Design And Application Of The Controller Based On The Theory Of Fractional Calculus

Fractional calculus theory is a new calculus theory which expands the calculus orderform the traditional integer to real numbers and even to the complex domain. With thedevelopment of society, design of the high-performance controller is more and morenecessary. Due to the superiority of the fractional calculus theory compared to integer one,The fractional order controller can meet this demand. Fractional order controller is a newresearch direction based on the fractional calculus operator and the fractional orderdifferential equations in the theory field of control.This paper first introduces several common methods of the fractional calculus operatorapproximation. Propose a new method of fractional calculus operator approximationmethod which based on the method of Oustaloup and the method of continued fraction.Then the corresponding Bode diagram is analyzed. According to the bode diagram thecurve of the new method is closer to the ideal curve than others.Secondly, this paper introduces two common conventional intelligent algorithms oftuning the PID controller parameters, named Particle Swarm Optimization and bacterialforaging algorithm. Then the dimension of both algorithms is expanded which can be usedto tune the fractional order controller. In this chapter some work is done for improving theglobal search ability of the two algorithms. The simulation results show that the improvedalgorithm has better parameter tuning results. According to the superiority features of antcolony algorithm in finding the function extreme an ant colony algorithm is designed whichcan find the time domain performance ITAE optimal value in tuning the fractional ordercontroller. The Simulation results show that this new intelligent algorithm is feasibility andapplicability.Finally, in some papers it is easily found that model predictive controller is good athandling large delay controlled objects and fractional order controller is adept in dealingwith inertia link which can achieve fast response. Then a controller is designed whichcombines the advantages of model predictive controller and fractional order controller. Thesimulation results show that the new controller has a superior performance when treat thecascade system. In the last chapter a fractional controllerPI λis designed based on theintelligent algorithm. Simulation and experimental results show thePI λcontroller has abetter speed tracking performance compared to conventional PI controller in controlling the speed loop of PMSM. Also for handling the speed loop of PMSM, a new control strategy isdesigned based on the fuzzy control theory which can adjust the fractional controllerparameters online and the simulation result shows that the new control strategy has a bettercontrol effect compared with the conventional PI controller.