H2 gain-scheduled state-feedback synthesis conditions applied to a quadruple tank system

Gabriel  P. Neves; Bruno  A. Angélico; Ricardo  C. L. F. Oliveira

doi:10.48011/asba.v2i1.1584

Gabriel P. Neves Polytechnic School of University of São Paulo
Bruno A. Angélico Polytechnic School of University of São Paulo
Ricardo C. L. F. Oliveira University of Campinas

DOI: https://doi.org/10.48011/asba.v2i1.1584

Keywords: Linear parameter-varying, Gain-schedule, State-feedback control, LMIs, Quadruple tank

Abstract

This article presents design conditions for controllers with polynomial dependence on the parameters for LPV systems.The technique is used to solve the problem of controlling a quadruple tank considering variations in valve opening. First, the nonlinear modeling of the system is presented as well with an analysis of its characteristics, and then an approximation to the dynamics is proposed in terms of a pure LPV polynomial model. As a main contribution, a sufficient condition based on LMIs is proposed for the design of scheduled controllers by state feedback with performance criterion based on the H2 norm. The design condition is general in the sense of treating LPV models with an arbitrary number of parameters and degree of polynomial dependence. Simulation in three distinct scenarios are presented to illustrate the design methodology and the quality of the controller designed for the quadruple tank.