Selected Topics on Constrained and Nonlinear Control: Textbook

1.1 Introduction......Page 16
1.3.1 Problem Formulation......Page 18
1.3.2 Partitioning into Sets of Active Constraints......Page 20
1.3.3 Eliminating the Lagrangian Multipliers......Page 21
1.4 Elimination for Systems of Linear Equations (Zero Loss Method)......Page 22
1.5 Elimination for Systems of Polynomial Equations......Page 26
1.5.1 Finding Invariant Controlled Variables for Polynomial Systems......Page 29
1.6 Switching Operating Regions......Page 31
1.7 Case Study......Page 32
1.7.2 Eliminating......Page 34
1.7.3 Eliminating Unknown Variables......Page 35
1.7.4 Using Measurement Invariants for Control and Region Identification......Page 37
1.8 Discussion......Page 38
References......Page 40
2.1 Introduction......Page 42
2.2 Sources of Poor Control Loop Performance......Page 45
2.2.1 Improper and Inadequate Controller Tuning and Lack of Maintenance......Page 46
2.2.2 Equipment Malfunction or Poor Design......Page 47
2.2.3 Poor or Missing Feedforward Compensation......Page 48
2.2.4 Inappropriate Control Structure......Page 49
2.3.1 Detection of Oscillating Control Loops......Page 50
2.3.2 The Oscillation Detection Method of Miao and Seborg (ACF Based)......Page 52
2.3.3 Oscillation Diagnosis......Page 57
2.4.1 Definitions: Stiction, Deadzone and Backlash......Page 59
2.4.2 Stiction Phenomenon in a Control Valve......Page 60
2.5.1 Physical Model......Page 61
2.5.2 Two Parameter Model......Page 63
2.5.3 One Parameter Model......Page 66
2.6 Diagnosis of Valve Stiction......Page 67
2.6.2 Method Based on Cross-correlation Function......Page 68
2.6.3 Stiction Detection Based on Curve Fitting......Page 70
2.6.4 Stiction Detection using an OP-PV Plot......Page 71
2.6.5 Stiction Detection using Higher Order Statistics......Page 72
2.6.7 Stiction Compensation......Page 75
2.6.8 Detection of Backlash......Page 76
2.6.9 Backlash Compensation......Page 78
2.7.1 Control Loop Performance Benchmarking......Page 79
2.7.2 Modifications to the Harris Index......Page 86
2.7.4 Advanced Benchmarks......Page 88
2.7.5 Multivariate Performance Measures......Page 89
2.8 Procedure for Controller Performance Assessment......Page 90
2.8.1 Preliminary Analysis of Data......Page 91
2.8.3 Evaluation of Level of Control Performance......Page 93
2.8.4 Improvement of Control Performance......Page 94
2.9 Issues in Multivariate Systems......Page 95
References......Page 97
Mikuláš Huba......Page 102
3.1 Introduction......Page 103
3.2 Innovation versus Conservativeness......Page 108
3.3 Advanced Modifications of PID Control......Page 112
3.4 Performance of PID Control......Page 116
3.4.1 Settling Time ts, IAE, TV, TV0, TV1 and TV2......Page 117
3.4.2 Basic Qualitative Shapes of Transient Responses......Page 119
3.4.3 Quantifying Qualitative Measures......Page 121
3.4.4  Performance Portrait (PP)......Page 125
3.5 Dynamical Classes (DC) of Control......Page 126
3.5.1 Dynamical Class 0 (DC0)......Page 130
3.5.2 Dynamical Class 1 (DC1)......Page 131
3.5.3 Dynamical Class 2 (DC2)......Page 132
3.6 Fundamental and ``ad hoc'' Solutions......Page 133
3.6.1 Setpoint Response......Page 134
3.6.2 Disturbance Response......Page 136
3.6.3 Internal and Zero Dynamics......Page 137
3.7 Dead Time Systems......Page 138
3.7.2 Fundamental Controllers – a New Concept?......Page 139
3.8 Table of Fundamental PID Controllers......Page 140
3.9 Generic and Intentionally Decreased DC......Page 143
3.10 Summary......Page 147
References......Page 149
4.1 I, I0 and FI0 Controllers......Page 154
4.1.1 Output Disturbance Reconstruction......Page 155
4.1.2 Input Disturbance Reconstruction......Page 156
4.1.4 Nonmodelled Dynamics Approximated by Dead-time – Analytical Treatment......Page 158
4.1.5 Nonmodelled Dynamics Approximated by Dead-time – Treatment by Performance Portrait......Page 161
4.1.6 Nonmodelled Dynamics Approximated by Time Constant – Analytical Treatment......Page 163
4.1.7 Nonmodelled Dynamics Approximated by Time Constant – Treatment by Performance Portrait......Page 164
4.1.8 Tuning Based on Maximal Sensitivity Ms=1.4......Page 165
4.1.9 Short Summary of Nominal I0-Controller Tuning......Page 167
4.1.10 Robust Controller Tuning and Characteristics......Page 169
4.2.1 Different Types of PI0 and FPI0 Controllers......Page 173
4.2.2 PI0-IM: Analytical Versus Numerical Robust Tuning......Page 177
4.2.3 PI0-IM: Impact of the Parameter Mismatch on Setpoint Steps......Page 180
4.2.4 PI0-IM: Impact of Parameter Mismatch for Disturbance Step......Page 183
4.2.5 Influence of the Nonmodelled Dynamics......Page 184
4.2.6 Effect of Measurement and Quantization Noise......Page 185
4.2.8 Performance Portrait of the FPI0 Controller for Tp=Tf......Page 186
4.3 Predictive I0 and Filtered Predictive I0 Controllers (PrI0 and FPrI0)......Page 187
4.3.1 Performance Portrait of the PrI0 and FPrI0 Controllers......Page 190
4.3.2 Robust Tuning of the PrI0 and FPrI0 Controllers......Page 191
4.4 Summary......Page 197
References......Page 199
5.1 Introduction......Page 202
5.1.1 Motivation and Main Ideas......Page 203
5.1.2 Historical Literature Review......Page 204
5.1.3 Notation......Page 206
5.2.1 Continuous-time Model, Discretization and Finite Parameterization......Page 207
5.2.2 Numerical Optimal Control......Page 211
5.2.3 Tuning and Stability......Page 217
5.2.4 Extensions and Variations of the Problem Formulation......Page 225
5.3.1 Basic Problem Formulation......Page 230
5.4.1 Problem Structure......Page 240
5.4.2 Nonlinear Programming......Page 241
5.4.3 Warm Start......Page 245
5.4.4 Computation of Jacobians and Hessians......Page 246
References......Page 248
6.1 Introduction......Page 256
6.2 Notation......Page 258
6.3 Explicit Model Predictive Control......Page 259
6.3.1 Quadratic Programming Definition......Page 261
6.3.2 Explicit Solution......Page 262
6.3.4 Numerical Example......Page 264
6.4.2 Theoretical Background......Page 267
6.4.3 Main Results......Page 268
6.4.4 Numerical Examples......Page 274
6.4.5 Random Systems......Page 275
6.4.6 Combination of Clipping and ORM......Page 279
6.5.1 Introduction......Page 280
6.5.2 Theoretical Background......Page 282
6.5.3 Main Results......Page 284
6.5.4 Numerical Example......Page 287
6.5.5 Real-time Control of a Thermo-Optical Device......Page 288
References......Page 300
Tomáš Polóni and Gergely Takács and Boris Rohal'-Ilkiv......Page 304
7.1 Introduction......Page 305
7.2.1 Introduction......Page 307
7.2.2 Problem Definition......Page 309
7.2.3 Theoretical Summary......Page 310
7.2.4 Experimental Setup......Page 318
7.2.5 Off-line properties......Page 321
7.2.6 On-line Properties......Page 323
7.2.7 Conclusion......Page 330
7.3.1 Introduction......Page 332
7.3.2 Basic Model Formulation......Page 333
7.3.3 Extended Kalman Filter......Page 335
7.3.4 Moving Horizon Estimation Algorithm......Page 336
7.3.5 Simulations......Page 340
7.3.6 Extended Kalman Filter Setup......Page 342
7.3.7 Moving Horizon Observer Setup......Page 343
7.3.8 Simulation Results and Discussion......Page 344
7.3.9 Conclusion......Page 349
7.4.1 Introduction......Page 350
7.4.2 Model Structure......Page 351
7.4.3 Predictive Controller Design......Page 355
7.4.5 Conclusion......Page 359
References......Page 360