Research On Integrated Design Method Of Fractional Order Compound PID Type Controller

As an important branch of mathematics,fractional calculus has been widely used in mathematics modeling,automatic control,signal processing,fluid control,biomedical engineering and so on.People realized that many systems existing in nature are fractional,the capacities are fractional,and even the human bodies are fractional with the deep discussion on the fractional calculus.Besides,fractional order systems can achieve better control performance only through fractional order controllers,so the design of fractional order controller is a crucial topic.In all fractional order controllers,fractional order PID type controllers are widely used fractional order controllers,not only inheriting the advantages of traditional PID controllers,but also have more adjustable parameters,so they can achieve more flexible and precise control performance.However,the design algorithm of the fractional-order controller is complex and the parameters tuning is difficult,so there need simpler controller's parameters tuning method.This paper focuses on the problem of designing a class of fractional order PID type feedforward-feedback controller.Firstly,a design method of fractional order PID type closed loop negative feedback controller is proposed by using the Bode's ideal transfer function.Then a mathematical model of DC motor is built,using this method to design a controller to control the DC motor and to validate it by MATLAB.It can be seen from the simulations that the proposed fractional order controller achieves excellent performance with reasonable overshoot,short rise time(fast response)and stronger robustness compared with other controllers.Secondly,from the closed loop feedback control to the feedforward control which is often neglected,a tuning method of all parameters adaptive fractional order PID type iterative learning controller is proposed by using flat phase method,fractional order iterative learning control and impulse response invariant discretization method which is first combined flat phase method with fractional order iterative learning control schemes.This method uses three formulas to tuning the three parameters of the fractional PID controller.Here,not only the correlation formula is deduced,but also the first order fractional order system,the second order fractional order system and the unknown structure system(Black box system)is used to verify this method.It can be seen from the simulations that the controller designed by this method can maintain its excellent performance and realize zero tracking error when the system parameters change in a certain range.In addition,combining the flat phase method with the manual method can also ensure the convergence and convergence speed of the fractional second order system and the black box system.Finally,combining fractional order feedback control with fractional order feedforward control,a designing method of fractional order feedforward-feedback controller is proposed.This is the ultimate goal of this paper.By selecting the first order system in the fractional iterative learning feedforward control as the controlled plant and retaining the fractional iterative learning feedforward control strategy,a feedback controller desining by the method of Bode's ideal transfer function is added in the control system.At the same time,a number of numerical simulations are built to valid the efficiency of this method.The simulation results show that the proposed controller does not change the convergence of the iterative learning control algorithm in feedforward control and can enhance the robustness of the system on the basis of preserving its adaptability.In general,the method of designing fractional order feedforward-feedback PID type controller in this paper is a comprehensive method which combines the advantages of feedback control and feedforward control.A lot of simulations validate the effectiveness of this method.