多變數動態系統之遞迴系統判別法則

Abstract

本論文主要目的在於建立一個線性多變數動態系統之遞迴系統判別法則。 基本上，本論文先對多輸入單輸出系統發展出遞迴最小平方估計法則而對 多輸入多輸出系統的判別，則是先針對每一個輸出所形成的多輸入單輸出 子系統一一判別出來之後，再利用最小實現法得出最後結果。由於多變數 系統的標準型並非唯一，在此我們引用奇異值分解的觀念。因為它穩定的 特性使得在此遞迴法則中，新的判別結果與先前已被判別出的數學模型間 ，僅有微小的修正。此舉正有利於日後控制法則的建立。模擬的結果顯示 此遞迴法則能平順地估計出系統參數並可收斂到正確值。 The main goal of this thesis is to develop a recursive (on- line) identification algorithm for linear multivariable dynamic systems. Basically, procedures for recursive least-squares estimation are developed for a multi-input single-output (MISO) system. For a multi-input multi-output (MIMO) system, modeling algorithm is accomplished by first identifying the MISO subsystems associated with each output of the MIMO system and then by minimal realization. Since the canonical form of an MIMO system is not unique, we introduce the concept of singular value decomposition (SVD) in the recursive scheme. Because of the stability property of SVD, the algorithm can provide a stable series of canonical forms, in which the new identified one is modified slightly from the previously identified one. Thus, the identification can be accomplished after all. The results of simulation show that the recursive scheme can estimate system parameters smoothly and converge to the exact values of these parameters.