Selected Topics on Constrained and Nonlinear Control

1.1 Introduction......Page 15
1.3.1 Problem Formulation......Page 17
1.3.2 Partitioning into Sets of Active Constraints......Page 19
1.3.3 Eliminating the Lagrangian Multipliers......Page 20
1.4 Elimination for Systems of Linear Equations (Zero Loss Method)......Page 21
1.5 Elimination for Systems of Polynomial Equations......Page 25
1.5.1 Finding Invariant Controlled Variables for Polynomial Systems......Page 28
1.6 Switching Operating Regions......Page 30
1.7 Case Study......Page 31
1.7.2 Eliminating......Page 33
1.7.3 Eliminating Unknown Variables......Page 34
1.7.4 Using Measurement Invariants for Control and Region Identification......Page 36
1.8 Discussion......Page 37
References......Page 39
2.1 Introduction......Page 41
2.2 Sources of Poor Control Loop Performance......Page 44
2.2.1 Improper and Inadequate Controller Tuning and Lack of Maintenance......Page 45
2.2.2 Equipment Malfunction or Poor Design......Page 46
2.2.3 Poor or Missing Feedforward Compensation......Page 47
2.2.4 Inappropriate Control Structure......Page 48
2.3.1 Detection of Oscillating Control Loops......Page 49
2.3.2 The Oscillation Detection Method of Miao and Seborg (ACF Based)......Page 51
2.3.3 Oscillation Diagnosis......Page 56
2.4.1 Definitions: Stiction, Deadzone and Backlash......Page 58
2.4.2 Stiction Phenomenon in a Control Valve......Page 59
2.5.1 Physical Model......Page 60
2.5.2 Two Parameter Model......Page 62
2.5.3 One Parameter Model......Page 65
2.6 Diagnosis of Valve Stiction......Page 66
2.6.2 Method Based on Cross-correlation Function......Page 67
2.6.3 Stiction Detection Based on Curve Fitting......Page 69
2.6.4 Stiction Detection using an OP-PV Plot......Page 70
2.6.5 Stiction Detection using Higher Order Statistics......Page 71
2.6.7 Stiction Compensation......Page 74
2.6.8 Detection of Backlash......Page 75
2.6.9 Backlash Compensation......Page 77
2.7.1 Control Loop Performance Benchmarking......Page 78
2.7.2 Modifications to the Harris Index......Page 85
2.7.4 Advanced Benchmarks......Page 87
2.7.5 Multivariate Performance Measures......Page 88
2.8 Procedure for Controller Performance Assessment......Page 89
2.8.1 Preliminary Analysis of Data......Page 90
2.8.3 Evaluation of Level of Control Performance......Page 92
2.8.4 Improvement of Control Performance......Page 93
2.9 Issues in Multivariate Systems......Page 94
References......Page 96
Mikuláš Huba......Page 101
3.1 Introduction......Page 102
3.2 Innovation versus Conservativeness......Page 107
3.3 Advanced Modifications of PID Control......Page 111
3.4 Performance of PID Control......Page 115
3.4.1 Settling Time ts, IAE, TV, TV0, TV1 and TV2......Page 116
3.4.2 Basic Qualitative Shapes of Transient Responses......Page 118
3.4.3 Quantifying Qualitative Measures......Page 120
3.4.4  Performance Portrait (PP)......Page 124
3.5 Dynamical Classes (DC) of Control......Page 125
3.5.1 Dynamical Class 0 (DC0)......Page 129
3.5.2 Dynamical Class 1 (DC1)......Page 130
3.5.3 Dynamical Class 2 (DC2)......Page 131
3.6 Fundamental and ``ad hoc\'\' Solutions......Page 132
3.6.1 Setpoint Response......Page 133
3.6.2 Disturbance Response......Page 135
3.6.3 Internal and Zero Dynamics......Page 136
3.7 Dead Time Systems......Page 137
3.7.2 Fundamental Controllers – a New Concept?......Page 138
3.8 Table of Fundamental PID Controllers......Page 139
3.9 Generic and Intentionally Decreased DC......Page 142
3.10 Summary......Page 146
References......Page 148
4.1 I, I0 and FI0 Controllers......Page 153
4.1.1 Output Disturbance Reconstruction......Page 154
4.1.2 Input Disturbance Reconstruction......Page 155
4.1.4 Nonmodelled Dynamics Approximated by Dead-time – Analytical Treatment......Page 157
4.1.5 Nonmodelled Dynamics Approximated by Dead-time – Treatment by Performance Portrait......Page 160
4.1.6 Nonmodelled Dynamics Approximated by Time Constant – Analytical Treatment......Page 162
4.1.7 Nonmodelled Dynamics Approximated by Time Constant – Treatment by Performance Portrait......Page 163
4.1.8 Tuning Based on Maximal Sensitivity Ms=1.4......Page 164
4.1.9 Short Summary of Nominal I0-Controller Tuning......Page 166
4.1.10 Robust Controller Tuning and Characteristics......Page 168
4.2.1 Different Types of PI0 and FPI0 Controllers......Page 172
4.2.2 PI0-IM: Analytical Versus Numerical Robust Tuning......Page 176
4.2.3 PI0-IM: Impact of the Parameter Mismatch on Setpoint Steps......Page 179
4.2.4 PI0-IM: Impact of Parameter Mismatch for Disturbance Step......Page 182
4.2.5 Influence of the Nonmodelled Dynamics......Page 183
4.2.6 Effect of Measurement and Quantization Noise......Page 184
4.2.8 Performance Portrait of the FPI0 Controller for Tp=Tf......Page 185
4.3 Predictive I0 and Filtered Predictive I0 Controllers (PrI0 and FPrI0)......Page 186
4.3.1 Performance Portrait of the PrI0 and FPrI0 Controllers......Page 189
4.3.2 Robust Tuning of the PrI0 and FPrI0 Controllers......Page 190
4.4 Summary......Page 196
References......Page 198
5.1 Introduction......Page 201
5.1.1 Motivation and Main Ideas......Page 202
5.1.2 Historical Literature Review......Page 203
5.1.3 Notation......Page 205
5.2.1 Continuous-time Model, Discretization and Finite Parameterization......Page 206
5.2.2 Numerical Optimal Control......Page 210
5.2.3 Tuning and Stability......Page 216
5.2.4 Extensions and Variations of the Problem Formulation......Page 224
5.3.1 Basic Problem Formulation......Page 229
5.4.1 Problem Structure......Page 239
5.4.2 Nonlinear Programming......Page 240
5.4.3 Warm Start......Page 244
5.4.4 Computation of Jacobians and Hessians......Page 245
References......Page 247
6.1 Introduction......Page 255
6.2 Notation......Page 257
6.3 Explicit Model Predictive Control......Page 258
6.3.1 Quadratic Programming Definition......Page 260
6.3.2 Explicit Solution......Page 261
6.3.4 Numerical Example......Page 263
6.4.2 Theoretical Background......Page 266
6.4.3 Main Results......Page 267
6.4.4 Numerical Examples......Page 273
6.4.5 Random Systems......Page 274
6.4.6 Combination of Clipping and ORM......Page 278
6.5.1 Introduction......Page 279
6.5.2 Theoretical Background......Page 281
6.5.3 Main Results......Page 283
6.5.4 Numerical Example......Page 286
6.5.5 Real-time Control of a Thermo-Optical Device......Page 287
References......Page 299
Tomáš Polóni and Gergely Takács and Boris Rohal\'-Ilkiv......Page 303
7.1 Introduction......Page 304
7.2.1 Introduction......Page 306
7.2.2 Problem Definition......Page 308
7.2.3 Theoretical Summary......Page 309
7.2.4 Experimental Setup......Page 317
7.2.5 Off-line properties......Page 320
7.2.6 On-line Properties......Page 322
7.2.7 Conclusion......Page 329
7.3.1 Introduction......Page 331
7.3.2 Basic Model Formulation......Page 332
7.3.3 Extended Kalman Filter......Page 334
7.3.4 Moving Horizon Estimation Algorithm......Page 335
7.3.5 Simulations......Page 339
7.3.6 Extended Kalman Filter Setup......Page 341
7.3.7 Moving Horizon Observer Setup......Page 342
7.3.8 Simulation Results and Discussion......Page 343
7.3.9 Conclusion......Page 348
7.4.1 Introduction......Page 349
7.4.2 Model Structure......Page 350
7.4.3 Predictive Controller Design......Page 354
7.4.5 Conclusion......Page 358
References......Page 359