investigation of simulator motion drive algorithms for

Investigation of Simulator Motion Drive Algorithms forAirplane Upset Simulation

by

Shuk Fai (Eska) Ko

A thesis submitted in conformity with the requirementsfor the degree of Master of Applied Science

Graduate Department of Applied Science and EngineeringUniversity of Toronto

Copyright c© 2012 by Shuk Fai (Eska) Ko

Abstract

Investigation of Simulator Motion Drive Algorithms for Airplane Upset Simulation

Shuk Fai (Eska) Ko

Master of Applied Science

Graduate Department of Applied Science and Engineering

University of Toronto

2012

Currently, it is uncertain how well a typical ground-based simulator’s hexapod motion

system can simulate the aggressive motion during airplane upset. To address this issue,

this thesis attempts to improve simulator motion for upset recovery simulation by defining

new motion fidelity criteria, implementing body frame filtering, and improving an existing

adaptive motion drive algorithm. The successfully improved adaptive algorithm was used

to conduct a paired comparison experiment to study the effects of trade-offs between

translational and rotational motion cues on pilot subjective fidelity and upset recovery

performance. Analysis of the experimental data found that pilots generally rejected

motion with false lateral cues and they preferred the presence of rotational cues for

moderate roll angles. Also, performance analysis suggested that roll cues helped improve

lateral control. Overall, pilots preferred to have simulator motion during upset simulation

and significant improvements in performance were observed when simulator motion was

present.

ii

Acknowledgements

I would like to express my sincerest gratitude to my supervisor, Professor Peter R. Grant,

for his guidance, patience and encouragement. His passion for our project inspired my

own continued fascination with the subject.

I would also like to thank my research committee members, Professor Hugh H.T.

Liu and Professor Christopher J. Damaren, for their thoughtful review and insightful

comments during the course of my study.

Special thanks go to Bruce Haycock and Stacey Liu for their active and generous

support for this research.

I would also like to take this opportunity to thank all the pilots who took part in the

upset recovery experiment, Robert Erdos, Larry Ernewein, Paul Kissmann, Tim Leslie,

and Peter Rebek, for their active participation and valuable feedback.

Thanks also go to Ruben Lakerveld, Vincent Lau, Richard Lee, Jake Li, Rhea Liem,

Amir Naseri, Tim Peterson, Bosco Tse, Diane Yang, and Jenmy Zhang for their kind

assistance along the way.

Last but not least, I would like to extend my heartfelt thanks to my parents, Chris

Ko, Henry Ko, Huan Wang, and Dat Chung for their endless support and encouragement.

iii

Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Scope and Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Reference Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Literature Review 9

3 Background 12

3.1 UTIAS Enhanced B-747 Flight Model . . . . . . . . . . . . . . . . . . . . 12

3.1.1 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1.2 Upset Recovery Experiment . . . . . . . . . . . . . . . . . . . . . 13

3.2 Platform Motion Cues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.1 Definition of Motion Cues and Motion Cueing Errors . . . . . . . 15

3.2.2 Benefits of Motion Cues for Upset Recovery Training . . . . . . . 16

3.3 UTIAS Classical Motion Drive Algorithm . . . . . . . . . . . . . . . . . . 17

3.3.1 General Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.4 UTIAS Adaptive Motion Drive Algorithm . . . . . . . . . . . . . . . . . 20

3.4.1 General Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4.2 Problems with the Original UTIAS Adaptive MDA . . . . . . . . 22

4 Motion Fidelity Criteria for Coordinated Roll Upsets 24

5 Body Frame Filtering 28

6 New UTIAS Adaptive Motion Drive Algorithm 34

6.1 Adaptive Surge/Pitch Channel Equations . . . . . . . . . . . . . . . . . . 35

6.2 Adaptive Sway/Roll Channel Equations . . . . . . . . . . . . . . . . . . 40

iv

6.3 Adaptive Heave Channel Equations . . . . . . . . . . . . . . . . . . . . . 45

6.4 Adaptive Yaw Channel Equations . . . . . . . . . . . . . . . . . . . . . . 46

6.5 A Comparison between the Original and the New Adaptive MDA . . . . 48

7 Upset Recovery Experiment 51

7.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.1.1 Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.1.2 Indications of Stall . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7.1.3 Motion Tuning Cases . . . . . . . . . . . . . . . . . . . . . . . . . 53

7.1.4 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . 62

7.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

7.2.1 Subjective Paired Comparison Analysis . . . . . . . . . . . . . . . 63

7.2.1.1 Non-parametric Analysis . . . . . . . . . . . . . . . . . . 63

7.2.1.2 Parametric Analysis . . . . . . . . . . . . . . . . . . . . 66

7.2.2 Objective Pilot Performance Analysis . . . . . . . . . . . . . . . . 70

7.3 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

8 Conclusions 79

8.1 Summary of Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Bibliography 82

A MDA Tuning Parameters 87

A.1 Body Frame Filter Parameters for Upset Simulation . . . . . . . . . . . . 87

A.2 Adaptive Filter Parameters for the Comparison between the Original and

New Adaptive MDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

A.3 Adaptive Filter Parameters for Upset Recovery Simulation . . . . . . . . 89

B Buffet Model Parameters 96

B.1 Filter Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

B.2 Angle of Attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

C Supplements for Subjective Paired Comparison Analysis 98

C.1 Paired Comparison Ordering . . . . . . . . . . . . . . . . . . . . . . . . . 98

C.2 Test Procedures for the extended Bradley-Terry Model . . . . . . . . . . 99

v

List of Figures

3.1 The UTIAS Classical MDA . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 The UTIAS Adaptive MDA . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1 Motion Fidelity Criteria Correlated with Rotational and Lateral Gains . 25

4.2 The Modified Sinacori Motion Fidelity Criteria for Rotational Motion . . 25

4.3 Motion Fidelity Criteria Correlated to Rotational Gain and False Lateral

Motion Cues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.4 Contour of the 3-D High-Medium Fidelity Boundary . . . . . . . . . . . 26

4.5 3-D Motion Fidelity Criteria (Color Intensity Increases with Increasing

Phase) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.1 Revised MDA Including Both Body Frame and Inertial Frame Filters . . 30

5.2 Comparisons of the Simulation Results Generated Using the Classical

MDA (in blue) and the Revised MDA (in red) for Upset Scenario 1 (Severe

Stall) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.3 Comparisons of the Simulation Results Generated Using the Classical

MDA (in blue) and the Revised MDA (in red) for Upset Scenario 4 (Rud-

der Hard-over) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6.1 The New UTIAS Adaptive MDA . . . . . . . . . . . . . . . . . . . . . . 34

6.2 Simulation of a Surge Acceleration Step Input Using the Original Adaptive

MDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.3 Simulation of a Surge Acceleration Step Input Using the New Adaptive

MDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

7.1 Buffet Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7.2 Scale Factor for Buffet Signal . . . . . . . . . . . . . . . . . . . . . . . . 54

7.3 Power Spectral Density of the Buffet Signal (Scale Factor = 1.2) . . . . . 54

vi

7.4 Fidelity of Baseline High-Pass Filters - Scenario 1 . . . . . . . . . . . . . 56






7.10 Translational Fidelity based on Both Baseline High-Pass and Low-Pass

Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

7.11 3-D Motion Fidelity Criteria . . . . . . . . . . . . . . . . . . . . . . . . . 59

7.12 Maximum Fidelity based on Both High-Pass and Low-Pass Filters - Sce-

nario 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60


nario 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60


nario 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60


nario 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61


nario 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61


nario 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

7.18 Total Scores for Motion Conditions . . . . . . . . . . . . . . . . . . . . . 64

7.19 Mean φmax for Severe Stall . . . . . . . . . . . . . . . . . . . . . . . . . . 72

7.20 Mean prms for Large Roll . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

7.21 Mean |θ|max for Rudder Hard-over . . . . . . . . . . . . . . . . . . . . . . 73

7.22 Mean prms for Rudder Hard-over . . . . . . . . . . . . . . . . . . . . . . 73

7.23 Mean qrms for Rudder Hard-over . . . . . . . . . . . . . . . . . . . . . . . 73

7.24 Mean rrms for Rudder Hard-over . . . . . . . . . . . . . . . . . . . . . . . 73

7.25 Mean nzmax for Rudder Hard-over . . . . . . . . . . . . . . . . . . . . . . 73

7.26 Mean qrms for Windshear . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7.27 Mean of First φmax after Control Handover for Severe Stall . . . . . . . . 76

vii

List of Tables

3.1 Information of Reference Upset Accidents/Incidents . . . . . . . . . . . . 14

7.1 Total Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

7.2 Overall Test of Significance . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7.3 Extended Bradley-Terry Model Fits . . . . . . . . . . . . . . . . . . . . . 69

7.4 Dependent Variables for ANOVA . . . . . . . . . . . . . . . . . . . . . . 71

7.5 Significant F-test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

A.1 Classical MDA Parameters for Upset Scenario 1 (Severe Stall) . . . . . . 87

A.2 Revised MDA Parameters for Upset Scenario 1 (Severe Stall) . . . . . . . 87

A.3 Classical MDA Parameters for Upset Scenario 4 (Rudder Hard-over) . . . 88

A.4 Revised MDA Parameters for Upset Scenario 4 (Rudder Hard-over) . . . 88

A.5 Parameters for the Gain Adaptive Surge High-Pass Filter . . . . . . . . . 89

A.6 UTIAS FRS Motion System Capabilities for Single DOF Motion . . . . . 89

A.7 Scenario 1 - F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.8 Scenario 1 - Ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.9 Scenario 1 - C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.10 Scenario 2 - F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.11 Scenario 2 - Ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.12 Scenario 2 - C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.13 Scenario 3 - F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.14 Scenario 3 - Ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.15 Scenario 3 - C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.16 Scenario 4 - F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.17 Scenario 4 - Ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.18 Scenario 4 - C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.19 Scenario 5 - F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

viii

A.20 Scenario 5 - Ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

A.21 Scenario 5 - C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

A.22 Scenario 6 - F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

A.23 Scenario 6 - Ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

A.24 Scenario 6 - C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

B.1 High-Pass Filters Parameters . . . . . . . . . . . . . . . . . . . . . . . . 96

B.2 Low-Pass Filters Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 96

B.3 Band-Pass Filter Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 96

B.4 Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

B.5 Angle of Attack for Buffet Model . . . . . . . . . . . . . . . . . . . . . . 97

C.1 Run Order for Pilot 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98





ix

Nomenclature

ai total score of motion condition i

aI scaled and limited aircraft acceleration in the inertial reference

frame, [m/s2 m/s2 m/s2]T

C simulator motion case representing the best compromise between

aircraft specific forces and angular rates

Ci non-dimensional aerodynamic coefficient: i = L (lift component),

l (rolling moment component), n (yawing moment component)

d simulator translational displacement capability, m

di transformation of scores, Dn =∑t

i=1 d2i has an asymptotic

chi-square distribution

||E|| norm of the perception vector in the revised MDA with body

frame filters

Erms root mean square of the errors in the revised MDA with body

frame filters

f specific force, [m/s2 m/s2 m/s2]T

f1

scaled and limited aircraft specific force in the aircraft reference

frame, [m/s2 m/s2 m/s2]T

fL

specific force due to tilt coordination, [rad rad rad]T

fthres human perception threshold for translational motions, m/s2

F simulator motion case representing the best matching specific forces

F ( , ) F-test result for the repeated-measures ANOVA

gi, hγ, hν equations for maximizing the logarithm of the likelihood function

g gravity vector, m/s2

Gx,y,z,ψ steepest descent step sizes in the adaptive algorithm

h altitude, ft

HPx/y/φ surge/sway/roll high-pass filter

x

Jx,y,z,ψ cost functions in the adaptive algorithm

kf matrix containing the translational scale factors,

kf = diag(kfx, kfy, kfz)

kω matrix containing the rotational scale factors,

kω = diag(kωp, kωq, kωr)

kx,y,z,ψ fixed filter parameters in the adaptive algorithm

Kfx/fy/ωp overall gains for surge/sway/roll motion

LIS transformation matrix from the simulator body frame to the

inertial frame

LIS× multiplication process using LIS

LIM tilt-rate and acceleration limiting function

LPx/y surge/sway low-pass filter

m stage counter for the iterative scheme

M iteration counter for the iterative scheme

n total number of comparisons between two conditions

ndata number of data points used to calculate the root mean square of

errors in the revised MDA with body frame filters

nz normal load factor, g

N simulator motion case with no motion but buffet

Oφ,θ,ψ order of the high-pass rotational filter in the classical algorithm

p roll rate, deg/s

P1/2/o probability of selecting the first condition/the second condition/

a tie when the conditions are the same

P probability

Px,y,z,ψ adaptive filter parameters in the adaptive algorithm

Px,y,z,ψ0 baseline values of the adaptive filter parameters in the adaptive

algorithm

q pitch rate, deg/s

r yaw rate, deg/s

rij total number of times the ordered pair (i, j) is compared

R correlation coefficient

R∗,+,− intermediate parameters for the critical range of the motion scores

s variable in the Laplace domain

S1,2,3 statistic with chi-square distribution

xi

SI simulator displacement in the inertial reference frame, [m m m]T

t simulation time, s

tc number of motion conditions

T1/2/o total number of preferences for the condition presented first/

the condition presented second/a tie

Ttotal total number of comparisons

T S transformation matrix from angular velocity to Euler rate

T S× multiplication process using T S

v simulator translational velocity capability, m/s

w1,ij/2,ij/o,ij/i,ij/j,ij frequencies of preference for the first case/the second case/

a tie/condition i/condition j for the ordered pair (i, j)

Wx,y,z,ψ weighing parameters in the adaptive algorithm

z variable in the z-domain

α angle of attack, deg

αb angle of attack for initial buffet, deg

αCLmax critical angle of attack, deg

αij total number of times condition i is selected over j plus half the

number of times conditions i and j are tied

αsig significance level

αW.D.P. angle of attack at the wing design plane, deg

β sideslip angle, deg

βC

scaled and limited aircraft Euler angle, βC

= [φC θC ψC ]T ,

[rad rad rad]T

βS

total simulator Euler angle, βS

= βSH

+ βSL

= [φS θS ψS]T ,

[rad rad rad]T

βSH

simulator Euler angle produced by the high-pass filter channel,

βSH

= [φSH θSH ψSH ]T , [rad rad rad]T

βSL

simulator Euler angle produced by the low-pass filter channel,

βSL

= [φSL θSL ψSL]T , [rad rad rad]T

γ model order effect

πi subjective merit of condition i

πij probability that condition i is selected over condition j, no order

effect

πi,ij/j,ij/o,ij probability that condition i/condition j/a tie is selected when

xii

the ordered pair (i, j) is presented

φ roll angle, deg

φlim, θlim tilt rate limit, rad/s

φlim, θlim tilt acceleration limit, rad/s2

θ pitch angle, deg

ψ yaw angle, deg

σ2 variance

ω1 scaled and limited aircraft angular velocity, ω1 = [p1 q1 r1]T ,

[rad/s rad/s rad/s]T

ωhp /lp second-order high-pass/low-pass break frequency, rad/s

ωhpb /lpb first-order high-pass/low-pass break frequency, rad/s

ωthres human perception threshold for rotational motions, deg/s

Ω simulator motion case representing the best matching angular

rates

χ2 chi-square distribution

ζhp /lp second-order high-pass/low-pass damping ratio

ν tie parameter

∆ small perturbation of variables

∆t simulation sample time, s

AA aircraft motion in the aircraft reference frame

b parameters in the simulator body reference frame

I motion in the inertial reference frame

( )LIM output from the tilt rate and acceleration limiting process

max maximum value

min,min( , ) minimum value

Pij motion variables calculated using the perturbed adaptive

parameters

rms root mean square value

SS, S simulator motion in the simulator reference frame

x/y/z, x/y/z surge/sway/heave components

ˆ estimated parameter

| | absolute value1s, 1s2

integrator, double-integrator in the Laplace domain

xiii

Chapter 1

Introduction

1.1 Motivation

Loss-of-Control (LOC) has surpassed Controlled-Flight-into-Terrain (CFIT) to become

the leading contributor of worldwide commercial aircraft fatalities in recent years [1].

LOC is defined in Reference [2] as motion that

• exceeds the normal operating flight envelopes;

• cannot be predictably altered by pilot control inputs;

• is characterized by nonlinear effects, such as kinematics/inertial coupling, dispro-

portionately large responses to small state variable changes, or oscillatory/divergent

behavior;

• involves high angular rates and displacements;

• causes the inability to maintain heading, altitude and wings-level flight.

To date, there is no widespread intervention strategies for preventing LOC [3]. Conse-

quently, the number of LOC accidents has remained relatively constant in the past few

years [4, 5, 6, 7] while the frequency of CFIT accidents have been significantly reduced

due to the development of the Enhanced Ground Proximity Warning System (EGPWS)

[1]. There is great concern within the aviation industry regarding the serious threat

of LOC on flight safety, and much current research is dedicated towards reducing the

number of accidents caused by LOC.

LOC often occurs following an airplane upset. Belcastro [8] reviewed the time se-

quencing of the causal and contributing factors of 126 LOC accidents to large transports

and smaller regional carriers between 1979 and 2009. This report found that “[w]hile

1

Chapter 1. Introduction 2

upsets [were] not usually the precipitating factor, many LOC sequences include[d] vehi-

cle upset somewhere in the chain of events” (P.402, [8]). This motivates the industry

to focus on mitigating LOC accidents resulting from aircraft upsets. Generally, an air-

plane is safe to be operated within its aerodynamic flight envelope which is defined by

the aircraft stall speeds, placarded maximum speeds and Mach numbers, and maximum

certificated altitudes [9]; however, when an airplane is upset, it unintentionally gets out-

side of its nominal flight envelope and approaches an unsafe condition [9]. During an

upset, the airplane may experience severe motions ranging from large attitude excursions

to the more serious situation involving aerodynamic stalls. An airplane upset recovery

team comprising of representatives from different branches of the aviation industry [9]

proposed a quantitative definition of upsets as one or more of the following situations:

• Pitch attitude greater than 25 nose-up or 10 nose-down;

• Bank angle exceeding ±45;

• Within the above parameters, but flying at inappropriate airspeeds.

Upsets can occur due to a variety of reasons. Based on the analysis of the 126 LOC

accidents, Belcastro [8] suggests that upsets are often due to an external hazard (such

as icing, windshear, collision or poor visibility) or an adverse onboard condition (such

as vehicle impairment, system failure or inappropriate crew response). Similarly, the

Airplane Upset Recovery Training Aid (URT Aid) [9] states that upsets can be induced

by environmental disturbances, system anomalies, and pilot errors, each acting alone or

in combination.

Different strategies are being used today to help reduce the probability of airplane

upsets, each with its own benefits and limitations. The advantages and disadvantages of

various strategies are discussed by Burki-Cohen and Sparko [1]. For example, airplane

control technologies, such as flight-envelope protection systems and assisted recovery

features, are automated systems being developed to deal with upsets. While flight-

envelope protection systems are designed to automatically keep the airplane within safe

operating limits, assisted recovery features aim to autonomously assist pilots to return

the airplane to a normal attitude. The problem of airplane control technologies arises

from the reliability of the automation, specifically whether pilots or automated systems

should have the ultimate authority in controlling the airplane [1]. Warning and advisory

systems have also been incorporated to alert pilots of potential upset events. In particular,

weather-forecasting displays, windshear detection systems, and icing detection systems


are used to detect and report possible environmental disturbances. In addition, aircraft

status displays are used to present onboard information, such as airplane’s attitude,

vertical situation and control surface status, that is crucial for pilots to recognize an

upset and to determine the appropriate actions for recovery [1]. Burki-Cohen and Sparko

suggest that warning and advisory systems may be the least controversial method to

prevent LOC. The main issue with warning and advisory systems is the accuracy of data

used in these systems [1].

In addition to the advanced technologies mentioned previously, three types of training

have been employed to prepare pilots for upset recovery and prevention: classroom,

aircraft and simulated aircraft training [1]. Classroom training teaches basic concepts

about airplane upsets, such as the aerodynamics and flight dynamics of aircraft during

upsets. It also teaches recovery techniques in a classroom setting without involving any

hands-on training. The industry guideline for classroom training is given in the URT

Aid [9]. The URT Aid states that classroom training will enhance the effectiveness of

subsequent hands-on training in aircraft or simulators [9]. Aircraft training is available

in aerobatic aircraft [1]. Although training in aerobatic aircraft provides perfect cues to

the pilot, it is somewhat impractical for upset prevention and recovery training (UPRT)

due to the danger of training accidents, the cost and scheduling issues for training the

large number of commercial pilots, and the uncertainty of transfer of training from an

aerobatic aircraft to a commercial jet [1]. Simulated aircraft training is employed for

UPRT using either an In-Flight Simulator (IFS) or a high fidelity ground-based full-flight

simulator (FFS). An IFS is an actual airplane which is computer-driven to simulate the

desired aircraft behavior with real visual and motion cues, but the usefulness of an IFS is

constrained by the accuracy of the flight model, the cost and scheduling issues, and the

danger of training in the air [1]. FFSs, in contrast, are ideal for UPRT in terms of safety,

training costs and time investments; however, the difficulty in developing accurate flight

models due to the lack of flight-test data outside the normal operating flight envelope and

the limited travel of the hexapod motion systems severely restrict the fidelity of upset

simulation in FFSs [1].

Certainly, the significant cost saving and safety make ground-based flight simulators

appealing for UPRT. However, whether UPRT in ground-based simulators would lead to

meaningful transfer of training between the simulator and the aircraft is a controversial

issue. The training limitations of existing ground-based simulators can be restated more

precisely as:


1. Critical upsets often occur outside the envelope of typical flight model’s aerody-

namic database. Simulation of critical upsets, therefore, requires extrapolation,

which often results in inaccurate aircraft response that may lead to negative trans-

fer of training;

2. It is unknown if conventional hexapod motion systems are sufficient for UPRT as

their typical motion drive algorithms (MDA) are designed to produce moderate

motions given the actuator limits of the motion system and they are unlikely to be

suitable for simulating the aggressive motion during airplane upset;

3. Even once improved MDAs are developed, it is unknown if the severe limitations

of the motion systems relative to the motions encountered during upsets will result

in poor or even negative transfer of training.

Given these limitations, ground-based simulators are currently used to perform a sub-

set of UPRT that occurs within the limits of the flight model’s aerodynamic database (i.e.

within the flight-test validated envelope)1 with or without simulator motion [1]. In other

words, existing UPRT only offers training for unusual attitude upsets (pre-stall/approach-

to-stall conditions) but not upsets involving actual stalls. In the well-known “Airplane

Upset Training Evaluation Report” [11], Gawron suggests that current UPRT is insuf-

ficient because pre-stall recovery and recovery from a complete stall require opposite

techniques2. Moreover, Gawron studied the effectiveness of airplane upset training using

piloted experiments and found that most pilots mistakenly used the techniques for re-

covering from an approach-to-stall situation to deal with a fully developed icing induced

stall [11]. In fact, investigation of recent LOC accidents also shows that pilots are in-

adequately trained for airplane upset recovery. In many cases, pilots fail to recognize

a stall, misinterpret instrument warnings and/or provide incorrect control inputs when

they encounter an aircraft upset [12, 13, 14]. It therefore seems prudent that UPRT

should be extended to include stalls and critical upsets that occur outside the nominal

flight envelope.

1Flight-test data are usually available to a certain angle of attack and sideslip. The limits of a flightmodel’s aerodynamic database are, therefore, defined by these boundaries of angle of attack and sideslipangle. An aircraft can exceed its normal flight envelope and undergo unusual attitude conditions, suchas large bank or pitch, while its angle of attack and sideslip are still within the limits of the flight model’saerodynamic database [10].

2“The recovery to prestall is add power and pull nose up so as not to lose altitude - powering outof the prestall condition. The correct recovery from a true stall is to reduce angle of attack and thisnecessitates pushing the yoke forward which will probably cause altitude loss” (P.181, [11]).


Significant effort has been made to extend the aerodynamic database of typical flight

models to accurately simulate upsets at extreme flight conditions. NASA Langley Re-

search Center (LaRC) collaborated with The Boeing Company to investigate extend-

ing the flight model of a commercial transport aircraft [15, 16, 17]. In this collabora-

tive research, wind tunnel tests were conducted on two subscale models of a generic,

medium-size, twin-jet commercial transport configuration to model the aerodynamics at

extreme flight conditions. The collected wind-tunnel data were incorporated to extend

the NASA’s baseline twin-jet transport aircraft flight model to create the Enhanced Up-

set Recovery (EUR) model [16]. Cunningham et al. at NASA/Boeing [16] compared

the EUR model to the baseline flight model using desktop and piloted simulations of

flight-test stalls and showed that the EUR model was a significant improvement over

the baseline model. Similarly, Liu [10] extended the aerodynamic database of an ex-

isting Boeing 747-100 flight model using the NASA LaRC wind tunnel data for the

on-going upset recovery research at the University of Toronto Institute for Aerospace

Studies (UTIAS) Flight Simulation Research Group. After the extended Boeing 747-

100 model was validated for aggressive roll-off and directional divergence at stall, Liu

conducted a pilot-in-the-loop experiment using the extended model to study the aircraft

behavior in six different upset scenarios. The Simulation of Upset Recovery in Aviation

(SUPRA) research project was also funded by the European Union 7th Framework Pro-

gram to develop an enhanced aerodynamic model for upset recovery simulation [18]. The

SUPRA aerodynamic model was developed for a generic, twin-engine, commercial trans-

port aircraft using the static and dynamic wind tunnel test data collected by the Central

Aerohydrodynamic Institute (TsAGI) to simulate the flight conditions both within and

outside the normal flight envelope [18]. The fidelity of the SUPRA model for simulating

aerodynamic autorotation was analyzed using computational fluid dynamic (CFD) meth-

ods and the wind tunnel data were combined with the CFD data to include Reynolds

number effects on the intensity of autorotation to simulate the desired lateral/directional

departure behavior [18]. The SUPRA model with modified departure characteristics was

then evaluated using a piloted experiment and it was rated to be representative of a

conventional jet transport both inside and outside the normal flight envelope [18].

In addition to the challenge of developing an accurate flight model, it is also a challenge

to produce useful motion cueing on a typical hexapod motion system for the extreme flight

motions encountered during upset. While platform motion may not be that important

for many flight training tasks [19], research has found that platform motion cues help to


improve pilot-vehicle performance in difficult skill-based tasks and for unstable vehicle

dynamics [20, 21, 22, 23, 24]. Since aircraft may become directionally and laterally

unstable during stalls, motion may be more important for UPRT than for regular training.

As a continuation of the UTIAS upset recovery research, this Master’s thesis is devoted

to study the improvement of simulator motion for airplane upset simulation.

1.2 Scope and Organization

This thesis studies the improvement of platform motion for UPRT in three steps: (1)

defines a set of motion fidelity criteria for upset simulation; (2) develops a new MDA to

more accurately simulate aircraft motion during upset; and (3) investigates the effects

of translational and rotational motion cues on subjective fidelity and pilot performance

during upset recovery simulation. The work of this thesis will be outlined as follows:

• Chapter 2 reviews past research on the development of platform motion cueing for

simulating upset recovery maneuvers.

• Chapter 3 reviews previous work done at UTIAS to get an upset recovery simula-

tion working. Liu [10] developed an Enhanced Boeing 747-100 Flight Model and

used this model to perform a fixed-base upset recovery experiment. Liu’s work is

important because the Enhanced Boeing 747-100 Flight Model and the simulation

data recorded during Liu’s upset recovery experiment are used throughout this

thesis for developing and testing new motion drive algorithms and for designing a

new upset recovery experiment. Second, the concepts of motion cues and motion

cueing errors will be presented. Also, the existing literature that found benefits

of simulator motion for flight conditions relevant to the airplane upset conditions

will be reviewed. Next, two existing MDAs will be described. The first is the

UTIAS Classical MDA, which is the basis MDA used in Chapter 5 for examining

the usefulness of body frame filtering during upset recovery simulation. The second

is the UTIAS Adaptive MDA, which forms the basis of a new improved adaptive

algorithm presented in Chapter 6.

• Chapter 4 proposes a set of three dimensional motion fidelity criteria that aims to

assess the fidelity of platform motion for simulating coordinated roll upsets. These

motion fidelity criteria are necessary requirements for upset recovery simulation


because the fidelity of simulator motion is at least partly dependent on its ability

to simulate a coordinated turn.

• Chapter 5 introduces the UTIAS Classical MDA extended with body frame filters.

The classical MDA performs high-pass filtering in the inertial reference frame to

ensure the commanded motions do not exceed the envelope of the hexapod motion

system. However, high-pass filtering in the inertial frame can introduce significant

cross-coupling among degrees-of-freedom (DOF) when the large angular motions

during upset are encountered. Therefore, we proposed to incorporate body frame

filters to the classical MDA to eliminate this cross-coupling. The modified classical

MDA has been tested using desktop simulation of six different upset maneuvers.

This chapter presents the simulation results and examines the effects of the addition

of body frame filters in improving motion fidelity during upset simulation.

• Chapter 6 presents a new adaptive MDA that is developed to maximize the fi-

delity of simulator cues for a typical hexapod motion system during upset recovery

simulation. This new adaptive MDA is an improvement over the original UTIAS

algorithm as it eliminates the undesired adaptation response found in the orig-

inal adaptive MDA by evaluating parameter adaptation rates using a numerical

approach.

• Chapter 7 contains the design and results of a piloted upset recovery experiment

utilizing the new adaptive MDA presented in Chapter 6. This experiment was con-

ducted to investigate the effects of different trade-offs between specific force and

angular rate on subjective motion fidelity and pilot performance during upset recov-

ery. In this experiment, six upset scenarios were tested by five pilots. Four different

sets of simulator motions, each representing a different trade-off between transla-

tional and rotational motions, were generated for each of the six upset scenarios by

changing the parameters within the new adaptive MDA. For each scenario, pilots

flew the simulated aircraft, recovered from the upset, and evaluated the fidelity of

the four sets of simulator motions using paired comparisons. The paired compari-

son data were then used to determine pilots’ rating on the fidelity of each motion

condition. Also, the aircraft state time histories, control time histories and actuator

lengths were recorded and used to investigate the effects of the four motion cases

on pilot recovery performance.


• Chapter 8 summarizes the findings of this thesis and suggests future directions for

UPRT research.

1.3 Reference Frames

The following reference frames will be used throughout this document:

The inertial reference frame (FI):

An Earth fixed inertial frame with its z-axis aligned with the inertial gravity vector. Its

origin and orientation are selected to suit the problem under study.

The simulator/body reference frame (FS /FB):

A body frame attached to the simulator cab with its origin placed at the centroid of the

upper bearing blocks for a hexapod motion system. The x-axis points forward and z-axis

points downward. The x-y plane is parallel to the floor of the simulator cockpit.

The aircraft reference frame (FA):

A body frame attached to the aircraft with its origin located at the same point relative

to the pilot in the aircraft as FS is in the simulator. The x-axis points forward and the

z-axis downward. The frame has the same orientation relative to the pilot as FS.

Chapter 2

Literature Review

Several studies devoted to the development of upset cueing for ground-based flight sim-

ulators were reported in the flight simulation literature. All of these studies focused on

enhancing conventional MDAs to improve simulator motion fidelity during the simulation

of airplane upset. Chung [25] investigated the achievable motion cueing for upset recov-

ery simulation using a typical MDA. In his analysis, a flight model built with the NASA

wind tunnel data was used to simulate a large roll attitude and a large pitch attitude

maneuver. Two sets of motion parameters, one based on the Medium Fidelity criteria

developed for rotorcraft operations [26] and the other being the typical MDA parameter

settings for a civil transport airplane, were used to simulate the aircraft motions for both

maneuvers [25]. Based on offline experimental results, Chung [25] demonstrated that

typical MDAs need to be improved in order to generate accurate motion cueing for upset

recovery simulation. In particular, he found that the simulation of sustained specific

forces demanded large responses from the tilt coordination circuits that occupied most of

the actuator travel. He also showed that significantly large lateral travel was required to

properly simulate a coordinated large roll upset. His findings suggest a tradeoff dilemma

between translational and angular motions for upset recovery simulation. For many of

the severe maneuvers encountered during UPRT, good angular roll cueing will lead to

large errors (false cues) in lateral specific force and similarly for pitch, there is little

actuator travel left for onset pitch cues if the simulator has large pitch angles for the

simulation of longitudinal specific forces.

As a part of the SUPRA research project, Zaichik et al. [27] developed a new al-

gorithm (referred to as the optimized algorithm) based on the UTIAS Classical MDA

(which will be introduced in Chapter 3) to take into account the effect of significant

9

Chapter 2. Literature Review 10

G-load on pilot’s perception of motion on other DOF, the influence of false cues, and the

motion fidelity requirements during upset recovery simulation. As stated by Zaichik et

al. [27], low frequency large amplitude G-loads can occur during airplane upset and cause

the human’s motion perception thresholds to increase. In order to simulate the reduced

motion sensitivity under the influence of low frequency large amplitude G-loads, adaptive

gains were added to the angular high-pass filters and the longitudinal low-pass filter in

the optimized algorithm to reduce the amount of motion generated in these DOF when

significant G-loads were present. In addition, a pre-defined nonlinear scale was imple-

mented into the high frequency vertical acceleration to enhance the G-break sensation.

Also, the sway low-pass filter that was originally implemented in the UTIAS Classical

MDA was replaced by a filter that passed mid-frequency motion and reduced phase dis-

tortion in the lateral DOF. The filter parameters of the optimized algorithm were tuned

based on the motion fidelity criteria, aiming to generate useful motion cues with little

false cues. The effectiveness of the optimize algorithm was tested using a piloted upset

recovery experiment and the algorithm was positively assessed by all pilots. In addition,

the recovery performance was analyzed based on the pilot’s control activities and the

flight controlled parameters (the aircraft pitch and roll rate) and it was found that both

the high-frequency components in the frequency spectra and the standard deviation of

the objective performance parameters decreased (suggesting improved control over the

aircraft) when simulator motion was generated using the optimize algorithm as compared

to the case when the experiment was conducted using a fixed-base configuration.

An algorithm was developed by Field et al. [28] as an alternative to the optimized

algorithm [27] for the SUPRA research project. The alternative algorithm (referred to

as the workspace algorithm) was also developed based on the UTIAS Classical MDA

and it was designed to more accurately simulate aircraft upset by maximizing the usage

of the simulator’s motion envelope. The filter gains of the workspace algorithm were

maneuver dependent. For each type of upset scenario, simulator motions in the sway,

heave, pitch, and roll DOF were prioritized in terms of the importance of the motion in

each DOF for recovering from the corresponding upset scenario. During the simulation

of any particular upset scenario, the filter gains were modified in real-time to maximize

the simulator motion in the prioritized DOF. In addition to the workspace algorithm,

Field et al. [28] also developed a buffet model to generate buffet signal that varied

depending on the aircraft angle of attack. Field et al. [28] combined the classical algo-

rithm, the workspace algorithm, the optimized algorithm, and the buffet model to form

Chapter 2. Literature Review 11

the SUPRA motion cueing filters. The goal of the SUPRA motion cueing filters was to

simulate different phases of an upset maneuver using different algorithms. In particular,

Field et al. [28] categorized an upset maneuver into five different phases: normal flight,

approach-to-upset, upset, recovery, and normal flight after recovery. During the simula-

tion of the two normal flight phases, simulator motions are generated using the classical

algorithm. In the approach-to-upset phase, buffeting cueing dominates and the classical

algorithm is gradually switched to the workspace algorithm. When the airplane is upset,

the workspace algorithm is then employed. During recovery, the workspace algorithm

is used if G-loads (relative to 1g) stay below 0.3g; otherwise, the optimized algorithm

is employed to account for the G-load effect on pilot’s motion perception. At the end

of this study, the fidelity of the SUPRA motion cueing filters was compared to that of

the classical MDA using a piloted upset recovery experiment for symmetric and asym-

metric stalls. The analysis of the subjective evaluation data showed that pilots generally

preferred the SUPRA motion cueing filters over the classical MDA. Also, it was found

that pilots experienced more false cues during the asymmetric stalls than the symmetric

stalls. In addition, the analysis of the pilot performance data found that the time to

recognize a stall was significantly shorter when the SUPRA buffet model was employed

than when buffet was presented in a constant amplitude.

In summary, conventional MDAs are unlikely to be suitable for airplane upset simu-

lation. Current studies focus on improving the classical MDA, by modifying solely the

filter gains in real-time in the attempt to more accurately simulate the aggressive motions

during upset. In addition to the real-time modification of the filter gains, there are other

possible ways to enhance the conventional MDAs. In the SUPRA project mentioned

previously, it has been demonstrated that algorithms developed based on the classical

MDA can generate simulator motions that lead to positive effects in both subjective mo-

tion fidelity and pilot performance during upset recovery. For this reason, more efforts

should be placed on enhancing the conventional MDAs, and any enhanced MDA should

maximize the fidelity of the simulator motion during upset recovery simulation. The

goal is to determine the ideal tradeoff between translational and rotational motions, and

thereby to better define motion criteria for upset recovery simulation.

Chapter 3

Background

3.1 UTIAS Enhanced B-747 Flight Model

3.1.1 Model Development

The UTIAS Enhanced Boeing 747-100 (B-747) Flight Model created by Liu [10] is one

of the few existing aircraft models that accurately predict aircraft dynamics in both the

pre-stall and post-stall regions. It was developed by extending the aerodynamic database

of an existing B-747 flight model using the wind tunnel data collected by NASA [10]. The

aerodynamic database of the original B-747 model contains the modeling data provided

by NASA/Boeing [29] and covers a flight envelope of α = [−5, 25] and β = [−15, 15]

[10]. Like typical flight models existing in the industry, the original B-747 model uses

look-up tables and simplified equations to calculate aerodynamic forces and moments [10].

Simulation of maneuvers outside the defined envelope using this original model would

require extrapolation or holding the last value in the look-up table, which would result in

inaccurate aircraft response that may lead to negative transfer of training. The data used

to extend the model were collected during a series of static and dynamic wind tunnel

tests conducted by NASA LaRC using subscale models of a generic, medium-size, twin-

engine commercial transport aircraft [15]. In particular, the static tests were conducted

on a 5.5%-scale model to measure the aerodynamic forces and moments with respect to

changes in α, β and control surface deflections [15]. The dynamic tests included two

parts: (1) force oscillation tests performed by sinusoidally oscillating a 5.5%-scale model

about its body axes at different frequencies and amplitudes to capture the aerodynamic

damping effects due to pitch, roll and yaw rates [15]; (2) rotary balance tests conducted

12

Chapter 3. Background 13

by rotating a 3.5%-scale model about its velocity vector at both positive and negative

rates to predict the aircraft steady-state spin dynamics [15]. Liu blended the NASA data

with the B-747 model’s original aerodynamic data to obtain a new model that covered

a flight envelope of α = [-5, 85] and β = [-45, 45] as well as high angular rates that

can occur during LOC. This is the first version of the UTIAS Enhanced B-747 Flight

Model and it will be referred to as the enhanced B-747 model in the following document.

Overall, the enhanced B-747 model behaves like the original B-747 model at small α,

β and angular rates, then gradually blends in the characteristics of the NASA data as

the attitudes and angular rates increase, and eventually follows the NASA data at large

values of α, β and angular rates where the database of the original B-747 model did not

cover [10].

In validating the enhanced B-747 model, Liu [10] simulated the NASA EUR stall ma-

neuver by applying the same control inputs to the enhanced B-747 model and compared

the simulation results to those of the NASA EUR model [16]. Liu [10] found that the

NASA EUR model demonstrated a more aggressive roll-off and directional divergence

at stall than the enhanced B-747 model. For this reason, Liu modified the lateral and

directional stability derivatives of the enhanced B-747 model by scaling Cl,Basic, Cn,Basic

and ∆Cl(α, p) of the NASA data to approximately match the Clβ/nβ/lp vs. α profiles of

the NASA EUR model. She also added the aerodynamic asymmetry data for Cl provided

by Foster et al. [17] to the database of the enhanced B-747 model [10]. The updated en-

hanced B-747 model then successfully matched the EUR model’s roll-off and directional

divergence at stall. In the following document, the updated model will be referred to as

“the enhanced B-747 roll model”.

3.1.2 Upset Recovery Experiment

Liu [10] conducted a piloted upset recovery experiment in the UTIAS Flight Research

Simulator (FRS) to examine the aircraft behavior at upset using both the enhanced B-

747 model and the enhanced B-747 roll model. In this experiment, six upset scenarios

were designed based on past accidents and flight test data for piloted recoveries. These

scenarios are summarized in Table 3.1.

Four pilots participated in Liu’s experiment [10]. All of them flew the simulated

aircraft and recovered from the six pre-programmed upset conditions using the enhanced

B-747 model with the motion-base turned off. In this part of the experiment, only


Scenario Registration No. Location Aircraft Date Type of Upset

1 B1816 Nagoya, Japan A300B4-622R 04/26/1994 Stall

2 G-THOF Hampshire, UK B737-3Q8 09/23/2007 Stall

3 HL-7451 London, UK B747-2B5F 12/22/1999 Large Roll Upset

4 N513AU Pittsburgh, U.S. B737-300 09/08/1994 Rudder Hardover

5 N954VJ Charlotte, U.S. DC-9-31 07/02/1994 Microburst

6 Flight Test N/A N/A N/A Pilot Induced Stall

Table 3.1: Information of Reference Upset Accidents/Incidents

Scenarios 1 and 2 were simulated with turbulence. In addition, two of the four pilots

repeated the experiment for Scenarios 1, 2 and 6 using the enhanced B-747 roll model.

In this section of the experiment, all of these three scenarios were simulated without

turbulence in order to examine the effect of the aerodynamic asymmetry data for Cl on

the aggressive roll-off and directional divergence at stall [10]. Throughout the experiment,

the aircraft state time histories and control time histories were recorded during each flight

for potential MDA design and tuning purposes.

Liu [10] analyzed her experimental data and concluded that Scenario 1 was the most

difficult scenario to handle as no pilot recovered from this scenario successfully in their

first attempt. In addition, Liu found that the maximum normal load factor in some

of the flights for Scenarios 3 and 4 reached 2.3g which was beyond the limit of 2.0g

recommended for flap-extended flights [9]. She also observed large angular rates in the

data of these scenarios. According to Liu [10], pilots could recover from Scenario 5

without any difficulty as pilots are familiar with windshear recovery. Also, Liu found that

pilots had the tendency to pull up too quickly before the airplane was fully recovered

in Scenario 6, thereby inducing a secondary stall that caused relatively large lateral

directional responses. In comparisons of the enhanced B-747 model and the enhanced

B-747 roll model, Liu showed that the latter generated larger sideslip and roll motions

in Scenarios 1 and 6. In particular, a pilot actually commented that the enhanced B-747

roll model was much more laterally unstable for Scenario 6 [10]. In addition to analyzing

the aircraft state time histories of the experiment, Liu [10] also used the Quantitative

Loss-of-Control Criteria (QLC) envelopes to identify which upset flights developed into

LOC. As defined by Wilborn and Foster [2], a maneuver that exceeds more than three

QLC envelopes can be classified as LOC. Based on this requirement, Liu examined one

example flight from each of Scenarios 1 to 4 and found that all of the four examples


resulted in LOC as they all exceeded more than three of the five QLC envelopes [10].

3.2 Platform Motion Cues

3.2.1 Definition of Motion Cues and Motion Cueing Errors

When flying flight simulators, pilots receive information representative of the actual mo-

tion which they would expect in an aircraft. They use this representative information as

cues to interpret the flight conditions and make decisions regarding their control inputs.

The most common cues presented in simulators are visual cues generated by the image

generator system and instruments, gravito-inertial cues generated by the simulator mo-

tion platform, proprioceptive cues created by the simulator force feel system, and aural

cues generated by the sound system [26]. According to Grant [30], motion cues could be

interpreted as any cue humans use to identify their motion, or any motion humans use as

a cue. This report will only focus on the latter because it is what MDAs directly control

and produce. For simplicity, this report will refer a motion cue to be “a signal generated

by motion through inertial space which is sensed by the pilot and/or guides the pilot’s

behavior” as defined in Reference (P.114, [30]). Grant emphasized that “[t]he signal it-

self is not the cue, only the human’s use or sense of the signal defines a cue” (P.113,

[30]). “Any simulator movement is therefore considered as motion, but not necessarily

as motion cue” (P.2, [31]).

All simulator motion platforms have very limited travel as compared to real aircraft.

During simulation, the desired aircraft motions are scaled, limited and filtered using

MDAs to produce representative motions without hitting the physical limits of the sim-

ulator [32]; therefore, almost all motion cues provided by the simulator differ from what

is expected in the aircraft [26, 33]. Grant [30] categorized motion cue errors into four

distinct types. According to Grant [30], false cues include motion cues in the simulator

which are in the opposite direction to what are in the aircraft, motion cues in the simu-

lator which are not expected in the aircraft and sustained motion cues in the simulator

which are distorted at relatively high frequency as compared to those in the aircraft. In

contrast, missing cues refer to motion cues that are not provided in the simulator, but

are expected in the aircraft. They do not degrade the motion fidelity as much as false

cues do and generally do not lead to significant pilot complaints [30]. Phase errors are

generated by high-pass filters in MDAs in the form of phase lead at frequencies near


and below the filters’ break frequencies. They are the most noticeable near the break

frequencies of the high-pass filters and become less significant as frequency decreases due

to the signal attenuation performed by the high-pass filters. Lastly, scaling errors are

resulted when the aircraft inputs are scaled down by MDAs and extreme scaling of the

aircraft motion can actually lead to missing cues.

3.2.2 Benefits of Motion Cues for Upset Recovery Training

The usefulness of simulator platform motion for training has always been debated. Re-

searchers are still uncertain as to whether motion leads to an improvement in transfer of

training. However, research has shown that motion strongly affects pilot performance in

certain situations [33]. In fact, the situations for which motion affects performance will

often arise during the extreme flight conditions experienced during aircraft upset. For

instance, White and Cooper [20] examined the lateral-directional stability at wings-level

flight at a poststall angle of attack. Their results showed that roll motion allowed pilots

to have significantly better lateral-directional control over the airplane. In the study of

Bergeron et al. [21], it was shown that the addition of motion did not alter the mean

square error appreciably in one-axis compensatory control tasks, but led to both an in-

crease in system bandwidth and a reduction in mean square error in tasks involving two

axes (pitch and roll, or pitch and yaw). Meiry [22] investigated the motion effects on

the human control characteristics in stable and unstable systems during a single-axis roll

tracking task. Meiry showed that although motion cues alone did not allow complete

control of the simulator attitude, the combination of motion and visual cues resulted in

better performance than when solely visual cues were presented. This was especially true

with unstable systems because motion cues further enhanced the pilot’s ability to stabi-

lize the system near the limit of controllability [22]. Stapleford et al. [23] also performed

a single-axis roll control task with a disturbance input and showed that the contribution

of motion feedback was higher if the task required more pilot lead, which means the

system was more unstable. The same result has been confirmed by Shirley and Young

[24]. In summary, previous research found evidence of the positive effects of simulator

motion on pilot performance in maneuvers comparable to airplane upset. Therefore, it

is worthwhile to research improvements in simulator motion to generate useful motion

cues during UPRT.


3.3 UTIAS Classical Motion Drive Algorithm

3.3.1 General Structure

A flight simulator platform moves due to the changes in its actuator extensions. In

comparison to an aircraft, it has very limited travel in all DOF. To resolve this ma-

jor restriction, MDAs are applied to modify aircraft motions using the techniques of

scaling, limiting, filtering and integration. The primary MDA used in the UTIAS FRS

is the classical washout filter algorithm developed by Reid and Nahon [32, 34]. The

classical MDA is simple and performs well in simulating aircraft motions for relatively

constant flight conditions, and therefore is widely used in the simulation industry. The

layout of the classical MDA is presented in Figure 3.1. The inputs to the algorithm are

the aircraft translational specific forces (fAA = [fxAA fyAA f

zAA]T ) and angular velocities

(ωAA = [pAA qAA rAA]T ) while the output is the simulator displacements (SI). In general,

the algorithm can be divided into three sections:

f

Scale

f

Limit

HP

FILT

1

s2LIS

x

RATE

LIMIT

LIS

fAA

f1 a I

.. S I

SI

f L

ω

Scale

ω

Limit

HP

FILT

1

s TS

xω1

.

βC βSH

+

++ LIS

TS

ωAA

TS

LIS

TS

βS

βSL

+ -

g

LP

FILTTILT

COORD

.

βSH

Figure 3.1: The UTIAS Classical MDA

1. High-Frequency Translational Motions

When aircraft translational specific forces are input to the algorithm, gravity (g)

is first added to the vertical body specific force. This step is necessary because

modifying the amplitude of gravity is undesirable [31]. Next, the amplitudes of the

accelerations are scaled uniformly across the entire frequency range using the scale


factor matrix kf defined as

kf =

kfx 0 0

0 kfy 0

0 0 kfz

(3.1)

Also, limiting is applied such that the surge and sway accelerations are limited to

± 10m/s2 while the heave acceleration is limited to ± (g + 10m/s2) [30]. Then, g

is subtracted from the accelerations. The resulted specific forces (f1) are converted

from the body reference frame into the inertial reference frame using the simulator

transformation matrix LIS (see Reid and Nahon [32] for the definition of LIS).

After that, g is added to the specific forces to create the inertial frame accelerations

(aI). The inertial accelerations are then subjected to the surge, sway and heave

high-pass filters which are respectively defined in Equations 3.2 to 3.4 to remove

the large displacement low-frequency motions. Note that all translational high-

pass filters must be of at least third-order in order to properly washout a sustained

translational acceleration input to zero translational displacement in the long term;

however, the surge and sway high-pass filters may be reduced to second-order when

tilt-coordination is applied since the use of tilt coordination effectively adds an

additional order to the surge and sway motions [32]. Lastly, simulator translational

displacements (SI) are obtained by double integrating the filtered accelerations

(SI).

SxI = Px1

(s2

s2 + 2ζhpxωhpxs+ ω2hpx

· s

s+ ωhpbx

)axI (3.2)

SyI = Py1

(s2

s2 + 2ζhpyωhpys+ ω2hpy

· s

s+ ωhpby

)ayI (3.3)

SzI = Pz1

(s2

s2 + 2ζhpzωhpzs+ ω2hpz

· s

s+ ωhpbz

)azI (3.4)

where Px1, Py1 and Pz1 are the high-pass filter gains and they are fixed constants

(with values equal to 1) for the classical MDA.

2. Sustained Translational Motions

The scaled and limited translational specific forces (f1) are subjected to tilt co-

ordination which transforms the translational motions into rotational motions by


tilting the simulator to get the component of the gravity equal to the scaled and

limited longitudinal and lateral specific forces. The algorithm of the TILT COORD

block is

fL

=

fxL

f yL

f zL

=

fx1 /g

−f y1 /g0

(3.5)

The specific forces due to tilt coordination (fL) are then low-pass filtered using

Equations 3.6 and 3.7 and subjected to tilt-rate and acceleration limiting. Note

that the tilt-rate and acceleration limiting process is performed in the intermediate

stages during the low-pass filtering process to limit the feedback circuits of the low-

pass filters so that the correct steady state tilt is reached. The purpose of tilt-rate

and acceleration limiting is to keep the tilt rate and acceleration motions below

the human perception thresholds, so that only the gravity component of the tilt

angle can be detected [32]. The result is the Euler angles simulating the sustained

translational motions, βSL

= [φSL θSL 0]T .

φSL =

(ω2lpy

s2 + 2ζlpyωlpys+ ω2lpy

· ωlpbys+ ωlpby

)f yL (3.6)

θSL =

(ω2lpx

s2 + 2ζlpxωlpxs+ ω2lpx

· ωlpbxs+ ωlpbx

)fxL (3.7)

3. High-Frequency Rotational Motions

Similar to the translational specific forces, the aircraft angular rates are first scaled

using the scale factor matrix kω defined as

kω =

kωp 0 0

0 kωq 0

0 0 kωr

(3.8)

and limited to ± 0.8 rad/s. The scaled and limited angular velocities (ω1) are then

transformed into Euler rates (βC

= [φC θC ψC ]T ) using the simulator transforma-

tion matrix T S (see Reid and Nahon [32] for the definition of T S). After that,

the Euler rates are high-pass filtered to generate βSH

= [φSH θSH ψSH ]T . The


high-pass angular filters are defined as

φSH =

Py4

(s2

s2 + 2ζhpφωhpφs+ ω2hpφ

)φC if Oφ = 2

Py4

(s

s+ ωhpφ

)φC if Oφ = 1

(3.9)

θSH =

Px4

(s2

s2 + 2ζhpθωhpθs+ ω2hpθ

)θC if Oθ = 2

Px4

(s

s+ ωhpθ

)θC if Oθ = 1

(3.10)

ψSH =

Pψ1

(s2

s2 + 2ζhpψωhpψs+ ω2hpψ

)ψC if Oψ = 2

Pψ1

(s

s+ ωhpψ

)ψC if Oψ = 1

(3.11)

where Px4, Py4 and Pψ1 are the high-pass filter gains which are fixed constants

(equal to 1) for the classical MDA, and Oφ, Oθ and Oψ define the orders of the

angular high-pass filters. Note that the rotational high-pass filters may be indepen-

dently reduced to first-order, but the filters have to be second-order to ensure that

sustained angular rates are properly washed out to zero angular displacements in

the long term [32]. By integrating the outputs from Equations 3.9 to 3.11, the Eu-

ler angles (βSH

) can be obtained. Using βSH

and βSL

resulting from the sustained

specific forces, the total simulator Euler angles (βS) can be calculated by

βS

= βSH

+ (βSL

)LIM (3.12)

where LIM represents the internal tilt-rate and acceleration limiting process.

3.4 UTIAS Adaptive Motion Drive Algorithm

3.4.1 General Structure

The UTIAS Adaptive Motion Drive Algorithm was originally developed by Reid and

Nahon [32, 34]. It was found to be slightly preferred over the classical MDA when tested

in piloted experiments [35, 36]. As shown in Figure 3.2, the adaptive MDA is a modifi-

cation of the classical MDA with high-pass filter parameters adapted in real-time based


f

Scale

f

Limit

HP

FILT

1

s2LIS

x

RATE

LIMIT

LIS

fAA

f1 a I

.. S I

SI

f L

ω

Scale

ω

Limit

HP

FILT

1

s TS

xω1

.

βC βSH

+

++ LIS

TS

ωAA

TS

LIS

TS

βS

βSL

+ -

gADAPTIVE

ALGORITHM

LP

FILTTILT

COORD

.

βSH

Figure 3.2: The UTIAS Adaptive MDA

on aircraft inputs and instantaneous simulator states. The idea behind the adaptation is

to open up the motion filters if the simulator is far from reaching its operational limits

while more subdued parameters will be assigned to the filters as the simulator’s displace-

ment and velocity increase [37]. In the adaptive algorithm, cost functions are defined

to penalize the (lack-of) fidelity of the simulator motions, the velocity of the simulator,

the displacement of the simulator and the values of the adaptive parameters. Parameter

adaptation rates are determined by minimizing these cost functions using the continuous

steepest descent method. In other words, the adaptation rate of a filter parameter is the

partial derivative of the cost function with respect to the parameter multiplied by the

negation of a step size.

Gain adaptation of a third-order heave high-pass filter is described below. For deriva-

tions of the complete UTIAS Adaptive MDA, see Reid and Nahon [32, 34]. The third-

order high-pass filter shown in Equation 3.4 is equivalent to that presented in Equation

3.13, except that Pz1 in Equation 3.13 is defined to be an adaptive gain rather than a fixed

constant. The heave cost function (Jz) is defined in Equation 3.14, where Wzi(i = 0, ..., 3)

are the weighing parameters and Pz10 is the baseline value of the adaptive gain. The adap-

tation rate of the filter gain (Pz1) is then shown in Equation 3.15 , where Gz1 is the step

size.

SzI = Pz1azI−(2ζhpzωhpz+ωhpbz)SzI−(2ζhpzωhpzωhpbz+ω

2hpz

)SzI−(ω2hpzωhpbz)

∫SzIdt (3.13)

Jz = 0.5[Wz0(azI − SzI )2 +Wz1(SzI )2 +Wz2(SzI )2 +Wz3(Pz1 − Pz10)2] (3.14)

Pz1 = −Gz1∂Jz∂Pz1

(3.15)


3.4.2 Problems with the Original UTIAS Adaptive MDA

In the original adaptive algorithm, the parameter adaptation rates are evaluated using an

analytical approach. O’Toole [37] investigated the performance of this analytical adap-

tive algorithm using the third-order gain adaptive heave filter and found two problems

in the algorithm. First, the simulated response of the original adaptive MDA to a heave

acceleration step input contained undesired oscillations [37]. O’Toole demonstrated that

errors in the integration process caused high frequency oscillations in the acceleration

response and this problem could be solved by using a higher integration rate or a high

order integration scheme. On the other hand, the transient response of the cost function

fidelity term resulted in large amplitude low frequency oscillations in the simulated heave

acceleration [37]. O’Toole suggests that the transient oscillations could be removed by

setting Wz0 to zero, but doing so would destroy the adaptation purpose of the algorithm.

Second, the gain adaptation of the third-order filter ceased regardless of the large differ-

ence between the aircraft acceleration and the simulator translational acceleration [37].

O’Toole studied the contribution of the cost function fidelity term to the gain adaptation

rate using a simplified cost function defined as

Jz = (azI − SzI )2 (3.16)

Ideally, large errors in the fidelity term should contribute to a positive gain adaptation

rate and force the filter gain to keep increasing in order to minimize the cost function. In

fact, without any other penalty and a large step size the gain should increase such that the

simulator acceleration almost matches the aircraft acceleration. O’Toole [37], however,

observed that the fidelity term barely affected the adaptation rate since it reached a

steady state of zero. In other words,

∂Jz∂Pz1

= −2(azI − SzI )∂SzI∂Pz1

→ 0 (3.17)

According to Equation 3.13, ∂SzI /∂Pz1 in Equation 3.17 can be expressed as

∂SzI∂Pz1

= azI −∂a

∂Pz1(3.18)

where a = (2ζhpzωhpz + ωhpbz)SzI + (2ζhpzωhpzωhpbz + ω2hpz

)SzI + (ω2hpzωhpbz)

∫SzIdt. As

defined by Reid and Nahon [32], it is assumed in the analytical algorithm of the original

adaptive MDA that

∂

∂Pz1

(d2SzIdt2

)=

d2

dt2

(∂SzI∂Pz1

)=

d

dt

(∂SzI∂Pz1

)(3.19)


O’Toole [37] argued that ∂a/∂Pz1 calculated based on the above assumption equaled azI

at steady state. As a result, ∂SzI /∂Pz1 and Equation 3.17 would reach a steady state of

zero and the gain adaptation would terminate regardless of any difference between the

aircraft input and simulator output.

In response to the problems of the original adaptive MDA, O’Toole [37] suggests

evaluating the gain adaptation rate numerically. In the numerical adaptive algorithm,

∂Jz/∂Pz1 which governs Pz1 is defined as

∂Jz∂Pz1

= lim4Pz1→0

[Jz(a

zI , S

zI , S

zI , S

zI , Pz1 +4Pz1)− Jz(azI , SzI , SzI , SzI , Pz1)

4Pz1

](3.20)

where the motion variables (SzI , SzI and SzI ) on the left cost function must be evaluated

using the perturbed gain (Pz1 +4Pz1) while those on the right cost function must be

determined based on Pz1 [37]. O’Toole then simulated the heave acceleration step input

again using the numerical approach. He showed that the numerical estimates of the

adaptation rates differed significantly from the analytical estimates while the numerical

estimates did not contain undesired oscillations or improper termination of the parameter

adaptation.

Chapter 4

Motion Fidelity Criteria for

Coordinated Roll Upsets

The ability to simulate a coordinated roll maneuver greatly affects the motion fidelity

of a simulator [38]. When an aircraft rolls and turns, the specific forces resulting from

the projection of gravity in the body-axis lateral direction is canceled by the centripetal

force. When a simulator rolls, however, no turning is performed and consequently, the

gravity component in the lateral body axis remains uncanceled and becomes a false

motion cue. One way to compensate these false lateral motion cues is to generate lateral

inertial acceleration as the simulator rolls. Unfortunately, this is not sufficient for upset

simulation because the simulator is unlikely to have enough travel to generate the required

lateral acceleration [25]. The other method for reducing the false cue is to high-pass filter

the aircraft roll motion so the onset cues are presented but the simulator rolls back to

zero roll-angle in the steady-state.

A previous study by Schroeder [26] proposed requirements on the simulator roll and

lateral translational motion for simulating coordinated roll maneuvers. In this study,

Schroeder examined the effects of false lateral motion cues on subjective motion fidelity

using a lateral displacement tracking task. A motion algorithm that consisted of pure

gains with no signal attenuation from washout filters was used to generate motion in

this experiment. The simulator roll motion was generated as the commanded roll motion

scaled by the roll gain. In addition, the simulator lateral specific force was produced as

the lateral translational motion required for coordination modified by the lateral gain.

For this particular motion algorithm, the false lateral motion cue, f ySS, can be expressed

24

Chapter 4. Motion Fidelity Criteria for Coordinated Roll Upsets 25

in the form of [26]: ∣∣∣∣ f ySSφAA

∣∣∣∣ = |g(Kfy − 1)Kωp| (4.1)

where φAA is the aircraft roll angle, g is the gravity vector, Kfy is the lateral gain and Kωp

is the roll gain [26]. Various amounts of false lateral motion cues were generated for the

tracking task by assigning different values of Kfy and Kωp to the motion algorithm. Pilot

fidelity ratings were collected for all motion cases. At the end of this study, Schroeder

combined the pilot fidelity ratings with the modified Sinacori motion fidelity criteria to

construct a new set of motion fidelity criteria correlated with roll and lateral gain to

define the motion requirements for simulating coordinated roll turns. These criteria are

shown in Figure 4.1.

The results from Schroeder’s study will be used to develop a new set of motion fidelity

criteria in the following section. The three dimensional (3-D) motion fidelity criteria

presented below suggest a way to estimate motion fidelity based on a combination of the

false lateral motion cues of the simulator and the phase and gain of the intended roll

motion. The development of these criteria consists of three main components:

1. The motion fidelity criteria correlated to rotational gain and phase

This is formed using the rotational motion fidelity plot defined in the modified

Sinacori criteria [26], see Figure 4.2.

2. The motion fidelity criteria correlated to rotational gain and∣∣∣ fySSφAA

∣∣∣To construct this part of the 3-D criteria, the x- and y- coordinates of each point on

the fidelity boundaries in Figure 4.1 are substituted into Kfy and Kωp in Equation

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Kfy

Kω

p

High fidelity

Medium fidelity

Low fidelity

Figure 4.1: Motion Fidelity Criteria Corre-

lated with Rotational and Lateral Gains

Figure 4.2: The Modified Sinacori Motion Fi-

delity Criteria for Rotational Motion


0 1 2 3 4 5 6

0

0.2

0.4

0.6

0.8

1

|fSS y /φ

AA| (m/s2/rad)

Ro

tati

on

al G

ain

High fidelity

Medium fidelity

Low fidelity

Figure 4.3: Motion Fidelity Criteria Corre-

lated to Rotational Gain and False Lateral

Motion Cues

0

2

40.40.6

0.810

10

20

30

40

|fSS y /φ

AA|(m/s2/rad)

Rotational Gain

Ph

ase

(deg

)

Figure 4.4: Contour of the 3-D High-Medium

Fidelity Boundary

4.1 respectively to determine∣∣∣ fySSφAA

∣∣∣. Then, the calculated∣∣∣ fySSφAA

∣∣∣ are plotted against

the corresponding Kωp to map the fidelity boundaries shown in Figure 4.3.

3. The combined effects of rotational gain, phase and∣∣∣ fySSφAA

∣∣∣When constructing the 3-D motion criteria, it is proposed that the phase error,

the gain error and the size of the lateral false cue all contribute to the simulator

fidelity. According to the modified Sinacori criteria, the rotational gain required

for a system with increased phase to stay in the same fidelity region increases. This

increase in the rotational gain is used to estimate the decrease in the allowable false

lateral motion cues such that:

∆

∣∣∣∣ f ySSφAA

∣∣∣∣ = − |g(Kfy − 1)|∆ |Kωp| (4.2)

Using the modified Sinacori criteria for rotational motion (Figure 4.2) and Equation

4.2, the fidelity boundaries of Figure 4.3 are extrapolated for different values of

phase. In Figure 4.4, the high-medium fidelity boundary correlated to rotational

gain and∣∣∣ fySSφAA

∣∣∣ (red line) is extrapolated for different phase values along the modified

Sinacori criteria for rotational motion (blue line) as an example. This was done

by simply scaling the zero-phase case such that it intersected the modified Sinacori

criteria.

The complete 3-D motion fidelity criteria are shown (in three different views) in Figure

4.5. It is proposed that this set of criteria can be applied to evaluate the fidelity of


general MDAs that include both gains and signal attenuation from the washout filters.

For general MDAs, there can be separate circuits for specific force and for cancelling the

lateral specific force due to rolling. In the UTIAS MDAs, however, the same high-pass

filter controls both. Therefore, the false lateral motion cue for the UTIAS MDAs can be

estimated by the maximum magnitude of the total lateral specific force transfer function

which is given as,

sup

∣∣∣∣ f ySSφAA

∣∣∣∣ = sup |gkωpHPφ(1−HPy)| (4.3)

where HPφ is the transfer function of roll high-pass filter and HPy is the transfer function

of sway high-pass filter. Moreover, the total rotational gain and the phase distortion can

be determined by the magnitude and phase of the simulator roll transfer function defined

in Equation 4.4 at the frequency of 1 rad/s 1 respectively.

φSS

φAA= kωpHPφ (4.4)

High fidelity (red) : Motion sensations are close to those of visual flightMedium fidelity (blue) : Motion sensation differences are noticeable but not objectionableLow fidelity (white) : Motion sensation differences are noticeable and objectionable

Figure 4.5: 3-D Motion Fidelity Criteria (Color Intensity Increases with Increasing Phase)

1The frequency of 1 rad/s is analyzed because it is where the vestibular system becomes the mostsensitive to motion stimuli [26]. Also, since it is a reasonable approximation of most pilot-vehicle crossoverfrequencies, the magnitude at 1 rad/s would indicate whether motion fidelity is sufficient to help pilotsgenerate the required lead equalization [33].

Chapter 5

Body Frame Filtering

Typical MDAs, including the UTIAS Classical MDA, are designed to perform high-pass

filtering in the inertial reference frame. The advantage of inertial high-pass filters is that

they ensure the simulator does not drift off into stops in the long term [32], but the

combination of the inertial high-pass filtering and the reference frame rotation between

the body and inertial reference frames can lead to significant cross-coupling among the

simulator body-axis specific force components [32]. For maneuvers with moderate aircraft

motions, the effects of cross-coupling can be assumed to be negligible; however, cross-

coupling could become significant when simulating upset conditions where the aircraft

and simulator attitudes can be large. According to Reid and Nahon [32], cross-coupling

can be avoided if body frame filters are used instead of inertial frame filters, with the

trade-off being drifting of the simulator position in the long term. This argument leads

to the idea of combining body frame filters with inertial frame filters in order to reduce

cross-coupling while ensuring motion commands remain within the motion system limits.

This chapter focuses on the experiment performed to investigate whether the com-

bination of body and inertial filters can reduce motion cue errors during upset recovery

simulation. In this experiment, the simulated aircraft state time histories of the six upset

scenarios collected by Liu as discussed in Section 3.1.2 were used as the aircraft inputs

to the MDAs. They were first simulated using the original classical MDA that involved

only inertial filters (see Section 3.3). The inertial filter parameters of the classical MDA

were tuned for each scenario to match the simulator specific forces with the correspond-

ing aircraft inputs and to minimize both the norm of the perception vector and the root

28

Chapter 5. Body Frame Filtering 29

mean square (RMS) of the errors which are defined in Equation 5.1 and 5.2 respectively.

||Ei|| =[(fxSSi/kfx − fxAAi

)/fthres]2 + [(f ySSi/kfy − f

yAAi

)/fthres]2

+ [(pSSi/kωp − pAAi)/ωthres]2 + [(qSSi/kωq − qAAi)/ωthres]2

+ [(rSSi/kωr − rAAi)/ωthres]212 , i = 1 : ndata

(5.1)

Erms =

√∑ndatai=1 ||Ei||2ndata

(5.2)

where f denotes specific forces, ndata denotes the number of data points collected in each

maneuver, the subscript SS denotes simulator motion in the simulator reference frame,

and the subscript AA denotes the aircraft motion in the aircraft reference frame. Note

that the errors in the vertical specific forces are not included in the norm calculation

because the fidelity of the simulator heave motion is constrained by the limited travel

of the simulator and the reduction of cross-couplings would not have much influence on

these errors. Also, each DOF is weighted equally in the metric and the errors of each

motion component are normalized by fthres = 0.05m/s2 or ωthres = 0.5 deg/s, which are

the estimates of the human perception thresholds for translational and rotational motion

respectively [39]. The purpose of normalizing the errors by the perception thresholds

was to put both translational and rotational motion cues on the same scale so that

a meaningful sum of errors across all DOF can be obtained. Moreover, the simulator

motion was divided by the scale factors to calculate the shape errors for analyzing how

well the trend of the simulator motion resembles that of the aircraft motion.

For the second step in this experiment, the upset scenarios were modeled using the

revised MDA that included both body and inertial filters. The layout of the revised MDA

is depicted in Figure 5.1. Note that the forms of the body filters are the same as those

of the inertial filters and they are presented in Equations 3.2 to 3.4 and Equations 3.9

to 3.11. When simulating the upset scenarios using the revised MDA, most of the signal

filtering was performed in the body reference frame and the inertial filters were only

used to control the drifting of the simulator position. For each scenario, the body filter

parameters of the revised MDA were set to be slightly smaller than the corresponding set

of classical inertial filter parameters, while the inertial filters of the revised MDA were

chosen to prevent the simulator from hitting the actuator limits. The goal was again to

match the simulator specific forces with the aircraft specific forces while minimizing the

norm of the perception vector and the RMS errors. The experimental results, however,

did not show any obvious reduction in motion cue errors with the aid of body filters.


f

Scale

f

Limit

FI HP

FILT

1

s2LIS

x

RATE

LIMIT

LIS

fAA

f1SI

f L

ω

Scale

ω

Limit

FI HP

FILT

1

s TS

xω1

.

βCβSH +

+ LIS

TS

ωAA

TS

LIS

TS

βS

βSL

+

+

-+

g

FB HP

FILT

gs

+

FB HP

FILT

LP

FILT

TILT

COORD

.

βSH

a I

.. S I

Figure 5.1: Revised MDA Including Both Body Frame and Inertial Frame Filters

Similar conclusions regarding the performance of the original and revised MDAs were

drawn from all six upset simulations. The simulation results of scenario 1 (a severe stall

scenario) and scenario 4 (a rudder hard-over scenario) are presented in Figures 5.2 and 5.3

respectively for analysis. The filter parameters tuned for these two scenarios are provided

in Tables A.1 to A.4 in Appendix A.1. Note that each motion component presented in

the simulation results was divided by the corresponding scale factor to illustrate the

shape errors. As shown in Figures 5.2b, 5.2c, 5.3b, and 5.3c, the simulator angular rates

and Euler angles generated by either MDA differed from the corresponding aircraft rates

and angles both in trend and magnitude. These errors suggest that tilt coordination

occupied most of the angular travel of the simulator platform, and the rotational motion

fidelity was sacrificed for the fidelity of translational motions. Moreover, the specific

forces generated using the classical MDA were compared to those generated using the

revised MDA (see Figures 5.2a and 5.3a) and it was found that no improvement in the

specific forces output from the revised MDA could be attributed to the reduction of cross-

coupling using the body filters. In general, cross-coupling only exists in high frequency

motions as low frequency motions are filtered in the body reference frame. According

to the errors in the simulated rotational motions, most specific forces in this experiment

were low frequency motions simulated using tilt-coordination and they should not contain

cross-coupling. Therefore, it was reasonable that the removal of cross-coupling did not

have any obvious impact on the simulation results. Lastly, Figures 5.2d and 5.3d show

that the application of body filters failed to reduce the norm of the perception vector

and the RMS of the errors. As discussed in Section 3.2, high-pass filters generate phase


lead and signal attenuation; therefore, adding body filters to the original classical MDA

could generate additional phase errors and magnitude errors to the system. As suggested

by the norm of the perception vector and the RMS values, the phase lead and signal

attenuation generated by the body filters might have produced more or less the same

amount of errors as those removed by the reduction of cross-coupling.

In summary, the simulation results showed that the addition of body filters in the

classical MDA did not help to improve motion fidelity in upset recovery simulation.

It, however, might be worthwhile to investigate whether the reduction of cross-coupling

would have a greater impact on simulating maneuvers that require little tilt coordination.

Also, since there is no guideline regarding the tuning of the filter parameters, it may be

possible to tune the body filter parameters in a different way to minimize all phase errors,

magnitude errors and cross-coupling; therefore, the usefulness of body filters should be

further analyzed before the method of body frame filtering is dismissed.


20 30 40 50 60 70 80 90 100

1

2

3

4

5

f x (

m/s

2 )

20 30 40 50 60 70 80 90 100

−1

0

1

f y (

m/s

2 )

20 30 40 50 60 70 80 90 100

−15

−10

−5

time(s)

f z (

m/s

2 )

AircraftInertial FiltersBody+Inertial Filters

(a) Specific Forces

20 30 40 50 60 70 80 90 100

−5

0

5

p (

deg

/s)

20 30 40 50 60 70 80 90 100−10

−5

0

5

q (

deg

/s)

20 30 40 50 60 70 80 90 100

−10123

time(s)r

(deg

/s)


(b) Angular Velocities

20 30 40 50 60 70 80 90 100

−505

1015

φ (d

eg)

20 30 40 50 60 70 80 90 100−20

0

20

40

θ (d

eg)

20 30 40 50 60 70 80 90 100

90

95

100

105

time(s)

ψ (

deg

)


(c) Euler Angles

20 30 40 50 60 70 80 90 100

5

10

15

20

25

30

35

40

time(s)

no

rm

RMS: Inertial Filters − 10.5115Body+Inertial Filters − 10.6322

Inertial FiltersBody+Inertial Filters

(d) Norm of the Perception Vector (Excluding

Vertical Specific Forces) and RMS Values

Figure 5.2: Comparisons of the Simulation Results Generated Using the Classical MDA (in

blue) and the Revised MDA (in red) for Upset Scenario 1 (Severe Stall)


10 20 30 40 50 60 70 80 900

2

4

f x (

m/s

2 )

10 20 30 40 50 60 70 80 90−3

−2

−1

0

f y (

m/s

2 )

10 20 30 40 50 60 70 80 90

−20

−15

−10

−5

time(s)

f z (

m/s

2 )


(a) Specific Forces

10 20 30 40 50 60 70 80 90−10

0

10

p (

deg

/s)

10 20 30 40 50 60 70 80 90

−5

0

5

q (

deg

/s)

10 20 30 40 50 60 70 80 90−6

−4

−2

0

2

time(s)r

(deg

/s)


(b) Angular Velocities

10 20 30 40 50 60 70 80 90−40

−20

0

20

φ (d

eg)

10 20 30 40 50 60 70 80 90

−20

−10

0

10

θ (d

eg)

20 30 40 50 60 70 80 90−50

0

50

time(s)

ψ (

deg

)


(c) Euler Angles

10 20 30 40 50 60 70 80 90

5

10

15

20

25

30

time(s)

no

rm

RMS: Inertial Filters − 11.0908Body+Inertial Filters − 11.6399

Inertial FiltersBody+Inertial Filters

(d) Norm of the Perception Vector (Excluding

Vertical Specific Forces) and RMS Values

Figure 5.3: Comparisons of the Simulation Results Generated Using the Classical MDA (in

blue) and the Revised MDA (in red) for Upset Scenario 4 (Rudder Hard-over)

Chapter 6

New UTIAS Adaptive Motion Drive

Algorithm

This chapter introduces a new adaptive MDA that was developed based on the original

UTIAS Adaptive MDA introduced in Section 3.4. As shown in Figure 6.1, the new

adaptive MDA has the same layout as the original adaptive MDA, except that the new

adaptive algorithm is developed based on the numerical algorithm suggested by O’Toole

[37] and the parameters of the low-pass filters are now also adapted. As discussed in

Section 3.3, the UTIAS Classical MDA which has fixed filter parameters is designed to

produce good motion for relatively constant flight conditions and is unlikely to be suitable

for upset simulation; therefore, the goal of the new adaptive MDA is to use parameter

adaptation to maximize the simulator cues resemblance to the large aircraft motions and

f

Scale

f

Limit

HP

FILT

1

s2LIS

x

RATE

LIMIT

LIS

fAA

f1 a I

.. S I

SI

f L

ω

Scale

ω

Limit

HP

FILT

1

s TS

xω1

.

βC βSH

+

++ LIS

TS

ωAA

TS

LIS

TS

βS

βSL

+ -

g

ADAPTIVE

ALGORITHM

LP

FILTTILT

COORD

.

βSH

Figure 6.1: The New UTIAS Adaptive MDA

34

Chapter 6. New UTIAS Adaptive Motion Drive Algorithm 35

high angular rates in upset recovery maneuvers without hitting the actuator limits. In

the following algorithm, f1

= [fx1 f y1 f z1 ] refers to the scaled and limited aircraft specific

forces and ω1 = [p1 q1 r1] represents the scaled and limited aircraft angular velocities.

Also, the Pij parameters are adaptive and the kij parameters are fixed.

6.1 Adaptive Surge/Pitch Channel Equations

The third-order surge adaptive high-pass filter is given as,

SxI =Px1axI − (kx1Px2 + kx3)SxI − [kx1kx3Px2 + kx2(Px2)2]SxI − [kx2kx3(Px2)2]

∫SxI dt

(6.1)

where Px1 is the adaptive surge high-pass gain, Px2 is the adaptive surge second-order

high-pass break frequency, kx1 is two times the surge high-pass damping ratio, kx2 is

unity, kx3 is the surge first-order high-pass break frequency, and axI is the scaled and

limited aircraft longitudinal acceleration expressed in the inertial reference frame,

axI = fx1 cos θS cos ψS + f y1 (sin φS sin θS cos ψS − cos φS sinψS)

+ f z1 (cos φS sin θS cos ψS + sin φS sinψS)(6.2)

The second-order pitch adaptive high-pass filter is given as,

θSH = Px4θC − kx4Px5θSH − kx5(Px5)2

∫θSH dt (6.3)

where Px4 is the adaptive pitch high-pass gain, Px5 is the adaptive pitch high-pass break

frequency, kx4 is two times the pitch high-pass damping ratio, kx5 is unity, and θC is

calculated by converting the scaled and limited body rates of the aircraft into the Euler

rates of the simulator,

θC = q1cos φS − r1sin φS (6.4)

The third-order surge low-pass filter is given as,

...θ SL = kx8Px7(Px8)2fxL − (kx6Px8 + kx8)(θSL)LIM − [kx6kx8Px8

+ kx7(Px8)2](θSL)LIM − [kx7kx8(Px8)2]θSL(6.5a)

(θSL)LIM =LIM

(∫...θ SL dt, ± θlim

)(6.5b)

(θSL)LIM =LIM

(∫(θSL)LIM dt, ± θlim

)(6.5c)


θSL =

∫(θSL)LIM dt (6.5d)

where Px7 is the adaptive surge low-pass gain, Px8 is the adaptive surge second-order

low-pass break frequency, kx6 is two times the surge low-pass damping ratio, kx7 is unity,

kx8 is the surge first-order low-pass break frequency, LIM is the internal tilt-rate and

acceleration limiting function 1, θlim = 100 rad/s2 is the tilt-acceleration limit for pitch

motion, θlim = 0.0698 rad/s is the tilt-rate limit for pitch motion, and fxL is the longitu-

dinal specific force due to tilt coordination,

fxL =fx1g

(6.6)

Using Equations 6.3 and 6.5, the total simulator pitch motions can be calculated as

θS = θSH + (θSL)LIM (6.7)

Based on the continuous steepest descent method, the parameter adaptation rates

are defined as

Pxi = −Gxi∂Jxi∂Pxi

, i = 1,2,4,5,7,8

= −Gxi

lim

∆Pxi→0

[Jxi(Pxi + ∆Pxi)− Jxi(Pxi)

∆Pxi

]= −Gxi

[lim

∆Pxi→0

(JxiPxi − Jxi

∆Pxi

)]≈ −Gxi

(JxiPxi − Jxi

∆Pxi

)if ∆Pxi 1

(6.8)

where Gxi are the step sizes, Jxi, which denote Jxi(Pxi), are the cost functions calculated

using the nominal adaptive parameters Pxi, and JxiPxi , which denote Jxi(Pxi+∆Pxi), are

the cost functions calculated using the perturbed adaptive parameters Pxi + ∆Pxi.

For i = 1,2:

Jxi = 0.5

Wx0

[axI − SxIfthres

]2

+Wx2

[SxIvxmax

]2

+Wx3

[SxIdxmax

]2

+Wx(i+5) [Pxi − Pxi0]2 (6.9a)

1For a function c and a variable d,

LIM (c,±d) =

d if c > d−d if c < −dc otherwise


JxiPxi = 0.5

Wx0

[axI − SxI Pxifthres

]2

+Wx2

[SxI Pxivxmax

]2

+Wx3

[SxI Pxidxmax

]2

+Wx(i+5) [Pxi + ∆Pxi − Pxi0]2 (6.9b)

For i = 4,5:

Jxi = 0.5

Wx0

[axI − SxIfthres

]2

+Wx1

[θC − θSωthres

]2

+Wx2

[SxIvxmax

]2

+Wx3

[SxIdxmax

]2

+Wx4

[θSqmax

]2

+Wx5

[θSθmax

]2

+Wx(i+5) [Pxi − Pxi0]2

(6.10a)

JxiPxi = 0.5

Wx0

[axI Pi − S

xI Pxi

fthres

]2

+Wx1

[θCPi − θSPxi

ωthres

]2

+Wx2

[SxI Pxivxmax

]2

+Wx3

[SxI Pxidxmax

]2

+Wx4

[θSPxiqmax

]2

+Wx5

[θSPxiθmax

]2

+Wx(i+5) [Pxi + ∆Pxi − Pxi0]2 (6.10b)

For i = 7,8:

Jxi =0.5

Wx0

fx1 − [SxI + gθSL

]fthres

2

+Wx1

[θC − θSωthres

]2

+Wx2

[SxIvxmax

]2

+Wx3

[SxIdxmax

]2

+Wx4

[θSqmax

]2

+Wx5

[θSθmax

]2

+Wx(i+5) [Pxi − Pxi0]2

(6.11a)

JxiPxi = 0.5

Wx0

fx1 − [SxI + gθSLPxi

]fthres

2

+Wx1

[θCPi − θSPxi

ωthres

]2

+Wx2

[SxI Pxivxmax

]2

+Wx3

[SxI Pxidxmax

]2

+Wx4

[θSPxiqmax

]2

+Wx5

[θSPxiθmax

]2

+Wx(i+5) [Pxi + ∆Pxi − Pxi0]2

(6.11b)


where fthres = 0.05m/s2 is an estimate of the human perception threshold for trans-

lational motions and ωthres = 0.5 deg/s (which is equivalent to 8.73 × 10−3 rad/s) is

an estimate of the human perception threshold for rotational motions [39]. Also, vxmax,

dxmax, qmax and θmax are the simulator maximum surge velocity, surge displacement, pitch

rate, and pitch angle respectively, Wxi(i = 0, ..., 13) are the weighing parameters, and

Pxi0(i = 1, 2, 4, 5, 7, 8) are the baseline values of the adaptive parameters.

For all cost functions, the motion variables without the subscript Pxi or Pi (axI ,SxI ,SxI ,SxI ,

θC , θS, θS, fx1 , and θSL) are defined in Equations 6.1 to 6.7. These motion variables, ex-

cept fx1 , are calculated based on the nominal adaptive parameters Pxi(i = 1, 2, 4, 5, 7, 8).

For JxiPxi(i = 1, 2, 4, 5, 7, 8), the motion variables with the subscript Pxi or Pi must

be calculated using the corresponding perturbed adaptive parameters Pxi + ∆Pxi(i =

1, 2, 4, 5, 7, 8). These variables are defined below:

The pitch motions calculated using perturbed parameters are:

θSPx4,5 = θSHPx4,5 + (θSL)LIM (6.12a)

θSPx4,5 = θSHPx4,5 + θSL (6.12b)

θSPx7,8 = θSH + (θSLPx7,8 )LIM (6.12c)

θSPx7,8 = θSH + θSLPx7,8 (6.12d)

where

θSHPx4 = (Px4 + ∆Px4)θC − kx4Px5θSH − kx5(Px5)2

∫θSH dt (6.13a)

θSHPx5 = Px4θC − kx4(Px5 + ∆Px5)θSH − kx5(Px5 + ∆Px5)2

∫θSH dt (6.13b)

θSHPx4,5 =

∫ t+∆t

t

θSHPx4,5 dt+ θSH (6.13c)

and...θ SLPx7 = kx8(Px7 + ∆Px7)(Px8)2fxL − (kx6Px8 + kx8)(θSL)LIM − [kx6kx8Px8

+ kx7(Px8)2](θSL)LIM − [kx7kx8(Px8)2]θSL

(6.14a)...θ SLPx8 = kx8Px7(Px8 + ∆Px8)2fxL − [kx6(Px8 + ∆Px8) + kx8](θSL)LIM − [kx6kx8(Px8

+ ∆Px8) + kx7(Px8 + ∆Px8)2](θSL)LIM − [kx7kx8(Px8 + ∆Px8)2]θSL

(6.14b)


(θSLPx7,8 )LIM =LIM

(∫ t+∆t

t

...θ SLPx7,8 dt+ (θSL)LIM , ± θlim

)(6.14c)

(θSLPx7,8 )LIM =LIM

(∫ t+∆t

t

(θSLPx7,8 )LIM dt+ (θSL)LIM , ± θlim)

(6.14d)

θSLPx7,8 =

∫ t+∆t

t

(θSLPx7,8 )LIM dt+ θSL (6.14e)

where t is the simulation time and ∆t = 0.005556 s is the sample time of the simulation.

θSPxi(i = 4, 5, 7, 8) are used to convert the aircraft motions from the body reference

frame to the inertial reference frame, so the aircraft inertial motions obtained after small

perturbation of adaptive parameters are:

axI P4,5=fx1 cos θSPx4,5 cos ψSPψ1,2

+ f y1 (sin φSPy4,5 sin θSPx4,5 cos ψSPψ1,2

− cos φSPy4,5 sinψSPψ1,2) + f z1 (cos φSPy4,5 sin θSPx4,5 cos ψSPψ1,2

+ sin φSPy4,5 sinψSPψ1,2)

axI P7,8=fx1 cos θSPx7,8 cos ψS + f y1 (sin φSPy7,8 sin θSPx7,8 cos ψS

− cos φSPy7,8 sinψS) + f z1 (cos φSPy7,8 sin θSPx7,8 cos ψS

+ sin φSPy7,8 sinψS)

(6.15a)

and

θCP4,5,7,8 = q1cos φSPy4,5,7,8 − r1sinφSPy4,5,7,8 (6.16)

where φSPyi(i = 4, 5, 7, 8) are the Euler roll angles perturbed by the lateral adaptive

parameters and ψSPψi(i = 1, 2) are the Euler yaw angles perturbed by the yaw adaptive

parameters. These variables will be defined later in Sections 6.2 and 6.4.

The surge motions calculated using the perturbed parameters are:

SxI Px1 = (Px1 + ∆Px1)axI − (kx1Px2 + kx3)SxI − [kx1kx3Px2 + kx2(Px2)2]SxI

− [kx2kx3(Px2)2]

∫SxI dt

(6.17a)

SxI Px2 =Px1axI − [kx1(Px2 + ∆Px2) + kx3]SxI − [kx1kx3(Px2 + ∆Px2)

+ kx2(Px2 + ∆Px2)2]SxI − [kx2kx3(Px2 + ∆Px2)2]

∫SxI dt

(6.17b)

SxI Px4,5,7,8 =Px1axI P4,5,7,8

− (kx1Px2 + kx3)SxI − [kx1kx3Px2 + kx2(Px2)2]SxI

− [kx2kx3(Px2)2]

∫SxI dt

(6.17c)


SxI Pxi =

∫ t+∆t

t

SxI Pxi dt+ SxI , i = 1,2,4,5,7,8 (6.17d)

SxI Pxi =

∫ t+∆t

t

SxI Pxi dt+ SxI , i = 1,2,4,5,7,8 (6.17e)

Note that the translational fidelity terms of Jx7 and Jx8 are defined to minimize

fx1 − (SxI +gθSL) where SxI +gθSL is the total simulator specific force estimated for a pure

longitudinal specific force maneuver based on small angle approximation and linearizing

[30]. By defining SxI + gθSL in these terms, the effects of motion on other DOF on

the longitudinal translational fidelity are neglected. The emphasis is therefore put on

increasing the longitudinal translational fidelity using the low-passed pitch motion. For

the same reason, SxI instead of SxI Px7,8 is used in the fidelity terms of JxiPxi(i = 7, 8)

because SxI Px7,8 are calculated using axI P7,8which are dependent on motions in other

DOF.

6.2 Adaptive Sway/Roll Channel Equations

The third-order sway adaptive high-pass filter is given as,

SyI =Py1ayI − (ky1Py2 + ky3)SyI − [ky1ky3Py2 + ky2(Py2)2]SyI − [ky2ky3(Py2)2]

∫SyI dt

(6.18)

where Py1 is the adaptive sway high-pass gain, Py2 is the adaptive sway second-order

high-pass break frequency, ky1 is two times the sway high-pass damping ratio, ky2 is

unity, ky3 is the sway first-order high-pass break frequency, and ayI is the scaled and

limited aircraft sway acceleration expressed in the inertial reference frame,

ayI = fx1 cos θS sinψS + f y1 (sin φS sin θS sinψS + cos φS cos ψS)

+ f z1 (cos φS sin θS sinψS − sin φS cos ψS)(6.19)

The second-order roll adaptive high-pass filter is given as,

φSH = Py4φC − ky4Py5φSH − ky5(Py5)2

∫φSH dt (6.20)

where Py4 is the adaptive roll high-pass gain, Py5 is the adaptive roll high-pass break

frequency, ky4 is two times the roll high-pass damping ratio, ky5 is unity, and φC is




φC = p1 + (q1sin φS + r1cos φS)tan θS (6.21)

The third-order sway low-pass filter is given as,

...φSL = ky8Py7(Py8)2f yL − (ky6Py8 + ky8)(φSL)LIM − [ky6ky8Py8

+ ky7(Py8)2](φSL)LIM − [ky7ky8(Py8)2]φSL(6.22a)

(φSL)LIM =LIM

(∫...φSL dt, ± φlim

)(6.22b)

(φSL)LIM =LIM

(∫(φSL)LIM dt, ± φlim

)(6.22c)

φSL =

∫(φSL)LIM dt (6.22d)

where Py7 is the adaptive sway low-pass gain, Py8 is the adaptive sway second-order low-

pass break frequency, ky6 is two times the sway low-pass damping ratio, ky7 is unity, ky8

is the sway first-order low-pass break frequency, φlim = 100 rad/s2 is the tilt-acceleration

limit for roll motion, φlim = 0.0698 rad/s is the tilt-rate limit for roll motion, and f yL is

the lateral specific force due to tilt coordination,

f yL = −fy1

g(6.23)

Using Equations 6.20 and 6.22, the total simulator roll motions can be calculated as

φS = φSH + (φSL)LIM (6.24)

The sway/roll parameter adaptation rates are defined as

Pyi = −Gyi∂Jyi∂Pyi

, i = 1,2,4,5,7,8

= −Gyi

lim

∆Pyi→0

[Jyi(Pyi + ∆Pyi)− Jyi(Pyi)

∆Pyi

]= −Gyi

[lim

∆Pyi→0

(JyiPyi − Jyi

∆Pyi

)]

≈ −Gyi

(JyiPyi − Jyi

∆Pyi

)if ∆Pyi 1

(6.25)

where Gyi are the step sizes. The cost functions are:


For i = 1,2:

Jyi = 0.5

Wy0

[ayI − S

yI

fthres

]2

+Wy2

[SyIvymax

]2

+Wy3

[SyIdymax

]2

+Wy(i+5) [Pyi − Pyi0]2 (6.26a)

JyiPyi = 0.5

Wy0

[ayI − S

yI Pyi

fthres

]2

+Wy2

[SyI Pyivymax

]2

+Wy3

[SyI Pyidymax

]2

+Wy(i+5) [Pyi + ∆Pyi − Pyi0]2 (6.26b)

For i = 4,5:

Jyi = 0.5

Wy0

[ayI − S

yI

fthres

]2

+Wy1

[φC − φSωthres

]2

+Wy2

[SyIvymax

]2

+Wy3

[SyIdymax

]2

+Wy4

[φSpmax

]2

+Wy5

[φSφmax

]2

+Wy(i+5) [Pyi − Pyi0]2

(6.27a)

JyiPyi = 0.5

Wy0

[ayIPi − S

yI Pyi

fthres

]2

+Wy1

[φCPi − φSPyi

ωthres

]2

+Wy2

[SyI Pyivymax

]2

+Wy3

[SyI Pyidymax

]2

+Wy4

[φSPyipmax

]2

+Wy5

[φSPyiφmax

]2

+Wy(i+5) [Pyi + ∆Pyi − Pyi0]2

(6.27b)

For i = 7,8:

Jyi =0.5

Wy0

f y1 − [SyI − gφSL]fthres

2

+Wy1

[φC − φSωthres

]2

+Wy2

[SyIvymax

]2

+Wy3

[SyIdymax

]2

+Wy4

[φSpmax

]2

+Wy5

[φSφmax

]2

+Wy(i+5) [Pyi − Pyi0]2

(6.28a)


JyiPyi = 0.5

Wy0

f y1 − [SyI − gφSLPyi]fthres

2

+Wy1

[φCPi − φSPyi

ωthres

]2

+Wy2

[SyI Pyivymax

]2

+Wy3

[SyI Pyidymax

]2

+Wy4

[φSPyipmax

]2

+Wy5

[φSPyiφmax

]2

+Wy(i+5) [Pyi + ∆Pyi − Pyi0]2

(6.28b)

where vymax, dymax, pmax and φmax are the simulator maximum sway velocity, sway displace-

ment, roll rate, and roll angle respectively, Wyi(i = 0, ..., 13) are the weighing parameters,

and Pyi0(i = 1, 2, 4, 5, 7, 8) are the baseline values of the adaptive parameters.

For all cost functions, the motion variables without the subscript Pyi or Pi (ayI ,SyI ,SyI ,SyI ,

φC , φS, φS, f y1 , and φSL) are defined in Equations 6.18 to 6.24. These motion variables, ex-

cept f y1 , are calculated based on the nominal adaptive parameters Pyi(i = 1, 2, 4, 5, 7, 8).

For JyiPyi(i = 1, 2, 4, 5, 7, 8), the motion variables with the subscript Pyi or Pi must

be calculated using the corresponding perturbed adaptive parameters Pyi + ∆Pyi(i =

1, 2, 4, 5, 7, 8). These variables are defined below:

The roll motions calculated using perturbed parameters are:

φSPy4,5 = φSHPy4,5 + (φSL)LIM (6.29a)

φSPy4,5 = φSHPy4,5 + φSL (6.29b)

φSPy7,8 = φSH + (φSLPy7,8 )LIM (6.29c)

φSPy7,8 = φSH + φSLPy7,8 (6.29d)

where

φSHPy4 = (Py4 + ∆Py4)φC − ky4Py5φSH − ky5(Py5)2

∫φSH dt (6.30a)

φSHPy5 = Py4φC − ky4(Py5 + ∆Py5)φSH − ky5(Py5 + ∆Py5)2

∫φSH dt (6.30b)

φSHPy4,5 =

∫ t+∆t

t

φSHPy4,5 dt+ φSH (6.30c)

and...φSLPy7 = ky8(Py7 + ∆Py7)(Py8)2f yL − (ky6Py8 + ky8)(φSL)LIM − [ky6ky8Py8

+ ky7(Py8)2](φSL)LIM − [ky7ky8(Py8)2]φSL

(6.31a)


...φSLPy8 = ky8Py7(Py8 + ∆Py8)2f yL − [ky6(Py8 + ∆Py8) + ky8](φSL)LIM − [ky6ky8(Py8

+ ∆Py8) + ky7(Py8 + ∆Py8)2](φSL)LIM − [ky7ky8(Py8 + ∆Py8)2]φSL

(6.31b)

(φSLPy7,8 )LIM =LIM

(∫ t+∆t

t

...φSLPy7,8 dt+ (φSL)LIM , ± φlim

)(6.31c)

(φSLPy7,8 )LIM =LIM

(∫ t+∆t

t

(φSLPy7,8 )LIM dt+ (φSL)LIM , ± φlim)

(6.31d)

φSLPy7,8 =

∫ t+∆t

t

(φSLPy7,8 )LIM dt+ φSL (6.31e)

φSPyi(i = 4, 5, 7, 8) are used to convert the aircraft motions from the body reference

frame to the inertial reference frame, so the aircraft inertial motions obtained after small

perturbation of adaptive parameters are:

ayIP4,5=fx1 cos θSPx4,5 sinψSPψ1,2

+ f y1 (sin φSPy4,5 sin θSPx4,5 sinψSPψ1,2

+ cos φSPy4,5 cos ψSPψ1,2) + f z1 (cos φSPy4,5 sin θSPx4,5 sinψSPψ1,2

− sin φSPy4,5 cos ψSPψ1,2)

(6.32a)

ayIP7,8=fx1 cos θSPx7,8 sinψS + f y1 (sin φSPy7,8 sin θSPx7,8 sinψS

+ cos φSPy7,8 cos ψS) + f z1 (cos φSPy7,8 sin θSPx7,8 sinψS

− sin φSPy7,8 cos ψS)

(6.32b)

and

φCP4,5,7,8 = p1 + (q1sin φSPy4,5,7,8 + r1cos φSPy4,5,7,8)tan θSPx4,5,7,8 (6.33)

The sway motions calculated using the perturbed parameters are:

SyI Py1 = (Py1 + ∆Py1)ayI − (ky1Py2 + ky3)SyI − [ky1ky3Py2 + ky2(Py2)2]SyI

− [ky2ky3(Py2)2]

∫SyI dt

(6.34a)

SyI Py2 =Py1ayI − [ky1(Py2 + ∆Py2) + ky3]SyI − [ky1ky3(Py2 + ∆Py2)

+ ky2(Py2 + ∆Py2)2]SyI − [ky2ky3(Py2 + ∆Py2)2]

∫SyI dt

(6.34b)

SyI Py4,5,7,8 =Py1ayIP4,5,7,8

− (ky1Py2 + ky3)SyI − [ky1ky3Py2 + ky2(Py2)2]SyI

− [ky2ky3(Py2)2]

∫SyI dt

(6.34c)


SyI Pyi =

∫ t+∆t

t

SyI Pyi dt+ SyI , i = 1,2,4,5,7,8 (6.34d)

SyI Pyi =

∫ t+∆t

t

SyI Pyi dt+ SyI , i = 1,2,4,5,7,8 (6.34e)

Note that the translational fidelity terms of Jy7 and Jy8 are defined to minimize

f y1 − (SyI − gφSL) where SyI − gφSL is the total simulator specific force estimated for a

pure lateral specific force maneuver based on small angle approximation and linearizing

[30]. By defining SyI − gφSL in these terms, the effects of motion on other DOF on the

lateral translational fidelity are neglected. The emphasis is therefore put on increasing

the lateral translational fidelity using the low-passed roll motion. For the same reason,

SyI instead of SyI Py7,8 is used in the fidelity terms of JyiPyi(i = 7, 8) because SyI Py7,8 are

calculated using ayIP7,8which are dependent on motions in other DOF.

6.3 Adaptive Heave Channel Equations

The third-order heave adaptive high-pass filter is given as,

SzI =Pz1azI − (kz1Pz2 + kz3)SzI − [kz1kz3Pz2 + kz2(Pz2)2]SzI − [kz2kz3(Pz2)2]

∫SzI dt

(6.35)

where Pz1 is the adaptive heave high-pass gain, Pz2 is the adaptive heave second-order

high-pass break frequency, kz1 is two times the heave high-pass damping ratio, kz2 is

unity, kz3 is the heave first-order high-pass break frequency, and azI is the scaled and

limited aircraft heave acceleration expressed in the inertial reference frame,

azI =− fx1 sin θS + f y1 sin φS cos θS + f z1 cos φS cos θS + g (6.36)

The heave parameter adaptation rates are

Pzi = −Gzi∂Jzi∂Pzi

, i = 1,2

= −Gzi

lim

∆Pzi→0

[Jzi(Pzi + ∆Pzi)− Jzi(Pzi)

∆Pzi

]= −Gzi

[lim

∆Pzi→0

(JziPzi − Jzi

∆Pzi

)]≈ −Gzi

(JziPzi − Jzi

∆Pzi

)if ∆Pzi 1

(6.37)


where Gzi are the step sizes. The cost functions are given by

Jzi = 0.5

Wz0

[azI − SzIfthres

]2

+Wz1

[SzIvzmax

]2

+Wz2

[SzIdzmax

]2

+Wz(i+2)[Pzi − Pzi0]2

(6.38a)

JziPzi = 0.5

Wz0

[azI − SzI Pzifthres

]2

+Wz1

[SzI Pzivzmax

]2

+Wz2

[SzI Pzidzmax

]2

+Wz(i+2) [Pzi + ∆Pzi − Pzi0]2 (6.38b)

where i=1,2, vzmax and dzmax are the simulator maximum heave velocity and heave dis-

placement respectively, Wzi(i = 0, ..., 4) are the weighing parameters, and Pzi0(i = 1, 2)

are the baseline values of the adaptive parameters.

For all cost functions, the motion variables azI , SzI , SzI , and SzI are calculated using

the nominal adaptive parameters Pzi(i = 1, 2). These variables are defined in Equations

6.35 to 6.36. For JziPzi(i = 1, 2), the motion variables with the subscript Pzi must be

calculated using the corresponding perturbed adaptive parameter Pzi + ∆Pzi(i = 1, 2).

These variables are defined below:

SzI Pz1 = (Pz1 + ∆Pz1)azI − (kz1Pz2 + kz3)SzI − [kz1kz3Pz2 + kz2(Pz2)2]SzI

− [kz2kz3(Pz2)2]

∫SzI dt

(6.39a)

SzI Pz2 =Pz1azI − [kz1(Pz2 + ∆Pz2) + kz3]SzI − [kz1kz3(Pz2 + ∆Pz2)

+ kz2(Pz2 + ∆Pz2)2]SzI − [kz2kz3(Pz2 + ∆Pz2)2]

∫SzI dt

(6.39b)

SzI Pzi =

∫ t+∆t

t

SzI Pzi dt+ SzI , i = 1,2 (6.39c)

SzI Pzi =

∫ t+∆t

t

SzI Pzi dt+ SzI , i = 1,2 (6.39d)

6.4 Adaptive Yaw Channel Equations

The second-order yaw adaptive high-pass filter is given as,

ψS = ψSH

=Pψ1ψC − kψ1Pψ2ψSH − kψ2(Pψ2)2

∫ψSH dt

(6.40)


where Pψ1 is the adaptive yaw high-pass gain, Pψ2 is the adaptive yaw high-pass break

frequency, kψ1 is two times the yaw high-pass damping ratio, kψ2 is unity and ψC is



ψC = (q1sin φS + r1cos φS)sec θS (6.41)

The yaw parameter adaptation rates are

Pψi = −Gψi∂Jψi∂Pψi

, i = 1,2

= −Gψi

lim

∆Pψi→0

[Jψi(Pψi + ∆Pψi)− Jψi(Pψi)

∆Pψi

]= −Gψi

[lim

∆Pψi→0

(JψiPψi − Jψi

∆Pψi

)]

≈ −Gψi

(JψiPψi − Jψi

∆Pψi

)if ∆Pψi 1

(6.42)

where Gψi are the step sizes. The cost functions are given by

Jψi =0.5

Wψ0

[ψC − ψSωthres

]2

+Wψ1

[ψSrmax

]2

+Wψ2

[ψSψmax

]2

+Wψ(i+2) [Pψi − Pψi0]2 (6.43a)

JψiPψi =0.5

Wψ0

[ψCP(i+3)

− ψSPψiωthres

]2

+Wψ1

[ψSPψirmax

]2

+Wψ2

[ψSPψiψmax

]2

+Wψ(i+2) [Pψi + ∆Pψi − Pψi0]2 (6.43b)

where i=1,2, rmax and ψmax are the simulator maximum yaw rate, and yaw angle respec-

tively, Wψi(i = 0, ..., 4) are the weighing parameters, and Pψi0(i = 1, 2) are the baseline

values of the adaptive parameters.

For all cost functions, the motion variables ψC , ψS, and ψS are calculated using the

nominal adaptive parameter Pψi(i = 1, 2). These variables are defined in Equations 6.40

to 6.41. For JψiPψi(i = 1, 2), the motion variables with the subscript Pψi or P(i+3) must be

calculated using the corresponding perturbed adaptive parameters Pψi + ∆Pψi(i = 1, 2)


as defined below:

ψSPψ1=ψSHPψ1

= (Pψ1 + ∆Pψ1)ψC − kψ1Pψ2ψSH − kψ2(Pψ2)2

∫ψSH dt

(6.44a)

ψSPψ2=ψSHPψ2

=Pψ1ψC − kψ1(Pψ2 + ∆Pψ2)ψSH − kψ2(Pψ2 + ∆Pψ2)2

∫ψSH dt

(6.44b)

ψSPψi =ψSHPψi , i = 1,2

=

∫ t+∆t

t

ψSHPψi dt+ ψSH(6.44c)

and

ψCPi = (q1sin φSPyi + r1cos φSPyi)sec θSPxi , i = 4,5 (6.45a)

6.5 A Comparison between the Original and the New

Adaptive MDA

A desktop simulation was conducted to compare the performance of the new (numeri-

cal) adaptive MDA to the performance of the original (analytical) adaptive MDA. The

comparison was based on the simulation of a surge acceleration step input of 10m/s2.

Similar to the study performed by O’Toole [37], the performance of the two MDAs was

investigated by examining the adaptation of the surge filter gain (Px1) using the cost

function translational fidelity term. By employing the surge high-pass filter parameters

listed in Table A.5 in Appendix A.2, the surge acceleration step input was first simulated

at 180Hz three times using the original MDA, each time with a different value assigned

to the surge fidelity weight (Wx0). Next, the same simulation was repeated using the new

MDA where the identical set of filter parameters was employed. The simulation results

produced by the original and the new algorithm are presented in Figures 6.2 and 6.3

respectively. As shown in Figure 6.2, the simulator response generated using the original

MDA reached a steady state of zero shortly after the start of the simulation without

properly minimizing the difference between the aircraft and the simulator acceleration.

This result is in agreement with the findings of O’Toole [37]. Moreover, it is depicted

in Figure 6.2 that the value of Wx0 had no positive effects on the improvement of the

simulator fidelity. In contrast, the new algorithm successfully maximized the simulator


fidelity during the simulation. As shown in Figure 6.3, the difference between the air-

craft acceleration and the simulator acceleration decreased as the value of Wx0 increased,

demonstrating that the simulator fidelity was properly controlled by Wx0 in the new

adaptive MDA. Based on these simulation results, it is therefore concluded that the find-

ings presented by O’Toole [37] were confirmed and that the new adaptive algorithm was

an improvement over the original algorithm.

0 1 2 3 4 5 6 7 8 9 10−2

0

2

4

6

8

10

12

time(s)

surg

e ac

cele

rati

on

(m

/s2 )

Step InputSimulator Response, Wx0 = 0.01Simulator Response, Wx0 = 0.05Simulator Response, Wx0 = 0.10

Figure 6.2: Simulation of a Surge Acceleration Step Input Using the Original Adaptive MDA


0 1 2 3 4 5 6 7 8 9 10

0

2

4

6

8

10

12

time(s)

surg

e ac

cele

rati

on

(m

/s2 )

Step InputSimulator Response, Wx0 = 0.01Simulator Response, Wx0 = 0.05Simulator Response, Wx0 = 0.10

Figure 6.3: Simulation of a Surge Acceleration Step Input Using the New Adaptive MDA

Chapter 7

Upset Recovery Experiment

During the tuning of the new adaptive MDA developed in Chapter 6, it was found

that specific force and angular rate cannot achieve good fidelity simultaneously when

the extreme flight motions encountered during upset were simulated. In order to better

understand the motion requirements of upset recovery simulation, a piloted experiment

was conducted in the UTIAS FRS to study the effects of trade-offs between specific force

and angular rate on pilot subjective motion fidelity and recovery performance. In this

experiment, four different types of trade-off between translational and rotational motions

were compared in six different upset scenarios and the simulator motion for all trade-off

conditions were generated using the new adaptive MDA. In the following sections, the

experimental setup will be described and the results of findings will be presented.

7.1 Experimental Setup

7.1.1 Tasks

The flying tasks were recoveries from the following six upset scenarios:

Scenario Type Descriptions

1 Severe Stall A stall resulting from the combination of full thrust and

full nose-up stabilizer trim during an instrument landing

system approach. During the stall, turbulence is applied

to introduce lateral disturbances. The pitch angle at

initial recovery is approximately 45.4.

51

Chapter 7. Upset Recovery Experiment 52

2 Modest Stall Same as scenario 1 except that the pitch angle at initial

recovery is approximately 19.7.

3 Large Roll A large roll upset resulting from the Attitude Direc-

tor Indicator (ADI) malfunction and incorrect wheel in-

put. In this scenario, the ADI is set to indicate zero roll

throughout the flight.

4 Rudder Hard-over A rudder hardover case where the rudder remains at the

jammed position and the pedals are deactivated.

5 Windshear A microburst where a powerful downdraft occurs follow-

ing an updraft.

6 Pilot Induced Stall A pilot induced stall maneuver whereby a pitch flight

director leads pilots into the stall condition.

These upset scenarios were originally designed by Liu [10] for a fixed-base upset

recovery experiment. In the current experiment, the aircraft’s behavior was simulated

for all six upset scenarios using the enhanced B-747 roll model (which was previously

introduced in Section 3.1.1). As per Liu’s experiment, Scenarios 1 to 5 were actual upset

recovery tasks. At the beginning of these scenarios, the simulated aircraft was flown into

the upset conditions using pre-programmed control inputs. After the simulated aircraft

was upset, an audible tone was generated to signal control handover to pilots. Then,

pilots took control of the aircraft and began recovery. Note that the controls were back-

driven during the entry to the upset so pilots could see the condition being entered.

Scenario 6 was a pilot induced stall and recovery task. For this scenario, pilots induced

a stall by tracking the pitch time history of a NASA flight test which was indicated by

a flight director shown on the ADI. After the simulated aircraft was stalled, the flight

director disappeared and pilots initiated recovery.

For all scenarios, the simulated aircraft was considered successfully recovered when it

was returned to a steady level flight such that the pitch attitude, roll attitude, airspeed

and altitude remained relatively constant for about 5 seconds. Landing was not required

in this experiment.

7.1.2 Indications of Stall

In this experiment, buffet was generated in the heave direction to simulate the buffet

that occurs in the real airplane. Also, a stick shaker was added onto the control column.


The data for the initial stick shaker angle of attack and the angle of attack for initial

buffet were provided by Hanke and Nordwall [29].

The buffet signal was generated using the Simulink model presented in Figure 7.1.

This buffet model was originally developed by Jiang [40]. The source of the buffet signal

was a white noise generator. The output from the white noise generator was multiplied

by a scale factor and then filtered by a set of high-pass filters, low-pass filters and band-

pass filters to generate the desired buffet signal. The parameters of the filters used in

the buffet model are listed in Appendix B.1. The magnitude of the buffet signal was

controlled by the scale factor as a function of the simulator angle of attack (α) and flap

setting. As shown in Figure 7.1, the simulator flap setting was used to determine the

angle of attack for initial buffet (αb) and the critical angle of attack (αCLmax). α, αb

and αCLmax were then input to an embedded function to determine the scale factor. The

algorithm of the embedded function is presented in Figure 7.2. For the data of αb and

αCLmax at each flap setting, see Appendix B.2. The power spectral density (PSD) of the

buffet signal generated using the maximum scale factor (scale factor = 1.2) is depicted

in Figure 7.3. The root mean square value of the buffet acceleration generated using the

maximum scale factor was approximately 0.28m/s2.

Figure 7.1: Buffet Model

7.1.3 Motion Tuning Cases

Four motion cases, each representing a different trade-off between translational and ro-

tational motions, were generated for each of the six upset scenarios. One of the motion


0

0.6

1.2

α

Bu

ffet

Sca

le F

acto

r

αb

αCLmax (2α

CLmax− α

b)

Figure 7.2: Scale Factor for Buffet Signal

100 10110−6

10−5

10−4

10−3

10−2

10−1

freq, Hz

PSD

, (m

/s2 )2 /Hz

Figure 7.3: Power Spectral Density of the Buffet

Signal (Scale Factor = 1.2)

cases involved no simulator motion except buffet (denoted as N). The other three cases

were simulator motions generated using the new adaptive MDA developed in Chapter

6 to represent aircraft motions in terms of best matching specific forces (denoted as F),

best matching angular rates (denoted as Ω), and best compromise between specific forces

and angular rates (denoted as C). No parameter tuning was required for the N cases.

In total, 18 parameter sets were generated by employing the aircraft state time histories

collected by Liu [10] as the aircraft inputs to the new adaptive MDA and by evaluating

the new adaptive MDA using the maximum motion capabilities of the UTIAS FRS given

in Table A.6 in Appendix A.3. The parameter sets are listed in Tables A.7 to A.24.

As a preliminary investigation, the modified Sinacori motion fideilty criteria were

used to estimate the fidelity of all motion cases before adaptation. The magnitude and

phase at 1 rad/s for the baseline angular and translational high-pass filters are plotted in

Figures 7.4 to 7.9. Overall, the fidelity of all F cases was rated as low for simulating either

rotational or translational motion, except that the fidelity was high in the yaw DOF for

Scenarios 1 and 5 as the yaw motions in these scenarios were not severe; the fidelity

of all Ω cases was estimated to be between medium and high for simulating rotational

motion and low for simulating translational motion; and the C cases were a compromise

between the F and Ω cases for both translational and rotational fidelity. The reason why

the translational fidelity of the F cases was rated as low was because the surge and sway

motions at upset were usually of low frequency and large amplitude, and therefore were

mostly simulated using tilt coordination. In order to take into account the contribution

of the low-pass filters, the translational fidelity was estimated again based on the total


specific force transfer function,

fx,ySS

fx,yAA

= kfx,y(LPx,y + (1− LPx,y)HPx,y) (7.1)

For all motion cases, the magnitude and phase at 1 rad/s for Equation 7.1 and those for

the heave high-pass filters are plotted in Figure 7.10. The fidelity of the F cases in the

surge and sway DOF was then estimated to be low but close to medium and of course the

fidelity in heave was of low fidelity due to the limited displacement envelope of hexapods.

The 3-D motion fidelity criteria were also used to estimate the fidelity of the motion

cases before filter adaptation. The magnitude and phase at 1 rad/s for the baseline roll

high-pass filters and the false lateral motion cues estimated by the maximum magnitude

of the total lateral specific force transfer function are plotted in Figure 7.11. Based on

these criteria, the fidelity of all F, Ω and C cases were low because either the specific forces

were poor or the angular rates were poor. This suggests that the fidelity based on solely

the magnitude and phase response of the angular high-pass filters could be overestimated.

Nevertheless, the 3-D criteria confirmed that the F cases produced relatively the least

amount of false lateral motion cues and very little rotational motion; the Ω cases provided

the largest amount of rotational motions which were likely to be uncoordinated; and the

C cases were the compromise between the F and Ω cases.

During the experiment, the fidelity of all motion cases varied depending on the adap-

tation of the filter parameters. In order to examine the performance of the motion cases

during adaptation, the maximum fidelity each tuning case could achieve during adapta-

tion was estimated by simulating the aircraft state time histories collected by Liu [10].

The magnitude and phase at 1 rad/s of Equation 7.1 evaluated using the most liberal

surge and sway filters and the magnitude and phase at 1 rad/s of the most liberal heave,

pitch, roll and yaw high-pass filters are plotted in Figures 7.12 to 7.17. During the simu-

lation, the F cases were only adapted in the surge and sway DOF to enhance translational

fidelity. For most of the F cases, the fidelity in these two DOF was rated as medium. The

exceptions were the sway DOF for Scenario 2 and the surge and sway DOF for Scenario

3, which all lay on the low-medium fidelity boundary. On the other hand, the Ω cases

were adapted only in pitch, roll and/or yaw DOF to enhance rotational fidelity. For most

of the Ω cases, the best fidelity was rated to be high in all rotational DOF. The exception

was the roll DOF for Scenario 6, which was rated to be of medium fidelity. The C cases

were adapted both in the translational and rotational DOF. Once again, the C cases were

a compromise between the F and Ω cases for both translational and rotational fidelity.


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity

F − xF − yF − zΩ − xΩ − yΩ − zC − xC − yC − z

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity

F − pitchF − rollF − yawΩ − pitchΩ − rollΩ − yawC − pitchC − rollC − yaw

Figure 7.4: Fidelity of Baseline High-Pass Filters - Scenario 1

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity



0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity




0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity



0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity



0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity




0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


(a) Scenario 1

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


(b) Scenario 2

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


(c) Scenario 3

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


(d) Scenario 4

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


(e) Scenario 5

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


(f) Scenario 6

Figure 7.10: Translational Fidelity based on Both Baseline High-Pass and Low-Pass Filters


(a) Scenarios 1 & 2 (b) Scenarios 3 & 4

(c) Scenarios 5 & 6

High fidelity (red) : Motion sensations are close to those of visual flight

Medium fidelity (blue) : Motion sensation differences are noticeable but not objectionable

Low fidelity (white) : Motion sensation differences are noticeable and objectionable

Figure 7.11: 3-D Motion Fidelity Criteria


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


Figure 7.12: Maximum Fidelity based on Both High-Pass and Low-Pass Filters - Scenario 1

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity



0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity




0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity



0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity



0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Translational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140

160

180

Rotational gain

Ph

ase

Highfidelity

Mediumfidelity

Lowfidelity




7.1.4 Experimental Procedure

The pilots’ task in this experiment was to fly each of the six upset scenarios for a set of

training trials followed by a set of evaluation trials. The order of the six scenarios assigned

to each pilot was randomized. For each scenario, the training trials were carried out with

no simulator motion except buffet to allow pilots to exercise the recovery techniques

required in the evaluation trials. During the training trials, pilots were required to fly

the scenario repeatedly for 10 minutes until they successfully recovered from it twice. If

no successful recovery was performed within the first 5 minutes, pilots would be supported

with instructions for recovering from the corresponding scenario. For the details of the

recovery techniques for each scenario, see Liu [10].

After pilots successfully recovered from a scenario twice, they proceeded to the evalu-

ation trials of the corresponding scenario. For each scenario, a paired comparison exper-

iment was run during the evaluation trials. Pilots flew the scenario twelve times in six

pairs to compare N to F, N to Ω, N to C, F to Ω, F to C, and Ω to C. The sequence of

these six pairs and the order of the two motion cases in each pair were assigned to pilots

using a randomized ordering. The pairing sequences were different for different scenarios

and the complete list of pairing sequences are shown in Tables C.1 to C.5 in Appendix

C.1. At the end of each paired run, pilots rated the motion fidelity of the motion cases

by choosing one of: (1) the fidelity of the first case was higher than that of the second

case, (2) the fidelity of the second case was higher than that of the first case, or (3) the

two cases were tied in terms of the motion fidelity.

At the end of each flight, the visual displays, excluding the electronic flight instrument

system, were turned off after the simulated aircraft was recovered. Then, the simulator

was brought back to the start-up position. In the meanwhile, pilots were asked to keep

the control column at the steady level flight attitude until the visual display was turned

back on. The purpose of this procedure was to reduce simulator sickness.

The entire experiment session took approximately 4.5 hours, including a 5 to 10

minute break after the completion of every second scenario. Five pilots, including one

flight training instructor and four test pilots, participated in the experiment. All pilots

had previous experience in upset recovery training and aerobatic flying experience. One

pilot had experience flying a B747-200 configuration. Four of the five pilots finished the

entire session in one day, and one pilot finished the session in two different days due to

the stick shaker malfunctioning on the first day.


7.2 Results

The analysis of the experimental results consists of two parts: (1) an analysis of the

subjective paired comparison data, and (2) an analysis of the objective pilot performance

data.

7.2.1 Subjective Paired Comparison Analysis

7.2.1.1 Non-parametric Analysis

The following non-parametric analysis for paired comparison experiments is based on

Butler [41] and it was developed by extending the non-parametric analysis given by

David [42] to allow ties and order effect. The probability that motion condition i is

preferred over motion condition j is given by the pair probability, πij, which is estimated

using

πij = αij/n (7.2)

where n is the total number of times conditions i and j are compared and αij is the total

number of times condition i is selected over j plus half the number of times conditions

i and j are tied. For this experiment, each pair of conditions was tested once by each

pilot, so n = 5 (5 subjects × 1 order). The total score for each motion condition is then,

ai =tc∑j=1

αij (7.3)

where tc is the number of conditions being compared, which is 4, and αii is 0 by definition.

The total scores for the four motion cases for all six scenarios are shown in Table 7.1 and

in Figure 7.18.

The first step in this analysis is to test the null hypothesis, H0, that all measured

scores are statistically equal (i.e. all motion conditions are equally preferred). According

to Butler [41], the expected values of all the scores is n/2× (tc− 1), which is 7.5 for this

experiment, and the variance of all the scores when all motion cases are equally preferred

is given by

σ2ai

=n(tc − 1)

2

[P1(1− P1) + P2(1− P2)− Po(1− Po)

2

](7.4)

The following probabilities are defined under H0,

P1, the probability of selecting the first condition when the conditions are the same


Scenario Severe Stall Moderate Stall

Motion Case N F Ω C N F Ω C

Scores 8.5 9 5.5 7 3.5 10 7.5 9

Scenario Large Roll Rudder Hard-over


Scores 6 11.5 3 9.5 3.5 8 10.5 8

Scenario Windshear Pilot Induced Stall


Scores 6.5 10 8 5.5 7.5 6 7.5 9

Table 7.1: Total Scores

0

2

4

6

8

10

Motion C ond it ion

Score

s

N F Ω C

(a) Severe Stall

0

2

4

6

8

10

12

Motion C ond it ion

Score

s

N F Ω C

(b) Modest Stall

0

2

4

6

8

10

12

Motion C ond it ionScore

sN F Ω C

(c) Large Roll

0

2

4

6

8

10

12

Motion C ond it ion

Score

s

N F Ω C

(d) Rudder Hard-over

0

2

4

6

8

10

12

Motion C ond it ion

Score

s

N F Ω C

(e) Windshear

0

2

4

6

8

10

Motion C ond it ion

Score

s

N F Ω C

(f) Pilot Induced Stall

Figure 7.18: Total Scores for Motion Conditions

P2, the probability of selecting the second condition when the conditions are the same

Po, the probability of selecting a tie when the conditions are the same

Also defining

di =ai − n(tc − 1)/2√

(ntc/2) [P1(1− P1) + P2(1− P2)− Po(1− Po)/2](7.5)


and taking into accounts ties and order effects, Butler [41] shows that for H0 the distri-

bution of Dn,

Dn =tc∑i=1

d2i =

2[∑tc

i=1 a2i − 1

4tcn

2(tc − 1)2]

ntc [P1(1− P1) + P2(1− P2)− Po(1− Po)/2](7.6)

can be approximated by the χ2 distribution with (tc − 1) DOF for both large and small

n(tc − 1).

Butler [41] suggests that the probabilities P1, P2, and Po can be estimated from the

experimental data, so

P1 = T1/Ttotal

P2 = T2/Ttotal

Po = To/Ttotal

(7.7)

where T1 is the total number of preferences for the condition presented first, T2 is the total

number of preferences for the condition presented second, To is the total number of ties,

and Ttotal = ntc(tc−1)/2 is the total number of comparisons, which is 30 for each scenario.

The estimated probabilities and the results of this analysis are presented in Table 7.2.

At the 5% level, significant motion differences were found for the Large Roll and Rudder-

Hardover scenarios and at the 10% level, there were significant motion differences for the

Modest Stall scenario. There was no preference between motion conditions for the Severe

Stall, Windshear, and Pilot Induced Stall scenarios.

Severe Stall Modest Stall Large Roll

P1 0.27 0.27 0.33

P2 0.43 0.40 0.43

Po 0.30 0.33 0.23

P of H0 0.53 0.06 * 0.01**

Rudder Hard-over Windshear Pilot Induced Stall

P1 0.30 0.17 0.27

P2 0.30 0.33 0.40

Po 0.40 0.50 0.33

P of H0 0.04** 0.18 0.71

Table 7.2: Overall Test of Significance

Post-hoc tests were conducted using the multiple comparison range test paralleling

the Tukey Honestly Significant Difference (HSD) method [42]. Butler [41] shows that


this test can be applied to the case with order and ties. He also suggests that the

probability of the range of scores being greater than or equal to the critical range (R−)

at a selected significance level (αsig) can be approximated by the probability of the

studentized range Wtc,αsig (with infinite DOF) being greater than or equal to the critical

range of di. According to David [42], R− at the αsig level is

R− = min(R∗, R+) (7.8)

where

R+ = n(tc − 1)− n/2 (7.9)

and R∗ is obtained by solving

Wtc,αsig =σ∆diR

∗ − 1/2

σ∆ai

(7.10)

where the right hand side of Equation 7.10 represents the critical range of di with a

continuity correction of half the usual size [42]. Using Equation 7.4 and 7.5, σ2∆di

, which

is the variance of the difference in di, is found to be 2 and the variance of the difference

in motion scores, σ2∆ai

, is given by

σ2∆ai

= ntc [P1(1− P1) + P2(1− P2)− Po(1− Po)/2] (7.11)

After rounding to the nearest 0.5, R∗ is

R∗ =1

2ceil

2√2

[Wtc,αsig

√ntc(P1(1− P1) + P2(1− P2)− Po(1− Po)/2) +

1

2

](7.12)

R− was calculated to be 7.5 at the 5% level for the Large Roll scenario, 7.0 at the 5%

level for the Rudder Hard-over scenario, and 6.5 at the 10% level for the Modest Stall

scenario. Thus for the Large Roll scenario only the F case was significantly preferred

to the Ω case (P = 0.046). For the Rudder Hard-over scenario only the Ω case was

significantly preferred to the N case (P = 0.034). Finally for the Modest Stall scenario

only the F case was somewhat preferred to the N case (P = 0.075).

7.2.1.2 Parametric Analysis

The previous non-parametric analysis allowed us to determine which motion cases were

significantly different from each other, but it provided little information on how much


more one motion case was preferred over another. In this section, a Bradley-Terry (B-

T) model is used to determine the merit for each motion condition. The merit values

estimated using the B-T model are on a linear scale and therefore (in case when the B-T

model fits well) the merit values would provide quantitative information on the relative

motion fidelity.

The following B-T model incorporating ties and order effects was developed by David-

son and Beaver [43]. For each ordered pair (i, j), the preference probabilities are given

as,

πi,ij =πi

πi + γπj + ν√πiπj

πj,ij =γπj


πo,ij =ν√πiπj


(7.13)

where πi,ij denotes the probability that i is preferred to j when i comes first, πj,ij denotes

the probability that j is preferred to i when i comes first, πo,ij denotes the probability

of a tie when i comes first, πi denotes the subjective merit of condition i, γ is the order

effect parameter, and ν is the tie parameter. For this model, it is required that πi ≥ 0,

γ ≥ 0, and ν ≥ 0. Note that the basic B-T model with no ties or order effects is obtained

when γ = 1, and ν = 0. When γ > 1, there is a bias to the condition presented second,

and when γ < 1, there is a bias to the first case presented.

The parameters of the extended B-T model can be estimated using the maximum

likelihood method. Unfortunately, the model incorporating ties and order effects is not

a generalized linear model; therefore, the maximum likelihood estimates have to be ob-

tained using an iterative approach. The following maximum likelihood estimation is

based on Davidson and Beaver [43]. For each ordered pair (i, j), let w1,ij, w2,ij and wo,ij

be the frequencies of preference for the first presented case (case i), the second presented

case (case j) and a tie respectively. Then, the total number of times each pair (i, j)

is compared in that order is rij = w1,ij + w2,ij + wo,ij. Also, as previously defined for

the non-parametric analysis, ai =∑

j[2(w1,ij + w2,ji) + wo,ij + wo,ji], T1 =∑

i

∑j w1,ij,

T2 =∑

i

∑j w2,ij, and To =

∑i

∑j wo,ij. The logarithm of the likelihood function is then

given by

ln L(π, γ, ν) =1

2

∑i

ai ln πi + T2 ln γ + To ln ν −∑∑

i 6=j

rij ln (πi + γπj + ν√πiπj)

(7.14)


By maximizing Equation 7.14 with an additional constraint of∑πi = 1, the maximum

likelihood estimates (π, γ, ν) of (π, γ, ν) can be obtained by solving the system of

equations shown in Equation 7.15 [43]. Note that π and π are vectors consisting all πi

and πi (i = 1, ... , tc) respectively.

ai/πi = gi(π, γ, ν) for i = 1, ... , tc

T2/γ = hγ(π, γ, ν)

To/ν = hν(π, γ, ν)

(7.15)

where

gi(π, γ, ν) =∑j

rij(2 + ν√πj/πi)


+∑j

rji(2γ + ν√πj/πi)

γπi + πj + ν√πiπj

hγ(π, γ, ν) =∑∑

i 6=j

rijπj


hν(π, γ, ν) =∑∑

i 6=j

rij√πiπj


The following iterative scheme is suggested by Davidson and Beaver [43] for solving

Equation 7.15. Davidson and Beaver suggest to set the initial conditions as π(0)i = 1/tc

(i = 1, ... , tc), γ(0) = T2/[Ttotal − (T2 + To)], and ν(0) = To/[Ttotal − (T2 + To)]. If order

effect is not considered, Davidson [44] suggests to set the initial conditions as π(0)i = 1/tc

(i = 1, ... , tc) and ν(0) = 2To/(Ttotal − To). Then, for the M th iteration (M ≥ 1),

1. Generate a new estimate of π in a cycle of tc stages by updating one of the tc

elements of π per stage. At the (m+ 1)th stage (m ≥ 0),

π(m+1)i = ai/gi(π

(m), γ(M−1), ν(M−1)) (7.16)

where i = m+ 1 (mod tc). Then, π(m+1) is obtained by replacing only π(m)i in π(m)

with π(m+1)i . At the end of each cycle of tc stages (i.e. when m ≡ tc (mod tc)), set

π(M) = π(m) (7.17)

2. Generate a new estimate of γ by evaluating

γ(M) = T2/hγ(π(M), γ(M−1), ν(M−1)) (7.18)

3. Generate a new estimate of ν by evaluating

ν(M) = To/hν(π(M), γ(M), ν(M−1)) (7.19)


As stated by Davidson and Beaver [43], a unique estimate of (π, γ, ν) which maximizes

the log-likelihood function (Equation 7.14) is guaranteed by the above iterative scheme

if and only if the following condition is met:

“In every partition of the objects into two non-empty sets I and J , there exist i ∈ I,

j ∈ J such that w1,ij > 0 and there exists k ∈ I, l ∈ J such that w2,kl > 0” (P.702, [43]).

Unfortunately, the paired comparison data for this study violated this assumption. In

order to confirm that the maximum likelihood estimates generated for the current paired

comparison data were unique, the iterative scheme was repeated nine times, each time

started with a random set of initial conditions. The results showed that all nine different

initial conditions converged to the same maximum likelihood estimates, suggesting that

the maximum likelihood estimates for the current experimental data were unique.

The results of the maximum likelihood estimates (π, γ, ν) are presented Table 7.3.

Note as only the difference in the merits are important, the merits for the N cases were

set to zero for reference. Also, as the data are on a ratio scale, the merits cannot be

meaningfully compared between scenarios. The results for a test of goodness of fit of the

model based on the likelihood ratio test (G.O.F), the correlation coefficient between the

measured probabilities and the probabilities estimated by the extended B-T model (R),

a test of the presence of an order effect (P (γ = 1)), and a test of overall equality of the

merits (P (πN = πF = πΩ = πC)) are also shown in Table 7.3. The procedures of the

three statistical tests and the measurement of the correlation coefficients are detailed in

Appendix C.2.

G.O.F R P (γ = 1) P (πN = πF πN πF πΩ πC γ ν

=πΩ = πC)

Severe Stall 0.45 0.49 0.32 0.53 0.00 0.05 -0.19 -0.11 1.00 0.90

Modest Stall 0.51 0.72 0.29 0.04** 0.00 0.42 0.14 0.28 1.00 1.27

Large Roll0.09 0.83

0.160.01** 0.00 0.51 -0.06 0.20 1.00 0.86

0.36 0.77 0.00** 0.00 0.57 -0.04 0.21 2.22 1.38

Rudder Hard-over 0.89 0.88 0.77 0.02** 0.00 0.17 0.55 0.17 1.00 1.84

Windshear 0.85 0.790.07

0.18 0.00 0.46 0.11 -0.04 1.00 2.40

0.34 0.56 0.09 0.00 0.59 0.13 -0.02 3.12 4.89

Pilot Induced Stall 0.97 0.61 0.20 0.71 0.00 -0.09 0.00 0.14 1.00 1.04

Table 7.3: Extended Bradley-Terry Model Fits

The presence of an order effect is somewhat significant only for the Windshear sce-

nario; therefore, for all other scenarios, excluding the Large Roll scenario, only the fit


for the B-T model incorporating ties but no order effect is presented. For the Large

Roll scenario, the order effect is not significant but the goodness of fit of the B-T model

without an order effect is very low and it contradicts the good fit suggested by the cor-

relation coefficient. The reason for this contradiction is that as described in Appendix

C.2, the estimated frequencies were used to evaluate the goodness of fit. For the Large

Roll scenario, one of the estimated frequencies is close to zero while the corresponding

measured frequency is close to unity. According to Davidson [44], the accuracy of the

approximated goodness of fit is low when the expected frequencies differ significantly

from the measured frequencies. In order to get a model with a more accurate model fit,

the B-T model incorporating both ties and order effects was used to fit the data for the

Large Roll scenario. The goodness of fit for this model is then found to be moderately

good. Overall, the ranking of the merits shows that the F case was rated the best for

the Severe Stall, Modest Stall, Large Roll, and Windshear scenarios. For the Rudder-

Hardover case, the Ω case was rated the best while the C case was rated the best for the

Pilot Induced Stall scenario. Moreover, significant motion differences were found only

for the Modest Stall, Large Roll and Rudder Hard-over scenarios. The results of this

analysis agree closely with those of the non-parametric analysis.

7.2.2 Objective Pilot Performance Analysis

The pilot performance data were analyzed for all scenarios. Repeated-measures univariate

analysis of variance (ANOVA) was conducted on the parameters listed in Table 7.4. For

the Severe Stall, Modest Stall, Large Roll, Rudder Hard-over, and Windshear scenarios,

the data for the performance analysis were extracted from the time of control handover to

the time when the sound switch was turned off to reset each flight. For the Pilot Induced

Stall scenario, data were extracted from the time when the flight director disappeared

to the time when sound was switched off. All pilots flew each scenario with each motion

case three times, but one file which was a third attempt of the C case for the Large Roll

Scenario was corrupted; hence, this case was not included in the analysis. For each pilot,

an average was computed for each parameter and each motion case. The ANOVA was

performed on these averaged data for each of the six upset scenarios.

The F-test found no significant motion differences in any of the performance param-

eters for the Modest Stall and Pilot Induced Stall scenarios. For the Severe Stall, Large

Roll, Rudder Hard-over, and Windshear scenarios, the F-test results which are significant


Maximum Pitch Angle (θmax) Minimum Pitch Angle (θmin) Absolute Maximum Pitch Angle (|θ|max)Maximum Roll Angle (φmax) Minimum Roll Angle (φmin) Absolute Maximum Roll Angle (|φ|max)Maximum Yaw Angle (ψmax) Minimum Yaw Angle (ψmin) Absolute Maximum Yaw Angle (|ψ|max)

RMS of Roll Rate (prms) RMS of Pitch Rate (qrms) RMS of Yaw Rate (rrms)

Maximum Normal Load Minimum Normal LoadMinimum Altitude (hmin)

Factor (nzmax) Factor (nzmin)

Table 7.4: Dependent Variables for ANOVA

at the 5% level are presented in Table 7.5. For cases where the assumption of sphericity

was violated, the stated P-values were corrected for the lack of sphericity in the covari-

ance matrix using the Huynh-Feldt method [45]. For the Rudder Hard-over scenario, the

F-test results were identical for θmax and |θ|max. Inspection of the data found that it was

because θmax = |θ|max for all data for this scenario. In the following analysis, therefore,

only |θ|max will be analyzed for the Rudder Hard-over scenario. For all parameters with

significant F-test, the means of the parameters and the standard error for each motion

case are shown in Figures 7.19 to 7.26. Post-hoc test was conducted using the Tukey

HSD multiple comparison method [45] to compare all motion cases pair-wise to find the

source of significant difference in the means. The Tukey HSD test results are presented

in Table 7.5 in terms of the ranking of the motion cases, where the leftmost motion case

in the ranking has the smallest mean for the corresponding parameter. Any two motion

cases which are not underlined by the same line are significantly different at the 5% level.


Scenario Sever Stall Large Roll Rudder Hard-over Windshear

θmax −− −−F (3, 12) = 6.570

−−P = 0.007

C F Ω N

|θ|max −− −−F (3, 12) = 6.570

−−P = 0.007

C F Ω N

φmax

F (3, 12) = 3.493

−− −− −−P = 0.050

Ω F C N

prms −−F (3, 12) = 3.996 F (3, 12) = 12.417

−−P = 0.035 P = 0.001

Ω C F N Ω F C N

qrms −− −−F (2, 10) = 5.777 F (3, 12) = 5.908

P = 0.019 P = 0.010

Ω C F N C Ω F N

rrms −− −−F (3, 11) = 13.364

−−P = 0.001

Ω F C N

nzmax −− −−F (3, 12) = 5.374

−−P = 0.014

Ω C F N

Table 7.5: Significant F-test Results

17

17.5

18

18.5

19

19.5

20

Ω F C N

Motion Condition

φ max

(de

g)

Figure 7.19: Mean φmax for Severe Stall

5

5.5

6

6.5

Ω C F N

Motion Condition

p rms (

deg/

s)

Figure 7.20: Mean prms for Large Roll


9.8

10

10.2

10.4

10.6

10.8

C F Ω N

Motion Condition

|θ| m

ax (

deg)

Figure 7.21: Mean |θ|max for Rudder Hard-over

3.8

4

4.2

4.4

4.6

4.8

5

Ω F C N

Motion Condition

p rms (

deg/

s)

Figure 7.22: Mean prms for Rudder Hard-over

0.8

1

1.2

1.4

1.6

Ω C F N

Motion Condition

q rms (

deg/

s)

Figure 7.23: Mean qrms for Rudder Hard-over

1.8

2

2.2

2.4

Ω F C N

Motion Condition

r rms (

deg/

s)

Figure 7.24: Mean rrms for Rudder Hard-over

1.25

1.3

1.35

1.4

Ω C F N

Motion Condition

n z max

(g)

Figure 7.25: Mean nzmax for Rudder Hard-over

1.4

1.5

1.6

1.7

1.8

C Ω F N

Motion Condition

q rms (

deg/

s)

Figure 7.26: Mean qrms for Windshear


7.3 Discussion of Results

For the Large Roll scenario, there was a strong preference for the F motion case and a

strong dislike for the Ω motion case with the compromise C being somewhat preferred

to the N case. The most likely explanation for this preference is the large lateral specific

force errors that occurred when an attempt was made to simulate the large roll motion.

In fact, three of the five pilots commented on the uncoordinated roll maneuvers and

mentioned that they did not prefer the strong side force in the Ω case of this scenario.

For other than the N case, the subjective fidelity ranking was identical to that given by

the minimization of the lateral specific force false cues. N was rated inferior to both F and

C likely because the false cues for these cases were not too large yet they still produced

motion. On the other hand, the performance analysis found that the root mean square

of the roll rate was significantly smaller for the Ω case than the N case. According to this

analysis, the value of prms was in fact inversely proportional to the fidelity of roll cues in

each motion case. As no significant differences were detected in the roll angle, a smaller

value of prms would mean that the aircraft was recovered using less aggressive dynamic

roll motions without causing the roll attitude to diverge, indicating better lateral control.

Hence, if prms is considered a representative measure of lateral control, the fidelity of roll

cues is then directly related to the degree of lateral control in the Large Roll scenario.

Also, the contradiction between the two analysis suggests that the specific force false

cues associated with the roll motion cues may in effect be subjectively cancelling out the

benefits of the improved lateral control.

For the Rudder Hard-over scenario, the Ω case was most preferred and the N case

was the least preferred. The other two cases were the same and fell between these two

extremes. This seems like a curious result given our previous explanation of lateral specific

force false cues. In fact, no pilots commented on the amount of lateral specific force false

cues during the testing of the Rudder Hard-over scenario. One possible explanation for

this is that the roll attitude for the Rudder Hard-over event was generally smaller than

that for the Large Roll scenario, so the roll cues could be generated for good lateral

motion cueing without the associated large false lateral cues. The benefit of the roll cues

was confirmed by the performance analysis. prms was found be to significantly smaller in

the Ω case than in any other motion cases for this scenario while no significant differences

were detected in the roll angle. Moreover, rrms was also found to be significantly smaller

for the Ω than the C and N cases with no significant differences found in the yaw angle.


This suggests that the presence of roll cues and yaw cues helped improve the lateral and

directional control in the event of rudder hard-over. The performance analysis also found

that the maximum normal load factor was significantly higher for the N case than any

other motion cases, suggesting that pilots tended to pull harder on the column in order to

roll aircraft back towards the wings-level flight when no motion cues were present. Lastly,

qrms was smaller for the Ω case than for the C and F cases while it was significantly smaller

than for the N case. In contrary, |θ|max was significantly smaller for the C case than both

the Ω and N cases. This suggests that high fidelity pitch motion does not necessarily lead

to improvements for the longitudinal control, but a compromise between specific force

cues and angular cues may lead to a good balance between the aircraft dynamic pitch

motion and pitch attitude for recovering a rudder hard-over scenario.

There was little preference for any of the motion conditions for the Windshear sce-

nario. In particular, the fit of the extended B-T model for this scenario determined a

high value for the tie parameter (ν = 4.89) and a probability of the presence of order

effect that was close to being significant at the 5% level. This suggests that pilots tended

to choose a tie or the motion case that was presented last in each pair. In fact, three

pilots found that the motions for this scenario were generally too subtle in all motion

cases. The performance analysis found that the root mean square values of the pitch rate

of both the C and Ω cases were significantly smaller than that of the N case. Although

no consensus was achieved between the subjective fidelity analysis and the performance

analysis, the results of this performance analysis agree with those of the Rudder Hard-

over scenario that a compromise between translational and rotational cues may lead to

better longitudinal control.

For the Severe Stall scenario, analysis of the performance data found that the max-

imum roll angle was significantly smaller for the Ω case than for the N case, but there

were no significant motion differences in terms of the minimum roll angle or the absolute

maximum roll angle. Generally, the maximum roll angle gives an indication of the pilot

performance for maintaining lateral control when the aircraft rolls to the right (with

smaller values indicating better control), and for this experiment, right was set as the

direction for the asymmetric stall roll-off. If the maximum roll angle is considered to be

a representative measure of lateral control, then it seems that the fidelity of roll cues was

closely related the degree of control for the aircraft’s initial divergent lateral-directional

responses. In order to confirm this claim, the data for the first maximum roll angle

that occurred after control handover (between control handover and about 10 seconds


after control handover) were examined for the Severe Stall scenario. The data for the

first maximum roll angle were almost identical to the overall maximum roll angle except

for one flight where a pilot got into a second lateral divergence. F-test found that the

effects of the motion types on the first maximum roll angle after control handover was

somewhat significant (P=0.063) and Tukey HSD test found that the first maximum roll

angle was significantly smaller for the Ω case than for the N case at the 10% level (see

Figure 7.27). It was therefore concluded that the presence of roll cues provided strong

alerting cues that helped improve the control for a divergent roll-off/directional response

during the Severe Stall scenario. On the other hand, no significant motion preferences

were measured by the pilot subjective fidelity. One possible reason for this is that during

the Severe Stall maneuver, the aircraft attained large roll and pitch angles and therefore

the specific force false cues associated with the Ω case may once again be subjectively

cancelling out the performance benefits of good angular cueing for controlling the aircraft

when it became laterally unstable at stall.

17

17.5

18

18.5

19

19.5

20

Ω F C N

Motion Condition

Initi

al φ

max

(de

g)

Figure 7.27: Mean of First φmax after Control Handover for Severe Stall

In contrast, no significant motion differences were detected by analyzing the perfor-

mance data for the Modest Stall scenario; however, analysis of the paired comparison

data showed that the F case was significantly preferred over the N case while the other

two motion cases were roughly equal and fell between the F and N cases. It is likely

that the minimization of false lateral cues once again led to F being preferred, but the

minimization of lateral specific force false cues does not explain everything in this case

as Ω (which should have produced the largest false cues) was not the least preferred. A

plausible reason is that the aircraft stalls at a much smaller pitch attitude in this scenario

than in the Severe Stall scenario (θmax ranged from 20.1deg to 28.3 deg in the Modest

Stall scenario and 46.1 deg to 47.4 deg in the Severe Stall case), so the aircraft can be


easily recovered without entering aggressive roll-off and directional divergence. Conse-

quently, roll and yaw motions were only generated to simulate the dutch-roll introduced

by turbulence for the Modest Stall scenario. During the experiment, the oscillatory roll

and sideslip responses were quickly countered by pilots. As a result, the roll attitude was

generally smaller in this scenario than in the Severe Stall scenario, so the roll cues could

provide useful cueing without generating large lateral specific force false cues. Moreover,

there was not much advantage to the roll cues for reducing the maximum roll angle likely

because the aircraft did not enter roll-off/directional divergence.

For the Pilot Induced Stall scenario, one would probably expect the same results as

those of the Severe Stall scenario since both scenarios involved aerodynamic stalling at

a high pitch attitude; however, no significant motion differences were found in either the

paired comparison data or the performance data for the Pilot Induced Stall scenario. The

differences in the results might be attributed to the differences in the nature of these two

stall conditions. As mentioned in Section 7.1.1, the upset condition for the Severe Stall

scenario was created by pre-programmed control inputs while pilots brought themselves

into a stall for the Pilot Induced Stall case. In general, no two pilots fly the same way

and how well a pilot follows the flight director to induce a stall might change from one

another; therefore, roll-off/directional divergence might only occur in some flights but not

all in the Pilot Induced Stall case. Consequently, the effects of roll cues on controlling

the asymmetric roll-off/directional divergence at stall could not be well determined for

this scenario. Moreover, the subjective preference for the roll cues would depend on

the amount of lateral specific force false cues associated with the roll attitude of each

flight. It is, in fact, interesting to find that although motion cases were not significantly

different, the compromise C case was subjectively rated the best for this scenario.

Overall, the presence of good roll cueing improved lateral control during both a severe

stall and unusual attitude upsets. This confirms with the results presented by Shirley

et al. [24] and Young [46] which suggest that roll cues improved control for unstable

vehicle dynamics. In particular, increasing the fidelity of roll cues at the expense of the

false lateral specific forces led to improvement in pilot performance but not in subjective

fidelity. This is in agreement with the findings of Grant et al. [47]. In another study by

Grant et al. [48], it was found that yaw motion and lateral translational motion improved

performance for a directional disturbance rejection task. Similarly, for the rudder hard-

over event, yaw cues led to the reduction in the dynamic yaw motion during upset;

however, the lateral specific forces did not have an impact on performance and it is likely


because the lateral translational motion examined in the study of Grant et al. [48] were

of high frequency while in the rudder hard-over scenario mainly low frequency lateral

specific forces were generated. In general, pilots rated at least one of the F, Ω, and C

cases higher than the N case for all scenarios. This suggests that the presence of simulator

motion, regardless of the trade-off between translational and rotational motion cues, was

preferred during piloted recovery. Moreover, in all the significant results found in the

performance analysis, the recovery performance was significantly better when simulator

motions were present (F, Ω or C case) than the performance when no simulator motion

was involved (N case). This important finding supports the hypothesis stated at the

beginning of this thesis that simulator motion may be important for UPRT.

Chapter 8

Conclusions

8.1 Summary of Work

In this thesis, a new set of 3-D motion fidelity criteria was defined for coordinated roll

upsets. These criteria were developed based on the modified Sinacori motion fidelity

criteria and Schroeder’s motion fidelity criteria correlated to roll and lateral gains. They

were proposed to estimate the fidelity of general MDAs based on a combination of the

simulator false lateral motion cues, the phase of the intended roll motion, and the gain

of the intended roll motion.

Body frame filters were incorporated into the UTIAS Classical MDA to reduce cross-

coupling among different DOF when simulating large amplitude motion during upset.

Desktop simulations were performed on six different upset scenarios and the results

showed that the elimination of cross-coupling effects did not lead to significant reduc-

tion of motion cue errors. Examination of the simulation results suggests that the upset

scenarios being studied were dominated by low frequency motion and the simulation

of low frequency motion required tilt coordination that did not contain cross-coupling.

Consequently, the motion cue errors reduced by removing cross-coupling effects might be

similar to the errors caused by the additional phase and magnitude errors introduced by

the body frame high-pass filters.

A new adaptive MDA was developed to adapt the gains and frequencies of all high-

pass and low-pass filters numerically without causing undesired oscillations and it has

weights and initial coefficients that can be tuned to adjust the parameter adaptation

rates. The goal of the parameter adaptation is to maximize the fidelity of platform

motion cues during upset recovery simulation. During the tuning of this new MDA, it

79

Chapter 8. Conclusions 80

was determined that for severe upset events both specific force and angular rate cannot

be of medium fidelity simultaneously; therefore, a paired comparison experiment was

performed to analyze the effects of different trade-offs between specific force and angular

rate on subjective motion fidelity and pilot performance during upset recovery. In this

experiment, four different motion conditions, each representing a different type of trade-

off between translational and rotational motion cues, were compared in six different upset

scenarios. All upset scenarios were simulated using the enhanced B-747 roll model and the

simulator motion of all motion cases were generated using the new adaptive MDA. A total

of 18 different sets of motion tuning cases were generated for this experiment. For all these

motion cases, the fidelity before adaptation and the maximum fidelity during adaptation

were evaluated using the modified Sinacori motion fidelity criteria. The fidelity analysis

showed that motion fidelity can be improved using parameter adaptation. In addition,

the roll fidelity of all 18 motion cases were evaluated using both the modified Sinacori

and the new 3-D motion fidelity criteria and it was found that the fidelity estimated

based on solely the magnitude and phase response of the roll high-pass filters could be

overestimated.

Analysis of the subjective paired comparison data found that pilots indicated strong

preference for the minimization of false lateral specific force false cues during large roll

excursions and they preferred angular motion cues when the roll attitude was moderate.

The preference for the minimization of false lateral specific force cues was also observed

in the case of a mild stall where a lateral disturbance was introduced by turbulence

but no aggressive lateral/directional divergence developed. On the other hand, analysis

of the pilot performance data suggests that the presence of roll cues helped improve

lateral control by reducing the first maximum roll angle after control handover as the

aircraft entered a lateral/directional divergence at stall, but no performance benefits were

detected for stall cases where divergent roll-off/directional response did not develop. It

was also found that during unusual attitude upsets, pilots tended to recover with less

aggressive dynamic roll motion when the fidelity of the roll cues was high, and in the

case of rudder hard-over and windshear, pilots tended to recover with less aggressive

dynamic pitch motion when the fidelity of the translational and rotational motion cues

was balanced. Lastly, pilots seemed to recover with a higher normal load factor when no

motion was presented in the Rudder Hard-over event. Overall, pilots indicated preference

for at least one of the three cases with simulator motions over the case with no motion

for all six upset events. Moreover, in all the significant results found in the performance

Chapter 8. Conclusions 81

analysis, the recovery performance was significantly better when simulator motions were

presented (either in terms of best matching specific forces, best matching angular rates,

or best compromise between specific forces and angular rates) than when no motion was

involved. Thus it is suggested by both the subjective fidelity data and the objective

performance data that simulator motion is important for UPRT.

8.2 Future Work

Continuous effort should be put to further improve MDAs for upset recovery simulation.

A possible solution that should be explored is the method of nonlinear scaling. Similar

to the adaptive MDA, nonlinear scaling can be applied to the classical MDA to constrain

aggressive aircraft motions from hitting the actuator limits while allowing moderate mo-

tions to make better use of the motion-base system. The difference being that nonlinear

scaling may be based on maneuver dependent parameters, such as altitude or angle of

attack, instead of the instantaneous simulator states that are used in the adaptive MDA

[25].

Regarding the upset recovery experiment, future work should include constructing a

set of measurements that defines “best specific forces”, “best angular rates” and “best

compromise between specific forces and angular rates” more precisely for tuning motion

parameters for the adaptive MDA. In addition, MDAs and their tuning method should be

improved to account for the tradeoff between false lateral motion cues and onset rotational

motion cues when simulating roll attitude excursions at upset. Finally, performance

criteria should be clearly defined in order to more accurately measure pilot performance

during upset recovery.

Bibliography

[1] J. Burki-Cohen and A. L. Sparko. Airplane upset prevention research needs. In AIAA

Modelling and Simulation Technologies Conference and Exhibit, number AIAA 2008-

6871, Honolulu, HI, August 2008.

[2] J. E. Wilborn and J. V. Foster. Defining commercial transport loss-of-control: A

quantitative approach. In AIAA Atmospheric Flight Mechanics Conference and

Exhibit, number AIAA 2004-4811, Providence, RI, August 2004.

[3] A. A. Lambregts, G. Nesemeier, J. E. Wilborn, and R. L. Newman. Airplane up-

sets: Old problem, new issues. In AIAA Modelling and Simulation Technologies

Conference and Exhibit, number AIAA 2008-6867, Honolulu, HI, August 2008.

[4] The Boeing Company. Statistical summary of commercial jet airplane accidents:

Worldwide operations 1959-2008. Technical report, Boeing Commercial Airplanes,

Seattle, WA, July 2009.






Seattle, WA, June 2011.




82

Bibliography 83

[8] C. M. Belcastro. Aircraft loss of control: Analysis and requirements for future

safety-critical systems and their validation. In Proceedings of the 8th Asian Control

Conference, pages 399–406, Kaohsiung, May 2011.

[9] D. Carbaugh and L. Rockliff. Airplane upset recovery: Training aid, revision 1.

August 2004.

[10] S. F. Liu. Ground-based simulation of airplane upset using an enhanced flight model.

Master’s thesis, University of Toronto Institute for Aerospace Studies, 2010.

[11] V. J. Gawron. Airplane upset training evaluation report. NASA/CR 2002-211405,

Veridian Engineering, Buffalo, NY, May 2002.

[12] Bureau d’Enquetes et d’Analyses. Safety investigation following the accident on 1ST

June 2009 to the Airbus A300-203, flight AF447. Technical report, Le Bourget, July

2012.

[13] National Transportation Safety Board. Loss of control on approach, Colgan Air,

Inc., Operating as Continental Connection Flight 3407, Bombardier DHC-8-400,

N200WQ, Clarence Center, New York, February 12, 2009. Technical Report

NTSB/AAR-10/01, NTSB, Washington, DC, February 2010.

[14] National Transportation Safety Board. Crash of Pinnacle Airlines Flight 3701, Bom-

bardier CL-600-2B19, N8396A, Jefferson City, Missouri, October 14, 2004. Technical

Report NTSB/AAR-07/01, NTSB, Washington, DC, January 2007.

[15] G. H. Shah, K. Cunningham, J. V. Foster, C. M. Fremaux, E. C. Stewart, J. E.

Wilborn, W. Gato, and D. W. Pratt. Wind-tunnel investigation of commercial

transport aircraft aerodynamics at extreme flight conditions. In World Aviation

Congress and Display, number SAE 2002-01-2912, Phoenix, AZ, November 2002.

[16] K. Cunningham, J. V. Foster, G. H. Shah, E. C. Stewart, R. N. Ventura, R. A.

Rivers, J. E. Wilborn, and W. Gato. Simulation study of flap effects on a commercial

transport airplane in upset conditions. In AIAA Atmospheric Flight Mechanics

Conference and Exhibit, number AIAA 2005-5908, San Francisco, CA, August 2005.

[17] J. V. Foster, K. Cunningham, C. M. Fremaux, G. H. Shah, E. C. Stewart, R. A.

Rivers, J. E. Wilborn, and W. Gato. Dynamics modeling and simulation of large

Bibliography 84

transport airplanes in upset conditions. In AIAA Guidance Navigation and Control

Conference and Exhibit, number AIAA 2005-5933, San Francisco, CA, August 2005.

[18] N. B. Abramov, M. G. Goman, A. N. Khrabrov, E. N. Kolesnoikov, L. Fucke, B. Soe-

marwoto, and H. Smaili. Pushing ahead - SUPRA airplane model for upset recov-

ery. In AIAA Modeling and Simulation Technologies Conference, number AIAA

2012-4631, Minneapolis, MN, August 2012.

[19] J. Burki-Cohen A. L. Sparko and T. H. Go. Transfer of training from a full-flight

simulator vs. a high level flight training device with a dynamic seat. In AIAA Mod-

elling and Simulation Technologies Conference, number AIAA 2010-8218, Toronto,

ON, August 2010.

[20] M. D. White and G. E. Cooper. A piloted simulation study of operational aspects

of the stall pitch-up. NASA TN D-4071, July 1967.

[21] H. P. Bergeron, J. J. Adams, and G. J. Hurt, Jr. The effects of motion cues and

motion scaling on one- and two-axis compensatory control tasks. NASA TN D-6110,

January 1971.

[22] J. L. Meiry. The Vesitbular System and Human Dynamic Space Orientation. T-65-1,

Massachusetts Institute of Technology, Man-Vehicle Control Laboratory, 1965.

[23] R. L. Stapleford, R. A. Peters, and F. R. Alex. Experiments and a model for pilot

dynamics with visual and motion inputs. NASA CR- 1325, May 1969.

[24] R. S. Shirley and L. R. Young. Motion cues in man-vehicle control: Effects of

roll-motion cues on human operator’s behavior in compensatory systems with dis-

turbance inputs. IEEE Transactions on Man-Machine System, MMS-9(4):121–128,

1968.

[25] W. W. Chung. A preliminary investigation of achievable motion cueing in ground-

based flight simulators for upset recovery maneuvers. In AIAA Modeling and Sim-

ulation Technologies Conference and Exhibit, number AIAA 2008-6868, Honolulu,

HI, August 2008. AIAA.

[26] J. A. Schroeder. Helicopter flight simulation motion platform requirements.

NASA/TP 1999-208766, Moffett Field, CA, July 1999.

Bibliography 85

[27] L. E. Zaichik, Y. P. Yashin, P. A. Desyatnik, and H. Smaili. Some aspects of upset

recovering simulation on hexapod simulators. In AIAA Modeling and Simulation

Technologies Conference, number AIAA 2012-4949, Minneapolis, MN, August 2012.

[28] J. Field, M. Roza, and H. Smaili. Developing upset cueing for conventional flight

simulators. In AIAA Modeling and Simulation Technologies Conference, number

AIAA 2012-4948, Minneapolis, MN, August 2012.

[29] C. R. Hanke and D. R. Nordwall. The simulation of a jumbo jet transport aircraft

Vol. II: Modeling data. NASA-CR- 114494, D6-30643, The Boeing Company/NASA,

Wichita, KS, September 1970.

[30] P. R. Grant. The Development of a Tuning Paradigm for Flight Simulator Mo-

tion Drive Algorithms, Volume I. PhD thesis, University of Toronto Institute for

Aerospace Studies, 1996.

[31] A. R. Naseri. Improvement of the UTIAS adaptive motion drive algorithm. Master’s

thesis, University of Toronto Institute for Aerospace Studies, 2006.

[32] L. D. Reid and M. A. Nahon. Flight simulation motion-base drive algorithms: Part 1

- Developing and testing the equations. Technical Report No. 296, UTIAS, December

1985.

[33] J. A. Schroeder and P. R. Grant. Pilot behavioral observations in motion flight

simulation. In AIAA Modelling and Simulation Technologies Conference, number

AIAA 2010-8353, Toronto, ON, August 2010.

[34] L. D. Reid and M. A. Nahon. Flight simulation motion-base drive algorithms: Part

2 - Selecting the system parameters. Technical Report No. 307, UTIAS, January

1986.

[35] L. D. Reid and M. A. Nahon. Flight simulation motion-base drive algorithms: Part

3 - Pilot evaluations. Technical Report No. 319, UTIAS, December 1986.

[36] R. V. Parrish and D. J. Martin, Jr. Comparison of a linear and a nonlinear washout

for motion simulators utilizing objective and subjective data from CTOL transport

landing approaches. NASA TN D-8157, June 1976.

Bibliography 86

[37] G. J. O’Toole. An investigation of the UTIAS Adaptive Washout Algorithm. Mas-

ter’s thesis, University of Toronto Institute for Aerospace Studies, 1995.

[38] J. B. Sinacori. The determination of some requirements for a helicopter flight re-

search simulation facility. NASA CR 152066, September 1977.

[39] G. L. Greig. Masking of Motion Cues by Random Motion: Comparison of Human

Performance With a Signal Detection Model. PhD thesis, University of Toronto

Institute for Aerospace Studies, 1988.

[40] C. Jiang. Buffet simulation of the UTIAS Flight Research Simulator. Technical

report, University of Toronto, April 2012.

[41] K. A. Butler. Some problems in paired comparisons and goodness of fit for logistic

regression. PhD thesis, Simon Fraser University, Burnaby, BC, 1997.

[42] H. A. David. The Method of Paired Comparisons. Oxford University Press, New

York, NY, 1988.

[43] R. R. Davidson and R. J. Beaver. On extending the Bradley-Terry model to incor-

porate within-pair order effects. Biometrics, 33(4):693–702, 1977.

[44] R. R. Davidson. On extending the Bradley-Terry model to accommodate ties in

paired comparison experiments. Technical Report No. 37, Florida State University,

August 1969.

[45] B. J. Winer, D. R. Brown, and K. M. Michels. Statistical Principles in Experimental

Design. McGraw Hill, Boston, MA, 3rd edition, 1991.

[46] L. R. Young. Some effects of motion cues on manual tracking. AIAA Journal of

Spacecraft, 4(10):1300–1303, 1967.

[47] P. R. Grant, M. Blommer, B. Artz, and J. Greenberg. Analysing classes of motion

drive algorithms based on paired comparison techniques. Vehicle System Dynamics,

47(9):1075–1093, 2009.

[48] P. R. Grant, B. Yam, R. Hosman, and J. A. Schroeder. Effect of simulator motion

on pilot behavior and perception. AIAA Journal of Aircraft, 43(6):1914–1924, 2006.

Appendix A

MDA Tuning Parameters

A.1 Body Frame Filter Parameters for Upset Simu-

lation

kfx = 0.5 kωq = 0.5

kfy = 0.5 kωp = 0.5

kfz = 0.5 kωr = 0.5

ζhpx = 1.0 ζlpx = 1.0 ζhpθ = 0.7

ζhpy = 1.0 ζlpy = 1.0 ζhpφ = 0.7

ζhpz = 1.0 ζhpψ = – –

ωhpx = 2.5 ωlpx = 2.0 ωhpθ = 1.5

ωhpy = 4.0 ωlpy = 2.5 ωhpφ = 1.5

ωhpz = 4.0 ωhpψ = 1.0

ωhpbx = 0.0 ωlpbx = 100 Oθ = 2

ωhpby = 0.0 ωlpby = 100 Oφ = 2

ωhpbz = 0.1 Oψ = 1

Table A.1: Classical MDA Parameters for Up-

set Scenario 1 (Severe Stall)

kfx = 0.5 kωq = 0.5

kfy = 0.5 kωp = 0.5

kfz = 0.5 kωr = 0.5

ζhpx = 1.0 ζlpx = 1.0 ζhpθ = 0.7

ζhpy = 1.0 ζlpy = 1.0 ζhpφ = 0.7

ζhpz = 1.0 ζhpψ = – –

ωhpx = 0.03 ωlpx = 2.0 ωhpθ = 0.05

ωhpy = 0.03 ωlpy = 2.5 ωhpφ = 0.05

ωhpz = 0.03 ωhpψ = 0.05



ωhpbz = 0.01 Oψ = 1

ζhpx b = 1.0 ζhpθ b = 0.7

ζhpy b = 1.0 ζhpφ b = 0.7

ζhpz b = 1.0 ζhpψ b = – –

ωhpx b = 2.3 ωhpθ b = 1.3

ωhpy b = 3.8 ωhpφ b = 1.3

ωhpz b = 3.8 ωhpψ b = 0.8

ωhpbx b = 0.0 Oθ b = 2

ωhpby b = 0.0 Oφ b = 2

ωhpbz b = 0.1 Oψ b = 1

Table A.2: Revised MDA Parameters for Up-

set Scenario 1 (Severe Stall)

87

Appendix A. MDA Tuning Parameters 88

kfx = 0.5 kωq = 0.5

kfy = 0.5 kωp = 0.5

kfz = 0.5 kωr = 0.5

ζhpx = 1.0 ζlpx = 1.0 ζhpθ = 0.7

ζhpy = 1.0 ζlpy = 1.0 ζhpφ = 1.0

ζhpz = 1.0 ζhpψ = – –

ωhpx = 3.0 ωlpx = 3.5 ωhpθ = 1.2

ωhpy = 2.0 ωlpy = 3.0 ωhpφ = 1.2

ωhpz = 5.0 ωhpψ = 0.5



ωhpbz = 0.2 Oψ = 1

Table A.3: Classical MDA Parameters for Up-

set Scenario 4 (Rudder Hard-over)

kfx = 0.5 kωq = 0.5

kfy = 0.5 kωp = 0.5

kfz = 0.5 kωr = 0.5

ζhpx = 1.0 ζlpx = 1.0 ζhpθ = – –

ζhpy = 1.0 ζlpy = 1.0 ζhpφ = – –

ζhpz = 1.0 ζhpψ = – –

ωhpx = 0.03 ωlpx = 3.5 ωhpθ = 0.01

ωhpy = 0.03 ωlpy = 3.0 ωhpφ = 0.01

ωhpz = 0.03 ωhpψ = 0.01



ωhpbz = 0.01 Oψ = 1

ζhpx b = 1.0 ζhpθ b = 0.7

ζhpy b = 1.0 ζhpφ b = 1.0

ζhpz b = 1.0 ζhpψ b = – –

ωhpx b = 2.8 ωhpθ b = 1.0

ωhpy b = 1.8 ωhpφ b = 1.0

ωhpz b = 4.8 ωhpψ b = 0.3

ωhpbx b = 0.0 Oθ b = 2

ωhpby b = 0.0 Oφ b = 2

ωhpbz b = 0.2 Oψ b = 1

Table A.4: Revised MDA Parameters for Up-

set Scenario 4 (Rudder Hard-over)

Note that for all simulation using either the classical or the revised MDAs, the tilt-rate

limit and tilt-acceleration limit were set to be 0.0698 rad/s and 100 rad/s2 respectively

for both the pitch and roll DOF.


A.2 Adaptive Filter Parameters for the Comparison

between the Original and New Adaptive MDA

kfx = 1.0 ζhpx = 1.0 ωhpx = 2.5 ωhpbx = 0

Gx1 = 0.1 Wx2,3,6 = 0 Px10 = 1.0 dPx1 = 0.01

Table A.5: Parameters for the Gain Adaptive Surge High-Pass Filter

A.3 Adaptive Filter Parameters for Upset Recovery

Simulation

Maximum Displacement Maximum Velocity

Surge 0.61m 0.7m/s

Sway 0.59m 0.7m/s

Heave 0.49m 0.7m/s

Roll 20 deg 30 deg/s

Pitch 21 deg 30 deg/s

Yaw 24 deg 30 deg/s

Table A.6: UTIAS FRS Motion System Capabilities for Single DOF Motion

The parameters of the new adaptive MDA are related to the variables used in Tables

A.7 to A.24 by:

Px20 = ωhpx, Py20 = ωhpy, Pz20 = ωhpz, Pψ20 = ωhpψ,

Px50 = ωhpθ, Py50 = ωhpφ, kz1 = 2ζhpz, kψ1 = 2ζhpψ.

Px80 = ωlpx, Py80 = ωlpy, kz3 = ωhpbz,

kx1 = 2ζhpx, ky1 = 2ζhpy,

kx3 = ωhpbx, ky3 = ωhpby,

kx4 = 2ζhpθ, ky4 = 2ζhpφ,

kx6 = 2ζlpx, ky6 = 2ζlpy,

kx8 = ωlpbx, ky8 = ωlpby,


Surge/Pitch Sway/Roll

kfx = 0.5 kfy = 0.5

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 4.0 ωhpy = 4.0

ωhpbx = 0 ωhpby = 0

ζlpx = 1.0 ζlpy = 1.0

ωlpx = 2.0 ωlpy = 3.0

ωlpbx = 100 ωlpby = 100

ζhpθ = 0.7 ζhpφ = 0.7

ωhpθ = 3.0 ωhpφ = 3.0

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0.01

Gx4 = 0 Gy4 = 0

Gx5 = 0 Gy5 = 0

Gx7 = 0 Gy7 = 0

Gx8 = 0.03 Gy8 = 0.3

Wx0 = 0.5 Wy0 = 0.03

Wx1 = 0 Wy1 = 0

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 3.0

Wx9 = 0 Wy9 = 0

Wx10 = 0 Wy10 = 0

Wx12 = 0 Wy12 = 0

Wx13 = 3.0 Wy13 = 0.3

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.001 ∆Py8 = 0.001

Heave Yaw

kfz = 0.5 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 4.0 ωhpψ = 0.1

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0

Gz2 = 0 Wψ0 = 0

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01

Table A.7: Scenario 1 - F


kfx = 0.4 kfy = 0.4

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 5.0 ωhpy = 5.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 0.1 ωlpy = 0


ζhpθ = 0.7 ζhpφ = 0.7

ωhpθ = 0.2 ωhpφ = 0.2

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0.001 Gy5 = 0.05

Gx7 = 0 Gy7 = 0

Gx8 = 0 Gy8 = 0

Wx0 = 0 Wy0 = 0

Wx1 = 0.03 Wy1 = 0.03

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 15.0 Wy10 = 5.0

Wx12 = 0 Wy12 = 0

Wx13 = 0 Wy13 = 0

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.001 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.4 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 5.0 ωhpψ = 0.1

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0.05

Gz2 = 0 Wψ0 = 0.01

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0.1

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.001

∆Pz2 = 0.01

Table A.8: Scenario 1 - Ω


kfx = 0.45 kfy = 0.45

kωq = 0.45 kωp = 0.45

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 4.0 ωhpy = 4.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 0.75 ωlpy = 1.0


ζhpθ = 0.7 ζhpφ = 0.7

ωhpθ = 1.0 ωhpφ = 1.0

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0.01 Gy5 = 0.05

Gx7 = 0 Gy7 = 0

Gx8 = 0.008 Gy8 = 0.15

Wx0 = 0.05 Wy0 = 0.002

Wx1 = 0.01 Wy1 = 0.01

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 1.0 Wy10 = 0.001

Wx12 = 0 Wy12 = 0

Wx13 = 5.0 Wy13 = 0.001

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.001 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.001 ∆Py8 = 0.001

Heave Yaw

kfz = 0.45 kωr = 0.45

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 4.0 ωhpψ = 0.3

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0.3

Gz2 = 0 Wψ0 = 0.005

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0.01

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.001

∆Pz2 = 0.01

Table A.9: Scenario 1 - C



kfx = 0.5 kfy = 0.5

kωq = 0.45 kωp = 0.45

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 2.5 ωhpy = 0.7


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 2.0 ωlpy = 2.0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 1.0 ωhpφ = 1.0

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0.0022

Gx4 = 0 Gy4 = 0

Gx5 = 0 Gy5 = 0

Gx7 = 0 Gy7 = 0

Gx8 = 0.004 Gy8 = 0.0015

Wx0 = 1.0 Wy0 = 1.0

Wx1 = 0 Wy1 = 0

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0.1

Wx9 = 0 Wy9 = 0

Wx10 = 0 Wy10 = 0

Wx12 = 0 Wy12 = 0

Wx13 = 0.1 Wy13 = 0.01

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.001

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.001 ∆Py8 = 0.001

Heave Yaw

kfz = 0.5 kωr = 0.45

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 4.0 ωhpψ = 0.8

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0

Gz2 = 0 Wψ0 = 0

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01



kfx = 0.5 kfy = 0.5

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 2.5 ωhpy = 2.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 0 ωlpy = 0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 0 ωhpφ = 0

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0 Gy5 = 0

Gx7 = 0 Gy7 = 0

Gx8 = 0 Gy8 = 0

Wx0 = 0 Wy0 = 0

Wx1 = 0 Wy1 = 0

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 0 Wy10 = 0

Wx12 = 0 Wy12 = 0

Wx13 = 0 Wy13 = 0

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 4.0 ωhpψ = 0

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0

Gz2 = 0 Wψ0 = 0

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01



kfx = 0.5 kfy = 0.5

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 4.0 ωhpy = 3.8


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 0.5 ωlpy = 1.0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 0.1 ωhpφ = 0.4

Gx1 = 0 Gy1 = 0

Gx2 = 0.0035 Gy2 = 0.15

Gx4 = 0 Gy4 = 0

Gx5 = 0 Gy5 = 0

Gx7 = 0 Gy7 = 0

Gx8 = 0.1 Gy8 = 0.1

Wx0 = 0.14 Wy0 = 0.105

Wx1 = 0 Wy1 = 0

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 10.0 Wy7 = 5.0

Wx9 = 0 Wy9 = 0

Wx10 = 0 Wy10 = 0

Wx12 = 0 Wy12 = 0

Wx13 = 1.0 Wy13 = 1.0

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 4.0 ωhpψ = 0.05

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0.04

Gz2 = 0 Wψ0 = 0.05

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 10.0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01




kfx = 0.5 kfy = 0.5

kωq = 0.4 kωp = 0.4

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 3.0 ωhpy = 2.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 2.0 ωlpy = 2.0


ζhpθ = 0.7 ζhpφ = 0.7

ωhpθ = 1.5 ωhpφ = 1.5

Gx1 = 0 Gy1 = 0

Gx2 = 0.005 Gy2 = 0.02

Gx4 = 0 Gy4 = 0

Gx5 = 0 Gy5 = 0

Gx7 = 0 Gy7 = 0

Gx8 = 0.15 Gy8 = 0.35

Wx0 = 0.1 Wy0 = 0.1

Wx1 = 0 Wy1 = 0

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 5.0 Wy7 = 1.0

Wx9 = 0 Wy9 = 0

Wx10 = 0 Wy10 = 0

Wx12 = 0 Wy12 = 0

Wx13 = 0.1 Wy13 = 0.01

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.4

ζhpz = 1.0 ζhpψ = 0.7

ωhpz = 4.0 ωhpψ = 1.5

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0

Gz2 = 0 Wψ0 = 0

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01



kfx = 0.3 kfy = 0.3

kωq = 0.4 kωp = 0.4

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 4.0 ωhpy = 4.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 0 ωlpy = 0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 0.3 ωhpφ = 0.05

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0.003 Gy5 = 0.02

Gx7 = 0 Gy7 = 0

Gx8 = 0 Gy8 = 0

Wx0 = 0 Wy0 = 0

Wx1 = 0.1 Wy1 = 0.001

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 13.0 Wy10 = 5.0

Wx12 = 0 Wy12 = 0

Wx13 = 0 Wy13 = 0

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.3 kωr = 0.4

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 5.0 ωhpψ = 0.25

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0.003

Gz2 = 0 Wψ0 = 0.035

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 3.0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01



kfx = 0.4 kfy = 0.4

kωq = 0.4 kωp = 0.4

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 3.0 ωhpy = 3.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 1.0 ωlpy = 3.0


ζhpθ = 1.0 ζhpφ = 0.7

ωhpθ = 0.7 ωhpφ = 1.0

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0.05 Gy5 = 0.07

Gx7 = 0 Gy7 = 0

Gx8 = 0.3 Gy8 = 0

Wx0 = 0.03 Wy0 = 0.01

Wx1 = 0.02 Wy1 = 0.01

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 2.0 Wy10 = 2.0

Wx12 = 0 Wy12 = 0

Wx13 = 0.1 Wy13 = 0.05

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.4 kωr = 0.4

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 4.0 ωhpψ = 0.4

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0.0013

Gz2 = 0 Wψ0 = 0.15

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 6.0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01




kfx = 0.5 kfy = 0.5

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 2.5 ωhpy = 1.5


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 3.0 ωlpy = 3.0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 2.5 ωhpφ = 2.5

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0 Gy5 = 0

Gx7 = 0 Gy7 = 0

Gx8 = 1.2 Gy8 = 6.0

Wx0 = 0.01 Wy0 = 0.015

Wx1 = 0 Wy1 = 0

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 0 Wy10 = 0

Wx12 = 0 Wy12 = 0

Wx13 = 0.005 Wy13 = 0.001

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 5.0 ωhpψ = 1.5

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0

Gz2 = 0 Wψ0 = 0

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01



kfx = 0.5 kfy = 0.5

kωq = 0.45 kωp = 0.45

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 4.0 ωhpy = 4.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 0 ωlpy = 0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 0.13 ωhpφ = 0.2

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0.009 Gy5 = 0.002

Gx7 = 0 Gy7 = 0

Gx8 = 0 Gy8 = 0

Wx0 = 0 Wy0 = 0

Wx1 = 0.01 Wy1 = 0.025

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 4.0 Wy10 = 0.1

Wx12 = 0 Wy12 = 0

Wx13 = 0 Wy13 = 0

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.45

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 5.0 ωhpψ = 0.16

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0.004

Gz2 = 0 Wψ0 = 0.005

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0.001

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01



kfx = 0.5 kfy = 0.5

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 3.5 ωhpy = 3.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 0.8 ωlpy = 1.0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 0.7 ωhpφ = 1.0

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0.03 Gy5 = 0.08

Gx7 = 0 Gy7 = 0

Gx8 = 0.17 Gy8 = 0

Wx0 = 0.01 Wy0 = 0

Wx1 = 0.01 Wy1 = 0.01

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 0.01 Wy10 = 1.0

Wx12 = 0 Wy12 = 0

Wx13 = 0.01 Wy13 = 0

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 5.0 ωhpψ = 0.7

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0

Gz2 = 0 Wψ0 = 0

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01




kfx = 0.5 kfy = 0.5

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 2.1 ωhpy = 2.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 3.0 ωlpy = 3.0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 1.3 ωhpφ = 2.5

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0.2

Gx4 = 0 Gy4 = 0

Gx5 = 0 Gy5 = 0

Gx7 = 0 Gy7 = 0

Gx8 = 0.25 Gy8 = 4.5

Wx0 = 0.1 Wy0 = 1.0

Wx1 = 0 Wy1 = 0

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0.01

Wx9 = 0 Wy9 = 0

Wx10 = 0 Wy10 = 0

Wx12 = 0 Wy12 = 0

Wx13 = 0.01 Wy13 = 0.005

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0


ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0

Gz2 = 0 Wψ0 = 0

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01



kfx = 0.5 kfy = 0.5

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 2.5 ωhpy = 2.5


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 0 ωlpy = 0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 0 ωhpφ = 0

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0 Gy5 = 0

Gx7 = 0 Gy7 = 0

Gx8 = 0 Gy8 = 0

Wx0 = 0 Wy0 = 0

Wx1 = 0 Wy1 = 0

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 0 Wy10 = 0

Wx12 = 0 Wy12 = 0

Wx13 = 0 Wy13 = 0

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0


ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0

Gz2 = 0 Wψ0 = 0

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01



kfx = 0.5 kfy = 0.5

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 3.0 ωhpy = 0.5


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 1.0 ωlpy = 2.0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 0.7 ωhpφ = 0.7

Gx1 = 0 Gy1 = 0

Gx2 = 0.05 Gy2 = 0.1

Gx4 = 0 Gy4 = 0

Gx5 = 0.15 Gy5 = 0.2

Gx7 = 0 Gy7 = 0

Gx8 = 0 Gy8 = 0

Wx0 = 0.01 Wy0 = 0.05

Wx1 = 0.01 Wy1 = 0.01

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0.012 Wy7 = 0.8

Wx9 = 0 Wy9 = 0

Wx10 = 0.05 Wy10 = 0.01

Wx12 = 0 Wy12 = 0

Wx13 = 0 Wy13 = 0

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0


ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0

Gz2 = 0 Wψ0 = 0

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01




kfx = 0.5 kfy = 0.5

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 3.0 ωhpy = 3.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 3.5 ωlpy = 2.5


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 2.5 ωhpφ = 2.5

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0 Gy5 = 0

Gx7 = 0 Gy7 = 0

Gx8 = 0.7 Gy8 = 0.45

Wx0 = 0.01 Wy0 = 0.1

Wx1 = 0 Wy1 = 0

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 0 Wy10 = 0

Wx12 = 0 Wy12 = 0

Wx13 = 0.02 Wy13 = 0.02

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 4.5 ωhpψ = 1.0

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0

Gz2 = 0 Wψ0 = 0

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01



kfx = 0.4 kfy = 0.4

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 5.0 ωhpy = 5.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 0 ωlpy = 0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 0.15 ωhpφ = 0.3

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0.01 Gy5 = 0.01

Gx7 = 0 Gy7 = 0

Gx8 = 0 Gy8 = 0

Wx0 = 0 Wy0 = 0

Wx1 = 0.005 Wy1 = 0.005

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 0.5 Wy10 = 1.0

Wx12 = 0 Wy12 = 0

Wx13 = 0 Wy13 = 0

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.4 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 5.0 ωhpψ = 0.05

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0.01

Gz2 = 0 Wψ0 = 0.01

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 1.5

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01



kfx = 0.5 kfy = 0.5

kωq = 0.5 kωp = 0.5

ζhpx = 1.0 ζhpy = 1.0

ωhpx = 3.0 ωhpy = 3.0


ζlpx = 1.0 ζlpy = 1.0

ωlpx = 2.0 ωlpy = 1.0


ζhpθ = 1.0 ζhpφ = 1.0

ωhpθ = 0.8 ωhpφ = 1.0

Gx1 = 0 Gy1 = 0

Gx2 = 0 Gy2 = 0

Gx4 = 0 Gy4 = 0

Gx5 = 0.015 Gy5 = 0.008

Gx7 = 0 Gy7 = 0

Gx8 = 0.07 Gy8 = 0.12

Wx0 = 0.01 Wy0 = 0.1

Wx1 = 0.01 Wy1 = 0.04

Wx2 = 0 Wy2 = 0

Wx3 = 0 Wy3 = 0

Wx4 = 0 Wy4 = 0

Wx5 = 0 Wy5 = 0

Wx6 = 0 Wy6 = 0

Wx7 = 0 Wy7 = 0

Wx9 = 0 Wy9 = 0

Wx10 = 1.0 Wy10 = 1.0

Wx12 = 0 Wy12 = 0

Wx13 = 0.1 Wy13 = 0.01

Px10 = 1.0 Py10 = 1.0

Px40 = 1.0 Py40 = 1.0

Px70 = 1.0 Py70 = 1.0

∆Px1 = 0.01 ∆Py1 = 0.01

∆Px2 = 0.01 ∆Py2 = 0.01

∆Px4 = 0.01 ∆Py4 = 0.01

∆Px5 = 0.01 ∆Py5 = 0.01

∆Px7 = 0.01 ∆Py7 = 0.01

∆Px8 = 0.01 ∆Py8 = 0.01

Heave Yaw

kfz = 0.5 kωr = 0.5

ζhpz = 1.0 ζhpψ = 1.0

ωhpz = 5.0 ωhpψ = 0.1

ωhpbz = 0.1 Gψ1 = 0

Gz1 = 0 Gψ2 = 0.009

Gz2 = 0 Wψ0 = 0.01

Wz0 = 0 Wψ1 = 0

Wz1 = 0 Wψ2 = 0

Wz2 = 0 Wψ3 = 0

Wz3 = 0 Wψ4 = 0.2

Wz4 = 0 Pψ10 = 1.0

Pz10 = 1.0 ∆Pψ1 = 0.01

∆Pz1 = 0.01 ∆Pψ2 = 0.01

∆Pz2 = 0.01


Appendix B

Buffet Model Parameters

B.1 Filter Parameters

The variable names used to denote the numerators and denominators of the filters in

this section were first presented in the buffet model shown in Figure 7.1 of Section 7.1.2.

In the tables below, s is the Laplace variable, z is the Z-transform variable, and the

numbers in the same row as the Laplace or Z-transform variables are the coefficients of

the corresponding variables. For example, “High-Pass Filter 1” in Figure 7.1 is

“num1”

“den1”=

0× s2 + 1× s1 + 0× s0

0× s2 + 1× s1 + 3× s0=

s

s+ 3(B.1)

num1 den1 num2 den2

s2 0 0 0 0

s1 1 1 1 1

s0 0 3 0 9

Table B.1: High-Pass Filters Parameters

num6 den6 num7 den7 num8 den8

s2 0 1 0 1 0 1

s1 0 30 0 15 0 240

s0 30 30 15 15 14400 14400

Table B.2: Low-Pass Filters Parameters

num3 den3 num4 den4 num5 den5

z2 0.0172 1.0000 0.0337 1.0000 0.0172 1.0000

z1 0 -1.9582 0 -1.8379 0 -1.9227

z0 -0.0172 0.9657 -0.0337 0.9325 -0.0172 0.9657

Peak Frequency (Hz) 2.5 9 6

Bandwidth (Hz) 1 2 1

Table B.3: Band-Pass Filter Parameters

K r1 K r2 K r3 K r4

0.7 1.0 0.7 0.3

Table B.4: Gains

96

Appendix B. Buffet Model Parameters 97

B.2 Angle of Attack

This section includes the angle of attack data used by the buffet model described in

Section 7.1.2. The αb data provided by Hanke and Nordwall [29] are presented in Table

B.5. In Reference [29], the data of the lift coefficient, C∗L, defined as

C∗L =CLbasic + (∆CL)αW.D.P.=0 deg+ ∆

(dCLdα

)αW.D.P.

+

(dCL

d ˆα

)(αc

2V

)+

(dCLd q

)( qc2V

)+

(dCLd nz

)nz

(B.2)

were provided for the maximum demonstrated CL for the clean configuration (flaps and

gear up). αCLmax for the flap setting of 0 deg was, therefore, estimated using Equation

B.2. The value of each term in Equation B.2 was interpolated from Reference [29]. For a

steady-state level flight at sea level with a Mach number of 0.3, it was determined that

(C∗L)CLmax = 1.06,(dCL

d ˆα

)(αc

2V

)= 0,

(∆CL)αW.D.P.=0 deg= 0.009,(

dCLd q

)( qc2V

)= 0,

∆

(dCLdα

)= 0.0065,(

dCLd nz

)= 0.0232,

nz = 1

αW.D.P. which is approximated as α and CLbasic which changes with α were estimated

iteratively by selecting an α value that allowed both sides of Equation B.2 to be close

to balanced. The desired α was then set as αCLmax . Using the values of α = 11 deg

and CLbasic(α = 11 deg) = 0.94, the right hand side of Equation B.2 was evaluated to

be about 1.04, which was considered to be a good approximation of the interpolated

(C∗L)CLmax . Thus αCLmax was set to be 11 deg for the flap setting of 0 deg. αCLmax at other

flap settings was then calculated by

αCLmax = αb ×αCLmax for flap = 0 deg

αb for flap = 0 deg' 1.2αb (B.3)

and the results are presented in Table B.5.

Flap Settings (deg) 0 5 10 15 20 25 30

αb (deg) 9 16.5 17.2 17.6 18.0 16.8 16.8

αCLmax (deg) 11 20.2 21.0 21.5 22.0 20.5 20.5

Table B.5: Angle of Attack for Buffet Model

Appendix C

Supplements for Subjective Paired

Comparison Analysis

C.1 Paired Comparison Ordering

In the following tables, the motion cases which are underlined are the preferred conditions.

Scenario 1 3 5 2 4 6

Ω N C Ω C N Ω C N F N Ω

Ω F C N Ω C N C C N N F

N C Ω N F C Ω F C Ω Ω F

C Ω Ω F N Ω N F Ω N C F

F C F C Ω F F C F C C Ω

F N N F F N Ω N Ω F N C

Table C.1: Run Order for Pilot 1


N F F C F N N F N C Ω F

C Ω C Ω C N C Ω N F N F

N Ω Ω F Ω C F C Ω N Ω C

F Ω N C N Ω C N Ω C N Ω

C N F N F C Ω N C F F C

F C N Ω F Ω F Ω Ω F N C



Ω C F Ω C Ω C N F C C F

N Ω C F C F N F C N N C

Ω F Ω C Ω N N Ω N F F N

F N F N N C F C Ω C C Ω

C N N C F N C Ω Ω N F Ω

F C Ω N F Ω F Ω F Ω Ω N



Ω F Ω C F Ω C Ω N C N C

F N N F N F F N C F C Ω

C Ω Ω N N Ω Ω F F Ω N Ω

C F F C Ω C F C Ω C N F

Ω N Ω F C N Ω N Ω N F Ω

N C N C C F C N F N F C



Ω F C N Ω C C F N F C F

N Ω Ω N F Ω C N C Ω F N

C F C F F N F Ω C N Ω C

N F C Ω N C F N C F Ω F

C N F Ω F C Ω C Ω N C N

C Ω F N Ω N N Ω Ω F N Ω


98

Appendix C. Supplements for Subjective Paired Comparison Analysis 99

C.2 Test Procedures for the extended Bradley-Terry

Model

This section describes the four methods used to analyze the results of the extended

Bradley-Terry model. The statistical tests below are based on Davidson and Beaver [43]

and Davidson [44].

1. Test for the presence of an order effect:

The hypothesis of no order effect is tested using the likelihood ratio test. For

the case of no order effect, the maximum likelihood estimates (πγ=1, νγ=1) can

be obtained by setting γ = 1 in the iterative estimation scheme. Under this null

hypothesis, the statistic

S1 = 2[ln L(π, γ, ν)− ln L(πγ=1, 1, νγ=1)

](C.1)

has a limiting chi-square distribution with 1 DOF [43].

2. Test of overall equality of preference:

The hypothesis of all merits are equal is tested using the likelihood ratio test.

Under this null hypothesis, the maximum likelihood estimates are πiequal = 1/tc

(i = 1, ... , tc), γequal = T2/[Ttotal − (T2 + To)], and νequal = To/[Ttotal − (T2 + To)]

[43]. If order effects are not considered, γequal = 1, and νequal = 2To/(Ttotal − To)[44]. The statistic

S2 = 2[ln L(π, γ, ν)− ln L(πequal, γequal, νequal

](C.2)

has a limiting chi-square distribution with (tc − 1) DOF [43, 44].

3. Test for the goodness of fit for the model:

According to Davidson [44], the statistic for the test of goodness of fit for the B-T

model with ties but no order effect is

S3 = 2∑∑

i<j

∑k

wk,ij ln (wk,ij/wk,ij) (C.3)

where k = i, j, o and wk,ij = rijπk,ij are the estimated frequencies. The statistic

S3 has an asymptotic central chi-square distribution with tc(tc−2) DOF. Davidson

[44] also suggests that S3 can be estimated by

S3 '∑∑

i<j

∑k

(wk,ij − wk,ij)2

wk,ij(C.4)

Appendix C. Supplements for Subjective Paired Comparison Analysis 100

with the same DOF. Davidson and Beaver [43] suggest that this test can be ap-

plied to the B-T model with both ties and order effect with a small change in the

summation such that

S3 = 2∑∑

i 6=j

∑k

wk,ij ln (wk,ij/wk,ij) (C.5)

and

S3 '∑∑

i 6=j

∑k

(wk,ij − wk,ij)2

wk,ij(C.6)

with 2tc(tc− 1)− (tc + 1) DOF. In this study, the goodness of fit of the B-T models

was estimated using Equations C.4 and C.6.

4. Evaluating the correlation between the measured and estimated data:

The fit of the model is examined based on the overall correlation coefficient between

the measured probabilities (πi,ij, πj,ij, πo,ij) and the estimated probabilities (πi,ij,

πj,ij, πo,ij).

investigation of simulator motion drive algorithms for

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