交流伺服系统的一种PIλDμ控制器设计方法

A Method of Designing PIλDμ Controller for AC Servo System

针对交流伺服系统,建立了数学模型,并设计了一种分数阶PIλDμ控制器设计。在利用传统PID参数整定方法确定比例增益k p、积分增益k i和微分增益k d的基础上,结合相位裕度定义,在相位裕度和截止频率给定的情况下完成积分阶次λ和微分阶次μ的设计。在求解积分阶次成λ和微分阶次μ时,采用一种简单易行的图解方法,巧妙地将求解一组非线性方程的问题转化为绘制两曲线求交点的问题。仿真结果表明,相对于传统PID控制器,本文设计的PIλDμ控制器,跟踪响应快,抗干扰能力强,鲁棒性好。

The mathematical model of AC servo system is built,and a method of designing fractional order PIλDμ controller is proposed for AC servo system. On the basis of the proportional gain kp,integral gain ki and derivative gain kd are obtained by using the classical PID tuning method. The fractional order of integrator A and fractional order of differentiator/x with the given phase margin and gain crossover frequency are given with combination of the phase margin specification. A graphical method is used when the fractional order of integrator A and fractional order of differentiator μ are obtained, and the method transforms the problem of solving a set of nonlinear equations into finding the intersection point of two graphs. The simulation results show that the proposed method has faster re- sponse, stronger anti-interference and better robustness than the classical PID controller.