Globally asymptotically stable saturated PID controllers for a double integrator with constant disturbance

摘要

This paper provides a deep insight into the saturated PID control of a double integrator with bounded disturbance. On the basis of the nested saturation functions, a simple PID-like controller is proposed. The main difficulty in saturation control with bounded disturbances is to prove that the unsaturated regions are invariant. By phase plane and singular perturbation analysis, we prove that the saturation restrictions on the controller can be removed one by one in finite time, and the closed-loop system can be finally reduced to a nonsaturated PID controlled double integrator. The sufficient conditions for the stability of the closed loop with disturbance are also derived. Finally, numerical simulations are conducted to validate the effectiveness of the proposed control scheme.