摘要
本文主要目的在於提出一種基於小波轉換之反覆學習控制機構，用以改善傳統反覆學習機構，在面臨具有不可學習動態系統時，可能發生學習率發散之問題。對於運動控制系統，即便組合了目前週期誤差(反饋誤差)的反覆學習機構，由於系統存在之非線性及非重覆性干擾，如:死區、齒隙及摩擦等，將使系統經由反覆學習之過程，造成其振動愈來愈激烈，換言之，具有不可學習動態之運動控制系統，其學習控制命令，經由學習之過程將使系統趨於不穩定。
為改善此一問題，我們使用小波轉換，將系統可學習之動態部份，從迴授信號中加以分離，並在下一次週期時，更新學習命令，此一小波轉換可將原始信號分解成許多低解析度之信號，這些信號分別包含了系統可學習與不可學習之部份，因此理想的學習控制命令，便可經由反覆學習的過程加以建立，而對於系統不可學習之動態部份，可經由反饋控制器加以壓制，本文中對於學習之收斂性也有理論之證明，利用一個直流馬達的轉速追蹤控制及一個皮帶驅動系統，做為受控對象，經由實驗證明對速度追蹤控制具有很好的性能改善。此外基於硬體簡單化、低成本及快速原型機發展，本文也利用單一的FPGA來完成此一基於小波轉換之反覆學習控制伺服晶片，此一晶片應用在噴墨印表機之速度控制上，其實驗結果顯示可以得到令人滿意的性能。

A wavelet-based iterative learning control (WILC) scheme is presented in this article. For motion control system using conventional current cycle error (CCE) type ILC scheme, undesired vibration may be induced by nonlinear disturbances such as dead-zone, backlash, friction or other non-smooth nonlinearities and the amplitude of vibration will rapidly grow up during the process of iterations. In other words, the unlearnable dynamics of the motion control system will corrupt the control profile and cause instability during the iterative operation.
To improve the learning behavior, wavelet transform is employed to extract the learnable dynamics from measured output signal before it can be used to update the control profile. The wavelet transform is adopted to decompose the original signal into many low-resolution signals that contain the learnable and unlearnable parts. The desired control profile is then compared with the learnable part of the transformed signal. Thus, the effect from unlearnable dynamics on the controlled system can be attenuated solely by a feedback controller design. Convergence analysis is also presented to provide theoretical background. A typical DC servo system and a belt-driven system are employed as the control target for experimental verification. Experimental results have shown a much-improved speed-tracking performance. Furthermore, in order to meet the requirements of simple hardware, fast rapid prototyping and cost down, we also design a wavelet based iterative learning control system servo-chip implemented on a signal field-programmable gate array (FPGA) system. The experiment results indicate that the WILC IC has shown a significant improvement in speed.

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