时滞对象PID控制器的参数稳定域求解方法

On Stabilizing Sets of PID Controllers for Time Delay Systems

研究时滞对象的PID控制器的参数稳定域的求解方法,通过引入Rekasius变换简化时滞特征多项式,并得到稳定域边界上PID控制器的3个参数所满足的方程。通过引入正弦变换,将对控制器参数在无穷范围内的遍历转为有限范围内的遍历,而特征多项式中的已知时滞被用以检验所遍历的点是否在稳定域边界上,在得到所有可能的稳定域边界后,使用Nyquist稳定性判据确定实际的稳定域。该方法适用于任意形式的单时滞对象,为实际应用中PID控制器的参数整定提供理论依据。

The problem to get the parameter stabilizing sets of PID controller with dead-time is studied. All possible values of control parameters are found out, which will result in pure imaginary roots of closed loop characteristic equation under all process parameters fixed. A simplifying substitution is used for delay component and the implicit equation of the PID parameter on the stability boundary is obtained. The ergodie search of PID control parameters are converted from the range of infinity to finite range by introducing trigonometric tangent function. After obtaining all possible stability boundaries, the Nyquist stability method is used to determine the actual stability region of the controller parameters. An illustrative example shows the effectiveness of the proposed method.