An H approach to linear iterative learning control design

Repetitive and iterative learning control are two modern control strategies for tracking systems in which the signals are periodic in nature. This paper discusses repetitive and iterative learning control from an internal model principle point of view. This allows the formulation of existence conditions for multivariable implementations of repetitive and learning control. It is shown that repetitive control can be realized by an implementation of a robust servomechanism controller that uses the appropriate internal model for periodic disturbances. The design of such controllers is discussed. Next it is shown that iterative learning control can be implemented in the format of a disturbance observer/compensator. It is shown that the resulting control stucture is dual to the repetitive controller, and that both constitute an implementation of the internal model principle. Consequently, the analysis and design of repetitive and iterative learning control can be generalized to the powerful analysis and design procedure of the internal model framework, allowing to trade-off the convergence speed for periodic-disturbance cancellation versus other control objectives, such as stochastic disturbance suppression.

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“…Several approaches exist in the literature to design L such that guaranteed and controlled convergence conditions exist, see e.g., [1].…”

Section: Existing Repetitive and Learning Control Algorithmsmentioning

confidence: 99%

“…In the literature on iterative learning control, schemes like (6) are called past error feedforward, see for example [1,14,12]. An alternative is to use current-error feedback, see e.g., [13,6,7], where:…”

Section: Existing Repetitive and Learning Control Algorithmsmentioning

confidence: 99%

Internal-model-based design of repetitive and iterative learning controllers for linear multivariable systems

Roover

Bosgra

Steinbuch

2000

International Journal of Control

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“…ILC was initially developed as a feedforward action applied directly to the open-loop system [2], [3], [6]. Several closed-loop ILC schemes were later developed in order to benefit from the feedback properties in the first iteration, e.g., [1], [7], [11], [15], and [22].…”

mentioning

confidence: 99%

“…The H ∞ and µ-synthesis approaches were used in [7] and [15] to design the learning filters, under model uncertainties, assuming that the feedback controller is already available. A two-step procedure based on the H ∞ optimization was proposed in [1] to design the feedback and learning controllers. However, as the authors pointed out in [1], this technique cannot be used for unstable systems, and the convergence condition can only be satisfied if there is no uncertainty.…”

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confidence: 99%

Robust Iterative Learning Control Design: Application to a Robot Manipulator

Tayebi

Abdul

Zaremba

et al. 2008

IEEE/ASME Trans. Mechatron.

102

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Abstract-This paper deals with robust iterative learning control design for uncertain single-input-single-output linear time-invariant systems. The design procedure is based upon solving the robust performance condition using the Youla parameterization and the µ-synthesis approachto obtain a feedback controller. Thereafter, a convergent iterative learning law is obtained by using the performance weighting function involved in the robust performance condition. Experimental results, on a CRS465 robot manipulator, are provided to illustrate the effectiveness of the proposed design method.

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“…An extension of this analysis uses a parametric uncertainty model for the lifted system representation [11]. Since H ∞ norm based design techniques are a common approach to deal with model uncertainty in robust feedback control design, they have also been exploited to design robust ILCs in both frequency-domain, using the z-domain representation, and time-domain, using the lifted system representation [12]- [15].…”

Section: Introductionmentioning

confidence: 99%

Robust optimal iterative learning control with model uncertainty

Son

Pipeleers

Swevers

2013

52nd IEEE Conference on Decision and Control

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Abstract-In this paper we present an approach to deal with model uncertainty in norm-optimal iterative learning control (ILC). Model uncertainty generally degrades the convergence and performance of conventional learning algorithms. To deal with model uncertainty, a robust worst-case norm-optimal ILC is introduced. The problem is then reformulated as a convex minimization problem, which can be solved efficiently to generate the control signal. The paper also investigates the relationship between the proposed approach and conventional norm-optimal ILC; where it is found that our design method is equivalent to conventional norm-optimal ILC with trial-varying learning gains. Finally, simulation results of the presented technique are given.

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An H approach to linear iterative learning control design

Cited by 18 publications

References 2 publications

Internal-model-based design of repetitive and iterative learning controllers for linear multivariable systems

Internal-model-based design of repetitive and iterative learning controllers for linear multivariable systems

Robust Iterative Learning Control Design: Application to a Robot Manipulator

Robust optimal iterative learning control with model uncertainty

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