LPV-based control of nonlinear compartmental model with input uncertainty

Abstract

In this study we introduce a Linear Parameter Varying (LPV) based controller design possibility for LPV systems with state and input uncertainties. Through the LPV framework the developed method can be used for the nonlinear system belongs to the given LPV system. The controller design approach effectively exploits the combination of the classical state feedback and matrix similarity theorems in order to realize a complementary LPV controller. By using this controller the necessary control action will be determined via a comparison to a given reference Linear Time Invariant (LTI) system which is given by the fixation of the parameter vectors in the parameter space. We proven the usability of the developed method on a highly nonlinear compartmental model. The results showed that the developed complementary controller structure performed well. We compared the dynamics of the reference LTI system, the LPV system and the original nonlinear system to each other by using a norm based error of the states. The magnitude of the error signals were small and acceptable in all cases. Moreover, the deviation between the LPV system and the original nonlinear system was negligible (only numerical error occurred), namely, the developed control structure can be used directly for the nonlinear system as well.