Multirate Iterative Learning Control Research Articles

Fast-Update Iterative Learning Control for Performance Enhancement With Application to Motion Systems

Iterative learning control (ILC) algorithms are typically used to improve the performance of repetitive processes. Numerous successful applications of ILC, such as computer numerical control (CNC) machining processes, robot manipulation, and lithography processes, have been reported. However, ILC often exhibits less than satisfactory performance since the control unit operates at a limited sampling rate in consideration of cost. In this study, the multiloop, multirate structure of servo motor control systems is taken advantage of and a fast-update multirate ILC (FILC) scheme is proposed for high-accuracy trajectory tracking, where compensation is updated at a rate faster than that of the original position loop without the need for redesigning the feedback controller. The key difficulty related to the design of the FILC lies in the extremely complex and time-varying dynamics inherent in multirate systems. To address this problem, a novel equivalent single-rate parametric model description of the multirate system is derived, which enables the use of the efficient norm optimal ILC algorithm. Consequently, a computationally efficient FILC is obtained to improve the performance. Subsequently, the proposed FILC is applied to the position control of the CNC motion stage. Simulation and experimental results are used to verify the effectiveness of the proposed method.

Case studies of filtering techniques in multirate iterative learning control

Iterative learning control (ILC) is a simple and efficient solution to improve tracking accuracy for systems that execute repetitively the same tracing operation. For engineering applications of ILC, the main concern is the monotonic decay of tracking errors, in the sense of infinity norm or peak error, along the trials. Low cost in implementation and robustness in performance are also critical factors. To achieve these important but sometimes contradicting goals, several multirate ILC schemes have been developed, in which different data sampling rates are used for feedback online loop and feedforward ILC offline loop. That is, multirate ILC uses a different (often lower) rate from the sampling rate of a feedback system to update input. Before the input signal is applied to the system for the next trial, it is upsampled to reach the original sampling rate. Since downsampling will cause distortion of frequency spectra, anti-aliasing and anti-imaging filters and signal extension are used together with downsampling and upsampling operations. In this paper, these technologies are integrated with three different multirate ILC schemes, pseudo-downsampled ILC, two-mode ILC, and cyclic pseudo-downsampled ILC, to achieve better performance. A series of experimental results on an industrial robot are presented to demonstrate the efficiency of multirate ILC schemes and compare the performance. The results demonstrate that multirate ILC schemes are able to achieve not only monotonic learning transient, but also much better tracking accuracy than conventional one-step-ahead ILC schemes.

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

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 [Zhang, B., Wang, D., Ye, Y., Zhou, K. and Wang, Y. (2009) ‘Cyclic Pseudo-downsampled Iterative Learning Control for High Performance Tracking’, Control Engineering Practice, 17, 957–965], 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.

Suppressing intersample behavior in iterative learning control

Iterative Learning Control (ILC) is a control strategy to improve the performance of digital batch repetitive processes. Due to its digital implementation, discrete time ILC approaches do not guarantee good intersample behavior. In fact, common discrete time ILC approaches may deteriorate the intersample behavior, thereby reducing the performance of the sampled-data system. In this paper, a generally applicable multirate ILC approach is presented that enables to balance the at-sample performance and the intersample behavior. Furthermore, key theoretical issues regarding multirate systems are addressed, including the time-varying nature of the multirate ILC setup. The proposed multirate ILC approach is shown to outperform discrete time ILC in realistic simulation examples.

Comparison Studies on Anti-Aliasing/Anti-Imaging Filtering and Signal Extension in Multi-rate ILC

Multirate iterative learning control (ILC) systems have different sampling rates for feedback online loop and feedforward (or ILC) offline loop. The implementation of multirate ILC requires to downsample the signal first and, after processing, upsample the signal again. In the process of downsampling and upsampling, aliasing and imaging may occur and need to be handled properly. In this paper, the multirate ILC with and without anti-aliasing/anti-imaging filters are compared with different types of low-pass filter. Furthermore, to satisfy the steady state frequency response, the signals are extended and different extension methods are evaluated. A series of simulation results is provided to demonstrate that anti-aliasing and anti-imaging filters significantly improve the tracking performance. However, the extension methods have little influence on the tracking accuracy.

Pseudo‐downsampled iterative learning control

AbstractIn this paper, a simple and effective multirate iterative learning control (ILC), referred as pseudo‐downsampled 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. Copyright © 2007 John Wiley & Sons, Ltd.