Model Predictive Control System Design and Implementation Using MATLAB

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1 Liuping Wang Model Predictive Control System Design and Implementation Using MATLAB Springer

2 List of Symbols and Abbreviations xxvii 1 Discrete-time MPC for Beginners Introduction Day-to-day Application Example of Predictive Control Models Used in the Design State-space Models with Embedded Integrator Single-input and Single-output System MATLAB Tutorial: Augmented Design Model Predictive Control within One Optimization Window Prediction of State and Output Variables Optimization MATLAB Tutorial: Computation of MPC Gains Receding Horizon Control Closed-loop Control System MATLAB Tutorial: Implementation of Receding Horizon Control Predictive Control of MIMO Systems General Formulation of the Model Solution of Predictive Control for MIMO Systems State Estimation Basic Ideas About an Observer Basic Results About Observability Kaiman Filter Tuning Observer Dynamics State Estimate Predictive Control Summary 37 Problems 39

3 xxii Contents 2 Discrete-time MPC with Constraints Introduction Motivational Examples Formulation of Constrained Control Problems Frequently Used Operational Constraints Constraints as Part of the Optimal Solution Numerical Solutions Using Quadratic Programming Quadratic Programming for Equality Constraints Minimization with Inequality Constraints Primal-Dual Method Hildreth's Quadratic Programming Procedure MATLAB Tutorial: Hildreth's Quadratic Programming Closed-form Solution of Л* Predictive Control with Constraints on Input Variables Constraints on Rate of Change Constraints on Amplitude of the Control Constraints on Amplitude and Rate of Change Constraints on the Output Variable Summary 81 Problems 83 3 Discrete-time MPC Using Laguerre Functions Introduction Laguerre Functions and DMPC Discrete-time Laguerre Networks Use of Laguerre Networks in System Description MATLAB Tutorial: Use of Laguerre Functions in System Modelling Use of Laguerre Functions in DMPC Design Design Framework Cost Functions Minimization of the Objective Function Convolution Sum Receding Horizon Control The Optimal Trajectory of Incremental Control Extension to MIMO Systems MATLAB Tutorial Notes DMPC Computation Predictive Control System Simulation Constrained Control Using Laguerre Functions Constraints on the Difference of the Control Variable Constraints on the Amplitudes of the Control Signal Stability Analysis Stability with Terminal-State Constraints Stability with Large Prediction Horizon 129

4 xxiii 3.8 Closed-form Solution of Constrained Control for SISO Systems MATLAB Tutorial: Constrained Control of DC Motor Summary 143 Problems 144 Discrete-time MPC with Prescribed Degree of Stability Introduction Finite Prediction Horizon: Re-visited Motivational Example Origin of the Numerical Conditioning Problem Use of Exponential Data Weighting The Cost Function Optimization of Exponentially Weighted Cost Function Interpretation of Results from Exponential Weighting Asymptotic Closed-loop Stability with Exponential Weighting Modification of Q and R Matrices Interpretation of the Results Discrete-time MPC with Prescribed Degree of Stability Tuning Parameters for Closed-loop Performance The Relationship Between P^ and J TO, ra Tuning Procedure Once More Exponentially Weighted Constrained Control Additional Benefit Summary 186 Problems 188 Continuous-time Orthonormal Basis Functions Introduction Orthonormal Expansion Laguerre Functions Approximating Impulse Responses Kautz Functions Kautz Functions in the Time Domain Modelling the System Impulse Response Summary 206 Problems 207 Continuous-time MPC Introduction Model Structures for CMPC Design Model Structure Controllability and Observability of the Model Model Predictive Control Using Finite Prediction Horizon Modelling the Control Trajectory Predicted Plant Response 218

5 6.3.3 Analytical Solution of the Predicted Response The Recursive Solution Optimal Control Strategy Receding Horizon Control Implementation of the Control Law in Digital Environment Estimation of the States MATLAB Tutorial: Closed-loop Simulation Model Predictive Control Using Kautz Functions Summary 244 Problems 245 Continuous-time MPC with Constraints Introduction Formulation of the Constraints Frequently Used Constraints Constraints as Part of the Optimal Solution Numerical Solutions for the Constrained Control Problem Real-time Implementation of Continuous-time MPC Summary 266 Problems 267 Continuous-time MPC with Prescribed Degree of Stability Introduction Motivating Example CMPC Design Using Exponential Data Weighting CMPC with Asymptotic Stability Continuous-time MPC with Prescribed Degree of Stability The Original Anderson and Moore's Results CMPC with a Prescribed Degree of Stability Tuning Parameters and Design Procedure Constrained Control with Exponential Data Weighting Summary 291 Problems 293 Classical MPC Systems in State-space Formulation Introduction Generalized Predictive Control in State-space Formulation Special Class of Discrete-time State-space Structures General NMSS Structure for GPC Design Generalized Predictive Control in State-space Formulation Alternative Formulation to GPC Alternative Formulation for SISO Systems Closed-loop Poles of the Predictive Control System Transfer Function Interpretation 310

6 xxv 9.4 Extension to MIMO Systems MNSS Model for MIMO Systems Case Study of NMSS Predictive Control System Continuous-time NMSS model Case Studies for Continuous-time MPC Predictive Control Using Impulse Response Models Summary 329 Problems Implementation of Predictive Control Systems Introduction Predictive Control of DC Motor Using a Micro-controller Hardware Configuration Model Development DMPC Tuning DMPC Implementation Experimental Results Implementation of Predictive Control Using xpc Target Overview Creating a SIMULINK Embedded Function Constrained Control of DC Motor Using xpc Target Control of Magnetic Bearing Systems System Identification Experimental Results Continuous-time Predictive Control of Food Extruder Experimental Setup Mathematical Models Operation of the Model Predictive Controller Controller Tuning Parameters On-line Control Experiments Summary 365 References 367 Index 373

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