Abstract
A solution to the following fundamental problem is presented in thisthesis."Given an adaptive controller with certain robustness properties, what isthe "size" of the class of plant uncertainties for which the stability ofthe adaptive closed-loop system can be ensured? and, if possible, find anassociated residual set for the tracking error."In more precise words, an adaptive control algorithm for the adaptivetracking problem, which requires no persistently exciting signals, and nopositivity condition needs to be checked, is proposed, for plants withbounded disturbances and nonlinear, time-varying, note necessarily stablefraction-type unmodeled dynamics. Then by virtue of an interestingstability theorem established here, it is shown that provided unmodeleddynamics are within an easily computable extent of permissible unmodeleddynamics, the adaptive close-loop system is guaranteed to be globallystable and, meanwhile, the tracking error will convwerge to an associatedresidual set (easily computable also), whose size is directly related tothe size of the relative dead zone and an assumed known magnitude upperbound on bounded disturbances; moreover, by comparing them with those forthe nonadaptive robuse control, both of them are, modestly, tight.Last but not least, a practical example is presented to illustrate theeffectiveness of the algorithm to complement the theoretical developments,wherein a converted lathe lathe is controlled by the strategy of theConstant Turning Force Adaptive Control (CTF AC); encouragingly enough, itis seen that, even when the cutting depth drastically varies duringoperation, good results are still obtained.本文針對下面問題提出一個答案．”給定一強健適應控制器，問它所能承受的未模式化動態（unmodeled dynamics）有多”大”（即尚能穩定受控廠）？並且，如果可能的話，找出一個相對應的追蹤誤差收斂區間．”較嚴密的說，本文針對受到均勻有界干擾和具有非線性，時變，及不一定穩定的分數型（fraction-type ）未模式化動態的受控廠，考慮追蹤的問題；文中提出一不需恆激（persistently exciting）外加輸入且不需驗證任何正實性（positivity ）條件的強健適應控制器．接著，運用吾人於文中所提出的穩定性定理，可證只要未模式化動態的”大小”小於一事先確知的範圍（很容易計算），即可確保整個閉迴路系統的全域（對任何初始條件）穩定；並且，可事先確知追蹤誤差的收斂區間（也是很容易計算），其中區間的大小直接和相對不作用區（relative dead zone）的大小及干擾的上界有關；而且，上述可事先確知的範圍和收斂區間大小經由和文中所導強健控制對應結果比較，結果令人滿意．最後但並非不重要，將上述強健適應控制器應用於定切削力車床適應控制系統的模擬，以配合本文發展的理論；結果顯示，即使切削過程中切深有很劇烈的變動，它仍能確保整個閉迴路系統有很好的性能．