- 期刊
Design of Optimal Fractional-Order PID Controllers
最適分數階次PID控制器之設計
摘要
本文探討分數階次PID控制器之設計問題，其中，積分器和微分器為非整數階次。吾人將決定控制器的三個增益值與二個實數階次，以符合最小化的誤差平方積分(ISE)性能參數，並且滿足所設定的增益邊限與相位邊限制條件。此設計問題將表示成含條件式之參數最適化，而微分演化演算法將應用於搜尋全域之最適控制參數。由於分數階次系統問題尚缺乏時域之解析方法，本文將整合一種有效率的數值方法用以計算ISE性能參數，同時完成頻率響應的穩定性測試。在設計範例中，吾人將對最適的分數階次與整數階次PID，各別用於整數和分數階次程序之情況作性能比較。
關鍵字
無資料並列摘要
In this paper we are concerned with the design of a Fractional-order PID controller which involves noninteger-order integrator and differentiator. The three controller gains and two real orders of the fractional-order PID controller are determined to minimize an integral square error (ISE)performance index while satisfying the specified gain and phase margins. We formulate the design problem as a constrained parametric optimization and apply a differential evolution algorithm to search globally the optimal controller parameters. Due to the problem lack of analytic time-domain analysis methods for fractional-order systems, and effective numerical method is utilized to compute the ISE performance index as well as to check the stability in the frequency domain. Design examples are given to compare the performance of the optimal fractional-order PID controller with the optimal integer-order PID controller in controlling integer-order as well as fractional-order processes.
延伸閱讀
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- 陳佳鴻（2009）。PID控制器之最佳化設計與感應馬達速度控制之研究〔碩士論文，崑山科技大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0025-0608200912034600
- 黃奇、黃志豪、呂政芳（2008）。解析PID控制器設計。化工，55(2)，18-36。https://doi.org/10.29803/CE.200804.0003
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