A Design Method of the Parameters of Fractional-order PI^λD^μ Controller -Poles-Orders Searching Method

Fractional-order PI^λD^μ controller expands the orders of integrator and differentiator of classical integer-order PID controller into fractional order.A PID controller can be designed flexibly by using the two parameters μ and λ.In this paper,an effective method for tuning the parameters of fractional-order PI^λD^μ controller-the poles-orders searching method-is proposed.The fundamental principle of the method is as follows: firstly proportional parameter K_P of the fractional-order PI^λD^μ controller is estimated;secondly a pair of poles with better stability measures are designed;thirdly the searching ranges of μ and λ are estimated;finally the known parameter K_P and the poles are introduced into the characteristic equation of fractional control system,and a group of parameters of the fractional-order PI^λD^μ controller in the ranges of μ and λ are found,which can meet performance requirements of the fractional control system in time domain.The simulation verifies that the fractional-order PI^λD^μ controller designed with poles-orders searching method can adjust the controlled system in a better way.