Sampled-data output regulation of unstable well-posed infinite-dimensional systems with constant reference and disturban
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Sampled-data output regulation of unstable well-posed infinite-dimensional systems with constant reference and disturbance signals Masashi Wakaiki1
· Hideki Sano1
Received: 27 January 2019 / Accepted: 27 November 2019 © Springer-Verlag London Ltd., part of Springer Nature 2019
Abstract We study the sample-data control problem of output tracking and disturbance rejection for unstable well-posed linear infinite-dimensional systems with constant reference and disturbance signals. We obtain a sufficient condition for the existence of finitedimensional sampled-data controllers that are solutions of this control problem. To this end, we study the problem of output tracking and disturbance rejection for infinitedimensional discrete-time systems and propose a design method of finite-dimensional controllers by using a solution of the Nevanlinna–Pick interpolation problem with both interior and boundary conditions. We apply our results to systems with state and output delays. Keywords Frequency-domain methods · Output regulation · Sampled-data control · State-space methods · Well-posed infinite-dimensional systems Mathematics Subject Classification 93B52 · 93C05 · 93C25 · 93C35 · 93C57 · 93D15
1 Introduction Due to the development of computer technology, digital controllers are commonly implemented for continuous-time plants. We call such closed-loop systems sampleddata systems. In addition to their practical motivation, sampled-data systems yield theoretically interesting problems related to the combination of both continuous-time
This work was supported by JSPS KAKENHI Grant Numbers JP17K14699.
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Masashi Wakaiki [email protected] Hideki Sano [email protected]
1
Graduate School of System Informatics, Kobe University, Nada, Kobe, Hyogo 657-8501, Japan
123
Mathematics of Control, Signals, and Systems
and discrete-time dynamics, and various techniques such as the lifting approach [5,52, 54] and the frequency response operator approach [1,15] have been also developed for the analysis and synthesis of finite-dimensional sampled-data systems. Sampled-data control theory for infinite-dimensional systems has been developed, e.g., in [18–20,25– 28,37–39,43]. Several specifically relevant studies will be cited below again. In this paper, we study the problem of sampled-data output regulation for unstable well-posed systems. The main objective of our control problem is to find finite-dimensional digital controllers achieving the output tracking of given constant reference signals in the presence of external constant disturbances. A theory for well-posed systems has been extensively developed; see, e.g., the survey [45,50] and the book [44]. Well-posed systems allow unbounded control and observation operators and provide a framework to formulate control problems for systems governed by partial differential equations with point control and observation and by functional differential equations with delays in the state, input, and output variables. Our output regulation method is based on the internal model pri
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