Control and Disturbance Rejection for Discrete Linear Repetitive Processes

Sulikowski, Bartłomiej; Gałkowski, Krzysztof; Rogers, Eric; Ownes, D.H.

doi:10.1007/s11045-005-6862-9

Cited by 7 publications

(6 citation statements)

References 14 publications

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“…Lemma 2. Given a scalar 2 > 0, the augmented system (42) is stochastically stable with an H ∞ disturbance attenuation level 2 Proof. Similar to the proof of Lemma 1, we introduce a stochastic Lyapunov function for augmented system (42) as…”

Section: Controller Design Conditionmentioning

confidence: 99%

“…Theorem 2. Given a scalar 2 > 0, the augmented system (42) is stochastically stable with an H ∞ disturbance attenuation level 2…”

Section: Controller Design Conditionmentioning

confidence: 99%

“…Dynamic systems generally have multi‐dimensional (m‐D) inherent characteristics. In all kinds of m‐D systems, two‐dimensional (2D) systems, in particular, have received extensive attention due to their widespread applications in practice, such as batch process, repetitive process, and digital filtering . In the past few years, a large number of topics on 2D systems have been extensively studied.…”

Section: Introductionmentioning

confidence: 99%

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Integrated fault detection and control for two‐dimensional Markovian jump systems

Ding

2019

Intl J Robust & Nonlinear

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Summary This paper is concerned with the problem of integrated fault detection and control for a class of two‐dimensional (2D) discrete‐time Markovian jump systems. The mathematical model of 2D Markovian jump systems is established upon the well‐known Roesser model, and a faults detection filter/controller is proposed to detect faults and meet some control specifications simultaneously. In this strategy, it takes into account both the fault detection objective and the control objective simultaneously through certain performance levels. The integrated design problem is then formulated as a multi‐objective optimization problem, which is nonconvex in essence. Furthermore, a two‐step algorithm is developed to solve this nonconvex problem. Sufficient conditions for existence of the desired fault detection filter/controller are established in terms of LMIs. A numerical example is used to demonstrate the effectiveness of the proposed method.

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Section: Controller Design Conditionmentioning

confidence: 99%

“…Theorem 2. Given a scalar 2 > 0, the augmented system (42) is stochastically stable with an H ∞ disturbance attenuation level 2…”

Section: Controller Design Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Integrated fault detection and control for two‐dimensional Markovian jump systems

Ding

2019

Intl J Robust & Nonlinear

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“…Proof The inequalities (16) and (18) are equivalent to r( A) < 1 and r( D 0 ) < 1, respectively (Sulikowski, Galkowski, Rogers, & Owens, 2005). Now consider the controlled process version of (8), i.e.…”

Section: Theorem 3 Suppose That a Control Law Of The Form (9) Is Applmentioning

confidence: 99%

Decoupling and iterative approaches to the control of discrete linear repetitive processes

Sulikowski

Gałkowski

Rogers

et al. 2007

Multidim Syst Sign Process

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This paper reports new results on the analysis and control of discrete linear repetitive processes which are a distinct class of 2D discrete linear systems of both systems theoretic and applications interest. In particular, we first propose an extension to the basic state-space model to include a coupling term previously neglected but which arises in some applications and then proceed to show how computationally efficient control laws can be designed for this new model.

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“…This represented a full survey on linear and nonlinear ILC. Disturbance rejection and control is seen in (Sulikowski et al, 2005) where convergence conditions of adaptive ILC is reported in Owens and Munde (2000). Exponential stability is investigated in Dymkov et al (2002) where French et al (2001) proposed a two-dimensional (2D)-approach discrete time ILC technique.…”

Section: Introductionmentioning

confidence: 99%

Sliding mode based fractional-order iterative learning control for a nonlinear robot manipulator with bounded disturbance

Ghasemi

Noei

Sadati

2016

Transactions of the Institute of Measurement and Control

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In this paper a new type of sliding mode based fractional-order iterative learning control (ILC) is proposed for nonlinear systems in the presence of uncertainties. For the first time, a sliding mode controller is combined with fractional-order ILC. This sliding mode based [Formula: see text] and [Formula: see text]-type ILC is applied on a nonlinear robot manipulator. Convergence of the proposed method is investigated when the stability is also proved. In this method, the control signal at any iteration is generated in two parts. The first section comes from the sliding mode controller while the second part is output of the fractional-order ILC. The latter signal is assessed using its previous amount and the sliding mode error signal. The achieved control law is capable of controlling nonlinear iterative processes, perturbed by bounded disturbances with high accuracy. The same frequent disturbance is eliminated by the iterative learning part, while the effect of nonrepetitive uncertainty is improved by the sliding mode part. The sliding mode based [Formula: see text]-type ILC (as an adaptive control law) is proposed to control a single-link arm robot. The controller is then improved to sliding mode based [Formula: see text]-type ILC. The effectiveness of the proposed method is again investigated on a single-link robot manipulator through a simulation approach. It is shown that the controller for [Formula: see text] provides performance by means of faster response together with more accuracy with respect to a conventional ILC.

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Control and Disturbance Rejection for Discrete Linear Repetitive Processes

Cited by 7 publications

References 14 publications

Integrated fault detection and control for two‐dimensional Markovian jump systems

Integrated fault detection and control for two‐dimensional Markovian jump systems

Decoupling and iterative approaches to the control of discrete linear repetitive processes

Sliding mode based fractional-order iterative learning control for a nonlinear robot manipulator with bounded disturbance

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