New Findings in the Stability Analysis of PI-state Controlled Systems with Actuator Saturation

Abstract

In this paper, a simple, generally valid stability proof for an anti-windup method for PI-state controlled systems is presented, with which it is possible to directly conclude the stability of the PI-state controlled system from a stable P-state controlled system with constraints in the manipulated variables, i.e. without having to perform a separate stability investigation of the anti-windup measures. The technique presented is based on the system description by means of state equations and Lyapunov's Direct Method using quadratic Lyapunov functions. Furthermore, the PI-state controller is designed in such a way that it provides the same command response as the P-state controller, for which a stability statement is already available. Both continuous-time and discrete-time systems are considered, which, apart from the saturation of the manipulated variables, show linear, time-invariant behavior. In addition, a general stability proof is given for discrete-time systems, which makes it possible to establish stable anti-windup methods for P- and PI-state controlled systems, which contain dead time elements in the path of the manipulated variables, without having to carry out separate stability investigations for them. For this purpose, the state controller design for the system with dead time elements in the manipulated variable paths is based on the principle that the same characteristics of the control behavior should be achieved as for the system without such dead time elements, but delayed by the dead time. The effectiveness of the presented methods is illustrated by an example from the field of electrical drives.