Limit cycle analysis of PID controller design

The main purpose of this paper is to predict limit cycles of nonlinear PID control systems with adjustable parameters by the approaches of stability equation, describing function and parameter plane. First, nonlinear elements are linearized by the classical describing function method. The stability of equivalent linearized system with adjustable parameters is then analyzed by using the stability equations and the parameter plane method. According to our study, the characteristics of limit cycles with PID control design in current literature can be improved. Finally, this approach is also extended to a sampled-data control system with broken line nonlinearity.