Nonlinear System Control And Circuit Analysis Based On Washout Filter

In the middle of the last century, it was predicted that chaos will lead mankind into a new scientific and technological revolution. A number of the branches of sciences are derived from development of the nonlinear dynamics, and nonlinear circuit arises at the historic moment. Nonlinear circuit is a master of the linear electronic circuits, and it is the cross field of nonlinear science and circuit, which marks the maturity of electronic circuit. The circuit are usually easy to accurately control and measure, so nonlinear circuits naturally became a powerful tool that simulates all kinds of nonlinear dynamical systems and chaos. However,chaos plays an uncertain role in the reality. We should get rid of harmful chaos henomenon, but the chaotic phenomenon are good for us to take advantage of it. Based on the analysis and control of existing generalized Chua’s circuit,a new oscillation circuit is structured by introducing a power source that is periodic changes in the voltage. According to the control principle of washout filter structure controlled system, and comparing the characteristics of circuits. Actually,the ample behaviors of two controlled systems disappeared basically,such as the hopf bifurcation, chaos attractor, chaotic crisis behavior and so on,which reached the purpose of the control.The main research contents of this paper are as follows:1.The development process and current situation of nonlinear electric circuit is briefly introduced. The purpose, significance and the current existing problems in this paper are res-earched at last.2. This paper introduces the definition of bifurcation and chaos, the basic characteristics of chaos, the path to chaos, the judgment method of chaos and chaos control.The characteristics of OGY control method for chaos is analysed. Compare washout filter control with conventional OGY method, we find that the former is superior to the latter in many ways, which make up for the part blank of OGY control method.3. Dynamic behavior is analysed and controled for a four dimensional autonomous oscillation circuit. In the first place, a four-dimensional generalized Chua’s circuit is introduced, and its equilibrium points and bifurcation set of the system are analysed preliminarily. Secondly, on the basis of given part parameters, dynamics behavior of the four dimensional autonomous oscillation system is analysed on resistor R1.We find that system has abundant dynamic behavior with chaotic crisis in the process of the formation of chaos through the study of the phase diagram, bifurcation diagrams and poincare section and time response figure. Finally, the controlled system is studied. Through Matlab numerical simulation analysis, we find that the washout filter can significantly change the characteristics of the system, and make it into a stable state, which can achieve the goal of chaos control. Circuit diagrams are structured based on the Multisim software circuit simulation experiment, which further illustrate the effectiveness of the controller.4. Dynamic behavior is analysed and controled for a four dimensional nonautonomous oscillation circuit. Based on four dimensional autonomous oscillation circuit, a new generalized chua’s circuit is constructed by introducing a voltage source of periodic change. On the basis of given part parameters, dynamics behavior of the four dimensional nonautonomous oscillation system is analysed on resistor R1.System has a wealth of almost periodic features with chaotic crisis in the process of the formation of chaos through the analysis of the phase diagram of the system, bifurcation diagrams and poincare section. Finally, based on the analysis of the controlled system, washout filter directly eliminate the chaotic phenomena of the system on a small scale, which achieved good control effect.