Robust anti-windup control design for PID controllers

This paper addresses an approximation-based anti-windup (AW) control strategy for suppressing the windup effect caused by actuator saturation nonlinearity in proportional-integral-derivative (PID) controlled systems. The effect of actuator constraint is firstly regarded a disturbance imported to the PID controller. The external disturbance can then be modeled by a linear differential equation with unknown coefficients. Using Stone-Weierstrass theorem, it is verified that these differential equations are universal approximators. An auxiliary control signal is finally designed to modify the error signal injected to the PID controller. The proposed AW control scheme is simple, system independent and applicable by digital or analog circuits. Analytical studies as well as simulation results demonstrate high performance of the proposed approach. It is shown that the proposed AW scheme renders the performance of the controlled system more robust toward the effects of windup than conventional PID AW schemes. The stability analysis is provided by Lyapunov's second method.