Research On Design Of Fractional Order PI～λD～μ Controller And Its Digital Implemetation

Fractional order calculus that is theory expansion of traditional calculus is new field in mathematic study fields. So far, a great achievement has been attained in fractional order calculus, which provides the new theory foundation for the development of fractional order calculus in other subjects.In this paper, fractional order PIλDμcontroller is researched deeply. First, the basic concepts and main properties of fractional order control system and fractional order PIλDμcontroller, the method for modeling fractional controlled system are introduced, coefficients computing and orders searching method.. Second, the methods for design of the parameters of fractional order PIλDμcontroller are concluded, including dominant roots method, gain and phase margin method, and optimization method. Because only three parameters of fractional order PIλDμcontroller can be worked out by dominant roots method and gain and phase margin method, the two methods have the disadvantages. In this paper, a new method called roots and orders searching method for designing the five parameters of fractional order PIλDμcontroller based on dominant roots method is proposed. Simulation outcomes verify that, compared with dominant roots method, fractional-order PIλDμcontroller designed by roots and orders searching method can adjust the controlled system better, and the closed system has better stable and dynamic performances. It is also approved that comparing with integer order PID controller, fractional closed control system with fractional order PIλDμcontroller has better stable and dynamic performance and more robust. Third, the digital implementation methods of fractional order PIλDμcontroller including time-domain and Z-domain numerical methods are researched. Fourth, the effect of parameters variation of fractional order PIλDμcontroller on closed control system is researched. Simulation outcomes verify that, the three parameters, Kp,Ki and Kd of fractional order PIλDμcontroller are same as the parameters of integer order PID controller, and they do same effect in both controllers. Another two parameters,differential orderμand integral orderλdecide differential effect and integral effect respectively.μaffects the overregulation of system andλaffects the steady precision. When the parameters of fractional order PIλDμcontroller vary in small ranges, the performances of the controller almost do not change. It can be concluded that fractional order PIλDμcontroller is more robust. At last, the main conclusion can be validated through real experiment of fractional order PIλDμcontroller.