在灰色預測控制系統中，有兩個重要的因素會影響控制的優劣，分別是灰色建模的精度及預測步距的調整，在灰色建模精度方面，傳統 GM(1,1) 在建模的過程中，利用一些假設及數學近似的技巧，將微分方程的解以離散的型式求出模型的響應，由於預測的資料通常都是以離散化的資料型態呈現，且從連續系統轉換成離散系統也容易產生建模的誤差，因此本研究提出一以差分方程為基礎的建模方式來取代傳統以微分方程為基礎的 GM(1,1) 建模。本研究亦以最佳化方法中的遺傳演算法，來調整模型的待定參數，以提高建模的精度，獲得良好的預測。另一方面在預測步距的調整上，許多文獻，皆指出不同的預測步距會有不同的效果，因此本研究將設計一動態調整步距的方法，來制定適當的步距。
最後本研究將結合灰差分建模及動態的步距調整設計一灰差分控制器，並實際應用於直流伺服馬達之速度控制，以驗證其可行性。
關鍵詞：灰色預測、GM(1,1)、灰色建模、灰差分建模、遺傳演算法

In grey prediction controller, there are two factors will effect the performance in control. Each of them is the precision of grey modeling and the adjustment of grey prediction step. In the grey modeling precision, the traditional GM(1,1) uses some hypothesis and mathematical approximation to transfer the solution of continuous differential equation to discrete difference equation in modeling process. Because of the forecasting sequence numbers of grey prediction are usually discrete sample data and it is easy to produce the error for the transform of continuous system to discrete system. Therefore, our research proposes the difference equation to replace the differential equation in traditional grey modeling in GM(1,1). Also, our research uses the genetic algorithm to adjust the parameters in our model. The other factor of grey prediction controller that will effect the output performance is the adjustment of the prediction step. Many researches point out that different steps will cause different performance. Hence, our research will design a dynamic method to make an appropriate prediction step.
Finally, our research will combine the difference grey modeling technique and the prediction step that using dynamic method to design a difference grey prediction controller. To verify the difference grey prediction controller, our research applies it to DC servomotor for speed control in practical.
Keywords : grey prediction、GM(1,1)、grey modeling、genetic algorithm difference grey modeling

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