Output regulation of periodic signals for DPS: an infinite-dimensional signal Generator

Immonen, Eero; Pohjolainen, Seppo

doi:10.1109/tac.2005.858643

Cited by 41 publications

(46 citation statements)

References 9 publications

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“…Finally, we will show that under the additional assumptions on the perturbations the conditions (19) are equivalent to ( R(iω k ,Ã e )B e φ k ) k∈Z ∈ ℓ 2 (C). Let k ∈ Z be such that |k| ≥ N and denoteỹ =P d (iω k )Ẽφ k +F φ k .…”

Section: If We In Particular Choosementioning

confidence: 96%

“…The controller is guaranteed to be robust with respect to all perturbations in O for which the strong closed-loop stability is preserved, {iω k } k∈Z ⊂ ρ(Ã e ), {iω k } |k|≥N ⊂ ρ(Ã) for some N ∈ N,P (iω k ) are invertible whenever |k| ≥ N , and for which (18) can again be replaced with (19) for the nominal plant. …”

Section: The Observer-based Controllermentioning

confidence: 99%

“…Such exogeneous signals can be generated with infinite-dimensional exosystems on the Hilbert space W = ℓ 2 (C) where S = diag(iω k ) k∈Z is an unbounded diagonal operator containing the frequencies {ω k } k∈Z that are present in the signals y ref (·) and w(·). In particular, any continuous τ -periodic signal can be generated with an exosystem of the form (2) where S = diag i 2kπ τ k∈Z [19]. Output tracking and disturbance rejection of nonsmooth signals with high accuracy have applications in the control of motor and disk drive systems and in power electronics [10].…”

Section: Introductionmentioning

confidence: 99%

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Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

Paunonen¹

2017

SIAM J. Control Optim.

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Abstract. We construct two error feedback controllers for robust output tracking and disturbance rejection of a regular linear system with nonsmooth reference and disturbance signals. We show that for sufficiently smooth signals the output converges to the reference at a rate that depends on the behaviour of the transfer function of the plant on the imaginary axis. In addition, we construct a controller that can be designed to achieve robustness with respect to a given class of uncertainties in the system, and present a novel controller structure for output tracking and disturbance rejection without the robustness requirement. We also generalize the internal model principle for regular linear systems with boundary disturbance and for controllers with unbounded input and output operators. The construction of controllers is illustrated with an example where we consider output tracking of a nonsmooth periodic reference signal for a two-dimensional heat equation with boundary control and observation, and with periodic disturbances on the boundary. IntroductionThe purpose of this paper is to construct controllers for robust output regulation of a regular linear system 1 [39, 40, 36]on an infinite-dimensional Banach space X. The main goal in the control problem is to achieve asymptotic convergence of the output y(t) to a given reference signal y ref (t) despite external disturbance signals w(t). In addition, it is required that the controller is robust in the sense that output tracking is achieved even under perturbations and uncertainties in the operators (A, B, B d , C, D) of the plant. The class of regular linear systems facilitates the study of robust output tracking and disturbance rejection for many important classes partial differential equations with boundary control and observation with corresponding unbounded operators B, B d and C [9,16,47,25]. In this paper we continue the work on designing robust controllers for regular linear systems begun recently in [26].The reference signal y ref (t) and the disturbance signals w(t) considered in the robust output regulation problem are assumed to be generated by an exosystem of the forṁ

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Section: If We In Particular Choosementioning

confidence: 96%

Section: The Observer-based Controllermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

Paunonen¹

2017

SIAM J. Control Optim.

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“…In the closed-loop system ' zðtÞ ¼ AzðtÞ þ BJxðtÞ þ ðBG þ PÞwðtÞ; t50 ð4aÞ We hasten to emphasize that the control law uðtÞ ¼ JxðtÞ þ GwðtÞ above does not involve a direct feedback from the state of the plant, as in References [11,12,18]. Furthermore, the feedforward part of the control is given by vðtÞ ¼ GwðtÞ ¼ Gy ref ðÁ þ tÞ; t50; where wð0Þ ¼ y ref ðÁÞ is the reference signal we want to track.…”

Section: The Feedforward-feedback Regulation Problemmentioning

confidence: 99%

“…In fact, there exist pairs ðA; BÞ which can only be stabilized strongly by a bounded feedback K; but sðA þ BKÞ \ iR ¼ |; and only AEi1 are points of accumulation for sðA þ BKÞ: This phenomenon is quite common in infinite-dimensional pole-placement problems; the reader is referred to Reference [32] for more details. We also assume throughout this section that plant (1) is a SISO system, but we do not restrict our attention to the case of p-periodic reference/disturbance signals as in References [12,18]. Our approach for solving the regulator equations (5) We can in this case choose the spaces H n ¼ spanff k j À n4k4ng for each n 2 N: This observation was the foundation of the method for solving the regulator equations (5) in References [12,18]; the same method has been shown to work for finite-dimensional exogenous systems in Reference [5].…”

Section: Solution Of the Regulator Equations For Siso Systemsmentioning

confidence: 99%

A feedforward–feedback controller for infinite-dimensional systems and regulation of bounded uniformly continuous signals

Immonen

2006

Int. J. Robust Nonlinear Control

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SUMMARYWe design a controller for infinite-dimensional linear systems (with bounded control, observation and feedthrough operators) which, under certain assumptions, achieves asymptotic tracking of arbitrary bounded uniformly continuous reference signals in the presence of disturbances. The proposed controller is of feedforward-feedback type: The dynamic feedback part is used to stabilize the closed-loop system consisting of the plant and the controller, whereas the feedforward part is tuned using the regulator equations to achieve the regulation of desired signals. We also completely solve the regulator equations for SISO systems, and we discuss robustness properties of the proposed controller. A useful feature in our design is that the feedforward part of the controller can be designed independently of the feedback part. This automatically leads to a degree of robustness in the stabilizing part of the controller, which is not present in the existing state feedback controllers solving the same output regulation problem.

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Internal‐model‐based control to reject an external signal generated by a class of infinite‐dimensional systems

Quan

Cai

2012

Adaptive Control & Signal

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SUMMARYIn this paper, an internal‐model‐based controller (IMBC) is designed to reject an external signal generated by a class of infinite‐dimensional systems for a class of nonlinear systems. First, a new description of the external signal is proposed. By this new description, the IMBC is designed, and the resulting closed‐loop error dynamics are analyzed with the help of a Lyapunov–Krasovskii functional. Compared with existing IMBCs, the designed IMBC provides the flexibility to cope with more types of external signals as well as to choose controller parameters to achieve a tradeoff between rejection performance and stability. Finally, the method is applied to attitude control of a quadrotor aircraft. Effectiveness of the IMBC is demonstrated by simulation. Copyright © 2012 John Wiley & Sons, Ltd.

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Output regulation of periodic signals for DPS: an infinite-dimensional signal Generator

Cited by 41 publications

References 9 publications

Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

A feedforward–feedback controller for infinite-dimensional systems and regulation of bounded uniformly continuous signals

Internal‐model‐based control to reject an external signal generated by a class of infinite‐dimensional systems

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