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E-book: Model Predictive Control System Design and Implementation Using MATLAB(R)

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Model Predictive Control System Design and Implementation Using MATLAB® 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® programs and exercises.

This book proposes methods for the design and implementation of MPC systems using basis functions that confer a number of advantages. As well as presenting the theory, the author covers industrial applications and explains the subject of quadratic programming.

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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 books 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)

List of Symbols and Abbreviations xxvii
1 Discrete-time MPC for Beginners 1
1.1 Introduction
1
1.1.1 Day-to-day Application Example of Predictive Control
1
1.1.2 Models Used in the Design
3
1.2 State-space Models with Embedded Integrator
4
1.2.1 Single-input and Single-output System
4
1.2.2 MATLAB Tutorial: Augmented Design Model
6
1.3 Predictive Control within One Optimization Window
7
1.3.1 Prediction of State and Output Variables
7
1.3.2 Optimization
9
1.3.3 MATLAB Tutorial: Computation of MPC Gains
13
1.4 Receding Horizon Control
15
1.4.1 Closed-loop Control System
16
1.4.2 MATLAB Tutorial: Implementation of Receding Horizon Control
20
1.5 Predictive Control of MIMO Systems
22
1.5.1 General Formulation of the Model
22
1.5.2 Solution of Predictive Control for MIMO Systems
26
1.6 State Estimation
27
1.6.1 Basic Ideas About an Observer
28
1.6.2 Basic Results About Observability
30
1.6.3 Kalman Filter
33
1.6.4 Tuning Observer Dynamics
34
1.7 State Estimate Predictive Control
34
1.8 Summary
37
Problems
39
2 Discrete-time MPC with Constraints 43
2.1 Introduction
43
2.2 Motivational Examples
43
2.3 Formulation of Constrained Control Problems
47
2.3.1 Frequently Used Operational Constraints
47
2.3.2 Constraints as Part of the Optimal Solution
50
2.4 Numerical Solutions Using Quadratic Programming
53
2.4.1 Quadratic Programming for Equality Constraints
53
2.4.2 Minimization with Inequality Constraints
58
2.4.3 Primal-Dual Method
62
2.4.4 Hildreth's Quadratic Programming Procedure
63
2.4.5 MATLAB Tutorial: Hildreth's Quadratic Programming
67
2.4.6 Closed-form Solution of λ*
68
2.5 Predictive Control with Constraints on Input Variables
69
2.5.1 Constraints on Rate of Change
70
2.5.2 Constraints on Amplitude of the Control
73
2.5.3 Constraints on Amplitude and Rate of Change
77
2.5.4 Constraints on the Output Variable
78
2.6 Summary
81
Problems
83
3 Discrete-time MPC Using Laguerre Functions 85
3.1 Introduction
85
3.2 Laguerre Functions and DMPC
85
3.2.1 Discrete-time Laguerre Networks
86
3.2.2 Use of Laguerre Networks in System Description
90
3.2.3 MATLAB Tutorial: Use of Laguerre Functions in System Modelling
90
3.3 Use of Laguerre Functions in DMPC Design
92
3.3.1 Design Framework
93
3.3.2 Cost Functions
94
3.3.3 Minimization of the Objective Function
97
3.3.4 Convolution Sum
98
3.3.5 Receding Horizon Control
98
3.3.6 The Optimal Trajectory of Incremental Control
99
3.4 Extension to MIMO Systems
106
3.5 MATLAB Tutorial Notes
108
3.5.1 DMPC Computation
108
3.5.2 Predictive Control System Simulation
115
3.6 Constrained Control Using Laguerre Functions
118
3.6.1 Constraints on the Difference of the Control Variable
118
3.6.2 Constraints on the Amplitudes of the Control Signal
121
3.7 Stability Analysis
127
3.7.1 Stability with Terminal-State Constraints
127
3.7.2 Stability with Large Prediction Horizon
129
3.8 Closed-form Solution of Constrained Control for SISO Systems
131
3.8.1 MATLAB Tutorial: Constrained Control of DC Motor
135
3.9 Summary
143
Problems
144
4 Discrete-time MPC with Prescribed Degree of Stability 149
4.1 Introduction
149
4.2 Finite Prediction Horizon: Re-visited
149
4.2.1 Motivational Example
150
4.2.2 Origin of the Numerical Conditioning Problem
150
4.3 Use of Exponential Data Weighting
152
4.3.1 The Cost Function
152
4.3.2 Optimization of Exponentially Weighted Cost Function
153
4.3.3 Interpretation of Results from Exponential Weighting
156
4.4 Asymptotic Closed-loop Stability with Exponential Weighting
158
4.4.1 Modification of Q and R Matrices
158
4.4.2 Interpretation of the Results
160
4.5 Discrete-time MPC with Prescribed Degree of Stability
165
4.6 Tuning Parameters for Closed-loop Performance
170
4.6.1 The Relationship Between Pinfinity and Jmin
171
4.6.2 Tuning Procedure Once More
176
4.7 Exponentially Weighted Constrained Control
179
4.8 Additional Benefit
182
4.9 Summary
186
Problems
188
5 Continuous-time Orthonormal Basis Functions 193
5.1 Introduction
193
5.2 Orthonormal Expansion
193
5.3 Laguerre Functions
194
5.4 Approximating Impulse Responses
197
5.5 Kautz Functions
202
5.5.1 Kautz Functions in the Time Domain
204
5.5.2 Modelling the System Impulse Response
205
5.6 Summary
206
Problems
207
6 Continuous-time MPC 209
6.1 Introduction
209
6.2 Model Structures for CMPC Design
209
6.2.1 Model Structure
211
6.2.2 Controllability and Observability of the Model
215
6.3 Model Predictive Control Using Finite Prediction Horizon
216
6.3.1 Modelling the Control Trajectory
217
6.3.2 Predicted Plant Response
218
6.3.3 Analytical Solution of the Predicted Response
219
6.3.4 The Recursive Solution
221
6.4 Optimal Control Strategy
224
6.5 Receding Horizon Control
227
6.6 Implementation of the Control Law in Digital Environment
234
6.6.1 Estimation of the States
234
6.6.2 MATLAB Tutorial: Closed-loop Simulation
237
6.7 Model Predictive Control Using Kautz Functions
240
6.8 Summary
244
Problems
245
7 Continuous-time MPC with Constraints 249
7.1 Introduction
249
7.2 Formulation of the Constraints
249
7.2.1 Frequently Used Constraints
249
7.2.2 Constraints as Part of the Optimal Solution
251
7.3 Numerical Solutions for the Constrained Control Problem
257
7.4 Real-time Implementation of Continuous-time MPC
262
7.5 Summary
266
Problems
267
8 Continuous-time MPC with Prescribed Degree of Stability 271
8.1 Introduction
271
8.2 Motivating Example
271
8.3 CMPC Design Using Exponential Data Weighting
274
8.4 CMPC with Asymptotic Stability
277
8.5 Continuous-time MPC with Prescribed Degree of Stability
283
8.5.1 The Original Anderson and Moore's Results
283
8.5.2 CMPC with a Prescribed Degree of Stability
284
8.5.3 Tuning Parameters and Design Procedure
286
8.6 Constrained Control with Exponential Data Weighting
288
8.7 Summary
291
Problems
293
9 Classical MPC Systems in State-space Formulation 297
9.1 Introduction
297
9.2 Generalized Predictive Control in State-space Formulation
298
9.2.1 Special Class of Discrete-time State-space Structures
298
9.2.2 General NMSS Structure for GPC Design
301
9.2.3 Generalized Predictive Control in State-space Formulation
302
9.3 Alternative Formulation to GPC
305
9.3.1 Alternative Formulation for SISO Systems
305
9.3.2 Closed-loop Poles of the Predictive Control System
307
9.3.3 Transfer Function Interpretation
310
9.4 Extension to MIMO Systems
313
9.4.1 MNSS Model for MIMO Systems
314
9.4.2 Case Study of NMSS Predictive Control System
315
9.5 Continuous-time NMSS model
320
9.6 Case Studies for Continuous-time MPC
323
9.7 Predictive Control Using Impulse Response Models
326
9.8 Summary
329
Problems
330
10 Implementation of Predictive Control Systems 333
10.1 Introduction
333
10.2 Predictive Control of DC Motor Using a Micro-controller
333
10.2.1 Hardware Configuration
334
10.2.2 Model Development
336
10.2.3 DMPC Tuning
337
10.2.4 DMPC Implementation
338
10.2.5 Experimental Results
339
10.3 Implementation of Predictive Control Using xPC Target
340
10.3.1 Overview
340
10.3.2 Creating a SIMULINK Embedded Function
342
10.3.3 Constrained Control of DC Motor Using xPC Target
347
10.4 Control of Magnetic Bearing Systems
349
10.4.1 System Identification
351
10.4.2 Experimental Results
352
10.5 Continuous-time Predictive Control of Food Extruder
353
10.5.1 Experimental Setup
355
10.5.2 Mathematical Models
357
10.5.3 Operation of the Model Predictive Controller
358
10.5.4 Controller Tuning Parameters
359
10.5.5 On-line Control Experiments
360
10.6 Summary
365
References 367
Index 373
Liuping Wang received her PhD in 1989 from the University of Sheffield, UK; subsequently, she was an adjunct associate professor in the Dept. of Chemical Engineering at the University of Toronto, Canada. From 1998 to 2002, she was a senior lecturer and research coordinator in the Center for Integrated Dynamics and Control, University of Newcastle, Australia before joining RMIT University where she is a professor and Head of Discipline of Electrical Engineering. She is the author of two books, joint editor of one book, and has published over 130 papers.

Liuping Wang has been actively engaged in industry-oriented research and development since the completion of her PhD studies. Whilst working at the University of Toronto, Canada, she was a co-founder of an industry consortium for the identification of chemical processes. Since her arrival in Australia in 1998, she has been working with Australian government organisations and companies in the areas of food manufacturing, mining, automotive and power services, including Food Science Australia, Uncle Bens Australia, CSR, BHP-Billiton, Pacific Group Technologies, Holden Innovation, Alinta, and ANCA. She leads the Control Systems program at the Australian Advanced Manufacturing Cooperative Research Center (AMCRC) that develops next generation technology platforms for the manufacturing industry. She is also on the Board of Directors of the Australian Power Academy that promotes power-engineering education and raises scholarships from the power industry to support undergraduate students.
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