| Fractional-order can accurately describe the physical conditions in today's world,and gradually become a new expression of mathematical states to solve natural science problems.The stability of fractional-order system plays a decisive role in practical engineering,and the study of its stability and synchronization is still in the development stage.The general control measures cannot be used in fractional-order chaotic systems because the development of control methods is not perfect enough to control fractional-order chaotic systems reasonably and accurately.With the development of time,people focus on the controller which can make fractional-order chaotic system stable.However,the study of passive control method in fractional-order field is still not deep enough,so there is more research space for passive synchronization control of fractional-order chaotic system.Based on the theory of fractional calculus and the stability theory of fractional Lyapunov,passive control of fractional-order chaotic systems with different dimensions,passive control of fractional-order hyperchaotic systems with time-varying gain and adaptive passive synchronous control of permanent magnet synchronous motors are carried out.The main research contents are as follows:Firstly,a passive feedback control scheme with time-varying gain is proposed for adaptive synchronization of fractional-order hyperchaotic systems.Different from the general feedback control law,this chapter only needs to control two signals.The fractional error dynamics system equivalent to the passive system can be obtained through the designed controller,so as to ensure the convergence of the synchronization error.After that,it is proved that the control method can be stable in finite time and enhance the robustness of the controller on the basis of nonlinear element parameters or structural uncertainty.Through the application in hyperchaotic system,it can be seen that this control method has certain practical value.Secondly,the passive synchronization control problem of Lorenz system with different fractal order is studied.According to fractional-order stability theory and passive control theory,a new passive controller is designed for the characteristics of the controlled system.Then the passive synchronization of fractional-order systems with different dimensions under different initial conditions is achieved.The passive control method used is from integer order of same dimension and same structure to fractional-order chaotic system of different dimension.Finally,through the comparison of control effect diagram,it can be concluded that the passive synchronization control method is better than the feedback control method.Finally,the adaptive passive synchronous control method is applied to the fractional-order model of permanent magnet synchronous motor.If the parameters of the permanent magnet synchronous motor dynamics system fall into a certain range,the system operation will be reduced due to chaotic behavior,then bad chaos will occur after the synchronization of the double-permanent magnet synchronous motor,and a passive control law is proposed to convert the fractional-order error system generated by the permanent magnet synchronous motor into the equivalent passive system.In order to eliminate the influence of uncertainties in the controlled system,an adaptive law is added to the controller to verify that the controlled system is asymptotically stable at the equilibrium point.By adjusting the internal parameters of the controller,different control effects are obtained. |
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