Modeling of a Continuous Stirred Tank Reactor and Controller Design Using LMI Approaches

Abstract

The design of non-linear control systems remains a challenge today, therefore through this work a procedure to obtain a vertex-reduced multi-model representation, without loss of convexity, is proposed as a suitable solution. That is, a novel approach which considers all parameter variations around the Continuous Stirred Tank Reactor (CSTR) system operating region is developed, resulting in a unique polytopic representation. After that, based on the linear matrix inequalities approach, a control scheme is developed to compute the optimal matrix gains, while the operating, states and inputs, constraints are satisfied and the stability conditions are ensured. Finally, the realistic simulation results highlight the model representation effectiveness in capturing the CSTR dynamic behavior in the operating region, despite parameter variations, allowing the optimal control law design, overcoming the non-linear system nature, to achieve the desired closed-loop system performance.