aa241x problem set 2 report team chimera - stanford …web.stanford.edu/~rsur/chimera...

Team Chimera – PS2

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AA241X Problem Set 2 Report

Team Chimera

April 29, 2013

CH

IME

RA


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Table of Contents

Listing of Tables ___________________________________________________ 3

Task 1: Experimental Determination of Trims for Bixler 2 _________________ 6

Task 2: Identification of Aircraft System Parameters _____________________ 9

Bixler 2 ________________________________________________________ 9

Chimera 1 and 2 ________________________________________________ 18

Task 3: Updated Mission Plan and Strategy ____________________________ 27

Task 4: Construction and Flight Testing of Chimera 1 ___________________ 31

Design and Construction of Chimera 1 _____________________________ 31

Construction Highlights for the Chimera 1 __________________________ 33

Aerodynamic Performance Estimations ____________________________ 39

Notes from RC Flight Testing & Considerations for Future Design

Iterations ______________________________________________________ 40

Task 5: Closing Control Loops ______________________________________ 42

Appendix A: Flight Data for Autonomous Flight (Day 1) _________________ 55

Appendix B: Flight Data for Autonomous Flight (Day 2) _________________ 65


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Listing of Tables

Table 1: Mass estimation for Bixler 2. ____________________________________________ 11

Table 2: Inertia estimates for Bixler 2. ____________________________________________ 11

Table 3: Flight dynamics of the Bixler 2. __________________________________________ 14

Table 4: Stability analysis of aileron and rudder gains. ______________________________ 15

Table 5: Stability derivatives for Bixler 2. _________________________________________ 17

Table 6: Weight estimation for the Chimera 1 and Chimera 2__________________________ 20

Table 7: Interia estimates for the Chimera 1 and Chimera 2 ___________________________ 20

Table 8: Flight dynamics of Chimera 1. ___________________________________________ 24

Table 9: Stability analysis of rudder gains. ________________________________________ 25

Table 10: Stability analysis of aileron gains. _______________________________________ 25

Table 11: Stability derivatives for Chimera 1. ______________________________________ 26

Listing of Figures

Figure 1: Variation of airspeed during a sample autopilot run. _________________________ 6

Figure 2: Variation of deflection angles at different airspeeds. __________________________ 7

Figure 3: Variation of the throttle setting at different airspeeds._________________________ 8

Figure 4: Aerodynamic model of the Bixler 2 (isometric view).__________________________ 9

Figure 5: Aerodynamic model of the Bixler 2 (top view). _____________________________ 10

Figure 6: Lift coefficient vs. angle of attack for Bixler 2. ______________________________ 12

Figure 7: Drag polar for Bixler 2. _______________________________________________ 12

Figure 8: CL/CD vs. angle of attack for Bixler 2. ____________________________________ 13

Figure 9: Longitudinal modes for Bixler 2. ________________________________________ 13

Figure 10: Lateral modes for Bixler 2. ____________________________________________ 14

Figure 11: Flight dynamics of Bixler 2. ___________________________________________ 15

Figure 12: Analysis images, distributed point mass is added along the body axis to account for

the fuselage. ________________________________________________________________ 16

Figure 13: Chimera 1 aerodynamic model (isometric view). ___________________________ 18

Figure 14: Chimera 1 aerodynamic model (top view). ________________________________ 18

Figure 15: Design of the Chimera 2 (isometric view). ________________________________ 19

Figure 16: Design of the Chimera 2 (top and front views). ____________________________ 19

Figure 17: CL vs. alpha for Chimera 1. ___________________________________________ 21

Figure 18: Drag polar for Chimera 1. ____________________________________________ 22

Figure 19: CL/CD vs. alpha for Chimera 1. ________________________________________ 22

Figure 20: Longitudinal modes for Chimera 1. _____________________________________ 23


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Figure 21: Lateral modes for Chimera 1. __________________________________________ 23

Figure 22: Flight dynamics of Chimera 1. _________________________________________ 24

Figure 23: Analysis images for the Chimera 1. _____________________________________ 25

Figure 24: Sample run 1 of the simulation. The plane starts at the outside of the field. In this run,

the score was 25. The time it took to find all three beacons was 78 seconds. The sum of the norms

of the estimation errors was 11.6 meters. Large blue circle: field; green circles: Field of View

when snapshot was taken; magenta circles: location of the plane; red circles: target position

estimate returned by snapshot; blue dots: estimates of the locations of the beacons; blue

asterisks (not easily visible, as they are covered by other lines): beacon locations. _________ 27

Figure 25: Sample run 2 of the simulation. The plane starts at the outside of the field. In this run,

the score was 33. The time it took to find all three beacons was 160 seconds. The sum of the

norms of the estimation errors was 9 meters (the minimum achievable value). Large blue circle:

field; green circles: Field of View when snapshot was taken; magenta circles: location of the

plane; red circles: target position estimate returned by snapshot; blue dots: estimates of the

locations of the beacons; blue asterisks (not easily visible, as they are covered by other lines):

beacon locations. ____________________________________________________________ 28

Figure 26: Score distribution for all simulations. Average score: 29.64. Standard Deviation:

4.83._______________________________________________________________________ 29

Figure 27: Time to find all beacons for all simulations. Average time: 162 seconds. Standard

Deviation: 83 seconds. ________________________________________________________ 29

Figure 28: Sum of the norms of the estimation errors. Average value of the sum: 10.5 meters.

Standard Deviation: 2.31 meters. ________________________________________________ 30

Figure 29: Chimera 1 assembled and ready to fly. Motor mount allows airflow to cool onboard

electronics and rubber band-secured wing provides easy access to flight hardware. ________ 31

Figure 30: The foam tail mount is designed for easy assembly, but made the tail less torsionally

rigid. ______________________________________________________________________ 33

Figure 31: First generation avionics chassis. ______________________________________ 34

Figure 32: Foam cutting of the two dihedral sections. ________________________________ 34

Figure 33: Vacuum bagging the five wing pieces. ___________________________________ 35

Figure 34: Cured wing pieces (after much sanding). _________________________________ 36

Figure 35: Alignment and curing set-up for joining wing segments. _____________________ 36

Figure 36: Joined wing piece. __________________________________________________ 37

Figure 37: Milling slots for servo installation. ______________________________________ 37

Figure 38: Fixturing for wing machining. _________________________________________ 38

Figure 39: Cutting the external shape of the fuselage. ________________________________ 38

Figure 40: Milling the internal cavity of the fuselage. ________________________________ 39

Figure 41: Chimera 1 on its virgin flight! _________________________________________ 41

Figure 42: Root locus of the pitch rate loop. _______________________________________ 43

Figure 43: Negative root locus of the pitch rate loop. ________________________________ 44

Figure 44: Block diagram of the pitch control loop. _________________________________ 45


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Figure 45: Block diagram of altitude hold control. __________________________________ 45

Figure 46: Simulink model for pitch control loop. ___________________________________ 46

Figure 47: Output of theta for a reference command of 26.25°. ________________________ 46

Figure 48: Simulink model for altitude control loop. _________________________________ 47

Figure 49: Output of altitude holding for a reference command to descend 3 meters. _______ 47

Figure 50: Block diagram of airspeed hold. ________________________________________ 48

Figure 51: Block diagram of the roll control loop. __________________________________ 49

Figure 52: Block diagram of the yaw loop. ________________________________________ 49

Figure 53: Block diagram of the sideslip loop. _____________________________________ 50

Figure 54: Simulink model for the roll control loop. _________________________________ 50

Figure 55: Simulink response of bank angle for reference command of 60° (alternating every 5

seconds). ___________________________________________________________________ 51

Figure 56: Simulink model for yaw loop. __________________________________________ 51

Figure 57: Simulink response of yaw angle for a refrence command of 30° (alternating every 25

seconds). ___________________________________________________________________ 52

Figure 58: First autopilot trial __________________________________________________ 52

Figure 59: Second autopilot trial. _______________________________________________ 53

Figure 60: Third autopilot trial. _________________________________________________ 53


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Task 1: Experimental Determination of Trims for Bixler 2 Primary contributors: Ritobrata Sur, Manuel Lopez, and Jack Tsai

The trim settings for the Bixler 2 were experimentally determined from the autopilot portions of

the flight where it held a straight course across Lake Lagunita at relatively uniform airspeed. A

sample plot of airspeed measurements from one of the autopilot sections is show below.

604 606 608 610 612 614 61613

14

15

16

17

18

19

20

Time [s]

Air

spee

d [

m/s

]

Figure 1: Variation of airspeed during a sample autopilot run.

Clearly it can be seen that the airspeed had a significant variation during this process and would

lead to significant uncertainties in these measurements. The mean deflection in the servo angles

were estimated from the log files of the Ardupilot. A large error (standard deviation of about

40% in some cases) in these measurements indicates that these obtained values are only valid up

to an order of magnitude.


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6 8 10 12 14 16 18

-5

0

5

Aileron Elevator Rudder

Trim

angle

s [d

egre

es]

Air speed [m/s]

Figure 2: Variation of deflection angles at different airspeeds.

The elevator trim had an unexpected trend. Ideally it should increase with airspeed. Instead, this

value initially increased, reached a maximum, and then started decreasing. This may be due to

the following reasons:

1. The noise in the data skewed the trend in the reverse direction. The standard deviation in the

elevator setting varied by over 40% in a few cases.

2. The motor throttle generated a lot of prop wash and altered the trim settings required to obtain

a certain amount of lift at the tail. Therefore, the amount of elevator trim required will decrease

due to this secondary effect. This influence is also expected to be seen more at higher throttle

speeds as was clearly displayed the figure above.

For the other two controllers however very reasonable data were obtained. The aileron was found

to be stabilized at a constant angle of around 4°. This could be due to the lateral asymmetry of

the weight distribution or the lift distribution due to imperfect manufacturing of the Bixler 2.

Nevertheless it remained constant for a steady flight. The rudder deflection was found to be very

near zero as expected.


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6 8 10 12 14 16 18

40

50

60

70

80

Th

rottle

settin

g [%

]

Air speed [m/s]

Figure 3: Variation of the throttle setting at different airspeeds.

The variation in the throttle settings followed a near to linear trend as expected. The first point

was close to stalling and hence may be ignored.

According to these measurements we can conclude that the following order may be followed for

a stable flight. First, the throttle setting must be fixed, then followed by the elevator. The

ailerons must be maintained at the trim settings when holding course. These settings may be

changed as and when necessary to balance the effects of wind, etc. The rudder may be the final

knob that we can change to fine tune the plane's orientation.


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Task 2: Identification of Aircraft System Parameters Primary contributor: Hao Dong and Marcel Nations

Bixler 2

1. Aerodynamic Modeling of Bixler2 in XFLR5

The Bixler 2 was modeled and analyzed using the XFLR5 software package. AVL and Vlaero

were also considered as analysis tools, but XFLR5 was selected as the most straightforward one

to use. Based on measured geometry from the Bixler 2, MM 300 was selected as the most

similar airfoil for analysis. The horizontal and vertical tail are modeled as NACA 0006 airfoils.

The wing, vertical tail (VT), and horizontal tail (HT) were modeled as trapezoidal sections. Each

section of the wing was defined by the root and tip chord, dihedral, and offset based on

measurements of the Bixler 2. Aileron, rudder, elevator are also defined according to measured

dimensions.

Figure 4: Aerodynamic model of the Bixler 2 (isometric view).


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Figure 5: Aerodynamic model of the Bixler 2 (top view).

2. Weight and Inertia Estimates

Weight and inertia estimation is very important for properly trimming the controls of an aircraft.

Without a proper estimation of these parameters, the stability derivatives cannot be accurately

calculated. In the case of the Bixler 2, it was possible to measure each component separately

using a digital balance. The propulsion hardware and avionics were then treated as point masses

in XFLR5.


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Table 1: Mass estimation for Bixler 2. Table 2: Inertia estimates for Bixler 2.

Mass Estimation (g)

Wing 250

Fuselage VT&HT 150

Propulsion 156

Motor 24

Propeller 18

Battery 118

Avionics 209

GPS 17

Pitot Tube 11

Servos (QTY. 4) 36

Transmitter 11

Autopilot

Transmitter 17

Votage Regulator 21

Autopilot Board 28

Speed Controller 38

Wiring 30

Total Mass (g) 765

3. Aerodynamic Performance Analysis

The analysis was performed in XFLR5. The XFLR5 analysis combines a three-dimensional

panel method and a vortex lattice method (VLM). Although VLM usually neglects viscosity,

XFLR5 has the viscous analysis function which interpolates from the airfoil analysis in 2D

viscous flow. The Reynolds number of the analysis ranges from 80,000 to 210,000 which

corresponds to a velocity of 6 to 15 m/s. The CL curve is treated as independent of velocity.

XFLR5 cannot interpolate beyond an angle of attack of 11.3 ; this indicates a stall angle of 11.3 .

The following diagrams plot CL as a function of angle of attack, the CL/CD polar, and CL/CD

versus angle of attack at different velocities.

Dimensions

Mass 765 g

Wing area 0.25 m^2

Wing span 1.48 m

HT area 0.05 m^2

VT area 0.02 m^2

X_CoG 0.085 m

Y_CoG 0

Z_CoG - 0.03

-

Ixx 0.028 kg-m2

Iyy 0.026 kg-m2

Izz 0.053 kg-m2

Ixz 0


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Figure 6: Lift coefficient vs. angle of attack for Bixler 2.

Figure 7: Drag polar for Bixler 2.


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Figure 8: CL/CD vs. angle of attack for Bixler 2.

4. Stability Analysis

The stability analysis is performed in XFLR5. The following diagrams show the eigenvalues of

longitudinal and lateral modes as a function of velocity (from 6.8 m/s to 16.4 m/s corresponding

to elevator angles of -10 to 0 ). The two longitudinal modes and dutch roll mode are

underdamped. The Spiral mode and rolling mode are overdamped.

Figure 9: Longitudinal modes for Bixler 2.


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Figure 10: Lateral modes for Bixler 2.

Table 3: Flight dynamics of the Bixler 2.

XCP =

0.066

Elevator -10 -8 -6 -4 -2 0

Velocity 6.807 7.413 8.249 9.49 11.6 16.366

XNP =

0.107

Alpha 11.51 9.3 7.08 4.85 2.61 0.36

CL 1.07 0.906 0.732 0.553 0.3705 0.186

Phugoid f 0.24 0.219 0.196 0.169 0.138 0.098

� 0.013 0.011 0.009 0.007 0.005 0.003

Short

period f 1.204 1.309 1.455 1.672 2.042 2.882

� 0.761 0.766 0.77 0.773 0.775 0.776

Dutch Roll f 0.784 0.818 0.876 0.977 1.165 1.617

� 0.364 0.329 0.298 0.271 0.251 0.238


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Figure 11. Damping ratio and Frequency of some modes of Bixler2

The stability analysis of aileron and rudder gains is also performed so as to get the stability

derivatives.

Table 4: Stability analysis of aileron and rudder gains.

XCP = 0.066 Rudder 0 4 8 12 16

Velocity 10.367 10.363 10.35 10.328 10.296

XNP = 0.107 alpha 3.76 3.76 3.78 3.81 3.85

Cl 0.463 0.464 0.465 0.467 0.46965

Phugoid f 0.155 0.155 0.155 0.155 0.155

0.006 0.007 0.008 0.009 0.006

Short f 1.823 1.822 1.82 1.816 1.81


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period

0.774 0.774 0.774 0.774 0.774

Dutch Roll f 1.074 1.07 1.065 1.062 1.059

0.265 0.265 0.264 0.264 0.265

XCP = 0.066 Aileron 0 4 8 12 16

Velocity 10.367 10.363 10.35 10.328 10.296

XNP = 0.107 alpha 3.76 3.76 3.78 3.81 3.85

Cl 0.463 0.464 0.465 0.467 0.46965

Phugoid f 0.155 0.155 0.154 0.154 0.153

0.006 0.008 0.015 0.025 0.041

Short

period f 1.823 1.823 1.823 1.822 1.821

0.774 0.774 0.775 0.775 0.775

Dutch Roll f 1.074 1.074 1.075 1.077 1.079

0.265 0.265 0.265 0.266 0.266

Figure 11: Analysis images, distributed point mass is added along the body axis to account

for the fuselage.


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5. Stability Derivatives

The stability derivatives for trim conditions in responses to changes of elevator angle are shown

below.

Table 5: Stability derivatives for Bixler 2.

Velocity

(m/s) 6.8070 7.4130 8.2490 9.4900 11.6000 16.3660

Elevator

-

10.0000 -8.0000 -6.0000 -4.0000 -2.0000 0.0000

Cla 4.8343 4.9479 5.0436 5.1199 5.1757 5.2101

CLq 9.4416 9.5599 9.6573 9.7327 9.7853 9.8146

Cma -1.4639 -1.4688 -1.4730 -1.4766 -1.4797 -1.4821

Cmq

-

16.6345

-

16.8134

-

16.9630

-

17.0822

-

17.1703

-

17.2268

CYb -0.2545 -0.2554 -0.2561 -0.2563 -0.2562 -0.2556

Cyp 0.0642 0.0443 0.0243 0.0044 -0.0153 -0.0347

CYr 0.2332 0.2347 0.2348 0.2333 0.2303 0.2256

Clb -0.0701 -0.0660 -0.0620 -0.0582 -0.0545 -0.0510

Clp -0.4906 -0.4930 -0.4949 -0.4963 -0.4974 -0.4980

Clr 0.2556 0.2161 0.1762 0.1361 0.0958 0.0555

Cnb 0.0866 0.0881 0.0898 0.0919 0.0943 0.0969

Cnp -0.1863 -0.1594 -0.1320 -0.1040 -0.0756 -0.0469

Cnr -0.0800 -0.0832 -0.0861 -0.0886 -0.0907 -0.0923

Cxe -0.0374 -0.0312 -0.0247 -0.0181 -0.0114 -0.0046

CYe 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Cze -0.5271 -0.5305 -0.5332 -0.5351 -0.5362 -0.5365

CLe 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Cme -1.6279 -1.6382 -1.6468 -1.6538 -1.6591 -1.6627

CNe 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000


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Chimera 1 and 2

1. Modeling of the Chimera 1 and 2

From the requirements of mission planning, the proposed aircraft should fly efficiently so as to

take as many pictures as possible. Thus a light-weight aircraft with a high-aspect-ratio, elliptical

wing is desired. Dihedral wing is also added to increase the lateral stability. Winglets are added

to reduce the induced drag. The airfoil was selected from low Reynolds number airfoils such as

SD 7043, S7075, Clark Y, etc. SD 7043 was ultimately selected because of its overall good

performance from Re = 60,000 to Re = 200,000 corresponding to airspeeds of 5 m/s to 15 m/s.

The following pictures show the Chimera 1 as modeled in XFLR5.

Figure 12: Chimera 1 aerodynamic model (isometric view).

Figure 13: Chimera 1 aerodynamic model (top view).

The following pictures show the preliminary design of Chimera 2. Instead of using foam, the

wing is made of balsa to reduce the weight of the aircraft. The wing loading of Chimera 2 is

almost the same as Chimeira 1, thus the wing area of Chimera 2 is smaller than Chimera 1. As


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for the fuselage, it has not been decided whether to use foam or balsa. Balsa construction is

lighter and (with the aid of the laser cutter) quicker to construct, but foam provides better

protection when landing.

Figure 14: Design of the Chimera 2 (isometric view).

Figure 15: Design of the Chimera 2 (top and front views).

2. Weight and Inertias Estimates


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Weight and inertia estimation is very important for properly trimming the controls of an aircraft.

Without a proper estimation of these parameters, the stability derivatives cannot be accurately

calculated. In the case of Chimera 1 and Chimera 2, estimates of weight were made for several

of the components (prior to manufacturing) based on the design volume and density of specified

materials.

Table 6: Weight estimation for the Chimera 1 and Chimera 2

Table 7: Dimensions and Interia estimates for the Chimera 1 and Chimera 2

Mass Estimation (g)

Wing (using foam) 265

Wing (using balsa) 120

VT & HT 28

Fuselage 70

Pod 50

Boom 20

Propulsion 186

Motor 50

Propeller 18

Battery (3 Cell) 118

Avionics 199

Servos (QTY. 4) 36

GPS 17

Pitot Tube 11

Transmitter 11

Autopilot Transmitter 17

Votage Regulator 21

Autopilot Board 28

Speed Controller 38

Other Wiring 20

Total Mass (g) (using

foam) 748

(using balsa) 603

Dimensions

Wing Area (foam) 0.241 m2

(balsa) 0.208

Wing Loading(foam) 3.1 kg/m2

(balsa) 3.0 kg/m2

Wing Span(foam wing) 1.50 m

HT Area 0.03 m2

Elevator Lever Arm 0.59 m

VT Area 0.01 m2

X_CoG - 0.009 m

Y_CoG 0

Z_CoG - 0.011 m

Inetias (Relative to C.G. Frame)

Aircraft

mass 748 g

Ixx 0.067 kg-m2

Iyy 0.022 kg-m2

Izz 0.087 kg-m2

Ixz 0


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3. Aerodynamic Performance Analysis

The analysis was performed in XFLR5. The Reynolds number of the analysis ranges from

80,000 to 210,000 which corresponds to a velocity of 6 to 14 m/s. The CL curve is treated as

independent of velocity. XFLR5 cannot interpolate beyond an angle of attack of 12.5 ; this

indicates a stall angle of 12.5 . The following diagrams plot CL as a function of angle of attack,

the CL/CD polar, and CL/CD versus angle of attack at different velocities.

Figure 16: CL vs. alpha for Chimera 1.


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Figure 17: Drag polar for Chimera 1.

Figure 18: CL/CD vs. alpha for Chimera 1.

4. Stability Analysis

The stability analysis is performed in XFLR5. The following diagrams show the eigenvalues of

longitudinal and lateral modes as a function of velocity (from 6.8 m/s to 16.4m/s corresponding

to elevator angles of -10 to 0 ). The two longitudinal modes and dutch roll mode are

underdamped. The Spiral mode and rolling mode are overdamped.


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Figure 19: Longitudinal modes for Chimera 1.

Figure 20: Lateral modes for Chimera 1.


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Table 8: Flight dynamics of Chimera 1.

XCP =

0.054

Elevator -5 -4 -3 -2 -1 0 1 2 3 4 5

velocity 6.857 7.138 7.465 7.85 8.313 8.883 9.605 10.56 11.902 13.978 17.833

XNP =

0.107

alpha 7.88 6.97 6.04 5.09 4.14 3.17 2.18 1.18 0.17 -0.85 -1.89

Cl 0.885 0.816 0.7466 0.675 0.6195 0.5272 0.451 0.373 0.294 0.2192 0.131

Phugoid f 0.236 0.226 0.216 0.205 0.193 0.18 0.166 0.151 0.134 0.114 0.09

� 0.028 0.026 0.024 0.021 0.019 0.016 0.013 0.011 0.008 0.004 0.0007

Short

period

f 0.975 1.006 1.043 1.086 1.14 1.207 1.294 1.41 1.576 1.836 2.324

� 0.724 0.728 0.732 0.736 0.74 0.744 0.747 0.75 0.753 0.756 0.759

Dutch

Roll

f 0.718 0.745 0.777 0.814 0.859 0.914 0.985 1.079 1.211 1.417 1.8

� 0.359 0.343 0.328 0.314 0.302 0.29 0.281 0.272 0.266 0.262 0.261

Figure 21: Flight dynamics of Chimera 1.


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The stability analysis of aileron and rudder gains is also performed so as to get the stability

derivatives.

Table 9: Stability analysis of rudder gains.

XCP =

0.054

Rudder -14 -12 -10 -8 -6 -4 -2 0

Velocity 8.612 8.681 8.746 8.805 8.737 8.851 8.877 8.883

XNP =

0.107

alpha 3.66 3.52 3.41 3.3 3.44 3.22 3.18 3.17

CL 0.561 0.552 0.544 0.537 0.546 0.531 0.528 0.527

Phugoid f 0.186 0.184 0.183 0.182 0.183 0.181 0.18 0.18

� 0.005 0.1 0.1 0.013 0.011 0.015 0.016 0.016

Short

period

f 1.174 1.184 1.193 1.202 1.185 1.203 1.207 1.207

� 0.742 0.743 0.742 0.742 0.744 0.744 0.744 0.744

Dutch Roll f 0.871 0.855 0.853 0.848 0.896 0.902 0.912 0.914

� 0.289 0.296 0.298 0.3 0.31 0.293 0.291 0.29

Table 10: Stability analysis of aileron gains.

XCP =

0.054

Aileron 0 4 8 12 16

Velocity 8.883 8.889 8.896 8.903 8.91

XNP =

0.107

alpha 3.17 3.16 3.15 3.14 3.13

CL 0.527 0.526 0.526 0.525 0.524

Phugoid f 0.18 0.18 0.18 0.18 0.18

� 0.016 0.015 0.013 0.1 0.07

Short

period

f 1.207 1.208 1.209 1.21 1.22

� 0.744 0.744 0.744 0.744 0.744

Dutch Roll f 0.914 0.915 0.916 0.917 0.918

� 0.29 0.29 0.29 0.29 0.29

Figure 22: Analysis images for the Chimera 1.


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5. Stability Derivatives The stability derivatives in response to changes in elevator angle are shown below.

Table 11: Stability derivatives for Chimera 1.

Elevator -5 -4 -3 -2 -1 0 1 2 3 4 5

Velocity (m/s) 6.857 7.138 7.465 7.85 8.313 8.883 9.605 10.56 11.902 13.978 17.833

Cla 4.651 4.687 4.72 4.75 4.777 4.801 4.822 4.838 4.851 4.86 4.865

CLq 7.454 7.482 7.508 7.532 7.553 7.573 7.59 7.605 7.618 7.628 7.635

Cma -1.59 -1.58 -1.56 -1.55 -1.53 -1.51 -1.49 -1.48 -1.46 -1.44 -1.42

Cmq -17.7 -17.8 -17.8 -17.8 -17.9 -17.9 -17.9 -17.9 -17.9 -17.9 -17.9

CYb -0.24 -0.24 -0.25 -0.25 -0.26 -0.26 -0.27 -0.27 -0.27 -0.28 -0.28

Cyp -0.14 -0.15 -0.16 -0.16 -0.17 -0.17 -0.18 -0.19 -0.19 -0.2 -0.2

CYr 0.289 0.287 0.285 0.283 0.281 0.278 0.275 0.272 0.269 0.266 0.262

Clb -0.09 -0.09 -0.09 -0.09 -0.09 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1

Clp -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.55 -0.55 -0.55 -0.55 -0.55

Clr 0.234 0.217 0.2 0.182 0.165 0.147 0.128 0.11 0.091 0.072 0.053

Cnb 0.084 0.087 0.09 0.092 0.095 0.098 0.101 0.104 0.106 0.109 0.112

Cnp -0.15 -0.14 -0.13 -0.12 -0.1 -0.09 -0.08 -0.06 -0.05 -0.04 -0.02

Cnr -0.11 -0.11 -0.11 -0.11 -0.11 -0.11 -0.11 -0.12 -0.12 -0.12 -0.12

Cxe 0 0 0 1.00E-04 0.001 0.002 0.003 0.004 0.005 0.007 0.008

CYe 4.00E-06 4.00E-06 4.00E-06 4.00E-06 4.00E-06 5.00E-06 5.00E-06 5.00E-06 5.00E-06 5.00E-06 6.00E-06

Cze -0.35 -0.35 -0.35 -0.35 -0.35 -0.35 -0.35 -0.35 -0.35 -0.35 -0.34

CLe 0 0 0 0 0 0 0 0 0 0 0

Cme -1.44 -1.44 -1.44 -1.45 -1.45 -1.45 -1.45 -1.45 -1.45 -1.45 -1.45

CNe 0 0 0 0 0 0 0 0 0 0 0


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Task 3: Updated Mission Plan and Strategy

Primary contributors: Manuel López and Ritobrata Sur

After the creation of a more realistic simulation, the strategy consists now of flying in a spiral

over the field. Given the fact that the camera can take pictures at a rate of 0.33Hz, it is possible

to take an average of six pictures of each beacon while flying slightly below the highest altitude

of 400 feet. The parameters described in Task 2 were used to approximate the maximum climb

rate, maximum speed, and battery consumption. The constant speed at which the aircraft flies in

these simulations is 9 meters per second. This is considered to be the most energy-efficient speed

of the propeller-motor combination given to the team.

Two sample runs are shown below.

-200 -150 -100 -50 0 50 100 150 200

-150

-100

-50

0

50

100

150

Longitude [m]

Latitu

de [

m]

Figure 23: Sample run 1 of the simulation. The plane starts at the outside of the field. In

this run, the score was 25. The time it took to find all three beacons was 78 seconds. The

sum of the norms of the estimation errors was 11.6 meters. Large blue circle: field; green

circles: Field of View when snapshot was taken; magenta circles: location of the plane; red

circles: target position estimate returned by snapshot; blue dots: estimates of the locations

of the beacons; blue asterisks (not easily visible, as they are covered by other lines): beacon

locations.


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In sample run 1, the strategy found all three beacons very quickly, but could not create a very

good estimate on the location of the beacons. Below is a sample run in which almost the

opposite happens: it takes a long time to find the beacons, but their location is estimated with

high accuracy.

-200 -150 -100 -50 0 50 100 150 200

-150

-100

-50

0

50

100

150

Longitude [m]

Latitu

de [

m]

Figure 24: Sample run 2 of the simulation. The plane starts at the outside of the field. In

this run, the score was 33. The time it took to find all three beacons was 160 seconds. The

sum of the norms of the estimation errors was 9 meters (the minimum achievable value).

Large blue circle: field; green circles: Field of View when snapshot was taken; magenta

circles: location of the plane; red circles: target position estimate returned by snapshot;

blue dots: estimates of the locations of the beacons; blue asterisks (not easily visible, as they

are covered by other lines): beacon locations.

To estimate the performance of the strategy, we ran the simulation 2,445 times. Below are the

results.


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Figure 25: Score distribution for all simulations. Average score: 29.64. Standard

Deviation: 4.83.

Figure 26: Time to find all beacons for all simulations. Average time: 162 seconds.

Standard Deviation: 83 seconds.


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Figure 27: Sum of the norms of the estimation errors. Average value of the sum: 10.5

meters. Standard Deviation: 2.31 meters.

It is important to note that the time it takes to find the beacons is more dependent on the

maximum speed of the aircraft than on any other factor. The accuracy of the estimated beacon

locations is on average fairly good, as the minimum value achievable here is 9 meters. Another

interesting observation is that the score hits a ceiling value of 33.5. This can be caused by the

fact that there is a ceiling in the accuracy with which we can estimate the location of the beacons

and a minimum amount of time necessary to find all beacons.

The simulation does not yet take into account the following:

1. The physics of the plane and the implemented control law

2. Constraints in the turning radius (with the strategy of flying in a spiral, the turning radius

is not so important in the simulation)

3. Constraints in the climb rate; the current model assumes the plane climbs at a constant

angle, which was measured during the test flights

4. Wind gusts

5. Accurate estimates of battery consumption; right now the simulation uses a drag

coefficient and the height to calculate the energy necessary to move the airplane. It would

be good to implement measurements of the real battery consumption in the simulation.

In conclusion, the simulations show that for a spiral flight, the accuracy with which the beacon

locations is estimated is very good, while the time it takes to find all of them depends strongly on

the speed of the aircraft. The next step in the devising of the strategy is to assess how beneficial

it would be to increase the speed of the aircraft. Even though higher speeds would help us attain

a higher score, the battery consumption limits would make it risky to try to fly the plane at high

but sub-optimal speeds.


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Task 4: Construction and Flight Testing of Chimera 1 Primary contributors: Matt and Albert (Construction), Rito and Manuel (Flight Testing)

Design and Construction of Chimera 1

Chimera 1, our team’s first prototype, was designed with the following considerations in mind:

- Easy insertion/removal of components

- Design adaptability

- Structural integrity

- Fast fabrication turn-around

Easy insertion/removal of components. The purpose of our first prototype is to provide a

platform for the iterative development of the UAV’s avionics, aircraft design, and mission

planning. This means that our test platform should facilitate frequent insertion and removal of

aircraft components (for example, downloading flight data, re-programming the APM,

recharging the Li-polymer battery pack, and switching out wing designs). Towards this aim, we

implemented a rubber band-secured wing, a wooden chassis, and an arming fuse. The rubber

band-secured wing allows easy access to flight hardware. In contrast, the Bixler 2’s cramped

cockpit made it difficult to install components and manually disconnect/reconnect the battery

between test flights. The mounting chassis has a two-fold benefit. First, the chassis will keep the

relative placement of parts, and therefore the Center of Gravity, consistent during midflight and

between flight tests. Second, the chassis simplifies installation because the hardware can be

assembled outside the fuselage then simply dropped in place. The arming fuse, which is

accessible from outside the plane, makes it easy to switch power on and off between testing.

Figure 28: Chimera 1 assembled and ready to fly. Motor mount allows airflow to cool

onboard electronics and rubber band-secured wing provides easy access to flight hardware.


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Adaptability. There is always imprecision between designs on the screen and dimensions that

are obtained in fabrication. For this reason, Chimera 1 was designed with adaptability in mind.

For example, the motor mount bulkhead is an open frame that allows air into the fuselage

because we experienced overheating issues with Bixler 2. The flat surfaces allow the bulkhead

to be easily Monokoted if this design proved to be aerodynamically unfavorable. Also, we were

concerned about cross-talk between the receiver, telemetry link, and high current near the

battery. So far, interference does not appear to be an issue after using the new receiver which

operates in the GHz range. However, a chassis that is separate from the fuselage allows us to

rearrange the flight hardware relative to the battery and/or motor controller if interference

becomes an issue. We can also reposition the hardware to adjust the Center of Gravity, in case

the fabricated plane differs from design specifications. A third example is our rubber band

harness system which allows us to test the same hardware and fuselage while modifying the

wing. This may prove especially helpful after we transition to a balsa wing to reduce the weight

of our next iteration. A fourth example is our control surface hinges. Tape allows us to easily

install larger control surfaces if the initial surfaces provide insufficient control authority.

Structural Integrity. It is critical for Chimera 1 to be durable, not only for the convenience of a

reusable test vehicle, but more importantly to protect the expensive flight hardware during

landing. Expanded polystyrene is used in the fuselage for impact absorption and flotation.

Likewise, the fiberglass-reinforced foam wing is also tough. By using a two-ply layup of

fiberglass (one lay at 0-90°, another at 45°-45° orientation), a study wing was produced that did

not require integration of a spar. After the autopilot on Chimera has matured to fly and land

autonomously, it would be safe to optimize aerodynamic considerations (e.g., smaller cross-

sectional area, and lighter construction) at the expense of durability. However, durability is only

one aspect of structural integrity. It is also critical for aircraft to be rigid so as to maximize the

responsiveness and consistency of the control inputs. The double-ply fiberglass proved to be

effective in maintaining the delicate trailing edge of our SD 7043 airfoil wing. The carbon fiber

rod used for the boom is very stiff in resisting bending, but we did not anticipate the rod to be

pliant in torsion. To exacerbate the situation, we did not realize that the expanded polystyrene

foam tail block is also pliant in torsion. This issue will be addressed later in this report.


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Figure 29: The foam tail mount is designed for easy assembly, but made the tail less

torsionally rigid.

Fast Fabrication. Almost immediately after the manufacturing training sessions, we began to

fabricate aircraft components with the CNC hot wire and laser cutter. To facilitate quick

fabrication, we always considered manufacturability in our designs. An obvious example of this

is the polygonal shape of the fuselage. A curved shape would be more aerodynamic and

aesthetically pleasing, but difficult to accomplish with the hot wire.

Summary of Chimera 1 Specifications:

- Tractor propelled glider

- 265g fiberglass-reinforced foam wing, 1.6 meter wingspan, 10 degree dihedral angle

- Laser-cut balsa and heat-shrink Monokote tail

- 7mm OD, carbon fiber boom

- Expanded polystyrene foam fuselage, wooden chassis, Velcro mounting

- Control surfaces: ailerons, rudder, and elevator

Construction Highlights for the Chimera 1

Avionics Chassis. The first generation avionics chassis was constructed out of 1/8” plywood

that assembled in a “puzzle-piece” fashion. A SolidWorks model was used to generate DXF

files for the laser cutter and to check for component interference before fabrication.

Cyanoacrylate (CA) was used to join the wooden pieces, and velco tape was used to mount the

avionics. This first attempt at a chassis has served its purpose well, but it could be optimized for

reduced weight on Chimera 2. First, the material will be changed to 1/8” balsa; plywood was


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used because that was the only material on-hand at time of fabrication. Design-wise, cut-outs

will be added to the roof and floor panels to remove material.

Figure 30: First generation avionics chassis.

Wing Assembly. Construction of the wing was by far the most complicated and time-

consuming process that went into creating Chimera 1. To start, a center span and two dihedral

segments were cut from blue foam using the CNC hot-wire foam cutter.

Figure 31: Foam cutting of the two dihedral sections.


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After cutting aileron sections from the two dihedral pieces, fiberglass-epoxy layup was

performed on a total of five pieces (center spar, two dihedrals, two ailerons). Keeping in mind

that Chimera 1 is designed to be used-and-abused as the team hones its manufacturing and

autonomous flight skills, two plys of fiberglass were used on each piece. All sections were cured

overnight in a vacuum bag before removing and sanding the finished items with increasingly fine

grades of sand paper. To join the dihedral sections to the center span, a hand layup was carefully

performed. A relatively precise dihedral angle was obtained by elevating the dihedral tips a set

distance above the table (distance determined via trigonometry based on the specified span

length and dihedral angle). The position of the parts was maintain through curing by shimming

with foam blocks and weighting with metal bocks as necessary. A final round of sanding was

performed after the hand layup had cured.

Heavy-duty packing tape was used to attach the ailerons to the wing. A Bridgeport milling

machine (manually-operated) was used to cut slots in the wing to reduce weight, install servos,

and route cables. The slot openings were covered and sealed with Monokote after installing the

servos. Pictures of the assembly process are provided below.

Figure 32: Vacuum bagging the five wing pieces.


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Figure 33: Cured wing pieces (after much sanding).

Figure 34: Alignment and curing set-up for joining wing segments.


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Figure 35: Joined wing piece.

Figure 36: Milling slots for servo installation.


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Figure 37: Fixturing for wing machining.

Fuselage. The fuselage external shape was cut from expanded polystyrene using the foam

cutter. The same milling machine that was used on the wing was then used to hollow out an

internal cavity to make room for avionics, servos, batteries, and propulsion hardware. Additional

modifications were made by hand using hobby knives and drill bits.

Figure 38: Cutting the external shape of the fuselage.


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Figure 39: Milling the internal cavity of the fuselage.

Aerodynamic Performance Estimations

It was a challenge to fly Chimera 1 for sustained durations due to the lack of responsiveness and

occasional loss of control. Therefore, we did not feel comfortable installing the APM to record

flight data. However, during flight tests it is quite obvious that Chimera 1 is more efficient and

flies more slowly than Bixler 2.

Based on visual inspection, we estimate that Chimera 1 has a sinking angle of about 5-6 degrees

while gliding. This yields an L/D ratio of 9.5 which is about ~12% larger than the Bixler 2.


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We are fortunate to have an experienced RC pilot on the team and he estimated Chimera 1’s stall

speed to be about 5.5 m/s.

For 15 °C, ρ = 1.225 kg/m3, S=0.266, W=0.748 kg *9.8=7.33 N, we estimate Chimera 1’s CL,max

to be about 1.48

Notes from RC Flight Testing & Considerations for Future Design

Iterations

The most noticeable observation from Chimera 1 flight tests was its lack of responsiveness and

the difficulty to make turns. This may be due to a combination of factors which include: (a) too

large of a dihedral that resists banking, (b) ailerons being too small, (c) pliant tail wings and

boom in the propeller wake, (d) wind gusts, and (e) trimming the neutral positions for the control

surface servos.

During the first few flights before setting the trims, Chimera 1 kept banking to the left and was

not responsive to RC commands to turn bank right. Out of curiosity, we shifted the rubber band-

mounted wing off center about 1 or 2 cm to the left so that more lift generated on the left wing

would oppose this tendency to bank left. This proved somewhat successful to cause Chimera 1 to

fly straight. Interestingly, at low speeds Chimera 1 would revert to its left banking tendencies but

at higher speeds the plane was more controllable, though it still lacked responsiveness. This is

due to the velocity dependence of lift.

After re-centering the wing and adjusting the trims, Chimera 1 was able to fly straight again

albeit still lacking responsiveness. It is worthwhile to mention that getting Chimera 1 to turn

involved moving the ailerons to maximum deflection. We did not try turning with the rudder

because on the Futaba controller, it is difficult to move the rudder without affecting the throttle.

Occasionally we would lose control of Chimera 1 for a few moments. We think this could be due

to separation due to maxing out the ailerons or gusts of wind.

To improve the responsiveness and turning radius of Chimera, we plan to implement a smaller

dihedral on the next wing design iteration. The dihedral will be reduced from 50cm dihedral

sections at a 10 degree angle to 30cm sections at a 6 degree angle. We plan to transition to balsa

wood construction for significant weight savings. As delineated in Task 2, we estimate a balsa

wing of the same design as Chimera 1 to be 120 grams. This would be less than half the weight

of our current 265 gram fiberglass-reinforced foam wing. During construction, we also plan to

add winglets for reduced drag.


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The new balsa wing will include longer ailerons, extended from 2.5cm ailerons on a 18cm chord

to 3cm ailerons on a 16cm chord. This should improve responsiveness as well as prevent

separation around the wing, because the ailerons will not need to be actuated as extremely.

Meanwhile a quick fix for more flight testing with Chimera 1 would be to extend the ailerons

with tape and balsa wood.

Chimera 2 will feature a redesign of horizontal and vertical tails. We are still debating between

materials selection. A balsa tail would prove to be lighter weight, whereas a foam wing would

allow us to use a NACA 0008 symmetric airfoil for reduced drag. The vibrational and torsional

rigidity of the boom and tail wings will be addressed in our next prototype in the following two

ways. First, our boom will employ a square carbon fiber rod that has a larger moment of inertia.

Second, we will avoid expanded polystyrene foam because the square rod provides a flat

mounting surface. Alternatively will use extruded polystyrene, which is more dimensionally

stable, should we choose to include a mounting block.

Figure 40: Chimera 1 on its virgin flight!


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Task 5: Closing Control Loops Primary contributors: Jack Tsai and Norman Wong

Before we derive a control law for altitude, heading and airspeed hold, we must obtain the

equations of motion for the aircraft. Having the equations, we can form the transfer function

between control surface displacement and attitude change.

Longitudinal Motion

The stick-fixed linearized longitudinal equation of motion can be represented in the state-space

form:

� Altitude Hold

We make the following assumption to derive a control law that maintains a desired altitude:

1. Altitude is a function of elevator input only, we decouple the input of the throttle

for the sake of simplicity.

2. Neglect the longitudinal-lateral coupling motion; that is, we restrict out aircraft

motion to the vertical plane.

For short period dynamics,

Taking the Laplace transform and dividing by yields our transfer function from elevator

input to pitch rate :


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Plugging in the numbers we identified in Task 2,

The root locus of is given as:

Figure 41: Root locus of the pitch rate loop.


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Since the DC gain is already negative, we apply a negative proportional gain to make the

closed loop stable for all gains. This modified root locus is shown below.

Figure 42: Negative root locus of the pitch rate loop.

Since ,

Our block diagram for the pitch feedback loops is shown as:


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Figure 43: Block diagram of the pitch control loop.

Closing the loop, our second order Closed Loop transfer function from is

Targeting and a settling time of 1 second gives . Matching

coefficients yields and .

For , we can use the small-angle approximation to yield:

Thus feedback loop of altitude hold is:

Figure 44: Block diagram of altitude hold control.

We use the same method as presented earlier and to close the loop.


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Simulation in SIMULINK:

Figure 45: Simulink model for pitch control loop.

Figure 46: Output of theta for a reference command of 26.25°.


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Figure 47: Simulink model for altitude control loop.

Figure 48: Output of altitude holding for a reference command to descend 3 meters.

.

� Airspeed Hold:

The aircraft dynamics can be approximated by the Pugoid mode

Taking the Laplace transform and dividing by yields

The airspeed hold can be implemented as


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Figure 49: Block diagram of airspeed hold.

where the engine plant G(s) can be modeled as a first order system

In general, the brushless electric motor’s time constant is less that 0.1 s, so

However, the stability derivatives found from Task 2 do not give information of the dynamics of

the throttle. Nevertheless, we can still expect to be in the form of a simple gain. We

simply guess the gain to be 1 and then we tweak the gain in flight test to maintain our airspeed.

Lateral Motion

� Course Hold

The control logic for lateral motion is more intertwined since it requires two control inputs

(ailerons and rudders) to execute a course hold. We again use the method of successive loop

closure developed previously here. We first evaluate the innermost loop—the roll loop. From

stick-fixed lateral dynamics, pure rolling motion may be modeled as:

Hence,

Since ,


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From Task 2, the dimensional stability and control derivatives are found and the transfer function

is :

We now have our inner loop block diagram as:

Figure 50: Block diagram of the roll control loop.

Next, we close the outer loop for heading. From the lateral equations of motion, a coordinated

turn occurs at . Thus our course hold loop becomes

Figure 51: Block diagram of the yaw loop.

Where is a simple gain .

Finally, we close the outermost loop for course angle. The mindset of this loop is to simply

regulate the sideslip acceleration to zero. The block diagram indicates this loop:


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Figure 52: Block diagram of the sideslip loop.

Simulation in Simulink:

Figure 53: Simulink model for the roll control loop.


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Figure 54: Simulink response of bank angle for reference command of 60° (alternating

every 5 seconds).

Figure 55: Simulink model for yaw loop.


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Figure 56: Simulink response of yaw angle for a refrence command of 30° (alternating

every 25 seconds).

Flight Test Results

On the morning of April 26, we successfully tested our autopilot for the first time by

demonstrating altitude hold, heading hold, and airspeed hold. We allowed the plane to fly

straight and level as we turned on the autopilot. The flight path trajectories for the three trials are

shown below (red indicates autopilot on):

Figure 57: First autopilot trial


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Figure 58: Second autopilot trial.

Figure 59: Third autopilot trial.


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The altitude and airspeed for these flight trials is provided as Appendix A. Although the lateral

autopilot works perfectly, the longitudinal motion seems a slightly underdamped; the elevator

fluctuated severely which caused the tail to wobble far too much. After decreasing the gain of

the pitch loop, the wobbling of the tail was mitigated in the afternoon trial. Generally speaking,

the three trials for autonomous control were successful.

In the afternoon of April 26, the autopilot was tested for the second time to demonstrate the altitude hold,

course hold (reference course angle 340°), and airspeed hold. The plane was allowed to fly straight and

level before turning on the autopilot. The flight path trajectory of the three trials along with plots of

control input/output data are provided as Appendix B.

As can be seen from the altitude plot, the altitude continues to decrease after turning. Therefore, the Kp,h

should be increased in future flight tests. Also, the fluctuations in the elevator are decreased in the last

trial, so there is still need to modify the gains in the pitch loop to smooth out the response. However, the

course angle was successfully held at 340°.

References:

[1] Robert C. Nelson, Flight stability and automatic control, McGraw-Hill Ryerson, Limited, 1989.

[2] Bernard Etkin, Lloyd Duff Reid, Dynamics of Flight: Stability and Control, Wiley, Oct 31, 1995.


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Appendix A: Flight Data for Autonomous Flight (Day 1)


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Appendix B: Flight Data for Autonomous Flight (Day 2)


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Second Trial


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Third Trial


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The third pilot test was done on 29th April, with better tuning of gains with only heading hold instead of

ground course hold. The side acceleration loop was enabled to have better conpensation of sideslip. The

throttle was kept at constant. The wind was strong on that day. The results are shown below:


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aa241x problem set 2 report team chimera - stanford …web.stanford.edu/~rsur/chimera...

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