| 摘要: | 本論文將探討灰色預測模型GM(1,1)之數學架構以及將應用於數位控制系統上，因而必須改良一般傳統灰色預測模型GM(1,1)所無法表達在數位控制系統上的影響因素，即取樣時間(T)的影響，此影響因素取樣時間(T)不僅是影響數位系統穩定的重要因素，也是有別於連續性控制系統的一個重要指標。因此，本論文將分析模型GM(1,1)的數學結構，且基於分析後所得到結果，因而定義出原級比值來作為使用灰色預測模型GM(1,1)的判斷依據。再進一步討論，將灰色預測模型GM(1,1)應用於數位系統上的改良型灰色預測模型，改良後的預測模型可以借由調整取樣時間(T)來改善傳統灰色預測模型的預測精確度，其改善的關點是使原始資料訊號的原級比值所構成的曲線趨勢變的較平滑，越平滑的曲線趨勢其預測的效果越好，且在本文中將提出一般應用於數位控制系統上的兩種灰色補償結構，並藉由調整取樣時間(T)的變化來觀看這兩種灰色補償結構的補償情況。 In this dissertation, we will explore the mathematical structure of gray prediction model GM(1,1) and will extend it to digital control system. In general, a traditional gray prediction model GM(1,1) which can not be used to express the sampling time and it is the affecting factor of stability of digital control systems, as well as it is an important index in contrast to analog systems. This work will analyze the mathematical structure. Based on the outcome of analysis, an original class rate is then defined and is used to decide whet hen the gray prediction model GM(1,1) is utilized to be adopted. Therefore, the model GM(1,1) has to be modified into the model GM(T,1,1). The model GM(T,1,1) is applied in the digital control systems, and the model GM(T,1,1) can improve the gray prediction model GM(1,1). The precision of the improved gray model GM(T,1,1) is modulated by the sampling time. The original data are used to construct a curve, which can enhance the precision of the original model (GM(1,1)). If the curve is smooth, then the GM(1,1) will have an accurate prediction. This work addresses two gray structures, and the compensation circumstances are observed by adjusting the change of the sampling time. |
