Download - Iver2 AUV Control Design Thesis Defense
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.
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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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Stern Fin Angle (rad)
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