發展一模糊比例微分控制器最佳化演算法於工程最佳化問題

Developing a Fuzzy Proportional-Derivative Controller Optimization Engine for Engineering Optimization Problems

劉子吉(Tzu-Chi Liu)

指導教授 ： 徐業良

元智大學/工程學院/機械工程學系/博士(2006年)

https://doi.org/10.6838/YZU.2006.00234

摘要

本研究提出一模糊比例微分控制器最佳化演算法以解決工程最佳化問題，工程設計問題通常有兩個特性：設計變數在目標函數與限制條件常具有單調性。而且，此目標函數與限制條件常為內隱式函數，也就是不能以設計變數來表示其外顯形式。
傳統的數值最佳化演算法在處理工程最佳化問題時將其視為一單純的數學問題，而工程方面的相關知識往往將其忽略，發展此模糊比例微分控制器最佳化演算法於工程最佳化問題，此動機為取代使用單純數值資訊來獲得新的迭代設計點，並運用模糊規則將工程知識如設計變數的單調性與限制條件的有效性，導入至最佳化演算法之中。
本論文發展此模糊比例微分控制器最佳化演算法透過三個階段，在前兩個階段之中，此最佳化演算法使用一最佳化準則方法來解決特定的工程最佳化問題。在第三階段中，則是將此模糊比例微分控制器最佳化演算法應用至一般的工程最佳化問題上，而此問題具有單調性的特性，並且，這些應用的工程最佳化問題亦常見於文獻之中來驗證最佳化演算法的實用性，最後，運用本論文發展的模糊比例微分控制器最佳化演算法都可成功的獲得最佳解，且在不同的初始值與移動限制下此最佳化演算法亦有不錯的強健性。

關鍵字

最佳化 ； 工程最佳化演算法 ； 模糊控制器

並列摘要

This paper proposes a fuzzy proportional-derivative (PD) controller optimization engine for engineering optimization problems. Engineering design problems have two characteristics: the design variables are often monotonic in the objective function and constraints. Moreover, the objective function and constraints are often implicit functions which cannot be expressed explicitly in terms of design variables.
Traditional numerical optimization algorithms treat engineering optimization problems as pure mathematical problems. Engineering heuristics are totally ignored. The idea of using the fuzzy PD controller in engineering optimization is that, instead of using purely numerical information to obtain the new design point in the next iteration, engineering knowledge, such as monotonicity of the design variables and activities of the constraints, are be modeled in the optimization algorithm using fuzzy rules.
The fuzzy PD controller optimization engine is developed through three stages. In the first two stages, the optimization engine is applied to solve engineering optimization problems with optimality criteria methods. In the third stage, the fuzzy PD controller optimization engine is extended to apply on more general engineering optimization problems with monotonicity. Several engineering design optimization problems commonly seen in research literature are used to demonstrate the practicality of the fuzzy PD controller optimization engine. Numerical optimal solutions are successfully obtained in all problems. The fuzzy PD controller seems to be robust to various initial design points and move limits.

並列關鍵字

Optimization ； Engineering Optimization Problems ； Fuzzy Controller

參考文獻

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