# Robust constrained MPC stabilization of a CSTR

**Juraj Oravec ^{ *}, Monika Bakošová**

*Slovak University of Technology in Bratislava, Faculty of Chemical and Food Technology,
Institute of Information Engineering, Automation, and Mathematics,
Radlinského 9, 812 37 Bratislava, Slovak Republic*

**E-mail:** ^{* }juraj.oravec@stuba.sk

**Abstract:** The paper addresses a case study of robust stabilization of a continuous stirred tank reactor using
robust model-based predictive control with constrained input variables. One exothermic reaction runs in
the reaction mixture and the reactor is modelled in the form of an uncertain polytopic system. The control
approach is based on solution of a set of linear matrix inequalities. This formulation enables to use convex
optimization methods to design a gain matrix of a state feedback controller in each control step. The task of
stabilization is solved in assumed control conditions with respect to symmetric constraints on control inputs.
The control performance achieved by robust constrained model-based predictive control is studied via simulations.
Obtained results confirm that the robust constrained model-based predictive control ensures the stability
demands and the quality requirements represented by chosen quadratic cost function.

**Keywords:** chemical reactor, constrained input, linear matrix inequality, parametric uncertainty, robust MPC

*Full paper in Portable Document Format:* acs_0123.pdf

Acta Chimica Slovaca, Vol. 5, No. 2, 2012, pp. 153—158