Applications Of Modified Differential Evolution In Fractional Order Control Systems

Fractional system is based on the fractional calculus, whose order is extended to theentire complex domain from the traditional integer domain to enrich the phenomenon whichinteger-order system can not accurately describe. The traditional calculus depends only on thelocal features of the function, while the fractional calculus considers the overall informationof the function by a weighted form. In many aspects, applying mathematical model of thefractional calculus can describe the actual dynamic response of the system more accurately, atthe same time improving design, characterization and control capabilities. In recent years,fractional calculus has raised a lot of concerns in various fields, and has begun to play a rolein engineering applications. Fractional control theory is a disciplinary branch that formed byintroducing the fractional calculus into classical control theory. It has proved that thefractional calculus in the control field can produce better results than the traditional integerorder.Differential evolution (DE) is a global optimization strategy based on the laws ofbiological evolution in continuous space. As for the disadvantages of traditional geneticalgorithm, DE uses floating-point encoding and arithmetic operations instead of binaryencoding and logic operations in order to solve the problems of slow convergence anddifficult control parameters determination. After nearly two decades of development, DE iswidely used in a variety of practical problems. Meanwhile, in order to meet the requirementsfor the convergence rate and resistance to premature, a variety of improved DE algorithmshave been formed, not only expanding the range of applications of the algorithm, but alsomaking the efficiency of the algorithm increased.This paper focuses on applications of DE and its improved algorithms in the fractionalcontrol system, the main contents are as follows:A parameter-adaptive improved DE has been proposed, the algorithm can adaptivelyadjust the scaling factor F according to the variance of the population fitness and individualfitness precision. Simulation results show that this method can effectively overcome theprecocious convergence of the traditional DE, in order to prevent the population falling into alocal optimum. As the fractional order system ensures the description precision by increasingthe degrees of freedom, yet will increase the difficulty of identification. In this paper, using the modified DE algorithm proposed, based on the time-domain response data of the systemand designing the rational fitness function, the fractional SISO system can be identified. Thesystem model structure and parameters can be identified simultaneously, and for the systemswith unknown model, it also has a better adaptation. PID controller has three parameters to betuned: proportional, integral and differential coefficient. However, fractional PID controllerintroduces two new variables: differential and integral order, to enlarge the tuning range of thefractional PID controller parameters. As for that feature, the paper selected the ITAEcriterion and weighted function with error and control signal, integer order and fractionalorder objects are analyzed and simulated respectively, and results show that the proposedcontroller meets the accuracy requirements.