Volume 25, 2019
|Number of page(s)||23|
|Published online||15 November 2019|
Output tracking and disturbance rejection for 1-D anti-stable wave equation*
School of Mathematics and Statistics, Central South University,
** Corresponding author: email@example.com
Accepted: 9 September 2018
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.
Mathematics Subject Classification: 37L15 / 93D15 / 93B51 / 93B52
Key words: Output tracking / disturbance rejection / wave equation / anti-damping / exponential stabilization
© EDP Sciences, SMAI 2019
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