Model Predictive Control System Design and Implementation Using MATLAB®

By: Liuping Wang

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Hardcover | 4 March 2009 | Edition Number 2009

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408 Pages

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24 x 16.2 x 2.9

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Model Predictive Control System Design and Implementation Using MATLAB^(R) proposes methods for design and implementation of MPC systems using basis functions that confer the following advantages: - continuous- and discrete-time MPC problems solved in similar design frameworks; - a parsimonious parametric representation of the control trajectory gives rise to computationally efficient algorithms and better on-line performance; and - a more general discrete-time representation of MPC design that becomes identical to the traditional approach for an appropriate choice of parameters.

After the theoretical presentation, coverage is given to three industrial applications. The subject of quadratic programming, often associated with the core optimization algorithms of MPC is also introduced and explained.

The technical contents of this book is mainly based on advances in MPC using state-space models and basis functions. This volume includes numerous analytical examples and problems and MATLAB^(R) programs and exercises.

Industry Reviews

From the reviews:

"This monograph gives an introduction to model predictive control and recent developments in its design and implementation using Matlab and Simulink. The book is aimed at a wide readership ranging from industrial control engineers to graduate students in the process and control disciplines." (IEEE Control Systems Magazine, Vol. 30, August, 2010)

"The book gives an introduction to Model Predictive Control (MPC), and recent developments in design and implementation. ... The book's approach is expected to appeal to a wide readership ranging from the industrial control engineer to the postgraduate student in the process and control disciplines. Both will find the MATLAB demonstrations of the control concepts a valuable tutorial route to understanding MPC in practice." (Karl-Heinz Waldmann, Zentralblatt MATH, Vol. 1200, 2011)

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Published: 21st October 2010

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List of Symbols and Abbreviations	p. xxvii
Discrete-time MPC for Beginners	p. 1
Introduction	p. 1
Day-to-day Application Example of Predictive Control	p. 1
Models Used in the Design	p. 3
State-space Models with Embedded Integrator	p. 4
Single-input and Single-output System	p. 4
MATLAB Tutorial: Augmented Design Model	p. 6
Predictive Control within One Optimization Window	p. 7
Prediction of State and Output Variables	p. 7
Optimization	p. 9
MATLAB Tutorial: Computation of MPC Gains	p. 13
Receding Horizon Control	p. 15
Closed-loop Control System	p. 16
MATLAB Tutorial: Implementation of Receding Horizon Control	p. 20
Predictive Control of MIMO Systems	p. 22
General Formulation of the Model	p. 22
Solution of Predictive Control of MIMO Systems	p. 26
State Estimation	p. 27
Basic Ideas About an Observer	p. 28
Basic Results About Observability	p. 30
Kalman Filter	p. 33
Tuning Observer Dynamics	p. 34
State Estimate Predictive Control	p. 34
Summary	p. 37
Problems	p. 39
Discrete-time MPC with Constraints	p. 43
Introduction	p. 43
Motivational Examples	p. 43
Formulation of Constrained Control Problems	p. 47
Frequently Used Operational Constraints	p. 47
Constraints as Part of the Optimal Solution	p. 50
Numerical Solutions Using Quadratic Programming	p. 53
Quadratic Programming for Equality Constraints	p. 53
Minimization with Inequality Constraints	p. 58
Primal-Dual Method	p. 62
Hildreth's Quadratic Programming Procedure	p. 63
MATLAB Tutorial: Hildreth's Quadratic Programming	p. 67
Closed-form Solution of $$	p. 68
Predictive Control with Constraints on Input Variables	p. 69
Constraints on Rate of Change	p. 70
Constraints on Amplitude of the Control	p. 73
Constraints on Amplitude and Rate of Change	p. 77
Constraints on the Output Variable	p. 78
Summary	p. 81
Problems	p. 83
Discrete-time MPC Using Laguerre Functions	p. 85
Introduction	p. 85
Laguerre Functions and DMPC	p. 85
Discrete-time Laguerre Networks	p. 86
Use of Laguerre Networks in System Description	p. 90
MATLAB Tutorial: Use of Laguerre Functions in System Modelling	p. 90
Use of Laguerre Functions in DMPC Design	p. 92
Design Framework	p. 93
Cost Functions	p. 94
Minimization of the Objective Function	p. 97
Convolution Sum	p. 98
Receding Horizon Control	p. 98
The Optimal Trajectory of Incremental Control	p. 99
Extension to MIMO Systems	p. 106
MATLAB Tutorial Notes	p. 108
DMPC Computation	p. 108
Predictive Control System Simulation	p. 115
Constrained Control Using Laguerre Functions	p. 118
Constraints on the Difference of the Control Variable	p. 118
Constraints on the Amplitudes of the Control Signal	p. 121
Stability Analysis	p. 127
Stability with Terminal-State Constraints	p. 127
Stability with Large Prediction Horizon	p. 129
Closed-form Solution of Constrained Control for SISO Systems	p. 131
MATLAB Tutorial: Constrained Control of DC Motor	p. 135
Summary	p. 143
Problems	p. 144
Discrete-time MPC with Prescribed Degree of Stability	p. 149
Introduction	p. 149
Finite Prediction Horizon: Re-visited	p. 149
Motivational Example	p. 150
Origin of the Numerical Conditioning Problem	p. 150
Use of Exponential Data Weighting	p. 152
The Cost Function	p. 152
Optimization of Exponentially Weighted Cost Function	p. 153
Interpretation of Results from Exponential Weighting	p. 156
Asymptotic Closed-loop Stability with Exponential Weighting	p. 158
Modification of Q and R Matrices	p. 158
Interpretation of the Results	p. 160
Discrete-time MPC with Prescribed Degree of Stability	p. 165
Tuning Parameters for Closed-loop Performance	p. 170
The Relationship Between P$$ and Jmin	p. 171
Tuning Procedure Once More	p. 176
Exponentially Weighted Constrained Control	p. 179
Additional Benefit	p. 182
Summary	p. 186
Problems	p. 188
Continuous-time Orthonormal Basis Functions	p. 193
Introduction	p. 193
Orthonormal Expansion	p. 193
Laguerre Functions	p. 194
Approximating Impulse Responses	p. 197
Kautz Functions	p. 202
Kautz Functions in the Time Domain	p. 204
Modelling the System Impulse Response	p. 205
Summary	p. 206
Problems	p. 207
Continuous-time MPC	p. 209
Introduction	p. 209
Model Structures for CMPC Design	p. 209
Model Structure	p. 211
Controllability and Observability of the Model	p. 215
Model Predictive Control Using Finite Prediction Horizon	p. 216
Modelling the Control Trajectory	p. 217
Predicted Plant Response	p. 218
Analytical Solution of the Predicted Response	p. 219
The Recursive Solution	p. 221
Optimal Control Strategy	p. 224
Receding Horizon Control	p. 227
Implementation of the Control Law in Digital Environment	p. 234
Estimation of the States	p. 234
MATLAB Tutorial: Closed-loop Simulation	p. 237
Model Predictive Control Using Kautz Functions	p. 240
Summary	p. 244
Problems	p. 245
Continuous-time MPC with Constraints	p. 249
Introduction	p. 249
Formulation of the Constraints	p. 249
Frequently Used Constraints	p. 249
Constraints as Part of the Optimal Solution	p. 251
Numerical Solutions for the Constrained Control Problem	p. 257
Real-time Implementation of Continuous-time MPC	p. 262
Summary	p. 266
Problems	p. 267
Continuous-time MPC with Prescribed Degree of Stability	p. 271
Introduction	p. 271
Motivating Example	p. 271
CMPC Design Using Exponential Data Weighting	p. 274
CMPC with Asymptotic Stability	p. 277
Continuous-time MPC with Prescribed Degree of Stability	p. 283
The Original Anderson and Moore's Results	p. 283
CMPC with a Prescribed Degree of Stability	p. 284
Tuning Parameters and Design Procedure	p. 286
Constrained Control with Exponential Data Weighting	p. 288
Summary	p. 291
Problems	p. 293
Classical MPC Systems in State-space Formulation	p. 297
Introduction	p. 297
Generalized Predictive Control in State-space Formulation	p. 298
Special Class of Discrete-time State-space Structures	p. 298
General NMSS Structure for GPC Design	p. 301
Generalized Predictive Control in State-space Formulation	p. 302
Alternative Formulation to GPC	p. 305
Alternative Formulation for SISO Systems	p. 305
Closed-loop Poles of the Predictive Control System	p. 307
Transfer Function Interpretation	p. 310
Extension to MIMO Systems	p. 313
MNSS Model for MIMO Systems	p. 314
Case Study of NMSS Predictive Control System	p. 315
Continuous-time NMSS model	p. 320
Case Studies for Continuous-time MPC	p. 323
Predictive Control Using Impulse Response Models	p. 326
Summary	p. 329
Problems	p. 330
Implementation of Predictive Control Systems	p. 333
Introduction	p. 333
Predictive Control of DC Motor Using a Micro-controller	p. 333
Hardware Configuration	p. 334
Model Development	p. 336
DMPC Tuning	p. 337
DMPC Implementation	p. 338
Experimental Results	p. 339
Implementation of Predictive Control Using xPC Target	p. 340
Overview	p. 340
Creating a Simulink Embedded Function	p. 342
Constrained Control of DC Motor Using xPC Target	p. 347
Control of Magnetic Bearing Systems	p. 349
System Identification	p. 351
Experimental Results	p. 352
Continuous-time Predictive Control of Food Extruder	p. 353
Experimental Setup	p. 355
Mathematical Models	p. 357
Operation of the Model Predictive Controller	p. 358
Controller Tuning Parameters	p. 359
On-line Control Experiments	p. 360
Summary	p. 365
References	p. 367
Index	p. 373
Table of Contents provided by Ingram. All Rights Reserved.

Model Predictive Control System Design and Implementation Using MATLAB®

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Hardcover

Industry Reviews

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