Design And Implement Of Fractional-order PID Controllers

The concepts of fractional calculus (FC) appeared three hundred years ago, however the research of fractional-order control theory is a new field in the area of control systems study. So far, a great achievement has been achieved in fractional-order calculus, which provides the new theory foundation for the development of fractional calculus in other subjects. With the development of industry, there are always heavy demands to the industrial process control mathematical models. The traditional integer-order controllers for some system may not be sufficient in control tasks. At the same time, with the rapid development of computer technology, in recent years, it is remarkable that the increasing number of studies related with application of fractional-order controllers, especially PIλDμ controllers, in many areas of science and engineering. Further research activities are running in order to develop new analysis and design methods for fractional-order controllers based on extension of traditional PID control theory.In the thesis, fractional calculus and control theory knowledge are adopted to design fractional-order controllers. The main contents are as followed:Firstly, the ideas in fractional calculus are systematically introduced, including:the basic functions have been extensive used in fractional calculus, the definitions of fractional calculus, the nature of fractional order calculus, the basic transformation formula and approximate methods the Oustaloup approximate method is chosen as the approximate algorithm in subsequent chapters.Secondly, the impact on system performances caused by the change of the parameters in fractional-order controller are analyzed and summarized. Through the simulation analysis it can be seen that the impact or the fractional-order controller parameters Kp, Ki, Kd are the same as those in the integer-order PID controllers. Because fractional-order PIAD" controller has the integral order λ and differentiation order μ, so it has more control contributions and more flexible than the integer-order PID controllers.Thirdly, a fractional-order PIλDμ controller tuning algorithm in frequency domain is presented. The presentation starts from design of simple fractional-order PDμ controller to and then is extended to design of fractional-order PIλDμ controllers. Through the simulation analysis the control effect of this kind of method to design the controller is validated. Simulation results show that fractional-order controllers may achieve can get better response speed, steady state performance and robustness than the integral-order PID controllers.At last, a method of fractional-order PIλDμ controller tuning based on genetic algorithm (GA) is presented. Since GA has been widely used in control research, and the integral-order PID controller has achieved the excellent control behavior in practical control. So GA is applied to the tuning of both integer-order PID controller and fractional-order PIλDμ controllers. Simulation results show that fractional-order controller can get better performance than integral-order PID controllers.