R∞ Based PI Controller Design for Coupled Tank System through Polytopic Modeling

This paper addresses a new technique to cater to the nonlinear dynamics involved in a coupled tank system. Earlier approaches to designing a linear controller for a nonlinear system are two-fold. The first considers linearizing the plant around some operating point, thereby ignoring the dynamics posed by higher-order terms while the second approach is to represent the system nonlinearities in the form of model uncertainties, without any approximation of the higher order terms. The latter method forms the basis of design considered in this paper. The nonlinear model of a coupled tank system is represented in the form of a polytopic system that allows for the implementation of a linear controller. The variation in nonlinear term is treated as an uncertain parameter for the system representation. A R∞ based Proportional Integral (PI) controller is designed combined with pole placement in a desired Linear Matrix Inequality (LMI) region to ensure better transient behavior of the system. Experimental results have been provided and compared with conventional design to illustrate the efficacy of the proposed design method.