Research On Design Method Of Fractional Order Controller

With the deepening of fractional order(FO)calculus theoretical studies in recent years,the theory of fractional calculus and control theory have attracted many scholars' attention in control areas,especially the FO-PID control,which combined the fractional theory with conventional integer order IO-PID controller.Compared with the traditional IO-PID controllers,the FO-PID controllers make the controller parameter tuning range of variable,and the possibility for a better control performance of the system was provided.However,the difficulty of controller parameter tuning was increased because of the fractional order.So it becomes a hot topic in the control area to design the FO-controller,which is simple in design,convenient in parameters tuning and strong in robust.In this paper,for IO systems,FO systems,FO processes with time-delay and high order processes,the design method of the FO-controllers were surveyed respectively.(1)For the IO systems,a design method of FO-(PID)? controller based on the principle of internal model control(IMC)was proposed.An FO-(PID)?controller was deduced by using the FO filter,and the controller only contained two adjustable parameters.So,the difficulty of FO-controller tuning was effectively reduced.Then,according to the phase stability margin index ?m and cut off frequency ?c of the system,the parameters tuning of FO-(PID)?controllers were realized.(2)For the FO systems,a design method of FO-PI?D? controller based on Bode's ideal transfer function was proposed.Firstly,the relationships between the gain K and the fractional calculus order y of the Bode's ideal transfer function and the dynamic performance and robustness of the system were analysed.Then,the Bode's ideal transfer function was chose as the reference system,and the order of the controlled object was selected as the fractional calculus order of the controller.Moreover,according to the dynamic performance and robustness of the system,the gain K of the PI?D? controller was tuned.So,the rules of the controller tuning were specified.(3)For a class of FO processes with time-delay,a designing method of FO-controller was raised.Stability of the processes was analyzed,and FO controller based on the IMC principles was presented.The the only one adjustable parameter can be derived by the maximum sensitivity index,and robustness of the system could be ensured.(4)For high order processes,a designing method of FO-controller was presented.Firstly,the model of high order processes was reduced by particle swarm optimization(PSO)technology,and then an FO-controller was designed for expected simplified FO-model based on the IMC principle.The controller has only one adjustable parameter,and the defects of FO-controller such as including more parameters and tuning complex were effectively overcome.Moreover,a robustness index and the analytical expression with only one controller adjusted parameter were given,and the robust tuning of the controller was realized.(5)For FO processes with time-delay,a design method of two degree of freedom FO-controllers based on IMC was proposed.IMC principle is used to design two-degree-of-freedom FO-controller and analyzed robust stability of systems with uncertain process parameters.Two adjustable parameters were adjusted independently based on the setting tracking characteristics and robustness of the system.The simulation results show that the proposed method was effective.