时滞系统PID控制器参数稳定域的实现

Realization of PID Controller Parameter Stable Regions for Time Delay Systems

基于广义Hermite-Biehler定理,运用时滞对象的逆Nyquist曲线,可确定PID控制器比例增益的稳定范围。在积分和微分增益平面上,针对多条边界直线,提出一种逆时针规律的判断方法,可快速确定该二维平面上参数的稳定区域,从而给出了一种确定时滞系统PID控制器参数稳定域的新算法。该算法适合软件实现,仿真实例验证了该算法的有效性。

Based on generalization of the Hermite-Biehler theorem,the stable regions of proportional gain of PID Controller can be determined by the inverse Nyquist plot of the time delay plant.In the integral and differential gain plane,an anti-clockwise rule of judgment method is proposed for more than a boundary line.It may quickly determine the parameter stable regions in this two-dimensional plane.Thus a new approach is given to determine the stable regions of PID controller parameter space for time delay systems.The given algorithm is suitable for software realization.The simulation examples demonstrate the validity of the proposed algorithm.