Parameter Identification Of Fractional System And Design Of The Fractional Order Controller

Fractional calculus with arbitrary fraction order, is different from the regular integercalculus, and it is a generalization of the regular integer calculus. Fractional calculus hasthe following advantages:(1) Fractional calculus has overall importance, and thefractional calculus can reflects very nicely the property, that the development of systemfunction depends on the history of the system;(2) The fractional calculus can describeaccurately the dynamic behavior of complex system and model it, and it overcomes theshortcoming that the regular integer calculus is inaccuracy to the description of thecomplex system. Therefore, the fractional calculus is applied to various fields. This papermakes a study of the identification of the fractional order system and the design offractional controller. This paper fulfills the following work:First, this paper proposes a method to solve the problem of parameter identification ofcommensurate fractional-order chaotic system. Firstly, the state vectors of the actualsystem and estimate system are obtained by solving the fractional order differentialequations of the two systems. By comparing the two groups’ vector, this paper adopts theaverage of the square sum of the difference as objective function. Therefore, parametersidentification problem is converted into parameter optimization problem. The differentialevolution algorithm is used to search for the optimal parameters. The proposed method isused to identify two different commensurate fractional order chaotic systems, Lu systemand Volta’s system. To the two systems, this paper identifies parameters and orders withthe order known and unknown, respectively. The experimental results proves that themethod is effective.Second, this paper presents a new method for designing fractional order PIDcontroller based on ideal reference model. The proposed method adopts the ideal Bodetransfer function as the reference model. The parameters of controller are determined byminimizing the integral absolute error between the output of reference model and the plant.The proposed method is applied to practical automatic voltage regulator. The experimentalresults proves that the method is effective.Third, this paper proposes the design method of fractional sliding mode controller forABS. An effective quarter-vehicle model is chosen as research object. The sliding surfaceis composed of two parts: the error between the desired slip value and the actual slip value;the fractional order derivative of the error. The equivalent control law can be obtained according to the quality of sliding mode control. The experimental results proves that themethod is effective.Finally, this paper proposes a novel self-tuning fuzzy control based on fractional-ordersliding mode control, because it exits high uncertainties in dynamic mathematical modelof ABS. The method adopts a fuzzy controller to mimic the error controller between theideal controller and the equivalent controller, and adopts a robust controller to compensatethe approximation error. Therefore, the final controller is composed of the equivalentcontroller、the fuzzy controller and the robust controller. This paper applies the proposedmethod to another quarter-vehicle model. The experimental results proves that the methodis effective.