Dynamic Analysis And Control Of Several Chaotic Systems

As a special operating state that exists in nonlinear systems,chaos phenomenon has a complex and far-reaching impact on various systems.As a high-order complex nonlinear system,the power system may have chaotic states due to the change of parameters and the combined operation of disturbance links or subsystems.This may cause irregular oscillations in the power system and even cause the power grid system to collapse.Aiming at the fractional order chaotic system,this paper takes Lorenz-Stenflo system and Sprott E system as the typical models,generalizes it to the fractional order,combines the fractional order field with the chaotic field,verifies the existence of chaotic behavior,analyzes its operating characteristics,A simultaneous study was conducted.Therefore,this paper studies the second-order power system,the fractional order Lorenz-Stenflo system and the fractional order Sprott E system,analyzes the chaotic operation state,and designs the corresponding controller according to the actual situation.Mainly summarized as follows:(1)The power system in the ideal state is analyzed,and for the second-order power system with disturbance links,the chaotic operation state is verified according to the Poincaré cross-section method,attractor phase diagram,power spectrum diagram,etc.Inversion adapts to the sliding mode control strategy,and the controller is designed.From the simulation results,it can be observed that the system has changed from an irregular chaotic operating state to a stable periodic operating state.(2)For the three-dimensional Lorenz system,it is extended to the four-dimensional Lorenz-Stenflo system.According to the judgment of the stable equilibrium point,the existence of hidden attractors is verified,and the chaotic running state is analyzed by Poincaré cross section and power spectrum.In this paper,the controller is designed according to the theory of fractional order stability,so that the fractional order Lorenz-Stenflo system reaches the synchronous operation state from the chaotic operation state in a short time.(3)Based on fractional calculus theory,the fractional Sprott to fractional Sprott E system,adopt the method of bifurcation diagrams to verify the existence of fractional order system,based on the analysis of basic operation of the system under the premise of the attractor phase diagram,the power spectra of verified the existence of chaotic behavior,and the integer order projective synchronization method of promotion to the fractional order system,synchronous controller is designed,the realization of fractional order system gradually stable.(4)Summarize the full text.The key research contents and innovative significance of the paper are summarized,which to some extent promotes the further development of chaos and fractional order fields,and prospects the future development.