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 |  موضوع: كتاب Computer-Aided Control Systems Design - Practical Applications Using MATLAB and Simulink الخميس 29 يوليو 2021, 1:25 am | |
| 
أخواني في الله
أحضرت لكم كتاب
Computer-Aided Control Systems Design
Practical Applications Using MATLAB and Simulink
Cheng Siong Chin
و المحتوى كما يلي :
Contents
Foreword .ix
Preface .xi
Acknowledgments xiii
Chapter 1 An Overview of Applied Control Engineering 1
1.1 Historical Review 1
1.2 Computer-Aided Control System Design 2
1.3 Control System Fundamentals .4
1.3.1 Open-Loop Systems .6
1.3.2 Closed-Loop Systems .7
1.4 Examples of Control Systems 8
1.4.1 Ship Control System .8
1.4.2 Underwater Robotic Vehicle Control System .8
1.4.3 Unmanned Aerial Vehicle Control System 9
1.5 Control System Design 10
Chapter 2 Introduction to MATLAB and Simulink . 13
2.1 What Is MATLAB and Simulink? 13
2.2 MATLAB Basic 13
2.2.1 Vector . 13
2.2.2 Matrices 15
2.2.3 Plot Graph . 17
2.2.4 Polynomials 17
2.2.5 M-Files and Function . 19
2.3 Solving a Differential Equation .20
2.3.1 MATLAB Open-Loop Transfer Function Modeling 22
2.3.2 Simulink Open-Loop Transfer Function Modeling .25
2.3.3 Simulink Open-Loop System Modeling 29
2.4 Simulink Closed-Loop Control System Design 45
2.4.1 PID Tuning Using Simulink . 45
2.4.2 PID Tuning Using the SISO Tool . 47
Chapter 3 Analysis and Control of the ALSTOM Gasifier Problem 51
3.1 Gasifier System Description and Notation 51
3.2 Inherent Properties Analysis . 52
3.3 Control Structure Design . 61
3.4 Gasifier System Analysis .64
3.5 Model Order Reduction (MOR) 72vi Contents
3.6 Linear Quadratic Regulator (LQR) .77
3.6.1 LQR Theory .77
3.6.2 LQR Design Steps 81
3.6.3 Performance Tests on LQR Design 81
3.7 Linear Quadratic Gaussian (LQG) 83
3.7.1 LQG Theory .83
3.7.2 Loop Transfer Recovery (LTR) 84
3.7.3 LQG/LTR Design Steps .86
3.7.4 Performance Tests on LQG/LTR .87
3.8 H-Infinity Optimization 87
3.8.1 Generalized Plant .89
3.8.2 H-Infinity Design Assumptions 90
3.8.3 H
∞ Optimization Routine 91
3.8.4 Mixed Sensitivity Problem Formulation 91
3.8.5 Selection of Weighting Function 93
3.8.6 H-Infinity Design Steps 95
3.8.7 Performance Tests on H-Infinity Design 105
3.9 H2 Optimization . 105
3.9.1 H2 Design Steps 107
3.9.2 Performance Tests on H2 Design 116
3.10 Comparison of Controllers 116
3.10.1 Sensitivity (S) . 116
3.10.2 Robust Stability (RS) 117
3.10.3 MIMO System Asymptotic Stability (MIMO AS) .117
3.10.4 Nyquist Type Criterion (NTC) . 118
3.10.5 Internal Stability (IS) . 118
3.10.6 Instantaneous Error (ISE) 119
3.10.7 Final Value Theorem (FVT) 119
3.10.8 Controller Order (CO) 120
3.10.9 Condition Number (CN) .120
3.11 Comparison of All Controllers 120
Chapter 4 Modeling of a Remotely Operated Vehicle 125
4.1 Background of the URV 125
4.2 Basic Design of a ROV and Tasks Undertaken .126
4.3 Need for ROV Control . 129
4.4 Dynamic Equation Using the Newtonian Method 130
4.5 Kinematics Equations and Earth-Fixed Frame Equation 135
4.6 RRC ROV Model . 138
4.6.1 Rigid-Body Mass and Coriolis and Centripetal
Matrix . 139
4.6.2 Hydrodynamic Added Mass Forces . 141
4.6.3 Hydrodynamic Damping Forces 154
4.6.4 Buoyancy and Gravitational Forces . 178
4.6.5 Thruster’s Configuration Model . 182Contents vii
4.7 Perturbed RRC ROV Model 186
4.7.1 Perturbation Bound on M and C Matrix 188
4.7.2 Perturbation Bound on D Matrix . 190
4.8 Verification of ROV Model . 190
Chapter 5 Control of a Remotely Operated Vehicle . 201
5.1 Nonlinear ROV Subsystem Model 201
5.1.1 Station-Keeping Model 202
5.1.2 Horizontal and Vertical Plane Subsystem Models .205
5.2 Linear ROV Subsystem Model 211
5.3 Nonlinear ROV Control Systems Design 215
5.3.1 Multivariable PID Control Design . 215
5.3.2 Sliding-Mode Control .229
5.3.3 Velocity State-Feedback Linearization 234
5.3.4 Fuzzy Logic Control . 239
5.3.5 Cascaded System Control on the Reduced ROV
Model 250
5.4 Linear ROV Control Systems Design 255
5.4.1 Inherent Properties of Linear ROV System .256
5.4.2 LQG/LTR Controller Design .264
5.4.3 H-Infinity Controller Design 267
References .277
Appendix A1: State-Space Matrices for ALSTOM Gasifier
System (Linear) .281
Appendix A2: LQR Simulation Model and Results .297
Appendix A3: LQG Simulation Model 309
Appendix A4: LQG/LTR Simulation Model and Results 321
Appendix A5: H2 Simulation Model and Results 333
Appendix A6: H∞ Simulation Model and Results .345
Index .
357
Index
A
AbsTol, 217
Acceleration
hydrodynamic added forces and moments
and, 141
state-feedback linearization, 234–235
system outputs, 141
Adaptive computed torque control, 234
Adaptive control, 201
Added mass, ROV dynamic equation, 134,
141–154, See also Hydrodynamic
added mass forces and moments
Adding/subtracting vectors, 14
Airy, G., 1
Algebraic Riccati equation (ARE), 78, 81, 86,
106, 265
ALSTOM gasifier system
bandwidth, 68–69, 98
control system specifications, 53t
description and notation, 51–52
ill-conditioned linear models, 51, 55, 58–59
I/O pairing, 61–63
ALSTOM gasifier system, controller comparison,
116–124
comparison of all controllers, 120–124
condition number, 120
controller order, 120
final value theorem, 119–120
instantaneous error, 119
internal stability, 118–119
MIMO system asymptotic stability, 117
Nyquist type criterion, 118
robust stability, 117
sensitivity, 116–117
ALSTOM gasifier system, control system design
control structure design, 61
Hankel singular values, 62–63
Niederlinski index, 63
relative gain array, 61–62
H
∞ control, See also H-infinity control
block diagram, 102t, 345
design steps, 95–105
optimization, 87–95, 345–356
performance tests, 105
H
2 optimization, 105–116, 333–344, See also
H
2 control
block diagrams, 114t, 333
design steps, 107–115
performance tests, 116
LQG, 83–87, 93–95, 309–320, See also
Linear quadratic Gaussian
block diagram, 85, 309
LQG/LTR, See LQG with LTR (LQG/LTR)
LQR, 77–83, 297–308, See also Linear
quadratic regulator
block diagram, 82t, 297
MATLAB GUI, 122–124
weighting matrices, 98–100
ALSTOM gasifier system, inherent properties
analysis, 52
condition number, 55, 60–61
condition number, Osborne preconditioning,
59–60
interaction test/direct Nyquist array, 57–59
minimal realization, 56–57
open-loop stability test, 53–55
RHP zeros test, 55
state-space model reduction, 56–57
transfer-function matrix, 60–61
ALSTOM gasifier system, model order reduction,
56–57, 72–77
Hankel singular values (HSVs), 74–75
impulse response matrix error, 73
system poles, 75
time response, 72–73
transmission zeros, 75–76
ALSTOM gasifier system, state-space matrices,
51–52, 281–296, See also State-space
representation
0% operating condition, 282–286
50% operating condition, 287–291
100% operating condition, 292–296
model reduction, 56–57, 72
ALSTOM gasifier system, system analysis, 64
bandwidth, 68–69
char input off-take rate, 66
design scaling, 70–71
frequency of highest interaction, 69–70
PI controller optimization, 64–66
transfer function matrix block diagonal
dominance, 66–68
Altimeter, 5, 9
ANSYS-CFX, 129, 154, 156, 159–160, 173,
176, 196
Applied control engineering, 1
computer-aided control system design, 2–4
historical review, 1–2
Artificial Intelligence (AI), 2
Asymptotic stability, 117358 Index
AutoCADTM, 11
Automated tuning, 49
Automatic control, 1
Autonomous underwater vehicle (AUV), 8, 125,
See also Underwater robotic vehicles
Autoscale, 29
B
Bandwidth, ALSTOM gasifier system,
68–69, 98
Bang-bang control, 7
Block diagonal dominance, 64, 66–68, 263–264
Block diagrams, 25, 345, See also Simulink
block diagrams, 333
buoyancy and gravitational force damping
matrix, 181
changing number and polarity of inputs, 36
classes, 26–27
Coriolis and centripetal matrix, 133
creating subsystems, 44
Euler’s transformation matrix, 136–137f
fuzzy logic control model, 247–248f
gasifier LQR, 82f
generalized plant, 89
H
2 design, 114f, 333
H
∞ design, 102f, 268f, 270f
linear open-loop ROV system, 257f
linear ROV LQG/LTR control, 266f
lines and signals, 27
LQG, 85, 309
LQG/LTR, 88f, 266t, 321
LQR, 82f, 297
multiplication (Gain block), 34, 39
perturbation model, 191
Pi-P cascaded controller, 253
relabeling, 32, 34
resizing, 36, 39
ROV control system, 130
ROV model overall view, 135f
ROV PID controller design, 218f
ROV real model, 194
Simulink block libraries, 26–27, 30
Simulink open-loop system modeling,
29–44
sliding-mode control, 231f
summation (Sum block), 36
velocity state-feedback linearization, 236f
Block Parameters, 34, 36
Bode diagrams, 80
Bode plot, 48
Body-fixed frame
mapping to earth-fixed frame, 128–129,
135–136
restoring force vector, 180
ROV dynamic equation, 131, 134
state-feedback linearization, 234
Buoyancy, 135, 171, 175, 178–183
block diagram, 181
PID controller design optimization, 221
simplifying assumptions, 180–181
C
Cascaded system control, reduced ROV model,
250–255
Cellular phone, open-loop system, 6–7
Center of buoyancy (CB), 135, 181–182
Center of gravity (CG), 135, 139, 175,
180–181, 206
Chattering, 230, 232
Closed-loop systems, 4, 7
control system examples, 8–10
Simulink control system design, 45–49
Closed-loop transfer function
generalized plant, 98, 108
H
∞ optimization routine, 91
Column vectors, 14
Commenting, using “%,” 19
Complementary sensitivity, 91
Computational fluid dynamics (CFD)
tools, 11, 129, 154, 156, 167, 173,
See also ANSYS-CFX; Wave
Analysis MIT
comparing experimental and simulation
results, 175–178
Computed torque control, 234
Computer-aided applied control engineering
(CAACE), 3
Computer-aided control system design (CACSD),
2–4, 10–12, See also Control systems
design; MATLAB
Condition number, ALSTOM gasifier system,
55, 58–59
controller comparison, 120
design scaling methods, 70–71
Osborne preconditioning, 59–60
RGA number, 62
Controllable inputs, 4
Controlled inputs, fuzzy logic control, 239
Controller order (CO), controller design
comparison, 120
Controllers, 201, See also Control
systems design
comparison
linear and nonlinear ROV, 274
sensitivity, 116–117
comparison for gasifier system, 116–124,
See also ALSTOM gasifier system,
controller comparison
fuzzy logic, See Fuzzy logic control
GUI, 275
H
∞, See H-infinity control
H
2, See H2 controlIndex 359
LQG, See Linear quadratic Gaussian
LQR, See Linear quadratic regulator
PI, 64–66
PID, See Proportional-integral-derivative
(PID) controller
PI-P cascaded controller, 252–253
ranking, 122
robustness issues, 215
ROV design, 129, See also Remotely
operated vehicles, modeling
sliding-mode, 201, 215, 229
state-feedback linearization, 215, 234–238
Zigler-Nichols tuning method, 45–47
Controller tuning, 45–49
Control structure design, gasifier system, 61–63,
See also ALSTOM gasifier system,
control system design
Control systems, See also Controllers; specific
types or applications
closed-loop systems, 4, 7
examples
ship, 8
underwater robotic vehicle, 8–9
unmanned aerial vehicles, 9–10
fundamentals, 4–5
open-loop systems, 6–7
Control systems design, 10–12, 215, See also
Controllers; specific tools, types, or
applications
computer-aided, 2–4
dynamic system modeling, 3
gasifier system, 61–124, See also ALSTOM
gasifier system, control system
design
historical review, 1–2
ROV, See Remotely operated vehicles, control
of
Simulink block diagrams, See Block
diagrams
Simulink closed-loop design, 45–49
step-by-step procedure, 3–4
Control Systems Toolbox, 13
Coriolis and centripetal matrix, 130, 132–133,
139–141
hydrodynamic added forces and moments,
142, 153
uncertainties and perturbation model, 190
Cost function optimization
H
∞, 87
H
2 and LQG optimization, 105–107
linear quadratic Gaussian, 83, 264
linear quadratic regulator, 77
C program, 19
Create Subsystem, 44
Critical gain, PID tuning, 46
Cube of a matrix, 16
Cylinder model, 146t
D
Damping forces, ROV, See Hydrodynamic
damping forces
Decoupled maneuver control scheme, 205–206
Deep Submergence Laboratory (DSL), 125
Defuzzifier, 240
demo command, 19
Density of seawater, 190t
Depth effects, hydrodynamic added forces, 145
Depth regulation, 8–9
Design Optimization Toolbox, Simulink,
219, 252
Design scaling, reducing system interactions,
70–71, 259–263
Differential equations, solving in MATLAB,
20–22
ODE Solvers, 216–217
Simulink block diagrams, 29–31
Simulink output to workspace, 42–43
state-space representation, 23–24
transfer function modeling, 22–25
Differentiation theorem, 22
Direct Nyquist array (DNA), 57–59, 71f, 259,
260–261f
Disturbance inputs, 4, 5
ALSTOM gasifier system, 51
H
∞ design, 101, 104
H
2 design, 111
controller sensitivity comparisons, 116–117
gasifier system sensitivity, 80
H-infinity control performance, 268, 273–274
LQG/LTR performance tests, 87
open-loop system vulnerabilities, 6
Docking station, 125
Doppler velocity log (DVL) sensor, 191
Dormand-Prince solver, 217
DOS, 11–12
Dot caret (.^), 15
Dot star (.*), 15
Drag coefficients, ROV hydrodynamic damping
model, 161–167, 175–176, See also
Hydrodynamic damping forces
Drawing Commands, 44
Drive-by-wire control systems, 10
Dulmage-Mendelsohn permutation, 57
Dynamic equations, ROV, 129, 130–135, 171,
182–183
station-keeping model, 202–203
E
Earth-fixed frame
mapping from body-fixed frame, 128–129,
135–136
ROV dynamic equation, 134
ROV kinematic equations, 135–136360 Index
Edmunds scaling, 70–71, 259–263
Eigenvalues, 16
ALSTOM gasifier open-loop stability test,
53–55
linear ROV open-loop stability test, 256
Perron-Frobenius plot, determining frequency
of highest interaction, 69–70
transmission zeros determination, 76
Error signal, 5
Euler’s transformation, 128, 135–136, 169,
179–180, 251, 255
block diagrams, 136–137f
PID controller modeling, 223–225
Experimental results, ROV hydrodynamics,
167–175, 196–197
improving accuracy, 200
pool test, 190–200
simulation results comparison, 175–178
F
Feedback, 7
Feedback amplifier design, 1
Feedback control systems, 45, See also Closedloop systems
Feedback linearization, 10, 215, 234–238
Filter algebraic Riccati equation (FARE), 84, 86,
106, 265
Final Value Theorem (FVT), 119–120
Flow speed specification, hydrodynamic damping
model, 156, 158
Fly-by-wire control systems, 10
FOR loops, 19
Forward velocity, 5
Free-decay experiment, 168–175
pool test, 191–200
French Research Institute for Exploration of the
Sea (IFREMER), 125
Fuzzy Inference System (FIS) Editor, 241–245
Fuzzy logic control (FLC), 2, 201, 215, 239–249
block diagram, 247–248f
controlled inputs, 239
defuzzifier, 240
fuzzy inference scheme, 239–240
Fuzzy Inference System (FIS) Editor,
241–245
GUI, Fuzzy Logic Toolbox, 240–241
Simulink model, 246–248
G
Gain block, 34, 39
Gasifier system, See ALSTOM gasifier system
Generalized plant, 89–90, 96–98, 268–269
Gershgorin disks, 57–59, 70–71, 259
GPS antenna, 200
Graphical user interface (GUI), 122–124, 194
Fuzzy Logic Toolbox, 240–241
ROV control system, 275
Gravitational forces, 178–183, 221
H H2
control, 105
block diagram, 114f, 333
comparison of controllers, 120–123
design steps, 107–115
generalized plant formulation, 107–108
MATLAB code, 110–113
weighting function selection, 108–110
LQG optimization, 105–107
optimization design, 333–344
0% load (sinusoidal pressure disturbance),
341–342, 344
0% load (step pressure disturbance),
340–341, 344
50% load (sinusoidal pressure
disturbance), 338–339, 344
50% load (step pressure disturbance),
337–338, 343
100% load (sinusoidal pressure
disturbance), 335–336, 343
100% load (step pressure disturbance),
334–335, 343
performance function specifications, 109t
performance tests, 111
Hankel singular values (HSVs), 62–63, 74–75
Hardware-in-the-loop testing, 11–12
Heading velocity, 5
Heave
experimental results, 168, 169, 172,
173t, 175
experimental results, pool test, 191, 195
horizontal plane model, 206
linear ROV open-loop stability, 258
modeling, 5, 144
PID controller modeling, 217, 219
skin friction effects, 174
station-keeping model, 202
thruster control, 125, 126
vertical plane model, 209
Help, 19
High-pass filter, 98, 99, 109
H-infinity control, 2
block diagram, 102f, 270f
comparison of controllers, 120–123
design steps, gasifier system, 95–105
block diagram, 102f
MATLAB code, 100–101, 104–105
weighting function selection, 98–100
linear ROV control systems design, 267–275
block diagram, 270f
generalized plant, 268–269
optimization, 87–95, 345–356Index 361
0% load (sinusoidal pressure disturbance),
353–354
0% load (step pressure disturbance),
352–353, 356
50% load (sinusoidal pressure
disturbance), 350–351, 356
50% load (step pressure disturbance),
349–350, 355
100% load (sinusoidal pressure
disturbance), 347–348, 355
100% load (step pressure disturbance),
346–347, 355
block diagram, 345
design assumptions, 90–91
generalized plant, 89–90, 96–98, 268–269
mixed sensitivity problem, 91–93
routine, 91
weighting function selection, 93–95,
98–99, 271–273
performance tests, gasifier system, 105
weighting matrices selection, 98–99
HINF.m, 97, 99
Horizontal plane subsystem model, 205–207, 214
Hovering (station-keeping), 202–205
Hybrid ROV-URV (HROV), 125
Hybrid switching control, 201
Hydrodynamic added mass forces and moments,
134, 141–154
CAD model, 143–148
comparing experimental and simulation
results, 175–178
convergence test, 148
depth effects, 145
experimental results, 167–175
multiple bodies effects, 148
perturbation model, 187
ROV scaled model, 147–148
simplifying assumptions, 142–143
thruster effects, 145–147, 175
Hydrodynamic damping forces, 154–178
block diagram, 181
CFD tools, 154, 156, 173
drag coefficients and Reynolds number,
161–167
experimental and simulation results
comparison, 175–178
experimental results, 167–175
flow speed specification, 156–158
initial values and time-step, 159–160
meshing domain, 161
perturbation model, 187
PID controller modeling, 223
simplifying assumptions, 155
skin friction effects, 154, 166, 174–175
thruster action, 175
turbulence model, 156, 158
wake formation, 162
wall-boundary conditions, 159
Hydrodynamics derivatives, 141
I
Ideal fluid assumptions, 130, 135, 142–143
IF-ELSE, 19
Image Processing Toolbox, 169
Impulse response matrix error, 73
Infinity-norm method, 59
Inline function, 18
Input/output (I/O) pairing, gasifier system control
structure design, 61–63
Hankel singular values (HSVs), 62–63
Niederlinski index, 63
relative gain array, 61–62
Input sensitivity
controller comparisons, 116–117, 122
H
∞, 91, 93–95, 272–273
H
∞ mixed sensitivity problem, 91–93
Instantaneous error (ISE), 119
Integral squared error (ISE), 64, 119, 122
Intelligent control, 2, 239
Interaction test, ALSTOM gasifier system,
57–59
design scaling methods, 70–71
determining highest interaction frequency,
69–70
Interaction test, linear ROV open-loop
stability, 259
Internal stability (IS), 118–119
Inverse function, 21
Inverse matrix, 16, 223
pseudo-inverse, 215
I/O pairing, design scaling methods, 70–71
J
JASON II/MEDEA system, 125
Java A mass applet, 148
K
Kalman filter, 2, 84
Kalman tests, 56–57
KEDDCTM, 3
Keulegan-Carpenter number, 172–173
Kinematics equations, ROV model, 135–138
horizontal plane model, 207
station-keeping model, 203–204
vertical plane model, 207–208, 209–210
L
Labeling lines and blocks, 32
Laplace transform, 22–23, 106
Least-squares method, 169–171362 Index
Linear damping, 154, 166, See also
Hydrodynamic damping forces
Linear differential equations, Laplace
transform, 22
Linear fractional transformation (LFT), 269
Linear-quadratic (LQ) control, 2
optimal control theory, 234, 235
Linear quadratic Gaussian (LQG), 2, 83–87,
309–320
0% load (sinusoidal pressure disturbance),
317–318, 320
0% load (step pressure disturbance),
316–317, 320
50% load (sinusoidal pressure disturbance),
314–315, 320
50% load (step pressure disturbance),
313–314, 319
100% load (sinusoidal pressure disturbance),
311–312, 319
100% load (step pressure disturbance),
310–311, 319
block diagram, 85, 309
comparison of controllers, 122
H
2 and optimization, 105–107, See also
H
2 control
loop transfer recovery (LQG/LTR), 84–86,
See also LQG with LTR
robustness properties, 87
theory, 83–84
Linear quadratic regulator (LQR), 77, 297–308
0% load (sinusoidal pressure disturbance),
305–306, 308
0% load (step pressure disturbance), 303–304
50% load (sinusoidal pressure disturbance),
302–303
50% load (step pressure disturbance),
300–301, 307
100% load (sinusoidal pressure disturbance),
299–300, 307
100% load (step pressure disturbance),
297–298, 306
block diagram, 82f, 297
comparison of controllers, 122
design steps, 81
gasifier system design, 81–83
generalized feedback system, 106f
robustness, 79–80
theory, 77–80
weighting matrices, 77, 81
Linear ROV control systems design, 255–275,
See also Remotely operated vehicles,
linear control systems design
Linear ROV subsystem model, 211–214,
See also Remotely operated
vehicles, modeling
Linear ROV system, inherent properties,
256–264
block diagonal dominance, 263–264
design scaling (Edmunds scaling), 259–263
interaction minimization, 259
interaction test/direct Nyquist array, 259
LHP/RHP zeros test, 259
open-loop stability test, 256–258
roll and pitch stability, 259
Lines in block diagrams, 27, 32
Linux, 11–12
Loop transfer recovery (LTR), 84–86, 264,
See also LQG with LTR
Lower functional transformation (LFT), 90, 98,
106, 108
Low-pass filter, 98–100, 109, 272–273
LQG with LTR (LQG/LTR), 84–86, 321–330
0% load (sinusoidal pressure disturbance),
329–330, 332
0% load (step pressure disturbance),
328–329, 332
50% load (sinusoidal pressure disturbance),
326–327, 332
50% load (step pressure disturbance),
325–326, 331
100% load (sinusoidal pressure disturbance),
323–324, 331
100% load (step pressure disturbance),
322–323, 331
block diagram, 88f, 266f, 321
comparison of controllers, 122
design steps, 86–87
linear ROV control systems design, 264–267
performance tests, gasifier system, 87
robustness properties, 89, 264
weight selection, 265–266
LTR, See Loop transfer recovery (LTR); LQG
with LTR
Lyapunov function, 223, 229
M
Macintosh, 13
MAGSHAPE, 95
Marine Dynamic Test Facility, 167
Masked subsystem, 44
Mass-spring-damper system
Simulink open-loop system modeling, 29–44
Simulink open-loop transfer function
modeling, 25–29
Mathematica , 3
Math Operations, 36, 39
Image Processing Toolbox, 169
MATLAB, 3, 10, 13, See also Simulink
fuzzy inference tools, 240–246
GUI, 122–124
H
∞ weight selection, 271–273
linear ROV open-loop stability test, 258
LQG/LTR weight selection, 265–266Index 363
RRC ROV modeling, 127
CAD tools and modeling, 144
SISO tool, 47–49
solving differential equations, 20–22
Simulink block diagrams, 29–31
transfer function modeling, 22–25
starting Simulink, 25
MATLAB, basics, 16
matrix operations, 15–17
M-files and functions, 19
plot graph, 17, 19, 42–43
polynomials, 17–18
vector operations, 13–15
Matrix operations, 15–17
characteristic polynomial, 16
eigenvalues, 16
Matrix simplifying assumptions, 143
Maxwell, J. C., 1
Medical robotic systems, 10
Membership Function Editor, 241, 242f
Meshing domain, hydrodynamic damping
model, 161
M-files and functions, 19–20
Mixed-sensitivity H∞ control, 91–93
Modal truncation, 72–74
Model order reduction (MOR), gasifier system,
56–57, 72–77, See also ALSTOM
gasifier system, model order
reduction
Model predictive control, 201
Moore-Penrose pseudo-inverse matrix, 215
Multi-Input, Multi-Output (MIMO) systems, 27
asymptotic stability comparison, 117
H
∞ optimization routine, 91
sensitivity function maximum value, 116
Multiplication, Simulink Gain block, 34, 39
Multiplication of matrices, 15
Multiplication of vectors, 15
MultiSurf, 141, 143–146, 148
Munk moments, 130
N
Navigation sensor block, 128–129
Neural network control, 201, 239
Newtonian method, ROV dynamic model, 129,
130–135
Niederlinski index, 63
Nonlinear ROV control systems design, 215–255,
See also Remotely operated vehicles,
nonlinear control systems design
Nonlinear ROV subsystem model, 201–211,
See also Remotely operated
vehicles, modeling
Norm reduction method, 59
Nyquist array, gasifier system, 57–59, 71f
Nyquist type criteria (NTQ), 118, 122
O
ODESET, 217
ODE Solvers, 216–217
ODIN ROV, 130
One norm method, 59, 70, 259
Open-loop stability test
ALSTOM gasifier model, 53–55
linear ROV system, 256–258
Open-loop systems, 6–7
Simulink modeling, 29–44
Open-loop transfer function modeling
ALSTOM gasifier system, 60–61
generalized plant, 96–98
MATLAB, 22–25
Simulink, 25–29
Optimal state-estimator gain, 86
Optimal state-feedback design, 77, 81, 84, 86,
264–265, See also Linear quadratic
Gaussian; Linear quadratic regulator
Optimum design, 2
Osborne preconditioning, 15, 59
Output sensitivity, controller comparisons,
116, 122
Output to workspace, 42–43
P
Parseval’s identity, 106
Pendulum experiment, 168–175, 196–197
Perron-Frobenius scaling, 69–70, 259
Perturbation model, ROV, 186–191
station-keeping mode, 205
vertical plane model, 208, 210–211
Pipeline inspection, 8, 125, 201, 250
ROV tracking control, 251
RRC ROV function, 126
station-keeping model, 202, 250
Pipeline-tracking planner, 127–128
Pitch, See Roll and pitch
Planar Motion Mechanism (PMM), 167
Plant, 4
plot, 17, 19, 42–43
Pole placement, 234, 235
Poly function, 16
Polynomials
converting linear transfer functions, 22
in MATLAB, 17–18
Polyval function, 18
Pontryagin minimum principle, 78
Pool tests, ROV, 190–200
Pro/ENGINEER, 11, 139, 180
Proportional control, 7
Proportional-derivative (PD) control, 221,
223, 225
Proportional-integral-derivative (PID) controller,
4–5, 45, 201, 215364 Index
nonlinear ROV control systems design,
215–229
block diagram, 218f, 226f
Simulink model, 215–221
perturbation assumptions, 215
Simulink design optimization, 219–221
Simulink model, 215–221
tuning using Simulink, 45–47
tuning using SISO tool, 47–49
Proportional-plus-Integral (PI) controller,
64–66, 252
Pseudo-inverse matrix, 215
Q
QNX, 11–12, 194
Quad-rotor helicopter, 9–10
R
Range-Kutta formula, 191
Relabeling blocks, 32, 34
Relative gain array (RGA), 61–62
RelTol, 217
Remotely operated vehicles (ROVs), 201, See also
RRC ROV
basic design, 126–129
control system example, 8–9
GUI, 194, 275
URV background, 125–126
Remotely operated vehicles, control of, 201–202
decoupled maneuver scheme, 202, 205–206
horizontal and vertical plane subsystems,
205–211, 213–214
linear control systems design, 255–275,
See also Remotely operated vehicles,
linear control systems design
linear subsystem model, 211–214
nonlinear control systems design, 215–255,
See also Remotely operated vehicles,
nonlinear control systems design
nonlinear subsystem model, 201–211
supervisory control, 201–202
Remotely operated vehicles, linear control
systems design, 255–275
block diagrams
H
∞-control, 268f
LQG/LTR, 266f
open loop, 257f
GUI, 275
H-infinity control, 267–275
inherent properties, 256–264, See also Linear
ROV system, inherent properties
LQG/LTR controller, 264–267
nonlinear ROV controller comparison, 274
station-keeping model, 255, 267
thruster dynamic, 255–256
Remotely operated vehicles, modeling, 128–129
added mass forces, 134, 141–154, See also
Hydrodynamic added mass forces
and moments
block diagrams, 130, 135f, 194
buoyancy and gravitational forces, 178–183
CAD tools and modeling, 139, 143–148
Coriolis and centripetal matrix, 130, 132–133,
139–141
damping forces, 154–178, See also
Hydrodynamic damping forces
dynamic equation, 129, 130–135, 138, 171,
182–183
station-keeping model, 202–203
experimental and simulation results
comparison, 175–178
experimental results, 167–175
higher-order model, 144
kinematics equations, 135–138
horizontal plane model, 207
station-keeping model, 203–204
vertical plane model, 207–208, 209–210
linear subsystem model, 211–214
mesh domain, 161
need for ROV control, 129–130
nonlinear subsystem model, 201–211
horizontal and vertical plane motion,
205–206
linearization, 211–212
station-keeping model, 202–205
notations, 131
perturbation model, 187–191
pool test, 190–200
property of body-fixed matrices, 139
rigid-body mass, 139
scaled model, 147–148, 175
simplifying assumptions, 130–131, 135,
142–143, 155
Simulink model, 127–129
state-space representation, 138
thruster configuration model, 182–186
thruster effect considerations, 200
Remotely operated vehicles, nonlinear control
systems design, 215–255
cascaded system control, reduced ROV
model, 250–255
fuzzy logic control, 239–249
linear ROV controller comparison, 274
multivariable PID control design, 215–229
block diagram, 218f, 226f
Simulink model and design optimization,
215–221
sliding-mode control, 229–234
station-keeping model, 250
thruster dynamic, 255–256
tracking control, 251
velocity state-feedback linearization, 234–238Index 365
Remotely operated vehicles, nonlinear
subsystem model, 201–211
Resizing blocks, 36, 39
Reynolds number, 156, 158
drag coefficient and, 161–167
RGA (relative gain array), 61–63
RGA number, 62
RHP zeros, 55, 83, 118–119, 256, 259
Riccati differential equation (RDE), 78
Right-hand plane (RHP) zeros, 55, 83, 118–119,
256, 259
Rigid body inertia matrix, 132–133, 139
Robotics Research Centre (RRC), 126, See also
RRC ROV
Robustness properties, 201
controller comparison, 117
controller design issues, 215
intelligent control, 239
LQG, 87
LQG/LTR, 89, 264
LQR, 79–80
Roll and pitch, 5, 202
asymptotic stability, 183
damping coefficients, 178
H-infinity control design, 267
horizontal plane model, 206
linear ROV open-loop stability, 258, 259
self-stabilization, 183, 202, 205, 215, 219,
221, 229, 232, 259, 267
station-keeping mode, 202
unactuated in RRC ROV, 126, 202
vertical plane model, 209, 213
Root locus plot, 48, 75–76
roots command, 16, 18, 20
ROV Dynamic, 129
Row vectors, 13–14
RRC ROV, 126, 215, See also Remotely
operated vehicles
added mass forces, 141–154, See also
Hydrodynamic damping forces
basic design, 126–129
cascaded structure, 250
components, 140f
damping forces, 154–178, See also
Hydrodynamic damping forces
experimental results, dynamics, 167–175
GUI, 194
H
∞-controller design, 267–275
higher-order model, 144
inherent properties, 256–264, See also
Linear ROV system, inherent
properties
linear control systems design, 255–275,
See also Remotely operated vehicles,
linear control systems design
model, 138–187, See also Remotely operated
vehicles, modeling
nonlinear control systems design, 215–255,
See also Remotely operated vehicles,
nonlinear control systems design
nonlinear dynamic parameters, 192–193t
perturbation model, 186–191
pool test, 190–200
scaled model, 147–148
sensors, 127f
simplifying assumptions, 130–131, 135,
142–143, 155
Simulink model, 127–129
navigation sensor block, 128–129
pipeline-tracking planner, 127–128
ROV Dynamic, 129
underactuated, 126, 129–130, 183, 202
S
Scalar signals, 27
Scaled model, ROV, 147–148
buoyancy, 171
experimental and simulation results
comparison, 175–176
experimental hydrodynamics results, 167–175
surface roughness, 175
Schur balanced truncation, 72–74
Scope block, 27
Scope sink, 39–42
Seawater density, 190t
Sensitivity function
controller comparison, 116–117
H
∞ optimization, 91–93
Sensitivity matrix, 119
Sensitivity shaping, H∞ optimization, 93–95,
98–99, 273–274
Sensors, 3, 5, 8–10
control system examples, 9, 10
RRC ROV, 127f
navigation sensor block, 128–129
Shaping filter design, 95
Shear stress transport (SST) model, 156
Ship control system, 5, 8
Signals in block diagrams, 27
Simplifying assumptions
buoyancy and gravitational forces, 180–181
dynamic equation using Newtonian method,
130–131
hydrodynamic added mass forces,
142–143, 155
RRC ROV modeling, 135
Simulink, 10, 13, 39, See also Block diagrams
block libraries, 26–27, 30
closed-loop control system design, 45–49
PID tuning, 45–47
Design Optimization Toolbox, 219, 252
fuzzy logic control model, 246–248
gasifier system LQG design, 87366 Index
gasifier system LQR design, 81, 82f
linear hydrodynamic damping matrix model,
178, 179f
Math Operations, 36, 39
open-loop system modeling, 29–44
open-loop transfer function modeling, 25–29
output to workspace, 42–43
PID controller modeling, 215–221
PI-P cascaded controller, 252–253
RRC ROV model, 127–129
running the simulation, 40
sliding-mode control, 230–231
starting, 25
starting new model, 26–27, 31
thruster configuration model, 185f
velocity state-feedback linearization,
235–236
Simulink Design Optimization, 219–221
Simulink Library Browser, 25, 31, 39, 42
Sine and cosine curves, 17
Single-Input, Single-Output (SISO) systems, 27
internal stability, 119
ROV PID controller design, 215
Single-Input, Single-Output (SISO) tool, 47–49
Singular Value Decomposition (SVD), 59
SIRENE, 125
Skin friction, 154, 166, 174–175
Skin friction (linear damping) drag, 190
Sliding-mode control, 201, 215, 229–234, 239
block diagram, 231f
chattering, 230, 232
Society of Naval Architects and Marine
Engineers (SNAME) notations, 131
SolidWorksTM, 11
Space robotic systems, 10
Sphere model, 144–145
Stability
ALSTOM gasifier system
LQR control approach, 80
open-loop stability test, 53–55
controller comparison, 117–119
internal, 118–119
linear ROV system, open-loop stability test,
256–258
MIMO system asymptotic stability, 117
ROV whirling motion due to cross-coupling
effects, 130
Stabilization about equilibrium, 202, See also
Station-keeping model
State estimator, LQG design, 83, 84, See also
Linear quadratic Gaussian
State-feedback linearization, 215, 234–238
State-space representation, 23–24
ALSTOM gasifier system, 51–52, 281–296
0% operating condition, 282–286
50% operating condition, 287–291
100% operating condition, 292–296
reduction, 56–57, 72
stochastic form, 83
generalized plant, 89, 97
linear subsystem model, 212–213
Nyquist type criteria, 118
ROV station-keeping model, 204
RRC ROV dynamics and kinematics
equations, 138
vertical plane model, 208
Station-keeping model, 202–205
cascaded system control, reduced ROV
model, 250
linear control systems design, 255, 267
perturbed model, 205
Step block, 27, 28
Step disturbance input, LQG/LTR performance
test, 87
Step parameters, 39
Step source, 39
Stochastic cost function, 83
Stochastic minimum least-squares, LQG
optimization, 105
Subsea docking station, 125
Subsystem block diagrams, 44
Sugeno inference, 240, 244
Sum block, 36
Supervisory control, ROV, 201–202
Supremum, 91
Surface roughness, 175
Surge
experimental results, 168, 169, 172, 173t, 175
experimental results, pool test, 191, 195,
197–198
horizontal plane model, 206
modeling, 144
PID controller modeling, 217, 219, 221
skin friction effects, 174
station-keeping model, 202
thruster control, 125, 126
vertical plane model, 209
Sway
experimental results, 168, 169, 172, 173t, 175
horizontal plane model, 206
linear ROV open-loop stability, 258
modeling, 5, 144
PID controller modeling, 217, 219
station-keeping model, 202
thruster control, 126
SWIMMER-PHENIX, 125
System error signal, 45
System model, 5
System poles and zeros, gasifier system, 75–76
T
Temperature control system, 7
Tether, ROV pool test, 194, 197Index 367
tf2ss command, 24
Thrusters
configuration model, 182–186
effects on model, 200
experimental measurement, 184–186, 256
hydrodynamic added forces, 145–147, 175
linear control systems design, 255–256
pool test, 190, 194
underactuated ROV, 126, 202
TIMDOMTM, 3
Time response
model order reduction, 72
optimization using PI controller, 64
Time-step specification, 159–160
Toeplitz structure, 240, 241f
Total mass inertial matrix, 206
To Workspace, 42–43
Tracking error, 251
Transfer Fcn block, 27
Transfer function
generalized plant, 96
H
∞ optimization routine, 91
LQG control, 84–86
MATLAB, 22–25
mixed sensitivity problem formulation,
91–93
Simulink, 24
SISO tool, 47–49
Transfer function matrix (TFM), ALSTOM
gasifier system, 60–61
block diagonal dominance, 66–68
Transmission zeros, 75–76
Transponder, 200
Tuning PID controller, 45–49
Turbulence model, 156, 158
U
Underactuated degrees of freedom, 126,
129–130, 183, 202
Underwater robotic vehicles (URVs), 125–126,
See also Remotely operated vehicles;
RRC ROV
basic control system, 4
basic design, 126–129
control system example, 8–9
depth regulation problem, 8–9
need for ROV control, 129–130
RRC ROV model, 138–187, See also
Remotely operated vehicles,
modeling
Unix, 13
Unmanned aerial vehicle (UAV) control system,
9–10
Update Compensator, 49
V
Vector-matrix equation, 21
Vector operations, 13–15
Vector signals, 27
Velocity state-feedback linearization, 234–238
Vertical plane subsystem model, 205–211,
213–214
VirtualDubMod, 169
Virtual Reality Modeling Language
(VRML), 127
W
Wake formation, 162
Wall-boundary conditions, 159
Watt, J., 1
Wave Analysis MIT (WAMIT), 129, 141,
143–145, 148, 154, 196
Weighting functions, 271–273
H
∞, 93–95, 98–100, 271–273
H
2, 108–110
Weighting matrices
H
∞, 98–100
LQG, 87
LQG/LTR, 265–266
LQR, 77, 81
WHILE, 19
White noise, 105, 106, 141
Windows, 13
Woods Hole Oceanographic Institution, 125
X
xPC TARGET, 11–12
Y
Yaw
experimental and simulation results
comparison, 178
experimental results, 168, 169, 172, 173t
experimental results, pool test, 191, 196
horizontal plane model, 206
linear damping, 166
linear ROV open-loop stability, 258
PID controller modeling, 217, 219
station-keeping model, 202
thruster control, 125, 126
vertical plane model, 209
Z
Zigler-Nichols controller tuning method
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