MPCtheoryRevised - – 1 – Model Predictive Controllers A...

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Unformatted text preview: – 1 – Model Predictive Controllers: A Critical Synthesis of Theory and Industrial Needs Michael Nikolaou 1 Chemical Engineering Dept. University of Houston Houston, TX 77204-4792 Abstract – After several years of efforts, constrained model predictive control (MPC), the de facto standard algorithm for advanced control in process industries, has finally succumbed to rigorous analysis. Yet successful practical implementations of MPC were already in place almost two decades before a rigorous stability proof for constrained MPC was published. What is then the importance of recent theoretical results for practical MPC applications? In this publication we present a pedagogical overview of some of the most important recent developments in MPC theory, and discuss their implications for the future of MPC theory and practice. 1 (713) 743 4309, fax: (713) 743 4323, email: [email protected] – 2 – TABLE OF CONTENTS 1 INTRODUCTION 3 2 WHAT IS MPC? 3 2.1 A TRADITIONAL MPC FORMULATION 6 2.2 EXPANDING THE TRADITIONAL MPC FORMULATION 7 2.3 MPC WITHOUT INEQUALITY CONSTRAINTS 8 3 STABILITY 10 3.1 WHAT IS STABILITY? 10 3.1.1 Stability with respect to initial conditions 11 3.1.2 Input-output stability 13 3.2 IS STABILITY IMPORTANT? 19 4 THE BEHAVIOR OF MPC SYSTEMS 19 4.1 FEASIBILITY OF ON-LINE OPTIMIZATION 19 4.2 NONMINIMUM PHASE AND SHORT HORIZONS 20 4.3 INTEGRATORS AND UNSTABLE UNITS 21 4.4 NONLINEARITY 23 4.5 MODEL UNCERTAINTY 25 4.6 FRAGILITY 27 4.7 CONSTRAINTS 28 5 A THEORY FOR MPC WITH PREDICTABLE PROPERTIES 29 5.1 STABILITY 29 5.1.1 MPC with linear model – A prototypical stability proof 29 5.1.2 MPC with nonlinear model 30 5.1.2.1 A prototypical stability proof for MPC with nonlinear model 31 5.1.3 The stability proof and MPC practice 31 5.2 ROBUST STABILITY AND FRAGILITY OF CONSTRAINED MPC 32 5.2.1 Robust stability 33 5.2.1.1 MPC tuning for robust stability 33 5.2.1.2 Modifying the MPC algorithm for robust stability 35 5.2.2 Fragility 37 5.3 PERFORMANCE AND ROBUST PERFORMANCE 38 6 HOW CAN THEORY HELP DEVELOP BETTER MPC SYSTEMS? 39 6.1 CONCEPTUAL UNIFICATION AND CLARIFICATION 39 6.2 IMPROVING MPC 39 6.2.1 Process models 40 6.2.1.1 Linear vs. nonlinear models 40 6.2.1.2 Input-output vs. state-space models 40 6.2.1.3 Moving horizon-based state estimation for state-space models 40 6.2.1.4 MPCI: Expanding the MPC/on-line optimization paradigm to adaptive control 41 6.2.2 Objective 43 6.2.2.1 Multi-scale MPC 43 6.2.2.2 Dynamic programming ( closed-loop optimal feedback) 45 6.2.3 Constraints 45 6.2.3.1 MPC with end-constraint 45 6.2.3.2 Chance constrained MPC: Robustness with respect to output constraint satisfaction 45 7 FUTURE NEEDS 45 7.1 IS BETTER MPC NEEDED? 45 7.2 IS MORE MPC THEORY NEEDED? 46 8 REFERENCES 46 – 3 – “ There is nothing more practical than a good theory. ” Boltzmann 1 Introduction The last couple of decades have witnessed a steady growth in the use of computers for advanced control of process plants. Rapid improvements in computer hardware, combined with stiff foreign and domestic competition andplants....
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This note was uploaded on 05/25/2011 for the course ECON 103 taught by Professor Poul during the Spring '11 term at American University of Central Asia.

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MPCtheoryRevised - – 1 – Model Predictive Controllers A...

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