The Anti-Windup Scheme for PID with a Switching Action Controller for Nonlinear Systems

The Proportional-Integral-Derivative with a Switching Action (PIDSA) controller, which incorporates PID and a switching action of sliding mode control (SMC), has been proposed to enhance the control performance of PID. However, the windup phenomenon can arise and cause excessive overshoot and instability when PIDSA is applied to systems with actuator saturation. This windup phenomenon is due to the integral term of PID and the integral terms of the double integral sliding surface. To address this issue, we propose anti-windup schemes specifically designed for PIDSA using a double integral sliding surface. For the integral term of PID, we use the back-calculation anti-windup scheme. However, this scheme alone cannot compensate for the windup effect caused by the integral term of PID. Therefore, we introduce a new sliding surface for the switching action that considers actuator saturation, and we propose the reset sliding surface scheme to match the sliding surface with the desired error dynamics of PID. To evaluate the effectiveness of the proposed scheme, we conduct experiments on a highly nonlinear system, a hydraulic vane motor. The experimental results demonstrate that our scheme effectively overcomes the windup problem of PIDSA.