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Iterative Learning Control - monotonicity and optimization

100%
Owens D., Daley S.
International Journal of Applied Mathematics and Computer Science
|
2008
|
tom 18
|
nr 3
279-293
EN
The area if Iterative Learning Control (ILC) has great potential for applications to systems with a naturally repetitive action where the transfer of data from repetition (trial or iteration) can lead to substantial improvements in tracking performance. There are several serious issues arising from the "2D" structure of ILC and a number of new problems requiring new ways of thinking and design. This paper introduces some of these issues from the point of view of the research group at Sheffield University and concentrates on linear systems and the potential for the use of optimization methods and switching strategies to achieve effective control.
2
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On the interaction between theory experiments and simulation in developing practical learning control algorithms

100%
Longman R. W.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 1
101-111
EN
Iterative learning control (ILC) develops controllers that iteratively adjust the command to a feedback control system in order to converge to zero tracking error following a specific desired trajectory. Unlike optimal control and other control methods, the iterations are made using the real world in place of a computer model. If desired, the learning process can be conducted both in the time domain during each iteration and in repetitions, making ILC a 2D system. Because ILC iterates with the real world, and aims for zero error, the field pushes the limits of theory, modeling, and simulation, to predict the behavior when applied in the real world. It is the thesis of this paper that in order to make significant progress in this field it is essential that the research effort employ a coordinated simultaneous synergistic effort involving theory, experiments, and serious simulations. Otherwise, one very easily expends effort on something that seems fundamental from the theoretical perspective, but in fact has very little relevance to the performance in real world applications.
3
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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.
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
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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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