In this paper, we solve the output tracking and disturbance rejection problem for a system described by a one-dimensional anti-stable wave equation, with reference and disturbance signals that belong to W1,∞[0, ∞) and L∞[0, ∞), respectively. Generally, these signals cannot be generated from an exosystem. We explore an approach based on proportional control. It is shown that a proportional gain controller can achieve exponentially the output tracking while rejecting disturbance. Our method consists of three steps: first, we convert the original system without disturbance into two transport equations with an ordinary differential equation by using Riemann variables, then we propose a proportional control law by making use of the properties of transport systems and time delay systems. Second, based on our recent result on disturbance estimator, we apply the estimation/cancellion strategy to cancel to the external disturbance and to track the reference asymptotically. Third, we design a controller using a state observer. Since disturbance does not appear in the observer explicitly (the disturbance is exactly compensated), the controlled output signal is exponentially tracking the reference signal. As a byproduct, we obtain a new output feedback stabilizing control law by which the resulting closed-loop system is exponentially stable using only two displacement output signals.
Accepté le :
DOI : 10.1051/cocv/2018049
Mots-clés : Output tracking, disturbance rejection, wave equation, anti-damping, exponential stabilization
@article{COCV_2019__25__A69_0,
author = {Zhou, Hua-Cheng},
title = {Output tracking and disturbance rejection for {1-D} anti-stable wave equation},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {25},
year = {2019},
doi = {10.1051/cocv/2018049},
mrnumber = {4031687},
zbl = {1441.93258},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2018049/}
}
TY - JOUR AU - Zhou, Hua-Cheng TI - Output tracking and disturbance rejection for 1-D anti-stable wave equation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2018049/ DO - 10.1051/cocv/2018049 LA - en ID - COCV_2019__25__A69_0 ER -
%0 Journal Article %A Zhou, Hua-Cheng %T Output tracking and disturbance rejection for 1-D anti-stable wave equation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2018049/ %R 10.1051/cocv/2018049 %G en %F COCV_2019__25__A69_0
Zhou, Hua-Cheng. Output tracking and disturbance rejection for 1-D anti-stable wave equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 69. doi : 10.1051/cocv/2018049. http://www.numdam.org/articles/10.1051/cocv/2018049/
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