Design of a modified repetitive-control system based on a continuous–discrete 2D model

International Journal of Engineering Mathematics

et al. 2014

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This paper presents a method of designing a state-observer based modified repetitive-control system that provides a given ∞ level of disturbance attenuation for a class of strictly proper linear plants. Since the time delay in a repetitive controller can be treated as a kind of disturbance, we convert the system design problem into a standard state-feedback ∞ control problem for a linear time-invariant system. The Lyapunov functional and the singular-value decomposition of the output matrix are used to derive a linear-matrix-inequality (LMI) based design algorithm for the parameters of the feedback controller and the state-observer. A numerical example demonstrates the validity of the method.

“…However, as pointed out by [7][8][9] and others, there are significant differences between them. First of all, the initial state of a period is different.…”

Section: Introductionmentioning

confidence: 95%

“…Choose ( ), ( ), and V( ) to be the state variables of the MRCS in Figure 1. Then, from the dynamic equations (1), (5), (8), and (9) yields the following state equation:…”

Section: Problem Descriptionmentioning

confidence: 99%

H∞ Controller Design for an Observer-Based Modified Repetitive-Control System

International Journal of Engineering Mathematics

et al. 2014

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“…Since we can view the past state as a kind of experience, the words control and learning mean that we use information about the present and previous periods, respectively, to produce the present control input (She et al, 2012). The 2D control law (28) contains the direct sum of the effects of control and learning.…”

Section: Design Of the Eid-based Rofmrcsmentioning

confidence: 99%

“…Employing the lifting technique (Yamamoto, 1994;Zhou et al, 2012), we convert a vector-valued continuous-time signal, ξ(t), in the EID-based ROFMRCS (Fig. 2), into a function-valued discrete-time sequence, ξ k (τ ).…”

Section: Design Of the Eid-based Rofmrcsmentioning

confidence: 99%

“…Many strategies have been proposed to try to resolve the trade-off (Pipeleers et al, 2009;Hu et al, 2011;Chung and Chen, 2012). As an effective solution, Zhou et al (2012;2013;2014b) and She et al (2012) exploited the periodicity and continuity of RC and developed a two-dimensional (2D) model-based method. It enables the preferential adjustment of control and learning actions, and the designed systems exhibit both satisfactory robustness and good control performance.…”

Section: Introductionmentioning

confidence: 99%

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Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

International Journal of Applied Mathematics and Computer Science

et al. 2016

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This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based ROFMRCS that accurately presents the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A robust stability condition for the closed-loop system is given in terms of a linear matrix inequality. It yields the parameters of the repetitive controller, the output-feedback controller, and the EID-estimator. Finally, a numerical example demonstrates the validity of the method.

Robust Repetitive Control and Disturbance Rejection Based on Two‐Dimensional Model and Equivalent‐Input‐Disturbance Approach

Asian Journal of Control

et al. 2016

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A new configuration of a modified repetitive-control system has been devised for a class of strictly proper plants that suppresses exogenous disturbances and uncertainties in the dynamics of the plant. It extends the applicability of the control system. The system consists of four parts: a two-dimensional augmented model of the plant, which takes into account the difference in characteristics between continuous control and discrete learning in repetitive control; an equivalent-input-disturbance estimator; a state observer; and a state-feedback controller. A robust-stability condition expressed in terms of a linear matrix equality is used to determine the gains of the observer and the controller. Finally, a comparison of our method with repetitive control based on linear active disturbance rejection control (LADRC) shows how effective our method is and that it is superior to LADRC-based repetitive control.