基于参数稳定裕度的低阶数字控制器设计

Design of a Low-Order Digital Controller Based on Parametric Stability Margin

工业中的控制系统大多含有复杂的不确定性,其模型参数有时会发生一定的波动.针对系统模型参数辨识不准确或发生波动的情况,需尽量选取控制器参数稳定域中稳定裕度最大的一组参数,以保证闭环系统的稳定性.根据工业中被控对象在工作点附近运行时的特点,基于二阶不确定数字控制系统进行比例-积分-微分(proportional-integral-derivative,PID)控制器设计.根据闭环系统稳定性条件给出PID参数稳定域的求解方法,其由一族平行的凸多边形构成.将坐标轴进行旋转,使构成稳定域的凸多边形垂直于其中一个坐标轴.利用线性规划方法,求出每个凸多边形的Chebyshev中心及其深度,选择深度最大的Chebyshev中心坐标.利用坐标轴逆旋转变换求出其在原坐标系下的坐标,即为对应的控制器参数.

Most control systems in the industry contain complex uncertainty and their model parameters sometimes may fluctuate.For inaccurate identification or fluctuation of system model parameters,the set of controller parameters with the largest stability margin in the parameters stabilizing sets should be selected in order to ensure the stability of the cloosed loop system.According to the characteristic of plants in industry when they run near the operating points,the proportional-integral-derivative(PID)controller is designed based on the second-order uncertain digital control system.First of all,the PID parameters stabilizing sets composed of a family of parallel convex polygons are obtained according to the stability condition of the closed loop system.Then coordinate axes are rotated to make the convex polygons perpendicular to one of the coordinate axes.Next,the Chebyshev center and its depth of each convex polygon are obtained by making use of the linear programming method.Finally,the coordinate of the Chebyshev center with the maximum depth is selected,and its coordinate in the original coordinate system is obtained by using the inverse axis rotation transformation,which is selected as the corresponding controller parameters.