Complex dynamics in linear PI control systems with saturations

Abstract

In this paper is shown how restrictions due to saturations can lead to unexpected responses in linear systems. A model for systems with saturations based on finite state machines is used to simulate a first order linear system with a proportional-integral (PI) controller with a saturation on the integral branch and on the actuator. The system simulations show how such saturations can determine the existence of six different configurations for the system. Numerical results let confirm that the contributions of each configuration to system dynamics lead to an isolated periodic orbit. This behavior is validated with experimental results of a PI servocontroller for a DC motor with anti-windup saturation on the integral branch.