Higher-Order Iterative Learning Control Algorithms for Linear Systems

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Iterative learning control (ILC) algorithms appeared in connection with the problems of increasing the accuracy of performing repetitive operations by robots. They use information from previous repetitions to adjust the control signal on the current repetition. Most often, information from the previous repetition only is used. ILC algorithms that use information from several previous iterations are called higher-order algorithms. Recently, interest in these algorithms has increased in the literature in connection with robotic additive manufacturing problems. However, in addition to the fact that these algorithms have been little studied, there are conflicting estimates regarding their properties. This paper proposes new higher-order ILC algorithms for linear discrete and differential systems. The idea of these algorithms is based on an analogy with multi-step methods in optimization theory, in particular, with the heavy ball method. An example is given that confirms the possibility to accelerate convergence of the learning error when using such algorithms.

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作者简介

P. Pakshin

Arzamas Polytechnic Institute of the Nizhny Novgorod State Technical University n.a. R.E. Alekseev

编辑信件的主要联系方式.
Email: pakshinpv@gmail.com
俄罗斯联邦, Arzamas

Yu. Emelianova

Arzamas Polytechnic Institute of the Nizhny Novgorod State Technical University n.a. R.E. Alekseev

Email: emelianovajulia@gmail.com
俄罗斯联邦, Arzamas

M. Emelyanov

Arzamas Polytechnic Institute of the Nizhny Novgorod State Technical University n.a. R.E. Alekseev

Email: mikhailemelianovarzamas@gmail.com
俄罗斯联邦, Arzamas

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1. JATS XML
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2. Fig. 1. Desired motion trajectory

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3. Fig. 2. Variation of learning RMS in the cases of the first-order algorithm (dashed line) and second-order algorithm (solid line) at τ1 = 0.8

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4. Fig. 3. Variation of learning RMS in the cases of the first-order algorithm (dashed line) and second-order algorithm (solid line) at τ1 = 1.2

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5. Fig. 4. Variation of learning RMS in the cases of the first-order (dashed line) and third-order (solid line) algorithm at τ1 = 0.8, τ2 = 0

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6. Fig. 5. Variation of learning RMS in the cases of the first-order algorithm (dashed line) and third-order algorithm (solid line) at τ1 = 0, τ2 = 0.8

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7. Fig. 6. Variation of training RMS in the cases of the first-order algorithm (dashed line) and third-order algorithm (solid line) at τ1 = 0.8, τ2 = 0.4

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8. Fig. 7. Variation of learning RMS in the cases of first-order (dashed line) and third-order (solid line) algorithm at τ1 = 0.6, τ2 = 0.7

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