參數空間法用於PID控制器之分析設計

Analysis and Design of PID Controllers Using Parameter-space Method

吳彥達(Yann-dar Wu)

指導教授 ： 韓光渭

元智大學/工程學院/電機與資訊工程研究所/碩士(1997年)

摘要

PID控制器被成功的用於工業界已有許多年了。其主要的優點是
架構簡單、有較好的模型誤差（modeling error）強健性、且很容易的
被實現（詳如附錄一）。另外，對於程序控制系統，這些控制器可由線
上所得到的即時資料（on-line data）來自動調整。由於具有這些優點
，有關之PID方面的研究工作在過去幾年相當的活躍。在Park先生等人
的文獻中有一較簡明的歷史回顧。本論文之主要目的是應用增益相位邊
際測試器和穩定方程式的方法作PID控制器設計，使系統能達到所要求
的增益邊際和相位邊際規格。另外本論文與一般文獻不同之處是用二自
由度的系統架構，在PID控制器之外，另加一個前置濾波器，同時考慮
干擾對系統的影響，並找出在系統規格內較佳的控制器參數。文中以鋼
板滾壓自動厚度控制系統和兩個飛機控制系統的例子來作設計，對所設
計結果，都用波德圖和時域響應來作對正。

關鍵字

PID控制器 ； 參數空間法 ； 增益邊際 ； 相位邊際

並列摘要

It is well known that the PID controllers have been
successful used in industry for many years.The advantages of
using PID controllers are : simple structure, robust to
modeling error, and easy to operate. Inaddition, for process
control systems, these controllers can be tuned automatically
using on-line data obtained from relay feedbacks. Due to
these advantabes has the research works are quite achive in
recent years. A brief hystorical review was given by Park et
al.The main purpose of this thesis is to design PID
controllers, by use of the gain-phase margin tester and the
stability-equation method, to meet specifications on
gain-margin and phase margin. In addition to the PID
controller, a prefilter is added, to make a system to have a
two DOF structure, then the effects of disturbance can be
considered, and the base values of parameters of the
controller can be found. For illustration, a steel mill
automatic-gauge-control system and two aircraft flight
control systems are considered. All the obtained results
are checked with Bode diagrams and time-domain responses.

並列關鍵字

PID Controller ； Parameter Space Method ； Gain Margin ； Phase Margin

參考文獻

[1] Wang, L., Cluett, W.R., "Tuning PID controllers for integrating processes," IEE Proc.-Control Theory Appl., Vol. 144, No. 5, pp. 385-392, September 1997.

[2] Wang, Q.G., Zou B. Lee, T.H., and Bi Q., "Auto-tuning of Multivariable PID Controllers from Decentralized Relay Feedback," Automatica, Vol.33, No.3, pp. 319-330, 1997.

[3] Park, J.H., Sung S.W. and Lee, I.B., "Improved Relay Auto-tuning with Static Load Disturbance," Automatica, Vol.33, No.4, pp. 711-715, 1997.

[4] Bi, Q., Wang, Q.G. and Hang C.C., "Relay-based Estimation of Multiple Points on Process Frequency Response," Automatica, Vol.33, No.9, pp. 1753-1757, 1997.

[5] Ho, W.K., Gan, O.P., Tay, E.B. and Ang, E.L., "Performance and Gain and Phase Margins of Well-Known PID Tunning Formulas," IEEE Trans. on Control Systems technology Vol.4, No.4, July 1996.