Output Tracking Control for the One-Dimensional Heat Equation with Unknown Disturbance by the Dirichlet Boundary Actuation

In this paper, output tracking problem for heat equation with general disturbance at left extremum and the Dirichlet control input at the right extremum is considered, which is solved by the Active Disturbance Rejection Control(ADRC) method. First, an infinite dimensional disturbance observer is constructed to estimate the disturbance. Secondly, we design an auxiliary system which used the estimate of the disturbance at left boundary and the reference signal at right boundary. Then, by using the hidden regularity of the right extremum of the auxiliary system to design the servo system, which contains the disturbance information transmitted from the left extremum and appear at the right extremum. As a result, the one-dimensional heat equation achieves the purpose of completing disturbance suppression and reference tracking. Finally, some simulation results are presented to illustrate the effectiveness of the proposed scheme.