Controller Design for Robust Output Regulation of Regular Linear Systems

Paunonen, Lassi

doi:10.1109/tac.2015.2509439

Cited by 102 publications

(87 citation statements)

References 27 publications

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“…In this section we construct a robust controller using the general internal model based structure introduced in [26,27]. The construction of the controller is completed in steps, and the required properties of the parts of the controller are verified in the proof of Theorem 16.…”

Section: The New Controller Structurementioning

confidence: 99%

“…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 …”

mentioning

confidence: 94%

“…The first construction is based on a new block triangular controller structure that was first introduced in [27,26] for control of regular linear systems with finite-dimensional exosystems. The second controller uses the observer based structure that was used to solve the robust output regulation problem for an infinite-dimensional exosystem in [17] in the case where the plant had bounded input and output operators.…”

Section: Introductionmentioning

confidence: 99%

“…In such a situation it is possible that the internal model in the controller can be replaced with a reduced order internal model containing smaller numbers of copies of some of the frequencies of the exosystem [29]. In this paper we generalize the controller achieving robustness with respect to a given class O 0 of perturbations presented in [27,26] for regular linear systems with infinite-dimensional exosystems. Finally, we use the new controller structure to construct a novel controller that achieves output tracking and disturbance rejection without the requirement for robustness with respect to perturbations in the parameters of the plant.…”

Section: Introductionmentioning

confidence: 99%

“…Controller design for robust output regulation for regular linear systems with finitedimensional exosystems has been studied previously in [35,26]. The output tracking and disturbance rejection for regular linear systems without the robustness requirement have been studied in [25,43].…”

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: The New Controller Structurementioning

confidence: 99%

mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

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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Adaptive output regulation for one‐dimensional parabolic equation with nonlocal term

LiuWeiwei

Wang

2021

Adaptive Control & Signal

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In this article, we develop the adaptive error feedback regulator design for one-dimensional heat equation with a nonlocal term and disturbances which are located all the channels. First, we construct a transformation to transform the original system into the first auxiliary system, and in this system the measurable tracking error becomes output, both the disturbances located at the in-domain and the control end are transformed to the uncontrolled end. Next, we design an observer for the first auxiliary system and an estimation mechanism for unknown parameters based on measurable tracking error.Then, by another transformation, we obtain the second auxiliary system, in which the disturbances and the reference signal are collocated with the control. Finally, the adaptive error feedback regulator is designed by using the backstepping method. The simulation results show that the regulator makes the tracking error asymptotically tend to zero and the state of the closed-loop system is bounded.

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Adaptive error feedback regulator problem for 1‐D anti‐stable wave equation with distributed harmonic disturbance

Jin

Guo

2022

Adaptive Control & Signal

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In this article, we are concerned with the error feedback regulator design for a one-dimensional anti-stable wave equation with harmonic reference signal and distributed disturbance. By the tracking error of the left end displacement, we first introduce a transport equation and a transformation to transform the original wave system to an auxiliary system, where the displacement at the left end is a scaling of the tracking error of the original system. Then an adaptive error-based observer is designed by using the tracking error to estimate the state of the auxiliary system and unknown amplitudes of the harmonic disturbance and reference signal. Next we propose an observer-based error feedback controller to regulate the tracking error to zero asymptotically and keep all the states uniformly bounded. Finally some numerical results are presented to illustrate the effectiveness of the controller.

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Controller Design for Robust Output Regulation of Regular Linear Systems

Cited by 102 publications

References 27 publications

Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

Adaptive output regulation for one‐dimensional parabolic equation with nonlocal term

Adaptive error feedback regulator problem for 1‐D anti‐stable wave equation with distributed harmonic disturbance

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