Robust output regulation problem for linear time-delay systems

Lu, Maobin; Huang, Jie

doi:10.1080/00207179.2014.1002111

Cited by 37 publications

(47 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Next, we introduce a necessary and sufficient condition for the solvability of the robust output regulation problem by the control law (40), and we demonstrate that the robust output regulation problem can be solved by the proposed control law. We note that the proofs of our results are slightly different from the equivalent results in due to the introduction of the predictor

{\overset{ζ}{true}}_{τ_{u}}

in our control law, and the differences in the state matrices of the closed‐loop system .Lemma Under Assumptions , , and , the following statements are equivalent. The controller (40) solves the robust output regulation problem. For each δ ∈ W , where W is an open neighborhood of δ = 0 such that the undisturbed closed‐loop system is asymptotically stable, there exists a unique matrix Π δ that satisfies the matrix equations

{normalΠ}_{δ} scriptS = Ā_{δ, 0} {normalΠ}_{δ} + \sum_{i = 1}^{N} Ā_{δ, i} {normalΠ}_{δ} e^{- τ_{i} scriptS} + {\overset{B}{true}}_{δ},

0 = {\overset{C}{true}}_{δ} {normalΠ}_{δ} e^{- τ_{e} scriptS} + {\overset{D}{true}}_{δ} .

Proof By Assumptions and and Lemma , there exists a unique solution Π δ to for any δ ∈ W .…”

Section: Robust Output Regulationmentioning

confidence: 76%

“…The state prediction

{\overset{ζ}{true}}_{τ_{u}}

and the prediction error

{\overset{ζ}{true}}_{τ_{u}}

are defined as in and , respectively. The pair ( G 1 , G 2 ) is the minimal s ‐copy internal model of matrix

scriptS

G_{1} = block diag \underset{s‐tuples}{\underset{︸}{(β, β, \dots, β)}}, G_{2} = block diag \underset{s‐tuples}{\underset{︸}{(σ, σ, \dots, σ)}},

where the constant matrix β has a characteristic polynomial equal to the minimal polynomial of

scriptS

, and constant column vector σ is chosen so that the pair ( β , σ ) is controllable. Next, we formally define the control problem at hand.Problem Robust output regulation problem .…”

Section: Robust Output Regulationmentioning

confidence: 99%

“…In order to present our solution to the robust output regulation problem, the next two preliminary results are extracted from Lemmas 2.1 and 4.2 in , respectively.Lemma Under Assumptions and , for each δ ∈ W and any matrix

{\overset{B}{true}}_{δ}

, there exists a unique matrix Π δ such that it satisfies the matrix equality

{normalΠ}_{δ} scriptS = Ā_{δ, 0} {normalΠ}_{δ} + \sum_{i = 1}^{N} Ā_{δ, i} {normalΠ}_{δ} e^{- τ_{i} scriptS} + {\overset{B}{true}}_{δ} .

Lemma Let pair ( G 1 , G 2 ) be the minimal s ‐copy internal model of

scriptS

, and Y is any constant matrix of appropriate dimensions. Then, if the matrix equation

X scriptS - G_{1} X = G_{2} Y

is satisfied for some real matrix X , then Y = 0.…”

Section: Robust Output Regulationmentioning

confidence: 99%

See 2 more Smart Citations

Robust output regulation of linear time-delay systems: A state predictor approach

Yoon

Lin

2015

Int. J. Robust. Nonlinear Control

View full text Add to dashboard Cite

Summary This paper considers the robust output regulation problem for linear systems in the presence of state, input, and output delays. First, a state feedback control law is constructed from a state predictor, recently developed for systems with state and input delays. Necessary and sufficient conditions for the existence of a solution to the regulator equations are presented. Next, an error feedback control law for the output regulation problem is constructed by means of an error‐based state predictor. Finally, the proposed error feedback solution is extended to solve the output regulation problem in the presence of model uncertainty. Numerical examples demonstrate the effectiveness of the proposed predictor‐based solutions. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

{\overset{ζ}{true}}_{τ_{u}}

{normalΠ}_{δ} scriptS = Ā_{δ, 0} {normalΠ}_{δ} + \sum_{i = 1}^{N} Ā_{δ, i} {normalΠ}_{δ} e^{- τ_{i} scriptS} + {\overset{B}{true}}_{δ},

0 = {\overset{C}{true}}_{δ} {normalΠ}_{δ} e^{- τ_{e} scriptS} + {\overset{D}{true}}_{δ} .

Proof By Assumptions and and Lemma , there exists a unique solution Π δ to for any δ ∈ W .…”

Section: Robust Output Regulationmentioning

confidence: 76%

“…The state prediction

{\overset{ζ}{true}}_{τ_{u}}

and the prediction error

{\overset{ζ}{true}}_{τ_{u}}

are defined as in and , respectively. The pair ( G 1 , G 2 ) is the minimal s ‐copy internal model of matrix

scriptS

G_{1} = block diag \underset{s‐tuples}{\underset{︸}{(β, β, \dots, β)}}, G_{2} = block diag \underset{s‐tuples}{\underset{︸}{(σ, σ, \dots, σ)}},

where the constant matrix β has a characteristic polynomial equal to the minimal polynomial of

scriptS

, and constant column vector σ is chosen so that the pair ( β , σ ) is controllable. Next, we formally define the control problem at hand.Problem Robust output regulation problem .…”

Section: Robust Output Regulationmentioning

confidence: 99%

{\overset{B}{true}}_{δ}

, there exists a unique matrix Π δ such that it satisfies the matrix equality

{normalΠ}_{δ} scriptS = Ā_{δ, 0} {normalΠ}_{δ} + \sum_{i = 1}^{N} Ā_{δ, i} {normalΠ}_{δ} e^{- τ_{i} scriptS} + {\overset{B}{true}}_{δ} .

Lemma Let pair ( G 1 , G 2 ) be the minimal s ‐copy internal model of

scriptS

, and Y is any constant matrix of appropriate dimensions. Then, if the matrix equation

X scriptS - G_{1} X = G_{2} Y

is satisfied for some real matrix X , then Y = 0.…”

Section: Robust Output Regulationmentioning

confidence: 99%

See 1 more Smart Citation

Robust output regulation of linear time-delay systems: A state predictor approach

Yoon

Lin

2015

Int. J. Robust. Nonlinear Control

View full text Add to dashboard Cite

show abstract

“…Technically, this paper is most relevant to Lu and Huang and Su et al Specifically, in the aforementioned work, we studied a special case of this paper with N =1 in system . For this case, since there is no communication constraint on the control law , we can use the full state feedback control or the full output feedback control to handle the problem.…”

Section: Introductionmentioning

confidence: 99%

Internal model approach to cooperative robust output regulation for linear uncertain time‐delay multiagent systems

Huang

2018

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

Summary In this paper, we study the cooperative robust output regulation problem for linear uncertain multiagent systems with both communication delay and input delay by the distributed internal model approach. The problem includes the leader‐following consensus problem of linear multiagent systems with time delay as a special case. We first generalize the internal model design method to systems with both communication delay and input delay. Then, under a set of standard assumptions, we have obtained the solution to the problem via both the state feedback control law and the output feedback control law. In contrast to the existing results, our results apply to general linear uncertain multiagent systems, accommodate a large class of leader signals, and achieve asymptotic tracking and disturbance rejection at the same time.

show abstract

“…In the nonlinear system setting, [48] extends the solvability conditions of the output regulation problem to systems with state delays. For systems with input delay, [49] introduces a robust solution to the output regulation problem. For continuous time linear time-invariant system with delays in the state, input and output, the output regulation problem has been studied in [50,51].…”

Section: Output Regulation For Input-delay System With Timeinvariant mentioning

confidence: 99%

Unbalance Compensation of AMB Systems with Input Delay: A Truncated Predictor Feedback Based Output Regulation Approach

Long

View full text Add to dashboard Cite

Active magnetic bearings (AMBs) adopt electromagnetic forces to support the rotating shaft and do not have physical contact with the rotary structure. Compared to conventional mechanical bearings, AMBs do not require lubrication; the non-contact working environment improves the e ciency and reduces maintenance cost caused by mechanical wear; the dynamic forces also help the machinery to achieve higher rotational speeds. These appealing features of AMBs have gradually expanded their application in di↵erent industries, especially those involving high speed rotating machineries, such as compressors, where e ciency and reliability are highly desired.Emerging applications in o↵shore drilling for oil and gas production require compressors to operate in a remote and harsh environment for long periods of time. By adopting AMB technologies, these remotely operated applications have become technically and economically more feasible. Motivated by the challenges in those applications, this dissertation first addresses controlling high speed compressors supported by AMBs in o↵shore oil and gas development, where the control and sensor measurement signals are transmitted through long cables between the control unit on the shore and the compressor on the seabed. These cables, which may extend for several kilometers, introduce significant time delays to the system and the delays can degrade the system performance and even cause instability. Therefore, control methods that e↵ectively contain the delay e↵ect become indispensable. In this dissertation, the truncated predictor feedback (TPF) control law is applied to handle the time delay. The TPF control method utilizes the prediction of future states in the control signal calculation ii iii to eliminate the delay e↵ect. The controller corresponding to the maximized input delay that the closed-loop system can tolerate is obtained iteratively from the solution of a linear matrix inequality (LMI) problem. It is demonstrated in the dissertation that the TPF controller can tolerate a significant amount of input delay for AMB system levitation and outperforms a properly designed µ-synthesis robust controller.The second topic of this dissertation is unbalance compensation of AMB systems at both constant and time-varying rotational speeds. Any rotating machines are subject to disturbance forces caused by residual unbalance and the disturbance force is synchronous to the rotational speed. Therefore, unbalance compensation is crucial for reducing rotor vibration and preserving the system stability in high speed rotating machines. A properly controlled compressor supported by AMBs needs to confine the vibration to a small level to satisfy industrial standards. To mitigate the adverse e↵ects of unbalance forces, this dissertation proposes a novel unbalance compensation technique based on the output regulation mechanism.The problem of output regulation is to design a controller for disturbance rejection and/or reference tracking, while the disturbance or reference signal is generated ...

show abstract

Robust output regulation problem for linear time-delay systems

Cited by 37 publications

References 6 publications

Robust output regulation of linear time-delay systems: A state predictor approach

Robust output regulation of linear time-delay systems: A state predictor approach

Internal model approach to cooperative robust output regulation for linear uncertain time‐delay multiagent systems

Unbalance Compensation of AMB Systems with Input Delay: A Truncated Predictor Feedback Based Output Regulation Approach

Contact Info

Product

Resources

About