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A framework for the analysis and control of hybrid systems


M. Morari

Mpumalanga, South Africa,, SAIChE, National Meeting, Secunda, presented by the South African Institution of Chemical Engineers

Over the last decade Model Predictive Control (MPC) has emerged as the standard for multivariable control in the process industries. Its ability to handle large complex systems involving hundreds of controlled and manipulated variables, dynamic interactions, time delays and constraints make it an attractive tool for many challenging control tasks. In this presentation we will point out several clearly discernible trends which point toward an extended need for new techniques to design control and supervisory schemes. We will show how this need can be met by expanding the scope of Model Predictive Controllers to deal with hybrid systems. The rapid advances in computer and information technology are enabling the closer integration of the various decision and control tasks which were traditionally distributed among a broad set of decision makers ranging from PLCs at the lowest level to planning and scheduling departments at the highest level. This integration should eventually lead to a smoother, more responsive and more competitive functioning of the entire organization. It requires the development of new modelling tools for such large complex systems involving continuous and discrete states whose behavior is governed by dynamics, logical statements and constraints. The models should facilitate the analysis of such systems and the efficient determination of optimal operating strategies. At the center of this new framework we envision the class of Mixed Logical Dynamical (MLD) systems. These MLD systems are described by discrete time linear dynamic equations subject to linear inequalities involving real and integer variables. The justification for the MLD form is that it is capable to model a broad class of systems arising in many applications, in particular constrained linear systems, finite state machines, some classes of discrete event systems, and nonlinear systems which can be approximated by piecewise linear functions. More importantly, the MLD form leads to the formulation of various verification, control and estimation problems in terms of Mixed Integer Quadratic Programs (MIQPs), for which efficient algorithms are available. These problems have not been successfully addressed by other tools or only with a much higher computational effort. Specifically, a predictive control scheme is proposed which is able to stabilize MLD systems on desired reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules. Many examples from a variety of fields are used to illustrate the concepts.


Type of Publication:

(05)Plenary/Invited/Honorary Lecture

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