Study Of Chaos And Chaos Control On Several Nonlinear Circuits

In this paper, we study the mechanisms of generating chaos and methods of chaos control with respect to several nonlinear circuits based on the characteristics of these systems. Better results are obtained.At first, a feedback chaos control method based on variables' proportional and differential is presented. and then it is applied to two autonomous classical physical systems Lorenz system and Chen system as well as two non-autonomous classical physical systems Rossler system and Buluser vibrator. Chaos in these systems are suppressed.In the next place, chaos control on chaotic and hyper-chaotic Chua's circuits are studied. First of all, a chaos control method based on variable's differential feedback is presented and applied to control chaos on chaotic chua's circuit. And then based on this chaos control method, two schematic circuits are designed, i.e. continuous differential feedback realization and impulse differential feedback realization. The circuit simulations are consistent with the theoretical analysis and numerical simulations. Then, chaos control on hyper-chaotic Chua's circuit is studied using feedback method of variables' proportional and differential. It is demonstrated that instead of feeding back one system variable to control chaos it needs at least two system variables to control hyper-chaos. Third, controlling chaos in the chaotic n-scroll Chua's circuit is studied. The approach taken is to use feedback of a single state variable in a simple PD (proportional and differential) format. First, the unstable fixed points in the n-scroll Chua's circuit are classified into two different types according to the characteristics of the eigenvalues of the linearized system matrix at the fixed points. Then, the controllability of these two-types of fixed points is studied. Theoretical analysis shows that the first type of unstable fixed points can be stabilized, at which Hopf bifurcation can also be generated. Control results of the n-scroll Chua's circuit are then demonstrated. Both theoretical analysis and numerical simulation results show that the proposed chaos control method is indeed effective. Forth, chaos control on buck converter in DC/DC converter is studied. At first, the mechanism of generating chaos on PWM buck converter is analyzed. It is found that when the switch S is on, the capacity charges too fast is the main reason why generating chaos in the circuit. Then based on above analysis, we present the method of using output voltage pulse differential feedback to control chaos in the buck converter. theoretical analysis, numerical calculation and circuit simulation demonstrate the validity of this chaos control method. Then, we present a schematic of buck converter by using sliding mode control and then design a circuit based on it. Circuit simulation demonstrated that the dynamic and static performances of buck converter controlling by sliding mode are better than that of PWM converter.