Chaotic Motion Of Fractional Order System And Its Control

Chaos belongs to an important branch of nonlinear dynamical sys-tems,and have been well studied in many fields such as biology,physic-s,chemistry and information.In this paper,the chaotic characteristics and chaos control and synchronization of a Synchronous Reluctance Motor(SynRM)are studiedFirstly,we discuss chaotic characteristic of the fractional SynRM by analyzing the bifurcation diagram,Lyapunov exponent,phase por-traits and time responses.Then we also study the influnce of system's order to the chaos.In the case of commensurate fractional order Syn-RM system,the lowest order at which chaos exists is turned out to be about 2.94.Then the chaotic characteristics of non equivalent frac-tional order SynRM are analyzed,and the minimum order difference between non equivalent fractional order SynRM and equivalent frac-tional order SynRMSecondly,in order to affect the normal operation of the fractional order SynRM in the chaotic state,a reasonable controller is designed for fractional order SynRM to achieve global asymptotic stability.T-wo different proving methods are put forward,and the stability of fractional order SynRM is proved from different angles.Finally,the validity of the method is verified by numerical simulationFinally,it is found that chaos is beneficial in some special situations In the case of chaotic SynRM with unknown parameters,the effect of parameters on chaos is studied.