高取樣頻率下之系統判別法則性能分析實驗與時延連續系統之參數估測

Abstract

近幾年來，由於數位電腦的廣泛使用，連續系統的主要控制技術與系 統判別方法已經走向數位化。而在數位化的情況下，為得到更好的控制效 果，我們可加快取樣頻率來達成它。但由於在實際數位計算時之有限位元 因素影響，一般以Shift model為基礎之最小平方估測法則，在高取樣頻 率及/或多參數情況下將導致數值上的錯誤發生。另一方面，若系統在我 們的判別過程中發生時間延遲的情形，但時間延遲參數卻未於估測模式中 被加以考慮，這對估測結果的影響程度，將隨著訊號頻率及取樣頻率的提 高而愈見其嚴重性。 在本文中，吾人採用Delta運算子來描述離散 時間模式。從硬體的實驗中，其結果顯示在高取樣頻率及/或多參數的判 別情況下，Delta model在數值上的計算及其估測結果都優於傳統的Shift model。同時實驗結果也指出由Delta model估測所得之結果，其將隨著取 樣頻率的提高而更加精確。此外，我們亦提出一個對時延參數小於一個取 樣間隔的時延連續系統的判別方法。而從電腦模擬與實驗的結果，其說明 了我們的方法是正確且可行的。吾人之研究成果對適應控制、系統監控等 ，都有相當之重要性。 In recent years, with the widespread use of the digital computers,the main control techniques and system identification methods for the continuous-time systems have been discretized. Moreover, we may raise the sampling rate to achieve a better control performance. However, since of the finite word length effect in practical computation, high sampling rate and/or a large number of estimation parameters will result in numerical errors for the usual least squares estimation based on shift model. On the other hand,if the pure time-lag occurs in the identification process and that is not taken into consideration at estimation model,the influence on the estimated results will be serious as the sampling rate increases. In this thesis, we take the delta operator to formulate discrete-time model. From hardware experiments, the results show that the delta model is numerically superior to the usual shift model under high sampling rate and/or for a large number of estimation parameters. Also, we have shown that the accuracy of estimated delta model improves as sampling rate increases. Moreover, we propose a new identification method to estimate the continuous-time system with unknown time-lag which is shorter than one sampling interval. The simulation and experimental results conform that our algorithm. Our identification methods are valuable in adaptive control, system monitoring, etc.