Design of multiple anti-windup loops for multiple activations

This paper considers anti-windup design for linear systems subject to actuator saturation. Three anti-windup gains are designed for activations immediately at the occurrence actuator saturation, after the saturation has reached a certain level and in anticipation of the occurrence of saturation, respectively. The design is based on the minimization of L₂ gain from the disturbance to the controlled output of the resulting closed-loop system. Traditional anti-windup scheme involves a single anti windup loop for immediate activation. A recent innovation is to design a single anti-windup loop for delayed or anticipatory activation, as well as to design two anti-windup gains, one for immediate activation and one for delayed activation. Our design of three anti-windup gains for three different activations is shown through simulation to lead to significant further performance improvement over the previous activation schemes.