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Stability and robustness analysis of cyclic pseudo-downsampled iterative learning control. (English) Zbl 1222.93179
Summary: Cyclic pseudo-downsampled Iterative Learning Control (ILC) has shown advantages to achieve good learning performance for trajectories containing high-frequency components and has been verified on industrial robot application. This scheme is a multirate ILC in nature and downsamples the fast rate signals (with a sampling period \(T\)) to slow rate signals (with a sampling period \(mT\)) with a ratio \(m\). Then ILC is carried out on the downsampled signals and interpolates its output to a fast rate signal. For the next iteration, ILC scheme downsamples the signals with the same ratio \(m\) but at different sampling points with a time shift \(T\). This process is repeated on the iteration axis so that ILC updates the input of all the sampling points once every \(m\) cycles. By experiments [B. Zhang, D. Wang, Y. Ye, K. Zhou and Y. Wang, ‘Cyclic pseudo-downsampled iterative learning control for high performance tracking’, Control Engineering Practice 17, 957–965 (2009)], this scheme has been shown effective and comparisons with other relevant schemes demonstrate its superior performance. In this article, this cyclic pseudo-downsampled ILC scheme is examined analytically and proved mathematically to be stable and robust. Extensions and insights are also established based on the theoretical developments and simulation verification. pseudo-downsampled ILC scheme.

MSC:
93D09 Robust stability
93C55 Discrete-time control/observation systems
68T05 Learning and adaptive systems in artificial intelligence
93C85 Automated systems (robots, etc.) in control theory
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