Control of homogeneous reaction systems using extent-based LPV models

This paper proposes the use of the extent decomposition on homogeneous reaction systems for control purposes. The decomposition results in a Linear Parameter-Varying (LPV) representation, upon which parametric feedback and feedforward strategies are developed. In the first part of the paper, three different ways to obtain the Extent-Based LPV (ELPV) representation of the system are proposed. The representation is advantageous since the physical meaning of all the variables are kept, and it has a Jordan type of structure which is used to establish controllability conditions. In the second part, general parametric feedback and feedforward control laws are proposed for the ELPV system. The nonlinear state-parameter dependence is first considered in the feedback term. This fact allows converting the original ELPV system into a Linear Time Invariant (LTI) system, which is used to design optimal control laws for reference tracking. Finally, the performance of the control strategy for the ELPV system is illustrated in simulation and compared with a controller based on a constant-parameter LTI model (ELTI).