UDE-based Robust Boundary Control of Heat Equation with Unknown Input Disturbance

Abstract

In this paper, a novel robust control strategy named uncertainty and disturbance estimator (UDE) is applied to the stabilization of an unstable heat equation with Dirichlet type boundary actuator and unknown time-varying input disturbance. The system is stabilized by the backstepping approach and the unknown input disturbance is compensated by the UDE-based method which constructs an estimation of the disturbance through filtering the system input U(t) and boundary state u(1, t). Compared to other existing disturbance compensation methods, the UDE-based method only requires the spectrum information of the disturbance signal. Furthermore, the output feedback version of the proposed control is also derived for the practical implementation purpose. Stability analysis of the closed-loop system for both state feedback and output feedback cases are carried out and simulation examples are also provided to verify the proposed method.