Performance output tracking for one-dimensional wave equation subject to unmatched general disturbance and non-collocated control

2018 ◽  
Vol 39 ◽  
pp. 39-52 ◽  
Author(s):  
Hua-Cheng Zhou ◽  
Bao-Zhu Guo
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
Output Tracking ◽  
Dimensional Wave ◽  
Collocated Control

Error-based output tracking for a one-dimensional wave equation with harmonic type disturbance

2020 ◽  
Vol 37 (4) ◽  
pp. 1447-1467
Author(s):  
Ziqing Tian ◽  
Xiao-Hui Wu
Keyword(s):  
Wave Equation ◽  
Closed Loop ◽  
Tracking Error ◽  
Difficult Case ◽  
Closed Loop System ◽  
One Dimensional ◽  
Output Tracking ◽  
Planning Approach ◽  
Uniformly Bounded ◽  
Dimensional Wave

Abstract In this paper, we consider output tracking for a one-dimensional wave equation, where the boundary disturbances are either collocated or non-collocated with control. The regulated output and the control are supposed to be non-collocated with control, which represents a difficult case for output tracking of PDEs. We apply the trajectory planning approach to design an observer, in terms of tracking error only, to estimate both states of the system and the exosystem from which the disturbances are produced. An error-based feedback control is proposed by solving a standard regulator equation. It is shown that (a) the closed-loop system is uniformly bounded whenever the exosystem is bounded; (b) when the disturbance is zero, the closed-loop is asymptotically stable; and (c) the tracking error converges to zero asymptotically as time goes to infinity. Numerical simulations are performed to validate the effectiveness of the proposed control.

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave
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