Circuit Simulation And Control Research Of Fractional-order Liu Chaotic System

Chaotic system is an extremely complex nonlinear system.Chaotic signal has the randomicity and extreme sensitivity to initial value.Sometimes,it may make system can't export according to the scheduled results,even make system collapse.However,its characteristics are suitable for research of secure communications.Therefore,how to eliminate chaos and how to achieve chaos synchronization have been a hot of research.As a natural extension of integer-order chaotic systems,fractional-order chaotic system has more complex dynamic characteristics,and it can truly describe the actual system.Research of its control and synchronization control has become a new hot problem.However,in the actual environment,the existence of external disturbances is inevitable,and it would affect the stability of system.So this thesis studies the control and synchronization control of fractional-order Liu chaotic system with perturbation based on sliding mode control.The main contents are as follows:Firstly,the dynamics characteristics of fractional-order Liu chaotic system and its implementation circuit are studied.Based on the stability theorem of fractional-order nonlinear system,the effect of system order a on fractional-order Liu system is studied,and it is concluded that the minimum order for fractional-order Liu system producing chaos is?=0.85.By numerical simulation,the conclusions are verified.At the same time,based on time domain-frequency domain transformation method,the implement circuit of fractional-order differential operator is designed,and the implement circuit of fractional-order Liu chaotic system with ?=0.9 is designed.By circuit simulation in Multisim,it is verified that the circuit is correct.Secondly,control of the fractional-order Liu chaotic system is studied.In view of fractional-order Liu chaotic system with disturbance,based on fractional-order sliding mode surface,fractional-order sliding mode controller and fractional-order adaptive sliding mode controller are designed,and they make system have faster response speed and strong robustness,and the latter overcame the constraints of the perturbation bound known,reducing conservatism of controller design.And the relationship between response speed of system and parameter r is studied,and it can be concluded that when parameter r is bigger,the response speed of system is faster.By simulation,the effectiveness of controllers is verified.At last,synchronization control of fractional-order Liu chaotic system is studied.In view of fractional-order Liu chaotic system and fractional-order Lorenz chaotic system with the boundary of disturbance known,based on fractional-order sliding mode surface,fractional-order sliding mode controller is designed,and synchronization of them is achieved.And it makes system have strong capability of anti-jamming.The effect of parameters k and? is studied,it is concluded that when parameters k and ? are bigger,the response speed of system is faster.In view of them with unknown boundary disturbance and unknown parameters,combined with adaptive methods,fractional-order adaptive sliding mode controller is designed,and achieved online identification for disturbances and parameters.At the same time,the relationship between response speed of system and parameter k is studied,and it is concluded that when parameter k is bigger,the response speed is faster.By simulation,the effectiveness of controllers is verified.