Fractional Order Model Reference Adaptive Control Research

The dynamic system discribed by the differential order with any real number ofdifferential equations called fractional order system. Using the fractional order modeldescribing a fractional characteristics of an object can better reveal the essence andbehavior of the object. The study showed using the fractional theory to design controller.In many cases, the controller designed by the conventional integer order theory cannotrealize the superiority but can achieve the stability of the robust,dynamic performanceand control accuracy well.Therefore, the study on the fractional order control systemcaused the experts’ and scholars’ in the control field wide concern. Although thefractional order control theory and application has developped futher in recent years, interms of theory,application and practice still exsit many studies and problems.Therefore,So on this system model reference adaptive control research has an important theoreticaland practical significance.The paper studied the fractional order control system and dothe work as follow on the foundation of the present reseach:1.The system analysized the defining relation,the description and common changeof the basic function and the method of solving of the fractional differential equation,and introduced the approximation, the optimal order reduction and the analysis of thestability theory. The paper combined the fractional calculus with the second method ofLyapunov, then got the Lyapunov stability criterion of the fractional order system.2.The paper elaborated the fractional model reference adaptive control law designmethod and explained the specific requirements of the reference model.According to theLyapunov stability criterion, it designed the fractional model reference adaptive controllaw. And in accordance with the fractional model reference adaptive algorithmstructure,the simulation experiments were carried out and verified the correctness andeffectiveness of the algorithm. 3.In view of the traditional Oustaloup filter deficiencies, it puts forward the improvedOustaloup filter in the numerical implementation par. It used the fractional order controlsystem model reduction and Simulink simulation experiment,designed the fractionalorder parameter module, simulate the numerical value on the selection of differentorders,like0.3, and different gain, and compared with the fractional order controlsystem. The simulation results show that the control effect of fractional model referenceadaptive control better than the integer order situation as selecting order in theadjustable parameter.