Performance Output Tracking for a One-Dimensional Wave Equation With Input Delay

• Published in: IEEE access Vol. 7; pp. 149996 - 150005
• Main Author: Liu, Yulong
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control systems design; Delay effects; Delays; Error analysis; Error feedback; Error signals; Feedback control; Mathematical model; Observers; output regulation; Propagation; Stability analysis; State feedback; time delay; Time lag; Tracking; Trajectory; unmatched disturbance; Wave equation; Wave equations
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2019.2947596

This paper is concerned with the performance output regulation problem for a wave equation with input delay and unmatched disturbance. Firstly, in the case of time delay, the input delay term is translated into a first-order hyperbolic equation and we obtain a cascade system. By applying the method of auxiliary trajectory, the unmatched disturbance is compensated and eliminated. Then, we design a state feedback controller. Meanwhile, with the measured error signal, we construct an observer for the cascade system. Based on the observer, an error feedback controller is developed by replacing the states with their estimations. By using Lyapunov functional method, we also prove the regulation error goes to zero exponentially. Thus, the problem of output tracking is solved for the wave equation in despite of input delay and unmatched disturbance. Finally, the numerical simulations are presented to validate the theoretical results.