Adaptive output regulator for wave PDEs with unknown harmonic disturbance. (March 2020)

• Record Type: Journal Article
• Authors: Yilmaz, Cemal Tugrul; Basturk, Halil Ibrahim
• Is Part Of: Automatica. Volume 113(2020)
• Publication Date: 2020-03
• Subjects: Wave PDE -- Disturbance rejection -- Observer design -- Adaptive control; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.108808
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper focuses on developing boundary controller for a wave PDE with two disturbances; ( i ) spatially varying and time-invariant in-domain disturbance, ( i i ) time-varying sinusoidal boundary disturbance. We consider the case that the sensor is collocated with the actuator and harmonic disturbance is anti-collocated with the sensor/actuator. We aim to regulate the rate of change of the opposite boundary, relative to the actuator, around a given constant reference. Towards that aim, we reformulate the opposite boundary equation as a linear system with known parameters, the sinusoidal disturbances and simultaneous input/output delays. In this way, the control input and sensor become collocated with the disturbance. Then, we parametrize the disturbance and represent the delays as a transport PDE. We develop an observer-based adaptive boundary controller for the ODE–PDE cascade system. We prove that all signals are bounded and the rate of change of the opposite boundary tracks a given constant reference. The performance of the controller is demonstrated in a numerical simulation.