Fractional Order Controller Design Method For Unstable System And Application Research

In view of the control problem for the unstable system,the traditional control method mainly adopts the PID control method.Although the traditional PID controller can stabilize unstable controlled objects,due to the existence of the right half part of the complex plane,the dynamic response characteristics of the system are not ideal after compensation.In this regard,this paper introduces the fractional order PID control method,the fractional order PID controller is the traditional integer order PID(IOPID)controller calculus operator'order extended to the fraction,it can more flexible control controlled object than the IOPID controller,so the fractional order PID controller has better dynamic response characteristics than the IOPID controller.For the fractional PD~?(FOPD)controller,this paper takes Bode ideal transfer function as the objective function to solve parameter,to match the open-loop transfer function and Bode ideal transfer function's amplitude,phase angle and Nyquist curve slope in the cut-off frequency ?_c,this method can solve controller parameters which has 3 elements.For the fractionalPI~?D~?(FOPID)controller,according to the Bode ideal transfer function's phase does not change with the frequency,this paper added two phase conditions in non cut-off frequency,proposed a FOPID parameters tuning method for unstable system.The unstable system can be abstracted as a set of systems whose center of gravity is on the top and the fulcrum on the below.The inverted pendulum system is a typical model of this kind of system,and it is also an ideal controlled object to verify the control method for the unstable system.The design method of fractional order controller for unstable system which proposed in this paper is applied to the linear inverted pendulum system(the pendulum transfer function is second-order system)and the single stage rotary inverted pendulum system(both the rotary arm and the pendulum transfer function are fourth-order system)to verify the stability control effect.For the linear inverted pendulum system,the FOPD controller and FOPID controller are designed for the transfer function of the pendulum and compared the response curve of pendulum with the IOPID controller.The results show that the stabilizing control effect of the FOPID controller is better than the other two controllers.For the single stage rotary inverted pendulum system,firstly analyzed swing pendulum control,take the idea of building energy function to design the swing pendulum controller.Then analized stablization pendulum control,due to it is a single input and double output system,the double closed-loop fractional PID control strategy is used to control the pendulum,and then designed FOPD controller and FOPID controller for the rotary arm transfer function and the pendulum transfer function.Finally,the above design controller is applied to the Quanser company's single stage rotary inverted pendulum hardware in the loop simulation platform and compared with the IOPID controller's control effect.The results show that the tracking and stabilizing control effect of the FOPID controller is better than the other two kinds of controllers,with the minimum tracking error of 1.6 degrees and the minimum peak peak of 1.2 degrees.