無過衝、下衝之直流伺服馬達PID控制

Abstract

本論文的主要目的是設計沒有步階響應過衝的三階轉移函數，進而將分析 的過程延伸到要求步階響應為單調漸增的三階轉移函數設計上，配合簡單 的無下衝法則，可適用在一般的直流馬達PID 控制上以及其他三階線性系 統。在分析上，本文以轉移函數的極點類型，依實數、複數或重根上的不 同，將三階轉移函數分成五類，分別從時域的觀點來討論已知極點下的滿 足無過衝和單調漸增的條件。並將這些充要或充分條件以轉移函數分子係 數作為參數表示出來，利用容易圖示的直線及二次曲線組合，決定出適用 的參數範圍，利用該範圍可得到定量的設計。從設計的簡易性和充分條件 包含的廣度考量，本文以轉移函數的分子係數取代零點作為暫態性能的控 制參數，藉由無過衝和單調漸增條件的特徵，可使某些充分條件得到進一 步的改良，而能以簡單的方法涵蓋到更廣泛的適合範圍。 The main objective of this thesis is to design third-order transfer functions satisfying non-overshoot step response. Furt- her, the process of analysis can be used to design third-order transfer functions with monotone-increasing step response.Simul- taneously, by obeying a simple non-undershoot rule, the results could be adopted in the general model of PID control DC motors and other third-order linear systems. In the analytical process, the transfer functions are classi- fied in five cases of poles, which are real, complex or multiple- order poles. In view of time domain, the conditions, the necessa- ry and sufficient conditions or only the sufficient ones, for non-overshoot systems are discussed. Finally the conditions are described in terms of the coefficients of the numerator of tran- sfer functions. Using these conditions to determine the range of the coefficients bounded by the combination of stright-lines and second-order curves, a suitable design can be achieved. For the sake of simplicity and the consideration about the capacities of the sufficient conditions, we substitute the coeff- icients of the numerator for the zeros of transfer functions as the controlled parameters of the transient perfermance index. By the characteristics of the non-overshoot step response curve and the monotone-increasing one, the sufficient conditions can be easily improved to contain.