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Model Predictive Control Toolbox For Use with MATLAB® Manfred Morari N. Lawrence Ricker Computation Visualization Programming User’s Guide Version 1

How to Contact The MathWorks: www.mathworks.com comp.soft-sys.matlab Web Newsgroup support@mathworks.com suggest@mathworks.com bugs@mathworks.com doc@mathworks.com service@mathworks.com info@mathworks.com Technical support Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 508-647-7001 The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 Phone Fax Mail For contact information about worldwide offices, see the MathWorks Web site. Model Predictive Control Toolbox User’s Guide  COPYRIGHT 1995 - 1998 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro- duced in any form without prior written consent from The MathWorks, Inc. FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by or for the federal government of the United States. By accepting delivery of the Program, the government hereby agrees that this software qualifies as "commercial" computer software within the meaning of FAR Part 12.212, DFARS Part 227.7202-1, DFARS Part 227.7202-3, DFARS Part 252.227-7013, and DFARS Part 252.227-7014. The terms and conditions of The MathWorks, Inc. Software License Agreement shall pertain to the government’s use and disclosure of the Program and Documentation, and shall supersede any conflicting contractual terms or conditions. If this license fails to meet the government’s minimum needs or is inconsistent in any respect with federal procurement law, the government agrees to return the Program and Documentation, unused, to MathWorks. MATLAB, Simulink, Stateflow, Handle Graphics, and Real-Time Workshop are registered trademarks, and Target Language Compiler is a trademark of The MathWorks, Inc. Other product or brand names are trademarks or registered trademarks of their respective holders. Printing History: January 1995 October 1998 First printing (Online only)

1 2 Contents Preface Tutorial Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 Target Audience for the MPC Toolbox . . . . . . . . . . . . . . . . . . . . 1-3 System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3 MPC Based on Step Response Models Step Response Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Model Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6 Unconstrained Model Predictive Control . . . . . . . . . . . . . . 2-11 Closed-Loop Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-18 Constrained Model Predictive Control . . . . . . . . . . . . . . . . . 2-20 Application: Idle Speed Control . . . . . . . . . . . . . . . . . . . . . . . 2-22 Process Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22 Control Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-24 Application: Control of a Fluid Catalytic Cracking Unit . 2-31 Process Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-31 Control Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33 i

Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-34 Step Response Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-34 Associated Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-36 Unconstrained Control Law . . . . . . . . . . . . . . . . . . . . . . . . . 2-36 Constrained Control Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-36 3 4 MPC Based on State-Space Models State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 Mod Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3 SISO Continuous-Time Transfer Function to Mod Format . . . . 3-3 SISO Discrete-Time Transfer Function to Mod Format . . . . . . 3-6 MIMO Transfer Function Description to Mod Format . . . . . . . 3-7 Continuous or Discrete State-Space to Mod Format . . . . . . . . . 3-9 Identification Toolbox (“Theta”) Format to Mod Format . . . . . . 3-9 Combination of Models in Mod Format . . . . . . . . . . . . . . . . . . 3-10 Converting Mod Format to Other Model Formats . . . . . . . . . . 3-10 Unconstrained MPC Using State-Space Models . . . . . . . . . 3-12 State-Space MPC with Constraints . . . . . . . . . . . . . . . . . . . . 3-20 Application: Paper Machine Headbox Control . . . . . . . . . . 3-26 MPC Design Based on Nominal Linear Model . . . . . . . . . . . . . 3-27 MPC of Nonlinear Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-38 Command Reference Commands Grouped by Function . . . . . . . . . . . . . . . . . . . . . . . 4-2 Index ii Contents

Preface

Preface Acknowledgments The toolbox was developed in cooperation with: Douglas B. Raven and Alex Zheng The contributions of the following people are acknowledged: Yaman Arkun, Nikolaos Bekiaris, Richard D. Braatz, Marc S. Gelormino, Evelio Hernandez, Tyler R. Holcomb, Iftikhar Huq, Sameer M. Jalnapurkar, Jay H. Lee, Yusha Liu, Simone L. Oliveira, Argimiro R. Secchi, and Shwu-Yien Yang We would like to thank Liz Callanan, Jim Tung and Wes Wang from the MathWorks for assisting us with the project, and Patricia New who did such an excellent job putting the manuscript into LATEX. iv

About the Authors About the Authors Manfred Morari Manfred Morari received his diploma from ETH Zurich in 1974 and his Ph.D. from the University of Minnesota in 1977, both in chemical engineering. Currently he is the McCollum-Corcoran Professor and Executive Officer for Control and Dynamical Systems at the California Institute of Technology. Morari’s research interests are in the areas of process control and design. In recognition of his numerous contributions, he has received the Donald P. Eckman Award of the Automatic Control Council, the Allan P. Colburn Award of the AIChE, the Curtis W. McGraw Research Award of the ASEE, was a Case Visiting Scholar, the Gulf Visiting Professor at Carnegie Mellon University and was recently elected to the National Academy of Engineering. Dr. Morari has held appointments with Exxon R&E and ICI and has consulted internationally for a number of major corporations. He has coauthored one book on Robust Process Control with another on Model Predictive Control in preparation. N. Lawrence Ricker Larry Ricker received his B.S. degree from the University of Michigan in 1970, and his M.S. and Ph.D. degrees from the University of California, Berkeley, in 1972/78. All are in Chemical Engineering. He is currently Professor of Chemical Engineering at the University of Washington, Seattle. Dr. Ricker has over 80 publications in the general area of chemical plant design and operation. He has been active in Model Predictive Control research and teaching for more than a decade. For example, he published one of the first nonproprietary studies of the application of MPC to an industrial process, and is currently involved in a large-scale MPC application involving more than 40 decision variables. v

Preface vi

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