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Parametric approach to the decoupling of linear distributed-parameter systems

IET CONTROL THEORY AND APPLICATIONS 2010年第12期4卷 2855-2866页

作者： Deutscher, J. Harkort, C. Univ Erlangen Nurnberg Lehrstuhl Regelungstech D-91058 Erlangen Germany

In this study the input-output decoupling of linear distributed-parameter systems with distributed control and distributed measurement is considered. The decoupling problem is formulated as an eigenstructure assignment problem for distributed-parameter systems, which is solved using the parametric approach. The resulting static state feedback controller exponentially stabilises the closed-loop system and decouples the reference transfer behaviour with respect to the first p dominant closed-loop modal states. The residual dynamics are taken into account by compensating further dominant eigenvalues with transmission zeros, so that they do not influence the reference transfer behaviour. A heat conductor is used to demonstrate the design procedure which is also compared with an early lumping approach.

关键词： input output decoupling distributed measurement parametric approach distributed control closed-loop system eigenstructure assignment linear distributed-parameter systems Control system analysis and synthesis methods decentralised control decoupling problem Multivariable control systems eigenstructure assignment problem linear distributed parameter systems closed loop systems

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Conditions for robustness and nonrobustness of the stability of feedback systems with respect to small delays in the feedback loop

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1996年第2期34卷 572-600页

作者： Logemann, H Rebarber, R Weiss, G UNIV NEBRASKA DEPT MATH & STATLINCOLNNE 68588 BEN GURION UNIV NEGEV DEPT ELECT ENGNIL-84105 BEER SHEVAISRAEL

It has been observed that for many stable feedback control systems, the introduction of arbitrarily small time delays into the loop causes instability. In this paper we present a systematic frequency domain treatment of this phenomenon for distributed parameter systems. We consider the class of all matrix-valued transfer functions which are bounded on some right half-plane and which have a limit at +infinity along the real axis. Such transfer functions are called regular. Under the assumption that a regular transfer function is stabilized by unity output feedback, we give sufficient conditions for the robustness and for the nonrobustness of the stability with respect to small time delays in the loop. These conditions are given in terms of the high-frequency behavior of the open-loop system. Moreover, we discuss robustness of stability with respect to small delays for feedback systems with dynamic compensators. In particular, we show that if a plant with infinitely many poles in the closed right half-plane is stabilized by a controller, then the stability is not robust with respect to delays. We show that the instability created by small delays is itself robust to small delays. Three examples are given to illustrate these results.

关键词： small time delays robust stabilization linear distributed parameter systems regular transfer functions dynamic stabilization

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CONTROL OF A LONG-LINE-TYPE PLANT

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OPTIMAL CONTROL APPLICATIONS & METHODS 1990年第2期11卷 111-126页

作者： SZYMKAT, M GORECKI, H POPEK, L Institute of Automatics Academy of Mining and Metallurgy al. Mickiewicza 30 30-059 Kraköw Poland

AbstractThis paper presents an approach to the feedback loop controller design problem for plants described by linear partial differential equations of a long‐line type. The classical frequency domain technique called ‘the optimal modulus criterion’ is applied. The different plant cases are classified and the corresponding recurrence formulae for derivatives of the transfer function inverse are derived. The applicability of the presented technique is discussed with particular emphasis on stability and performance aspects. The conclusions for different types of controllers are illustrated with several examples. This analysis uses an originally developed computer pa

关键词： Feedback loop control Frequency design Long‐line plant Optimal modulus criterion linear distributed parameter systems

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Optimal control of diffusions

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APPLIED MATHEMATICS AND OPTIMIZATION 2002年第2-3期46卷 207-230页

作者： Fattorini, HO Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA

We prove a version of Pontryagin's maximum principle for time and norm optimal control of linear diffusion processes. This result includes both necessary and sufficient conditions and implies a "concentration... 详细信息

关键词： linear distributed parameter systems optimal controls

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Vanishing of the costate in pontryagin's maximum principle and singular time optimal controls

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JOURNAL OF EVOLUTION EQUATIONS 2004年第1期4卷 99-123页

作者： Fattorini, HO Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA

We provide examples of time and norm optimal controls that satisfy Pontryagin's maximum principle in an interval 0 less than or equal to t less than or equal to T but with a costate that vanishes in 0 less than or equal to t less than or equal to T - delta with delta < T. A refinement of this construction produces time optimal controls which do not satisfy the maximum principle, even in weak form. On the positive side, we show that when we drive to zero the costate is nonzero in the whole control interval.

关键词： linear distributed parameter systems boundary control systems optimal controls

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The maximum principle for control systems described by linear parabolic equations

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2001年第2期259卷 630-651页

作者： Fattorini, HO Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA

关键词： linear distributed parameter systems boundary control systems optimal controls

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Some aspects of the optimal control of distributed parameter systems /

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1972年

作者： Lions Jacques Louis.

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