Analysis And Control Of Multi-scale Bifurcation And Chaos In The Piece-wise Smooth Circuit

The complex behavior in nonlinear circuit has become an important research subject in the modern circuit, which include extremely abundant contents and wide application prospects. In this dissertation, as an important part of nonlinear circuit research, the complex behavior in the piece-wise smooth circuit is investigated and the details are presented as follows:1. The multiple chaotic attractor in autonomous piece-wise smooth circuit is studied. Two kinds of multi-scroll chaotic attractor and another kind of multi-folded torus chaotic attractor in the autonomous piece-wise smooth circuits are constructed and analyzed. The mathmatical models are established, the effects of parameters on the chaos of the circuit and the route to chaos of the circuit are analyzed. Moreover, the relationship between the number of chaotic attractor and the number of closed switches are given.2. The multi-scale bifurcation in the one-cycle controlled DC-DC circuit is studied. The fast-scale bifurcation in the one-cycle controlled Buck circuit and the slow-scale bifurcation in one-cycle controlled Boost circuit are invesigated respectively with the circuit simulation, theoretical analysis and circuit experiment. The results shows: the main reason for the occurrence of fast-scale bifurcation in the one-cycle controlled Buck circuit is that the operation frequency of the circuit is lower than the clock frequency. But, for the slow-scale bifurcation in the one-cycle controlled Boost circuit, in fact, it is that the Hopf bifurcation happens in the area where the frequency is much lower than the switching frequency.3. The multi-scale bifurcation in average current controlled Boost PFC circuit is studied. By establishing the simplified models, the medium-scale bifurcation is investigated based on the small-sigal model, and the slow-scale bifurcation is investigated based on the harmonic balance method and Floquet theory, and also, the subslow-scale bifurcation is investigated based on the nonlinear model. The under mechanism of the above three kinds of bifurcaton are given. Finally, the effectiveness of the simplified models and the validity of the theoretical analyses are confirmed by the circuit simulations and circuit experiments. 4. The multi-scale bifurcation in the averge current controlled Boost PFC with an input filter is studied. The mathematical models of the circuit are constructed, the slow-scale bifurcaiton in the circuit is analyzed by means of the harmonic balance method and Floquet theory and the subslow-scale bifurcation is analyzed by means of the nonlinear model. The results show that the stable area may be enlarged when the extra input filter is added into the average current controlled Boost PFC circuit. These results change the conclusions that the extra input filter will only degrade the stability of the average current controlled Boost PFC circuit.5. The multi-scale bifurcation in the multi-stage PFC circuit is studied. Based on certain suitable assumptions, the simplified model of the cascade PFC circuit are established. And then, the medium-scale bifurcation is analyzed by using the small-signal model, and the slow-scale bifurcation is analyzed by using the method of incremental harmonic balance and Floquet theory. The effectiveness of the simplified model and the validity of the theoretical analysis are both confirmed by the circuit simulation and circuit experiment. Furthermore, the slow-scale bifurcation in parallel PFC circuit is analyzed by using the method of harmonic balance and Floquet theory. It is found that there are very important differences between the single-stage PFC circuit and the parallel PFC circuit.6. Control of multi-scale bifurction and chaos in the piece-wise smooth circuit is studied. Firstly, the linear feedback control is proposed to realize the synchronization of the Chua's circuit. Secondly, based on the passive control theory, the passive controller is designed to realize the synchronization of the modified Chua's circuit. Thirdly, the current feedback control is applied to realize the control of the slow-scale bifurcation in the one-cycle controlled Boost circuit. The span of the control parameters for maintaining the circuit in stable operation are fixed. Moreover, the effectiveness of the control method and the validity of the theoretical analysis are confirmed by the circuit simulation and circuit experiment. Finally, the load current feedback control is applied to control the slow-scale bifurcation in average current controlled Boost PFC circuit. Based on the simplified model, the span of control parameters for maintaining the circuit in stable operation is analzed by using the method of harmonic and Floquet theory, and then the effectiveness of the control method and the validity of the theoretical analysis are confirmed by the circuit simulation and circuit experiment.