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Variable-structure repetitive control for discrete-time linear systems with multiple-period exogenous signals

Kurniawan Edi, Harno Hendra G., Wijonarko Sensus, Widiyatmoko Bambang, Bayuwati Dwi, Purwowibowo Purwowibowo, Maftukhah Tatik

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 2

207--218

EN

A new method to construct a discrete-time variable-structure repetitive controller for a class of linear systems perturbed by multiple-period exogenous signals is presented. The proposed control scheme combines the features of the discrete-time multiple-period repetitive control (MP-RC) and variable-structure control (VSC) techniques. The MP-RC part is assigned to simultaneously track and reject periodic signals consisting of multiple uncorrelated fundamental frequencies. The VSC part is then integrated to provide a fast transient response and robustness against plant parameter variations. Stability and robustness analyses are also elaborated to ensure that the resulting closed-loop system satisfies the desired control objectives. Moreover, it is shown through an example that the repetitive control system constructed using the proposed control method can effectively track a sinusoidal reference signal despite the presence of a multiple-period disturbance.

2

Ufnalski B., Grzesiak L M., Kaszewski A., Galecki A.

Przegląd Elektrotechniczny

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2018

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R. 94, nr 5

38--46

EN

There are two main techniques to solve the reference tracking problem for repetitive references and under repetitive disturbances, namely multiresonant (a.k.a. multioscillatory) controllers and iterative learning controllers. Nevertheless, neither of the approaches is a deﬁnitive winner, which is to be demonstrated herein. Both have their strengths, weaknesses and challenges. A grid-tie converter will be the case study here. The goal is to draw or inject sinusoidal currents under distorted grid voltage conditions. The supporting feedforward controller will be addressed within the context of the discussed repetitive control task. The case will be illustrated using numerical simulations. Our main goal is to make practitioners familiar with the relationships between these two control methods.

PL

Istnieją dwia główne sposoby rozwiązywania zadania regulacji nadążnej dla powtarzalnego sygnału zadanego w obecności powtarzalnego zakłócenia, jest to zastosowanie regulatorów wielorezonansowych (zwanych też wielooscylacyjnymi) oraz regulatorów z uczeniem iteracyjnym. Jednak żadnego z tych rozwiązań nie można uznać za jednoznacznie lepsze, co zostanie tutaj pokazane. Oba cechują zarówno mocne strony, jak i pewne słabci oraz wyzwania implementacyjne. Przekształtnik sieciowy posłuży tutaj za przykład. Celem jest pobieranie lub oddawanie sinusoidalnego prądu sieci pomimo odkształconego napięcia. Omówione zostanie również sprzężenie w przód od zakłócenia w kontekście zadania sterowania powtarzalnego. Zagadnienie zostanie zilustrowane przy użyciu symulacji komputerowych. Naszym głównym celem jest pokazanie praktykom związków pomiędzy tymi dwiema metodami sterowania.

3

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

Zhou L., She J., Li C., Pan C.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 2

285--295

EN

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.

4

Repetitive neurocontroller with disturbance feedforward path active in the pass-to-pass direction for a VSI inverter with an output LC filter

Ufnalski B., Grzesiak L. M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 1

115--125

EN

An enhancement to the previously developed repetitive neurocontroller (RNC) is discussed and investigated in the paper. Originally, the time-base generator (TBG) has been used to produce the only input signal for the neural approximator. The resulting search space makes the dynamic optimization problem (DOP) of shaping the control signal solvable with the help of a function approximator such as the feed-forward neural network (FFNN). The plant under consideration, i.e. a constant-amplitude constant-frequency voltage-source inverter (CACF VSI) with an output LC filter, is assumed to be equipped with the disturbance load current sensor to enable implementation of the disturbance feed-forward (pDFF) path as a part of the non-repetitive subsystem acting in the along the pass p-direction. An investigation has been undertaken to explore potential benefits of using this signal also as an additional input for the RNC to augment the approximation space and potentially enhance the convergence rate of the real-time search process. It is numerically demonstrated in the paper that the disturbance feed-forward path active in the pass-to-pass k-direction (kDFF) improves the dynamics of the repetitive part as well indeed.

5

A plug-in direct particle swarm repetitive controller for a single-phase inverter

Ufnalski B., Grzesiak L M.

Przegląd Elektrotechniczny

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2014

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R. 90, nr 6

6--11

EN

The paper presents an online particle swarm optimizer (PSO) as an iterative learning controller for the single phase inverter with an output LC filter. The novelty of the solution lies in the fact that the swarm directly stores samples of the control signal. The swarm optimizes, according to a user-defined performance index, in online mode the control signal to reject the repetitive disturbance (the load current drawn, for example, by the diode rectifier). The concept of the direct swarm controller is investigated with the help of numerical simulations.

PL

W artykule opisano regulator rojowy realizujący sterowanie z uczeniem iteracyjnym dla jednofazowego falownika napięcia z wyjściowym filtrem LC. Oryginalność rozwiazania polega na fakcie bezpośredniego przechowywania próbek sygnału sterujacego przez rój cząstek. Rój optymalizuje w trybie on-line sygnał sterujący eliminując wpływ okresowego zakłócenia (prądu obciążenia pobieranego, na przykład, przez prostownik diodowy z filtrem pojemnościowym) na jakość napięcia wyjściowego. Sygnał sterujący jest optymalny z uwagi na zdefiniowany przez użytkownika wskaźnik jakości. Koncepcja bezpośredniego regulatora rojowego została zbadana przy użyciu technik modelowania numerycznego.

6

A 2D system approach to the design of a robust modified repetitive-control system with a dynamic output-feedback controller

Zhou L., She J., Zhou S.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 2

325--334

EN

This paper is concerned with the problem of designing a robust modified repetitive-control system with a dynamic output feedback controller for a class of strictly proper plants. Employing the continuous lifting technique, a continuous-discrete two-dimensional (2D) model is built that accurately describes the features of repetitive control. The 2D control input contains the direct sum of the effects of control and learning, which allows us to adjust control and learning preferentially. The singular-value decomposition of the output matrix and Lyapunov stability theory are used to derive an asymptotic stability condition based on a Linear Matrix Inequality (LMI). Two tuning parameters in the LMI manipulate the preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the effectiveness of the method.

7

DSP Based Hardware Implementation of Repetitive Current Controller for Interleaved Grid Connected Inverter

Jamil M., Sharief F., Yasin A., Ahmed A., Gulfam S. M., Khaqan A., Riaz R. A.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 2a

251-255

EN

The performance of the repetitive controller (RC) for classical inverters (e.g. two-level LCL filter based inverter) can decline if the system bandwidth is not sufficient enough due to much larger LCL filter component values. The novel interleaved inverters can provide higher bandwidth than the classical inverters because of low filter values. This paper reflects upon the analysis and hardware implementation of the RC for interleaved inverter using DSP. High quality (very low THD) output current is demonstrated through simulation and experimental results.

PL

W artykule przedstawiono analizę i implementację na DSP sterowania powtarzalnego dla badanego falownika typu interleaved. Przedstawione wyniki badań symulacyjnych, pokazują wysoką jakość (niskie THD) prądu wyjściowego przekształtnika.

8

System Identification from Multiple-Trial Data Corrupted by Non-Repeating Periodic Disturbances

Phan M. Q., Longman R. W., Lee S. C., Lee J. W.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 2

185-192

EN

Iterative learning and repetitive control aim to eliminate the effect of unwanted disturbances over repeated trials or cycles. The disturbance-free system model, if known, can be used in a model-based iterative learning or repetitive control system to eliminate the unwanted disturbances. In the case of periodic disturbances, although the unknown disturbance frequencies may be the same from trial to trial, the disturbance amplitudes, phases, and biases do not necessarily repeat. Furthermore, the system may not return to the same initial state at the end of each trial before starting the next trial. In spite of these constraints, this paper shows how to identify the system disturbance-free dynamics from disturbance-corrupted input-output data collected over multiple trials without having to measure the disturbances directly. The system disturbance-free model can then be used to identify the disturbances as well, for use in learning or repetitive control. This paper represents the first extension of the interaction matrix approach to the multiple-trial environment of iterative learning control.

9

Comparison of the Stability Boundary and the Frequency Response Stability Condition in Learning and Repetitive Control

Songschon S., Longman R. W.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 2

169-177

EN

In iterative learning control (ILC) and in repetitive control (RC) one is interested in convergence to zero tracking error as the repetitions of the command or the periods in the command progress. A condition based on steady state frequency response modeling is often used, but it does not represent the true stability boundary for convergence. In this paper we show how this useful condition differs from the true stability boundary in ILC and RC, and show that in applications of RC the distinction between these conditions is of no practical significance. In ILC satisfying this frequency condition is important for good learning transients, even though the true stability boundary is very different.