應用QFT於變動參數系統之PID控制器設計

Abstract

在現實世界中，任何系統都含有不確定因素，無論是外在環境改變，或人為操作過程產生誤差，或系統本身(元件，材質)等因素，皆會使系統產生變化，因此現實受控系統並不如我們所學習之典型控制中所描述之固定參數系統。本論文應用量化回授理論(QFT)之設計方法在尼可圖上(Nichols chart)，繪出“一片”符合開迴路邊界之開迴路轉移函數曲線，每一條曲線軌跡即代表一個PID控制器，並利用次序最佳化(Ordinal Optimization)理論，以盲目選擇法(Blind Pick)，選出一相位邊限(phase margin)或增益邊限(gain margin)最小之PID控制器，使變動參數之受控系統經由此PID控制器控制後，系統輸出響應能符合規格之要求。

In practical world, there are uncertainties in any control system. These uncertainties occur due to models themselves or the environment which the equipments are exposed to changes. So, we can not view the plants as fixed parameter plants which we learned in classical control system. In this thesis, the Quantitative Feedback Theory (QFT) design methods are used to draw a band of open-loop transfer function curves which satisfy the open-loop specification bounds on Nichols chart. Each curve represents a PID controller. Then we utilize the Blind Pick (BP) in Ordinal Optimization theory to pick the worst PID controller among the PID controllers which we had drawn.” Worst” here means the gain margin (GM) or the phase margin (PM) of the designed system is the smallest one. Though the PID controller we had chosen, the output response of the parametric uncertain system meets whether the time domain specifications or the frequency domain specifications.