Robust Control Engineering. Practical QFT Solutions

569 Pages·2017·66.584 MB·English

by  Mario Garcia-Sanz

Robust Control Engineering
Robust Control Engineering
Practical QFT Solutions
Mario García-Sanz
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“If you want to ind the secrets of the universe, think in terms of energy, frequency and
vibration”. Nikola Tesla (1856–1943).
“If you believe in the frequency domain, you believe in QFT”. Isaac Horowitz to Mario
García-Sanz (Pamplona, Spain), 2000.
“QFT provides one of the most practical robust control design methods available... It is
now becoming a much more accessible and valuable method, mainly because the avail-
ability of good design software... Prof. Garcia-Sanz has developed a very easy to use
design package”. Michael Grimble, founder of the industrial control centre (Glasgow,
UK), E-news August 2016.
“The most valuable companies in the future won’t ask what problems can be solved
with computers alone. Instead, they’ll ask: how can computers help humans solve hard
problems”. Peter Thiel, co-fouder of PayPal and Palantir, in his book Zero to One, 2014.
“Thanks for making this amazing toolbox!!”. “The QFT Control Tollbox proved to be
an excellent tool for robust controller design!!”. “One of the best courses I’ve taken!!”.
CWRU students who attended Prof. Garcia-Sanz QFT control courses.
“The investment in training will pay off in the long term. People can’t deliver on what
they do not know how to do... you have to upgrade capabilities... A well-trained team
is often a company’s most signiicant advantage—and an incompetent one its biggest
liability”. David Hoffeld, CEO Hoffeld Group, in his book The Science of Selling, 2016.
To Marta, María, Pablo, and Sofía
Contents
Preface .............................................................................................................................................xv
Acknowledgments ......................................................................................................................xix
Author ...........................................................................................................................................xxi
1 Introduction .............................................................................................................................1
1.1 The Control Engineer’s Leadership ............................................................................1
1.2 QFT Robust Control Engineering ...............................................................................4
1.3 Book’s Outline ...............................................................................................................7
1.4 Courses and Modules .................................................................................................11
2 QFT Robust Control .............................................................................................................17
2.1 Introduction .................................................................................................................17
2.2 Plant Modeling: Step 1 ...............................................................................................19
2.3 The Nominal Plant: Step 2 .........................................................................................28
2.4 QFT Templates: Step 3 ................................................................................................28
2.5 Stability Speciications: Step 4 ...................................................................................30
2.6 Performance Speciications: Step 5 ...........................................................................31
2.7 QFT Bounds: Steps 6 through 8 ................................................................................34
2.8 Controller Design, G(s)—Loop Shaping: Step 9 ......................................................39
2.9 Preilter Design, F(s): Step 10 ......................................................................................41
2.10 Analysis and Validation: Steps 11 through 13 ........................................................42
2.11 Model Matching ..........................................................................................................54
2.12 Feedforward Control ..................................................................................................59
2.13 PID Control: Design and Tuning with QFT ............................................................63
2.14 Practical Tips ................................................................................................................69
2.14.1 Selection of Speciications .............................................................................69
2.14.1.1 Stability W ......................................................................................69
s
2.14.1.2 Sensitivity δ (ω) ...............................................................................69
3
2.14.1.3 Reference Tracking δ (ω), δ (ω) ................................................71
6-lo 6-up
2.14.2 Loop Shaping—Designing G(s)....................................................................74
2.14.3 Preilter—Designing F(s) ...............................................................................77
2.15 Summary ......................................................................................................................78
2.16 Practice ..........................................................................................................................78
3 Unstable Systems and Control Solutions ........................................................................79
3.1 Introduction .................................................................................................................79
3.2 Understanding Gain and Phase Margins, and W Circles ....................................82
s
3.3 The NSC ........................................................................................................................84
3.4 Nyquist Stability Criterion in the Nichols Chart ....................................................86
3.5 Examples ......................................................................................................................89
3.6 Guidelines to Design Controllers .............................................................................91
3.6.1 Parity Interlacing Property ...........................................................................91
3.6.2 Fundamental Theorem of Feedback Control .............................................92
ix
x Contents
3.6.3 Examples .........................................................................................................92
3.7 Analysis of the First Case ..........................................................................................95
3.8 Summary ......................................................................................................................97
3.9 Practice ..........................................................................................................................98
4 Time-Delay and Non-Minimum Phase Systems ...........................................................99
4.1 Time-Delay Systems ...................................................................................................99
4.2 Robust Design of the Smith Predictor ......................................................................103
4.2.1 First Algorithm .............................................................................................107
4.2.2 Second Algorithm ........................................................................................107
4.3 Non-Minimum Phase Systems ...................................................................................114
4.3.1 Analysis .........................................................................................................114
4.3.2 Control Methodology ..................................................................................115
4.4 Summary ....................................................................................................................118
4.5 Practice ........................................................................................................................118
5 Distributed Parameter Systems .......................................................................................119
5.1 Introduction ...............................................................................................................119
5.2 Modeling Approaches for PDE ...............................................................................120
5.3 Generalized DPS Control System Structure .........................................................121
5.4 Extension of QFT to DPS ..........................................................................................124
5.5 Summary ....................................................................................................................134
5.6 Practice ........................................................................................................................134
6 Gain Scheduling/Switching Control Solutions ...........................................................135
6.1 Introduction ...............................................................................................................135
6.2 System Stability Under Switching ..........................................................................135
6.3 Methodology ..............................................................................................................141
6.4 Examples ....................................................................................................................142
6.5 Summary ....................................................................................................................147
6.6 Practice ........................................................................................................................150
7 Nonlinear Dynamic Control ............................................................................................151
7.1 Introduction ...............................................................................................................151
7.2 The Circle Stability Criterion...................................................................................151
7.3 Nonlinear Dynamic Control: One Nonlinearity ..................................................153
7.4 Anti-Windup Solution for PID Controllers ...........................................................156
7.5 Nonlinear Dynamic Control: Several Nonlinearities ..........................................163
7.5.1 Describing Functions ..................................................................................164
7.5.2 Isolines ...........................................................................................................169
7.6 Summary ....................................................................................................................182
7.7 Practice ........................................................................................................................183
8 Multi-Input Multi-Output Systems: Analysis and Control .......................................185
8.1 Introduction ...............................................................................................................185
8.2 Formulation for n × n Systems ................................................................................192
8.3 MIMO Systems—Description and Characteristics ..............................................196
8.3.1 Loop Coupling and Controller Structure .................................................196
8.3.2 Interaction Analysis .....................................................................................197
Contents xi
8.3.3 Multivariable Poles and Zeros ...................................................................199
8.3.4 Directionality................................................................................................201
8.3.5 Gain and Phase ............................................................................................201
8.3.6 Effect of Poles and Zeros .............................................................................202
8.3.7 Disturbance and Noise Signals ..................................................................202
8.3.8 Uncertainty ...................................................................................................202
8.3.9 Stability ..........................................................................................................203
8.4 MIMO QFT Control—Overview ............................................................................204
8.5 Non-Diagonal MIMO QFT—Method 1 ..................................................................207
8.5.1 The Coupling Matrix ...................................................................................208
8.5.2 Tracking .........................................................................................................209
8.5.3 Disturbance Rejection at Plant Input ........................................................211
8.5.4 Disturbance Rejection at Plant Output .....................................................212
8.5.5 The Coupling Elements ...............................................................................213
8.5.6 The Optimal Non-Diagonal Compensator ..............................................214
8.5.6.1 Tracking .........................................................................................215
8.5.6.2 Disturbance Rejection at Plant Input .........................................215
8.5.6.3 Disturbance Rejection at Plant Output .....................................215
8.5.7 The Coupling Effects ...................................................................................215
8.5.7.1 Tracking .........................................................................................216
8.5.7.2 Disturbance Rejection at Plant Input .........................................216
8.5.7.3 Disturbance Rejection at Plant Output .....................................216
8.5.8 Quality Function of the Designed Compensator ....................................217
8.5.9 Design Methodology ...................................................................................218
8.5.10 Some Practical Issues...................................................................................220
8.6 Non-Diagonal MIMO QFT—Method 2 ..................................................................220
8.6.1 Non-Diagonal MIMO QFT Reformulation ...............................................221
8.6.2 Case 1: Reference Tracking and Disturbance Rejection at Plant
Output ...........................................................................................................221
8.6.2.1 Methodology .................................................................................222
8.6.3 Case 2: Disturbance Rejection at Plant Input ...........................................226
8.6.4 Stability Conditions and Final Implementation ......................................227
8.6.5 Translating Matrix Performance Speciications ......................................228
8.6.5.1 Case n × n ......................................................................................228
8.6.5.2 Case 2 × 2 .......................................................................................234
8.7 Comparison of Methods 1 and 2 .............................................................................238
8.8 Heat Exchanger, Example 8.1—MIMO QFT Method 1 ........................................240
8.9 Heat Exchanger, Example 8.1—MIMO QFT Method 2 ........................................248
8.10 Summary ....................................................................................................................259
8.11 Practice ........................................................................................................................259
9 Control Topologies .............................................................................................................261
9.1 Introduction ...............................................................................................................261
9.2 Cascade Control Systems .........................................................................................261
9.2.1 Challenge 9.1 .................................................................................................261
9.2.2 Solution 9.1: Cascade Control .....................................................................262
9.3 Feedforward Control Systems .................................................................................263
9.3.1 Challenge 9.2 .................................................................................................263
9.3.2 Solution 9.2a: For Disturbance Rejection ..................................................264
xii Contents
9.3.3 Solution 9.2b: For Reference Tracking. Model Matching ........................266
9.3.4 Solution 9.2c: For Disturbance Rejection and Reference Tracking .......266
9.4 Override Control Systems ........................................................................................267
9.4.1 Challenge 9.3 .................................................................................................267
9.4.2 Solution 9.3: Override Control ....................................................................267
9.5 Ratio Control Systems ..............................................................................................269
9.5.1 Challenge 9.4 .................................................................................................269
9.5.2 Solution 9.4: Ratio Control ..........................................................................269
9.6 Mid-Range Control Systems ....................................................................................270
9.6.1 Challenge 9.5 .................................................................................................270
9.6.2 Solution 9.5: Mid-Range Control ................................................................271
9.7 Load-Sharing Control Systems ...............................................................................272
9.7.1 Challenge 9.6 .................................................................................................272
9.7.2 Solution 9.6: Load-Sharing Control ...........................................................272
9.8 Split-Range Control Systems ...................................................................................273
9.8.1 Challenge 9.7 .................................................................................................273
9.8.2 Solution 9.7 Split-Range Control ................................................................274
9.9 Inferential Control Systems .....................................................................................274
9.9.1 Challenge 9.8 .................................................................................................274
9.9.2 Solution 9.8: Inferential Control .................................................................275
9.10 Auctioneering Control Systems ..............................................................................276
9.10.1 Challenge 9.9 .................................................................................................276
9.10.2 Solution 9.9: Auctioneering Control ..........................................................277
9.11 Summary ....................................................................................................................277
9.12 Practice ........................................................................................................................278
10 Controller Implementation ...............................................................................................279
10.1 Introduction ...............................................................................................................279
10.2 Analog Implementation ...........................................................................................279
10.3 Digital Implementation ............................................................................................284
10.3.1 Sample and Hold ..........................................................................................285
10.3.2 Computer Control Algorithms ..................................................................288
10.3.3 Positional and Velocity Algorithms ..........................................................292
10.3.3.1 Positional Algorithm ....................................................................293
10.3.3.2 Velocity Algorithm .......................................................................293
10.3.4 Switching and Bumpless Algorithms .......................................................294
10.3.5 Pulse Width Modulation .............................................................................294
10.4 Fragility Analysis with QFT ....................................................................................296
10.5 Summary ....................................................................................................................299
10.6 Practice ........................................................................................................................300
Case Study 1: Satellite Control................................................................................................301
Case Study 2: W ind Turbine Control .....................................................................................317
Case Study 3: Wastewater Treatment Plant Control ...........................................................343
Case Study 4: R adio-Telescope Control .................................................................................365
Case Study 5: Attitude and Position Control of Spacecraft
Telescopes with Flexible Appendages .........................................................395