Relaxed distributed fuzzy controller design with input constraints for a class of nonlinear first-order hyperbolic PDE systems

Mardani, Mohammad Mehdi; Shasadeghi, Mokhtar; Safarinejadian, Behrouz

Relaxed distributed fuzzy controller design with input constraints for a class of nonlinear first-order hyperbolic PDE systems

Authors

Mohammad Mehdi Mardani

Mokhtar Shasadeghi

Behrouz Safarinejadian

M.Sc. Students, Control Dept., Electrical and Electronic Engineering Faculty, Shiraz University of Technology, Shiraz, Iran.

Abstract

In this paper, the stability problem of nonlinear first order hyperbolic partial differential equations (PDE) systems is investigated. Based on Lyapunov stability theorem, the sufficient conditions to guarantee the stability of Takagi-Sugeno (TS) fuzzy hyperbolic PDE model are achieved in terms of spatially varying linear matrix inequalities (SVLMI). To investigate the exponentially stabilization of nonlinear first order hyperbolic PDE systems, a fuzzy Lyapunov function is considered. Then, some new space varying slack matrices are introduced to conduct the stability analysis. The proposed stability conditions are more relaxed than the newly published one. Furthermore, the problem of applying some constraints on control input is studied through this paper. Hence, the performance of the controller is improved in the proposed approach. Finally, in order to evaluate the validity of the proposed approach, a practical application of nonisothermal plug flow reactor (PFR) is considered.

Keywords

First order hyperbolic PDE systems

TS fuzzy PDE model

Fuzzy Lyapunov function

Slack matrices

Space varying LMI