Abstract

Discrete Model Predictive Control (MPC) became one of the most widespread modern control principles. Process controls with a finite number of admissible values are common in a large number of relevant applications. For this type of optimization problems, the computational complexity is exponential in the number of binary optimization variables. The solver is based on a standard branch-and-bound method and interior point method is used for solution of the relaxed problem. The simulation experiment involved controlling the temperature of a batch reactor by using two on/off input valves and a discrete-position mixing valve.

Highlights

  • Model Predictive Control (MPC) has become of the most widespread modern control strategies which have been successfully applied in many industrial applications

  • Process controls with a finite number of admissible values are common in a large number of relevant applications

  • 4 Relaxation of Mixed Integer Quadratic Program (MIQP) In order to reduce the complexity of MIQP the constraints of binary variables can be relaxed, i.e. binary variables are allowed to span over the continuous interval [0,1] and the problem can be solved as a quadratic programming (QP) problem

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Summary

Introduction

Model Predictive Control (MPC) has become of the most widespread modern control strategies which have been successfully applied in many industrial applications. Bemporad and Morari [1] introduced a special class of hybrid systems called Mixed Logical Dynamical (MLD) systems They can effectively model a variety of systems: hybrid automata, nonlinear systems with the nonlinearity represented by the piece-wise affine functions, linear systems with constraints, etc. Hybrid systems arise naturally in areas such as automotive systems [2], chemical systems [3] or power systems [4] In all of these applications, there are several operation modes in the plant that justify the implementation of a hybrid MPC controller. CPLEX and GUROBI represent a commercial optimization software that is able to solve the MIQP problems and several toolboxes for MATLAB exists (OPTI Toolbox which uses SCIP solver [10], Hybrid toolbox [11]). MLD approach is used for modelling and predictive control of a batch reactor as a switched linear system

Mixed logical dynamical systems
Predictive control of MLD systems
Relaxation of MIQP
Simulation results
Conclusion
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