• Journal of Korean Institute of Industrial Engineers
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• v.23 no.1
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• pp.1-22
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• 1997

Learning control refers to controllers that learn to improve their performance at executing a given task, based on experience performing this specific task. In a previous work, the authors presented a theory of indirect decentralized learning control based on use of indirect adaptive control concepts employing simultaneous identification and control. This paper extends these results to apply to the indirect repetitive control problem in which a periodic (i.e., repetitive) command is given to a control system. Decentralized indirect repetitive control algorithms are presented that have guaranteed convergence to zero tracking error under very general conditions. The original motivation of the repetitive control and learning control fields was learning in robots doing repetitive tasks such as on an assembly line. This paper starts with decentralized discrete time systems, and progresses to the robot application, modeling the robot as a time varying linear system in the neighborhood of the desired trajectory. Decentralized repetitive control is natural for this application because the feedback control for link rotations is normally implemented in a decentralized manner, treating each link as if it is independent of the other links.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.79-82
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• 2002

In this paper, we propose an adaptive repetitive control algorithm for the system the task of which is repetitive. The feedforward controller in the repetitive control system is modified by using the system parameter identifier in order to improve the convergence characteristics. The proposed algorithm is applied to the tracking control of a linear BLDC motor to which a periodic reference input is applied. It is illustrated by simulation results that the proposed adaptive repetitive control method yields better control performance than existing repetitive control even when modeling errors exist.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.7
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• pp.668-673
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• 2010

Given a periodic reference signal or disturbance, repetitive control is a special control scheme to reduce a tracking error effectively by the periodic signal generator in the repetitive controller. In general, a repetitive controller is added on the existing feedback control system to improve the tracking performance. However, because the information used in the design of the feedback controller is not taken into account, the design problem of the repetitive controller is totally another problem irrespective of that of the feedback controller. In this paper, we present a more general method to design an add-on type repetitive controller using the information on the performance of the existing feedback control system. We first show that a robust stability condition of repetitive control systems is obtained using the well-known robust performance condition of general feedback control systems. It is also shown that we can obtain a steady-state tracking error described in a simple form without time-delay element if the robust stability condition is satisfied for the repetitive control system. From the obtained results, several design criterions for repetitive controller are provided. Through the simulation study, the feasibility of the proposed method is verified.

• International Journal of Control, Automation, and Systems
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• v.6 no.6
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• pp.960-967
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• 2008

This paper shows that design of a robustly stable repetitive control system is equivalent to that of a feedback control system for an uncertain linear time-invariant system satisfying the well-known robust performance condition. Once a feedback controller is designed to satisfy the robust performance condition, the feedback controller and the repetitive controller using the performance weighting function robustly stabilizes the repetitive control system. It is also shown that we can obtain a steady-state tracking error described in a simple form without time-delay element if the robust stability condition is satisfied for the repetitive control system. Moreover, using this result, a sufficient condition is provided, which ensures that the least upper bound of the steady-state tracking error generated by the repetitive control system is less than or equal to the least upper bound of the steady-state tracking error only by the feedback system.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.2
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• pp.117-123
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• 2003

Rotational machines such as optical disk drives, hard disk drives, and so on are subject to periodic disturbances caused by their mechanical characteristics. In the meanwhile, it is well known that repetitive control rejects periodic disturbance effectively. This paper presents a practical application of repetitive control to the track-following servo of an optical disk drive. The repetitive control system is composed of two repetitive controllers which compensate for periodic disturbances generated by track geometry and eccentric rotation of disk and a feedback controller stabilizing the feedback loop. A robust stability for all plant uncertainties is proved using linear matrix inequalities (LMIs). In the controller design, a weighting function is introduced for the feedback controller to ensure a minimum loop gain and a sufficient phase margin. The repetitive controllers and the feedback controller are designed by solving an optimization problem which can consider the robust stability condition and the system performance. The developed repetitive control system is implemented in the digital control system with a 16-bit fixed-point digital signal processor (DSP). Through simulation and experiment. The feasibility of the proposed repetitive control system is verified.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.1051-1059
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• 1992

Two types of digital repetitive control systems are analyzed and designed to reduce the error spectrum including not only harmonic but also non-harmonic components. First, a novel gain scheduling algorithm is suggested for conventional and modified repetitive controller is scheduled to reduce the infinite norm of error in frequency domain. For this, the relative error transfer function is mewly defined as the ratio of the error spectrum for the system with a repetitive controller to the error spectrum for the system with a repetitive controller to the error spectrum for the system without a repetitive controller. Secondly, as an alternative of a repetitive control system with the gain scheduling, a repetitive control system with higher order repetitve function is analyzed and designed, where instead of equal weightings, weightings of the higher order repetitive function is determined in such a way that the infinite norm of relative error transfer function is minimized. To show the validities of proposed methods, computer simulation results are illustrated for a typical disk drive head positioning servo system.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.779-782
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• 1996

Repetitive control is a proposed control strategy in view of the internal model principle and achieves a high accuracy asymptotic tracking property by implementing a model that generates the periodic signals of period into the closed-loop system. Since the repetitive control system contains a periodic signal generator with positive feedback loop, which reduces the stability margin, in the overall closed-loop system, the stability of the closed-loop system should be considered as an important problem. In case that a real system has plant uncertainties which are not represented through modeling, the robust stability problem of the repetitive control system has not been considered sufficiently. In this paper, we propose the robust stability condition for the system with modeling uncertainty. The proposed robust stability condition will be obtained using the robust performance condition in the H$_{\infty}$ control. Moreover, by use of the proposed robust stability condition, we propose a procedure that designs a repetitive controller and a feedback controller simultaneously which can stabilize the overall closed-loop system robustly and which can also do the closedloop system without repetitive controller..

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.4
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• pp.420-426
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• 1998

It is the purpose of this paper to make a preliminary study on the use of repetitive control to improve velocity accuracy by eliminating repetitive disturbances caused by machining inaccuracies of the axis of rotation location. If the control system can be intelligent enough to compensate for such machining errors, then one may be able to improve the accuracy of the velocity control, or alternatively, one may maintain the same accuracy and relax the machining tolerances required. This could decrease cost significantly. Experiments are performed testing repetitive control methods on a constant speed rolling operation testbed. The experimental results show very substantial decreases in the tracking error of the system. Spectral data of the output motion are given to demonstrate the attenuation of the disturbance frequencies and harmonics, related to the bandwidth being used. It is seen that the simplest form of repetitive control which is very easily implemented, can produce striking improvement in control system performance in such belt drive rolling operations, and the learning can be accomplished in a short time.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.1
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• pp.6-11
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• 2014

Repetitive control is a specialized control scheme to track and/or attenuate a periodic reference trajectory and/or disturbance. Most researches about repetitive control have been performed in the frequency domain. Recently, several approaches to deal with repetitive control systems in the state space are developed by representing a q filter as a state-space equation. This paper presents a design method of a repetitive control system in the state space to satisfy $H_{\infty}$ performance. The overall system is composed of a plant, a repetitive controller, and a state-feedback controller, which can be converted to a standard form used in $H_{\infty}$ control. A LMI (Linear Matrix Inequality)-based stability condition is derived for fixed state-feedback gains. Under a given q filter, another LMI condition is derived to improve $H_{\infty}$ performance and is employed to find state-feedback gains by solving an optimization problem. Finally, to verify the feasibility of the proposed method, a numerical example is demonstrated.

• Journal of Electrical Engineering and Technology
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• v.11 no.3
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• pp.618-628
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• 2016

Active power filter (APF) has been proved as a flexible solution for compensating the harmonic distortion caused by nonlinear loads in power distribution power systems. Digital repetitive control can achieve zero steady-state error tracking of any periodic signal while the sampling points within one repetitive cycle must be a known integer. However, the compensation performance of the APF would be degradation when the grid frequency varies. In this paper, an improved repetitive control scheme with frequency adaptive capability is presented to track any periodic signal with variable grid frequency, where the variable delay items caused by time-varying grid frequency are approximated with Pade approximants. Additionally, the stability criterion of proposed repetitive control scheme is given. A three-phase shunt APF experimental platform with proposed repetitive control scheme is built in our laboratory. Simulation and experimental results demonstrate the effectiveness of the proposed repetitive control scheme.