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Internal model based tracking and disturbance rejection for stable well-posed systems. (English) Zbl 1028.93012
In this very important and useful paper the tracking and disturbance rejection problem for infinite-dimensional linear systems with reference and disturbance signals that are finite superpositions of sinusoids, is solved. The authors explore two approaches, both based on the internal model principle. In the first approach a low gain controller is used. These results are a partial extension of results given by Hämäläinen and Pohjolainen (here the plant is required to have an exponentially stable transfer function on the Callier-Desoer algebra). Main results: The authors only require the plant to be well-posed and exponentially stable. These conditions are sufficiently unrestrictive to be verifiable for many partial differential equations in more than one space variable. Moreover the second approach concerns the case where the second component of the plant transfer function (from control input to tracking error) is positive. In this case, a very simple stabilizing controller which comes from an internal model, but which does not require a low gain, is identified.
Finally the authors apply the proposed results to two problems involving systems modelled by partial differential equations: the problem of rejecting external noise in a model for structural acoustics, and a similar problem for two coupled beams.

MSC:
93B51 Design techniques (robust design, computer-aided design, etc.)
93C73 Perturbations in control/observation systems
93C25 Control/observation systems in abstract spaces
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