标题: 变动区间系统PID控制器之设计
Design of PID Controller for Interval Plants
作者: 陈俊光
Jung-Guang Chen
邓清政
Ching-Cheng Teng
电控工程研究所
关键字: PID控制器;变动区间系统;PID controller;Interval Plants
公开日期: 2001
摘要: 摘 要
以往的古典控制理论,乃是利用一些基本方法如根轨迹图(Root Locus)、罗斯稳定准则(Routh Stability Criterion)、奈氏图(Nyquist Plot)、波德图(Bode Plot)及尼可图(Nichols Chart)来判断固定参数受控体(Plant)的稳定性,并依据所需规格(时域或频域)来设计控制器。
本论文先介绍变动区间系统的相关理论,包括Kharitonov定理、Mikhailov准则、剔零原理(Zero Exclusion Principle)及极值系统(Extremal System)等,并讨论变动区间多项式的稳定度。
然后将变动区间系统套入奈氏图、波德图及尼可图中,讨论该系统的稳定度,并定义增益边限(Gain Margin,GM)及相位边限(Phase Margin,PM)。
最后则是以基本的二阶变动区间系统为主,配合增益波德图的上边界(upper bound)及相位波德图的下边界(lower bound),透过简单的数学推导,来设计符合所需规格的PID控制器,并举例说明如何设计,再以奈氏图、波德图及尼可图来检查受控系统补偿后的稳定度。并且说明本论文所提方法优点及可行性。
ABSTRACT
In classic control theory, we can usually apply methods including root locus, Routh stability criterion, Nyquist plot, Bode plot and Nichols chart to design the controllers such that the resulting systems meet the specifications of time or frequency domain.
In the thesis, we first introduce some theory about interval system including Kharitonov theory, Mikhailov criterion, zero exclusion principle and extremal system to discuss the stability of interval parametric polynomial.
Then, we use the methods of Nyquist plot, Bode plot and Nichols chart to check the stability of an interval system and define the gain and phase margins.
Lastly, we use the upper bound of Bode plot in gain and the lower bound of Bode plot in phase to design a PID controller of an interval system. We also use Nyquist plot, Bode plot and Nichols chart to check the system stability after compensation.
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT900591046
http://hdl.handle.net/11536/69419
显示于类别:Thesis