Finite spectrum assignment problem for systems with delays

Manitius, A.; Olbrot, A.W.

doi:10.1109/tac.1979.1102124

Cited by 1,018 publications

(471 citation statements)

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“…The existence of time delay may result in unexpected degradation in control performance and even instability. 1 Hence, how to effectively attenuate the effect of time delay has always been the research hotspot during the latest several decades, with numerous control schemes proposed, such as previous studies [2][3][4][5][6][7][8][9][10][11][12] for input delay and other studies [13][14][15][16][17][18] for state delay. Especially in Sun et al 17 and Sun and Liu, 18 stabilization of high-order uncertain nonlinear systems with state delays were investigated by using adaptive approach.…”

Section: Introductionmentioning

confidence: 99%

“…19,20 This paper focuses on the problem of input delay, ie, the time delay that occurs between the control input and the plant. Specifically, predictor-based techniques such as Artstein model reduction 2 and finite spectrum assignment, 3 which originate from classic Smith predictor method, 4 are typically exploited to compensate for the input delay. The core design in these predictor-based approaches is to transform the delayed system to a delay free one by using finite integrals over past control values.…”

Section: Introductionmentioning

confidence: 99%

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Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

Deng

Yao

2017

Intl J Robust & Nonlinear

119

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SummaryThis paper addresses the output feedback tracking control of a class of multipleinput and multiple-output nonlinear systems subject to time-varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory-based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time-varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady-state tracking accuracy in spite of the presence of time-varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a LyapunovKrasovskii functional. A specific study on a 2-link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme. | INTRODUCTIONTime delay that includes state delay and input delay is a pervasive phenomenon encountered in many practical engineering applications such as robotic systems, electrical networks, and hydraulic actuation systems. The existence of time delay may result in unexpected degradation in control performance and even instability. 1 Hence, how to effectively attenuate the effect of time delay has always been the research hotspot during the latest several decades, with numerous control schemes proposed, such as previous studies 2-12 for input delay and other studies [13][14][15][16][17][18] for state delay. Especially in Sun et al 17 and Sun and Liu, 18 stabilization of high-order uncertain nonlinear systems with state delays were investigated by using adaptive approach. 19,20 This paper focuses on the problem of input delay, ie, the time delay that occurs between the control input and the plant. Specifically, predictor-based techniques such as Artstein model reduction 2 and finite spectrum assignment, 3 which originate from classic Smith predictor method, 4 are typically exploited to compensate for the input delay. The core design in these predictor-based approaches is to transform the delayed system to a delay free one by using finite integrals over past control values. 21 In addition, many predictive controllers have also been synthesized based on the fact that the input delayed systems can be modeled as

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

Deng

Yao

2017

Intl J Robust & Nonlinear

119

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“…The control law obtained from the above controllers becomes [6,12,13,16,17], to achieve prefixed suitable either delay-independent or delay-dependent closed-loop spectrum. This more general problem statement may be beneficial in some applications where the suitable closed-loop spectrum is reallocated, but still delaydependent, due to the intrinsic delayed nature of the original open-loop plant [3,4,18].…”

Section: Controller Parametrization and Control Lawmentioning

confidence: 99%

“…Usually, R υ (s) is a rational function and S υ (s) is a polynomial. (A1) means that system (2.1) is spectrally controllable and spectrally observable [8,16]. This is an obvious requirement for the existence of a control law for prefixed spectrum assignment via output-feedback controllers.…”

Section: A(s)r(s) + B(s)s(s)mentioning

confidence: 99%

Pole placement controllers for linear time-delay systems with commensurate point delays

Sen

2004

Anal. Theory Appl.

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We investigate the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement-type controllers for single-input singleoutput linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled Diophantine equations of polynomials. An extra complexity is incorporated in the above design to cancel extra unsuitable dynamics being generated when solving the above Diophantine equations. Thus, the complete controller tracks any arbitrary prefixed (either finite or delay-dependent) closed-loop spectrum. However, if the controller is simplified by deleting the above-mentioned extra complexity, then robust stability and approximated spectrum assignment are still achievable for a certain sufficiently small amount of delayed dynamics. Finally, the approximate spectrum assignment and robust stability problems are revisited under plant disturbances if the nominal controller is maintained. In the current approach, the finite spectrum assignment is only considered as a particular case of the designer's choice of a (delay-dependent) arbitrary spectrum assignment objective.

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“…the standard delay system has been extensively studied in the literature, see e.g. [26], [22], [23], [25] in the case of X = R n and [8], [18], [21], [24] in the case of infinite dimensional spaces.…”

Section: Introductionmentioning

confidence: 99%

Feedback stabilizability of infinite dimensional neutral systems

Hadd

Nounou

2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-A new functional analytic approach to the concept of feedback stabilizability of infinite dimensional linear neutral systems is presented. We first reformulate this systems as an infinite dimensional open-loop systems with appropriate semigroups and unbounded control operators. We introduce conditions for which such semigroups are eventually compact. In addition, when the image of the control operator is finite dimensional, we give necessary and sufficient conditions for the feedback stabilizability of neutral system. Our approach is based on the concept of regular linear systems in the Salamon-Weiss sens.

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Finite spectrum assignment problem for systems with delays

Cited by 1,018 publications

References 8 publications

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

Pole placement controllers for linear time-delay systems with commensurate point delays

Feedback stabilizability of infinite dimensional neutral systems

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