Pseudo‐downsampled iterative learning control

Abstract

SUMMARYIn this paper, a simple and effective multirate iterative learning control (ILC), referred as pseudodownsampled ILC, is proposed to deal with initial state error. This scheme downsamples the tracking error and input signals collected from the feedback control system before they are used in the ILC learning law. The output of the ILC is interpolated to generate the input for the next cycle. Analysis shows that the exponential decay of the tracking error can be expected and convergence condition can be ensured by downsampling. Other advantages of the proposed pseudo-downsampled ILC include no need for a filter design and reduction of memory size and computation. Experimental results demonstrate the effectiveness of the proposed scheme.

Using basis functions in iterative learning control: analysis and design theory

“…Note that in terminal ILC, the reference signal consists of only one sample. Hillenbrand and Pandit (1999) and Zhang, Wang, Zhou, Ye, and Wang (2008) downsample the i/o signals of the system using time windows to achieve specific convergence properties of the ILC controlled system. In this case, the reference signal is defined using the lower sample rate.…”

“…As a result, in this article we do not focus on, e.g. robustness aspects of ILC in the presence of model uncertainty (Moore, Ahn, and Chen 2008;Donkers, van de Wijdeven, and Bosgra 2008), or initial condition disturbances due to errors in the resetting of the system between two trials (Lee and Bien 1991;Zhang et al 2008).…”

Multirate iterative learning control schemes

“…For system (11), when the sampling ratio changes from 1 to 10, 1/C s B s for these different sampling ratios are larger than 1. Therefore, Γ is selected conservatively as 0.5.…”

Stability and robustness analysis of cyclic pseudo-downsampled iterative learning control

“…However, in most cases it cannot be satisfied for a given system with feedback controller encapsulated. We observe that by reducing the sampling rate, Moore's condition is easier to be satisfied (Zhang, Wang, Ye, Wang, and Zhou 2006, 2008Zhang, Wang, Ye, Zhou, and Wang 2009).…”

“…Based on this idea, we proposed a pseudo-downsampled ILC (Zhang et al 2008) in which ILC is implemented on signals at a downsampled slow rate. The output of ILC is upsampled through a zero-order holder.…”