Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4999975 | Automatica | 2017 | 9 Pages |
Abstract
This contribution presents the backstepping design of output feedback regulators for boundary controlled linear 2Ã2 hyperbolic systems, that achieve regulation in finite time. It is assumed that the disturbances can act in-domain, at both boundaries and at the output to be controlled. The latter need not be available for measurement and consists of in-domain pointwise, distributed or boundary outputs. Firstly, a solution of the finite-time state feedback regulator problem is given on the basis of the regulator equations. They are formulated in backstepping coordinates so that a solution is attainable in closed-form. This leads to a very straightforward regulator design for 2Ã2 hyperbolic systems with a general class of outputs. Then, a finite-dimensional reference observer that converges in finite-time is introduced, which consists of two observers and a delay. This result is extended to the backstepping design of finite-time disturbance observers for 2Ã2 hyperbolic systems with a collocated measurement. In particular, two backstepping disturbance observers are determined so that after introducing a delay the disturbance model and plant states can be estimated in finite-time. Hence, by combining the state feedback regulator with these observers a finite-time output feedback regulator is obtained. For the state feedback regulator and the disturbance observer existence conditions are derived in terms of the plant transfer behaviour. A simple example with an in-domain pointwise and distributed output illustrates the theoretical results.
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Physical Sciences and Engineering
Engineering
Control and Systems Engineering
Authors
Joachim Deutscher,