Nonsmooth PI Controller for Uncertain Systems

Abstract

This paper investigates the problem of nonsmooth feedback stabilization for the higher order uncertain chain of integrators. For achieving the specified goal, the integral term of classical Proportional-Integral (PI) controller is replaced by an integral of the discontinuous function. Replacing this integrator, the overall control becomes absolutely continuous rather than discontinuous as in the first order sliding mode control. With this proposed scheme, the property of invariance concerning the matched Lipschitz uncertainty is still preserved. The main technical contribution of the paper is a sound and non-trivial Lyapunov analysis of the closed loop system controlled by nonsmooth PI controller. The effectiveness of the proposed controller is illustrated with the help of numerical simulation on the magnetic suspension system.

Keywords

• Nonsmooth PI
• stability and stabilization
• strict Lyapunov function