Controller synthesis for a class of nonlinear systems with time delay based on stability region of PID controllers

Abstract

The analysis of nonlinear system with time delay is more complex compared with that of the linear system and the system without time delay. This paper considers the problem of stabilizing a nonlinear plant with known time delay using a low-order controller and designing controller synthesis to satisfy different performance criteria. Firstly, for second-order nonlinear system, by characteristic modeling and system identification, the characteristic model which contains both dynamic characteristics of controlled plants and performance specifications of original nonlinear system can be acquired. According to the characteristic model, the stabilization parametric region of low-order controller for the nonlinear system is presented by employing an extended Hermite–Biehler Theorem applicable to quasi-polynomials. Then, in order to obtain corresponding optimal controllers that satisfy different performance criteria, an analytical algorithm based on the stabilizing sets presented previously and controller synthesis is presented. Numerical simulations verify the feasibility and effectiveness of the proposed approach.