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Journal ArticleDOI: 10.1080/00207178508933401

On the design of a sensitivity-reducing optimal dead-beat controller

01 Oct 1985-International Journal of Control (Taylor & Francis Group)-Vol. 42, Iss: 4, pp 877-886
Abstract: A method is proposed for the design of constant-gain feedback-control laws for linear multivariable discrete-time systems which reduce trajectory sensitivity to small system parameter variations and ensure the closed-loop eigenvalues at the origin The given quadratic index of performance including a sensitivity term is minimized in an average sense An efficient computational procedure based on direct cost optimization using gradient type algorithm is also reported An example is worked out to illustrate the proposed technique

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Citations
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Book ChapterDOI: 10.1016/S0090-5267(96)80006-5
Abstract: This chapter explores the development of deadbeat control and one-step-ahead control Deadbeat control and one-step-ahead control, each have a long history, the two were developed in separate research streams, and it was many years before these streams merged It compares and contrast deadbeat and one-step-ahead control strategies, to contribute to the unification of the two areas, and to clear up some possible points of confusion The chapter discusses that system identification, deadbeat control, and one-step-ahead control are possible because discrete-time systems are described by difference equations, which define an algebraic relation between the system inputs and outputs Such procedures cannot be applied to continuous-time systems, whose inputs and outputs are related by differential equations As a result, for example, deadbeat response in a continuous-time system cannot be achieved via linear time invariant feedback No matter how rapid the step response of a continuous-time control system is made, the exponentially decaying error vanishes only as time goes to infinity

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Topics: Step response (54%), Control system (52%), LTI system theory (50%)

13 Citations


Journal ArticleDOI: 10.1115/1.3152655
Abstract: This paper shows that the sensitivity of state feedback control systems can be re­ duced by additional state derivative feedback, for a fixed closed loop eigenstructure. The price of this sensitivity reduction is in general noise response amplification. Two indices which quantify stability robustness and response sensitivity are given for time invariant continuous time and discrete time systems, together with an index of response to disturbances and noise. Closed form expressions for the gradients of these indices are given. A two step design procedure is proposed which consists of first selecting a closed loop eigenstructure, then minimizing one of the sensitivity in­ dices under a magnitude constraint on the noise response. Examples are given to il­ lustrate this original design procedure.

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11 Citations


Journal ArticleDOI: 10.1016/0167-6911(90)90022-M
Chun-Hsiung Fang, Fan-Ren Chang1Institutions (1)
Abstract: Explicit formulas for doubly coprime matrix-fraction descriptions (MFDs) of the transfer matrix of a linear time-invariant state-space system are given in terms of a controllable and observable state-space realization of the transfer matrix. These formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime MFDs of multivariable systems.

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Topics: Realization (systems) (57%), Coprime integers (55%), Matrix (mathematics) (53%) ...read more

9 Citations


Book ChapterDOI: 10.1007/978-3-662-01632-9_6
Mansour Eslami1Institutions (1)
01 Jan 1994-
Abstract: In Chapters Two to Five we devote our attentions primarily to issues regarding parameter-sensitivity analysis. In spite of different uncertainties which may exist in a dynamical system, we expect that our controller will ultimately maintain qualitatively and/or quantitatively the overall system operation as desired. Or it will maintain this operation within a prespecified class of such operations which this is really the key issue in any robustness methodology. Therefore we must incorporate in control synthesis algorithm any information regarding possible discrepancies in system “output”, in order to generate new controllers that can stand against the consequences of some possible uncertainties. This incorporation is by no means a simple task, and before we let our expectations exceed our means, we examine some of our earlier assumptions and review the class of problems which currently can be analyzed.

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7 Citations


Open accessProceedings ArticleDOI: 10.23919/ACC.1987.4789375
10 Jun 1987-
Abstract: This paper presents a control design procedure for linear time invariant systems using output proportional plus derivative feedback. The traditional linear quadratic performance index is used with additional terms to penalize disturbance and noise response and eigenvalue and response sensitivities. The sensitivity terms represent measures of stability robustness. It is shown that the derivative feedback improves the measure of performance. This design procedure has been applied to obtain an improved autopilot for the lateral dynamics of an L1011 aircraft.

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Topics: Linear system (57%), Proportional control (56%), LTI system theory (54%) ...read more

2 Citations

References
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Journal ArticleDOI: 10.1109/TAC.1970.1099363
William S. Levine1, Michael Athans1Institutions (1)
Abstract: The optimal control of linear time-invariant systems with respect to a quadratic performance criterion is discussed. The problem is posed with the additional constraint that the control vector u(t) is a linear time-invariant function of the output vector y(t) (u(t) = -Fy(t)) rather than of the state vector x(t) . The performance criterion is then averaged, and algebraic necessary conditions for a minimizing F\ast are found. In addition, an algorithm for computing F\ast is presented.

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Topics: Linear-quadratic-Gaussian control (56%), State vector (54%), Linear system (54%) ...read more

886 Citations


Proceedings ArticleDOI: 10.1109/TAC.1976.1101355
B. Moore1Institutions (1)
01 Dec 1975-
Abstract: A characterization is given for the class of all closed loop eigenvector sets which can be obtained with a given set of distinct closed loop eigenvalues using state feedback. It is shown, furthermore, that the freedom one has in addition to specifying the closed loop eigenvalues is precisely this: to choose one set of closed loop eigenvectors from this class. Included in the proof of this result is an algorithm for computing the matrix of feedback gains which gives the chosen closed loop eigenvalues and eigenvectors. A design scheme based on these results is presented which gives the designer considerable freedom to choose the distribution of the modes among the output components. One interesting feature is that the distribution of a mode among the output components can be varied even if the mode is not controllable.

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Topics: Loop fission (62%), Do while loop (62%), Loop gain (59%) ...read more

578 Citations


Journal ArticleDOI: 10.1109/TAC.1982.1102995
M. Fahmy1, J. O'ReillyInstitutions (1)
Abstract: The eigenvalue-assignment approach of Brogan [1], [2] is generalized and extended to the assignment of the entire closed-loop eigenstructure of linear multivariable systems The set of assignable eigenvectors and generalized eigenvectors emerges naturally in the solution and is given, moreover, in an explicit parametric form Two numerical examples are worked out to demonstrate the application of the procedure

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157 Citations


Journal ArticleDOI: 10.1109/TAC.1977.1101435
G. Klein1, B. Moore1Institutions (1)
Abstract: In a recent paper [1], a characterization has been given for the class of all closed-loop eigenvector sets which can be obtained with a given set of distinct closed-loop eigenvalues. This note extends these results to characterize the class of generalized eigenvector chains which can be obtained with a given set of nondistinct eigenvalues. Included is an algorithm for computing a feedback matrix which gives the selected closed-loop eigenvalues and generalized eigenvector chains. Although there are limitations on the Jordan structure of the closed-loop system, this algorithm allows one to realize any "allowable" closed-loop Jordan configuration.

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143 Citations


Journal ArticleDOI: 10.1080/00207177108931949
Abstract: Optimal sampled-data controls for linear processes with quadratic criteria are determined through application of the discrete minimum principle. The effect of sampling on the closed-loop system's performance is investigated and the asymptotic behaviour of the optimal cost for large sampling periods is determined. The resulting design method is applicable to continuous, sampled-data and discrete regulators.

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Topics: Sampling (statistics) (66%)

123 Citations