Analysis, Redesign and Verification of the Iver2 Autonomous Underwater Vehicle Motion Controller

A Thesis inElectrical Engineering

by Eric A. Leveille

Submitted in Partial Fulfillment of theRequirements for the Degree of

Master of Science

July, 2007

Committee Members

• Professor Steven Nardone: Co-advisor

• Professor Gilbert Fain: Co-advisor

• Associate Professor Howard Michel: Committee Member

• Jon Crowell - Director of Engineering, OceanServer Technology: Committee Member

Presentation Overview

• Introduction

• Modeling the Iver2 AUV

• Linear Control Design

• Controller Nonlinearities

• Field-testing the Depth Controller

• Conclusion

Motivation for Research

• Typical AUV applications [1] : – surveillance– reconnaissance– mine countermeasures– tactical oceanography– communications– navigation– anti-submarine warfare

• Control system failures may lead to a failed mission or loss of vehicle

The Iver2 AUV

• Dimensions: 4 foot long by 6 inch diameter

• Weight: 46 pounds• Cost: $50k• Nearest competitor’s

cost: $500k

Original Motion Controller Design

• Proportional gains control pitch, depth, heading and roll.

• Trial and error design technique is used.

• An analytical approach may improve the overall system response. 550 560 570 580 590 600 610

3

4

5

6

7

8

9

X: 589.9Y: 7.61

Time (s)

Dep

th F

rom

Sur

face

(ft

) X: 592.4Y: 6.64

DepthGoal Depth

Iver2 Model Development

• Vehicle model needed for analytical controller redesign.

• Modeling process relies heavily on Verification of a Six-Degree of Freedom Simulation Model for the REMUS Autonomous Underwater Vehicle [2].

Controller Design and Implementation

• Controller designs based upon linear transfer function models

• Root locus, frequency domain, and time plots are used to design each controller.

• Field tests performed to verify the designed depth controller

Vehicle Coordinate Systems

Vehicle Kinematics

• Kinematic equations [3] convert body-fixed velocities and rotation rates to changes in inertial position or attitude.

• Integrating the kinematic equations provides the solution for new position and attitude.

r

q

p

w

v

u

z

y

x

cos/coscos/sin0000

sincos0000

tancostansin1000

000coscossincossin

000cossinsinsincossinsinsincoscoscoscos

000sincoscossinsinsinsincoscossincoscos

Control Coordinate System

• Center of buoyancy is the point to be controlled.• Center of gravity is typically located directly

below the center of buoyancy for improved stability.

Rigid Body Dynamics

• Dynamic equations are given by Standard Equations of Motion for Submarine Simulation [4,5].

Xqprzrqxwqvrum GG 22

Yrqpxpqrzurwpvm GG

Zqrpxqpzvpuqwm GG 22

KurwpvzmqrIIpI Gyzx

MvpuqwxwqvruzmrpIIqI GGzxy

NurwpvxmpqIIrI Gxyz

.

External Forces and Moments

• Each component of the sum of external forces is calculated based on current states and vehicle coefficients.

• Vehicle coefficients, such as the axial drag coefficient, are found based on measured vehicle parameters and the hull shape.

CONTROLMASSADDEDDRAGLIFTCHYDROSTATIEXT FFFFFF

uuACF fdDRAGAXIAL )2

1(

6-DOF Nonlinear Model

• Combines equations for kinematics, dynamics, and external forces and moments.

• Simulates how control and hydrodynamic forces affect both the body-fixed velocities and overall change in position and attitude.

),( iii uxfx

Ti zyxrqpwvux

Linear Depth Plane Model

GӨ

δs(t) Ө(t)GZ

z(t)

qYqY

q

qY

s

MIM

sMI

Ms

MI

M

s

ssG

s

2)(

)()(

5203.0007.1

147.12

ss

s

U

s

szsGZ

)(

)()(

s

1

Depth Plane Control Structure

• Two available measurements: depth and pitch• Cascade control structure is used for increased

disturbance rejection.

KDEPTH KPITCH GӨ GZ

- -

+ + δs(t) Ө(t) Z(t)Depth Reference

(m)

Inner Pitch Loop (Fast)

Outer Depth Loop (Slow)

Depth Sensor Feedback

Pitch Sensor Feedback

Inner Pitch Loop Design

• Main goal is disturbance rejection.

• A proportional-derivative (PD) controller is chosen to meet requirements.

• Use of derivative action frequently leads to problems with high frequency signals.

Type A PD Controller [6]

KP GӨ

-

+ δs(t)

Ө(t)

Pitch Sensor Feedback

Pitch ReferenceFrom Outer Control Loop

(radians)

d/dt

+

KD

+

Inner Pitch Loop (Fast)

GsKK

sKKS

DP

DPI )(1

• Amplifies high-frequency noise on the feedback path and on the time-varying pitch reference.

Type B PD Controller

KP GӨ

-

+ δs(t)

Ө(t)

Pitch Sensor Feedback

Pitch ReferenceFrom Outer Control Loop

(radians)

d/dt

-+

KD

Inner Pitch Loop (Fast)

• Avoids the differentiation of the time-varying pitch reference, which reduces fin flutter.

GsKK

KS

DP

PI )(1

Pitch Controller Step Response

• Type B PD controller designed using Root Locus techniques.

• Rise Time: 2 sec• Critically damped

for a quick rise time with no overshoot.

• Steady-state error is allowable.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Step Response of Pitch Controller

Time (sec)

Pitc

h (

deg

)

Outer Depth Loop Controller

• Outer depth loop must be slower than the inner pitch loop for the cascade structure to work correctly.

• P and PI depth controllers are designed.

KP GZ

-

+ Ө(t) Z(t)Depth Reference

(m)

Depth Sensor Feedback

TP

Closed-Loop TF forInner Pitch Loop

Effective Depth Plant

KI

+

+

dt

P Controller Depth Response

• Slower depth loop has a rise time of 8 seconds, which is 4x faster than the inner pitch loop.

• Overshoot should be kept less than 20%.

0 5 10 150

0.2

0.4

0.6

0.8

1

System: TzTime (sec): 8.15Amplitude: 0.907

Step Response of Depth Loop with P Controller

Time (sec)

Dep

th (

m)

PI Controller Depth Response

• Integral action added to offset effects of tow-float.

• Integral action has a destabilizing effect due to phase lag introduced.

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

System: Tz2Time (sec): 7.31Amplitude: 0.917

1m Depth Change with PI Control using Linear Model

Time (sec)

Dep

th (

m)

Nonlinear Depth Plane Simulation

• 6-DOF model used to verify the results of the designed PI controller.

• Nonlinear model simulation produces similar results to the linear simulations.

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

X: 8.233Y: 0.8952

Time (s)

Dep

th (

m)

1m Depth Change with PI Depth Control using 6-DOF Model

Linear Control Signals

• Linear control signals travel to extreme values.

• Limiting their values will change the designed response.

0 20 40 60 80 100-100

-50

0

50

100

150

200

250Commanded Pitch and Stern Fin Angle During 5m Depth Change

Time (s)

Ang

le (

de

g)

Reference PitchStern Control Fin

Saturating Nonlinearities

• Designs so far assumed linear controllers.• Control fin angles and commanded pitch angle

are both limited in practice.

KDEPTH KPITCH GӨ GZ

--

+ + δs(t) Ө(t)

Z(t)

Depth Reference

(m)

Inner Pitch Loop (Fast)

Outer Depth Loop (Slow)

Depth Sensor Feedback

Pitch Sensor Feedback

LP Lδs

n

n

+

+ +

+

Linear and Saturated Responses

• Saturation in the controller slows the rise time and increases overshoot.

• Rise time varies due to pitch limiting.

• Increased overshoot is unacceptable.

0 50 100 1509

10

11

12

13

14

15

16

17

Time (s)

Dep

th (

m)

Saturated and Linear 5m Depth Changes with 6-DOF Model

LinearSaturated

Integrator Windup

KP GZ

-

+ Ө(t)Z(t)

Depth Reference

(m)

Depth Sensor Feedback

TP

Closed-Loop TF forInner Pitch Loop

Effective Depth Plant

dt KI

+

+

Pnom Psat

e

• Integrator continues to “wind up” the depth error when the reference pitch is saturated.

• Integrator windup can lead to an undesired response and even instability.

Preventing Integrator Windup [7]

1. Integrator Limiting

2. Conditional Freeze

3. Freeze

4. Preloading

5. Anti-windup Bumpless-transfer

6. Variable-structure PID Control

Simulated Anti-windup Techniques

• Conditional Freeze and Freeze methods present the best results for the Iver2 application.

0 50 100 1508

10

12

14

16

18

20

22

24

Time (s)

Dep

th (

m)

Comparison of Anti-Windup Methods during 10m Depth Change

CI-ILIMCI-CFRZCI-FRZAWBTVSPIDNo Anti-windup

Dive Video

Implemented Depth Controller

• PI Outer Depth Loop Control• Integrator Freeze Antiwindup Method• Type A PD Inner Pitch Loop Control

KP

-

+ δs(t)

Pitch Sensor Feedback

Commanded Pitch

d/dt

+

KD

+

KP

-

+

Depth Sensor Feedback

KI

+

+

To ControlFin Motors

Goal Depth

dt

Integrator Freeze Antiwindup

Old vs New Depth Responses

550 560 570 580 590 600 6103

4

5

6

7

8

9

X: 589.9Y: 7.61

Time (s)

Dep

th F

rom

Sur

face

(ft

) X: 592.4Y: 6.64

DepthGoal Depth

Old Controller New Controller

• New controller removes steady-state error, decreases overshoot, and removes the steady-state oscillations.

45 50 55 60 65 70 75 80 85 90 952

3

4

5

6

7

8

Time (s)

Dep

th F

rom

Sur

face

(ft

)

Goal DepthActual Depth

Old vs New Pitch Responses

550 560 570 580 590 600 610-20

-15

-10

-5

0

5

10

15

20

Time (s)

Ang

le (

de

g)

PitchGoal Pitch

Old Controller New Controller

• New controller removes the steady-state oscillations and is more-capable of tracking the goal pitch.

45 50 55 60 65 70 75 80 85 90 95-20

-15

-10

-5

0

5

10

15

20

Time (s)

Ang

le (

de

g)

Goal PitchPitch

Old vs New Control Fin AnglesOld Controller New Controller

• New controller slightly increases fin flutter due to the use of derivative action in the inner pitch loop.

550 560 570 580 590 600 610-30

-20

-10

0

10

20

30

Time (s)

Ang

le (

de

g)

45 50 55 60 65 70 75 80 85 90 95-30

-20

-10

0

10

20

30

Time (s)

Fin

Ang

le (

de

g)

Future Improvements

• Reprogram the controller to fit the Type B structure.

• Introduce a lowpass filter in the derivative path of the pitch controller.

• Investigate online-tuning procedures for the cascade control structure to automatically tune the depth controller.

Conclusion

• Nonlinear and linear models were developed for the Iver2 AUV.

• Analytical redesign of the depth plane controller reduced overshoot, removed steady-state error and removed steady-state oscillations, and is a good addition to the Iver2 platform.

• Room for further improvement remains.

References• [1] Robert L. Wernli. Low-Cost UUV’s for Military Applications: Is the Technology

Ready? Space and Naval Warfare Systems Center San Diego. 2001 • [2] Timothy Prestero. Verification of a Six-Degree of Freedom Simulation Model for

the REMUS Autonomous Underwater Vehicle. M.S. Thesis, 2001• [3] Thor I. Fossen. Guidance and Control of Ocean Vehicles. John Wiley & Sons Ltd.

1994.• [4] Morton Gertier and Grant R. Hagen. Standard Equations of Motion for Submarine

Simulation. Naval Ship Research and Development Center. June, 1967.• [5] J. Feldman. DTNSRDC Revised Standard Submarine Equations of Motion. David

W. Taylor Naval Ship Research and Development Center. June, 1979.• [6] Yun Li, Kiam Heong Ang, Gregory C.Y. Chong. PID Control System Analysis and

Design: Problems, Remedies and Future Directions. IEEE Control Systems Magazine. February, 2006.

• [7]A. Scottedward Hodel, Charles E. Hall. Variable-Structure PID Conrol to Prevent Integrator Windup. IEEE Transactions on Industrial Electronics, Vol. 48, No. 2, April 2001.

Thank You!

QUESTIONS?

Simulink Model

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[u v w p q r]

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[x y z phi theta psi]

Body -f ixed State

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Rudder Fin Angle (rad)

Stern Fin Angle (rad)

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Sum of Forces Vector

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Body to Inertial Rotation Matrix

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Stern FinAngle (rad)

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Rudder FinAngle (rad)