Numerically Efficient Fuzzy MPC Algorithm with Advanced Generation of Prediction—Application to a Chemical Reactor

Abstract

In Model Predictive Control (MPC) algorithms, control signals are generated after solving optimization problems. If the model used for prediction is linear then the optimization problem is a standard, easy to solve, quadratic programming problem with linear constraints. However, such an algorithm may offer insufficient performance if applied to a nonlinear control plant. On the other hand, if a model used for prediction is nonlinear, then non–convex optimization problem must be solved at each algorithm iteration. Then the numerical problems may occur during solving it and the time needed to calculate the control signals cannot be determined. Therefore approaches based on linearized models are preferred in practical applications. A fuzzy algorithm with an advanced generation of the prediction is proposed in the article. The prediction is obtained in such a way that the algorithm is formulated as a quadratic optimization problem but offers performance very close to that of the MPC algorithm with nonlinear optimization. The efficiency of the proposed approach is demonstrated in the control system of a nonlinear chemical control plant—a CSTR (Continuous Stirred–Tank Reactor) with van de Vusse reaction.