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Comparison of the stability boundary and the frequency response stability condition in learning and repetitive control

100%
Songschon S., Longman R. W.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 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.
2
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A 2D system approach to the design of a robust modified repetitive-control system with a dynamic output-feedback controller

88%
Zhou L., She J., Zhou S.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 2
325-334
EN
This paper is concerned with the problem of designing a robust modified repetitive-control system with a dynamic outputfeedback 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.
3
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Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

88%
Zhou L., She J., Li C., Pan C.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 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
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System identification from multiple-trial data corrupted by non-repeating periodic disturbances

88%
Phan M. Q., Longman R. W., Lee S. C., Lee J.-W.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 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.
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