結合線性近似法則之灰色估測器應用於離散型順滑模態之控制

Abstract

灰色模型GM(1,1)適合用於單一指數變化率的數列估測。然而，對於其他非單一指數變化率或是非單調數列(non-monotone sequence)而言，則需要採用高階的灰色模型或者以其他方法來降低估測誤差。由於高階灰色模型的運算太過繁雜，並不適用於微處理器的即時運算。基於快速運算效能的需求，本論文提出一種簡單而有效的誤差補償方法，來提高估測的精確度。 類似的問題，也可以應用於離散型順滑模態控制(discrete sliding-mode control)系統，其未知範圍的外部匹配式干擾訊號估測。離散型滑模控制針對系統不定值與干擾的穩健性已被普遍證明並加以應用。不過，在實際應用上卻經常面臨無法得知系統外部干擾訊號界限或是干擾訊號太大的窘境。為了解決此一問題，本論文根據可量測的狀態變數、系統動態方程式以及順滑函數，首先透過代數運算，求得系統外部匹配式干擾(external matched disturbance)訊號的歷史資料。然後，再以灰色模型GM(1,1)結合傳統線性近似的補償法則，得到干擾訊號的估測值。接著，以其估測結果作為受控體的前饋控制輸入，並與離散型滑模控制器整合成為離散型灰色滑模控制器(discrete grey sliding-mode controller, DGSMC)。 最後，以模擬的方式說明以灰色估測器應用於離散型滑模控制器的可行性，同時比較GM(1,1)模型經過誤差補償與修正之後的效能。

The grey model GM(1,1) is applicative to the prediction of a monotone sequence. For those multiple-rate or non-monotone sequences, however, it needs another method to alleviate prediction errors by means of a grey model of higher order or some other compensation algorithms. Unfortunately, the use of higher order grey model implies the demand of more complicated computations, and thus makes it difficult for real-time process in microprocessors. To achieve an efficient real-time process, this thesis introduces a novel and simple scheme not only to save the computation time, but also improve the prediction accuracy. The proposed simple scheme is also suitable for the discrete sliding-mode control (DSMC) system to forecast the unbounded external matched disturbances. Recently, the DSMC has been widely adopted to deal with system uncertainties and perturbations. Nevertheless, there often exist quandaries about unknown disturbances in physical utilizations. To overcome this issue, at first, the historical data of external matched disturbances are obtained by algebraic computations based on the measurable states, system dynamic equation, and sliding function. The modified grey model GM(1,1), combined with linear approximation, shows a more precise prediction. The integration of the DSMC and the proposed prediction algorithm results in a discrete grey sliding-mode controller (DGSMC). Numeric simulation results are given to illustrate the feasibility and successfulness of the DGSMC.