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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
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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.
2
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Iterative learning control for over-determined under-determined, and ill-conditioned systems

63%
Avrachenkov K. E., Longman R. W.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
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nr 1
113-122
EN
This paper studies iterative learning control (ILC) for under-determined and over-determined systems, i.e., systems for which the control action to produce the desired output is not unique, or for which exact tracking of the desired trajectory is not feasible. For both cases we recommend the use of the pseudoinverse or its approximation as a learning operator. The Tikhonov regularization technique is discussed for computing the pseudoinverse to handle numerical instability. It is shown that for over-determined systems, the minimum error is never reached by a repetition invariant learning controller unless one knows the system exactly. For discrete time uniquely determined systems it is indicated that the inverse is usually ill-conditioned, and hence an approximate inverse based on a pseudoinverse is appropriate, treating the system as over-determined. Using the structure of the system matrix, an enhanced Tikhonov regularization technique is developed which converges to zero tracking error. It is shown that the Tikhonov regularization is a form of linear quadratic ILC, and that the regularization approach solves the important practical problem of how to intelligently pick the weighting matrices in the quadratic cost. It is also shown how to use a modification of the Tikhonov-based quadratic cost in order to produce a frequency cutoff. This robustifies good learning transients, by reformulating the problem as an over-determined system.
3
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Comparison of the stability boundary and the frequency response stability condition in learning and repetitive control

63%
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

51%
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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