植基於加權因子小腦模型控制器之設計

林立人

指導教授 ： 洪欽銘 ； 許全守

國立臺灣師範大學/科技學院/工業教育學系/碩士(2002年)

摘要

小腦模型控制器(CMAC)為類神經網路的一支系，構造簡單與演算法撰寫容易是此控制器的特色之一。但本研究發現，當使用簡單迭代法進行演算時，CMAC的誤差曲線會呈現巨幅地振盪然後收歛，此種情形於實際的控制應用裡是不被允許的，因此本研究提出加權因子的概念，改進了控制器在收歛曲線中所發生之振盪現象。
整合加權因子與小腦模型控制器，將此新的控制器命名為「加權因子小腦模型控制器」(WCMAC)。為測試其實用性，本論文之研究範圍包括WCMAC的原理分析、函數學習性能測試和實際控制測試，茲概述如下：
在WCMAC的原理分析裡，本研究採用條件數為測度依據，以實驗說明加權因子的施用能改善CMAC之關聯矩陣，使迭代運算次數明顯地減少。
就函數學習性能測試裡，以Sayil於2002年所整理之資料為依據，分別對連續型函數與非連續型函數進行學習記錄，其中配合殘差理論，發現WCMAC在此項測驗中，就學習的精度而言，WCMAC的性能測試明顯地不遜於他種演算法。
最後的實際控制測試，採用球-桿平衡系統為實驗對象，此為典型控制實驗室裡的測試工具，為一非最小相位系統。本論文以二次型最佳化控制理論設計一主控制器，然後施加WCMAC作為輔助控制器，實驗發現WCMAC能提高響應品質並且不會有學習發散的現象。

關鍵字

類神經網路 ； 小腦模型控制器 ； 二次型最佳化控制 ； 殘差演算法 ； 迭代演算法 ； 球-桿平衡系統 ； 非最小相位系統

並列摘要

The Cerebellar Mode Articulation Controller (CMAC), one kind of Neural Network, is well known of its simple architecture and easily developed algorithm. We found that the curve of error is oscillational, and its situation is not acceptable for real time control, but after the heavy oscillation, it goes steady for some time when CMAC applied simple iterative algorithm. The concept of weighted factor is hereby proposed in order to improve the curve of error in a smoother converging curve.
This paper presents a novel WCMAC, weighted CMAC, to discuss whether or not that it can be suitably applied in the future. The following discussions are focuses on the 1) theory of WCMAC, 2) its learning ability for specific mathematical function and 3) experiment with WCMAC on Ball on Beam Control System.
Firstly, the numbers of iterative applied by WCMAC can be reduced after concluding the result of experiment that is based on the criteria of mathematical condition number.
Secondly, the responses of the WCMAC, when integrated with principle of residual are accurate as well as the other algorithms of CMAC based on the learning specific mathematical function that was adapted from the table from Sayil in 2002.
Finally, this study chooses the Ball on Bean System, a well-known nonminimum phase system, as a tester. We designed a main controller using theory of quadratic optimal control for the purpose of implementing WCMAC as an auxiliary controller. The responses of results found that the control system worked well with WCMAC applied.

並列關鍵字

Neural Network ； Cerebellar Model Articulation Controller ； Quadratic Optimal Control ； Residual Method ； Iterative Method ； Ball on Beam Control System ； Nonminimum Phase System

參考文獻

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[2] J.S. Albus,”Data storage in the Cerebellar Model Articulation Controller (CMAC)”, Trans. ASME, Dyn. Syst. Meas., and Control, 1975, pp.228 – 233.

[3] J.S. Albus,” Theory of Cerebellar Function”, Mathematical Biosciences, Vol.10, No.1/2, 1971, pp. 25-61.

[4] W.S. Mischo, “A CMAC-type neural memory for control applications”, IEEE Conf. Microelectronics for Neural Networks, 1996, pp. 161 -167.

[5] L.G. Kraft and D.P. Campagna, “Comparison of Convergence Properties of CMAC neural network and Traditional Adaptive Controllers”, IEEE Proc. Decision and Control, vol.2, 1989, pp. 1744 -1745.