| Compared with the traditional chaotic system,the topological structure of the hyperchaotic system is more complex and the nonlinear dynamic behavior is also richer.Therefore,it has broader application prospects in the fields of signal detection and secure communication.In this paper,three problems are studied: How to construct hyperchaotic system by using feedback control method,how to design controller to realize chaos control of chaotic system and hyperchaotic system,and how to use chaos theory to detect power harmonic signal under noise background.The main contents include:(1)First,a three-dimensional chaotic system is introduced.Through MATLAB numerical simulation,the trajectory of the phase plane and the time-domain waveform diagram of each state variable can be directly observed,and the Lyapunov exponent and0-1 test results of the system are analyzed.At the same time,an analog circuit is built based on the chaotic circuit design principle,and the phase diagram obtained from the simulation verifies the correctness of the theoretical derivation and numerical simulation.Then two controllers are designed,one is a linear state feedback controller designed based on Barbashin-Krasovskii theory,and the gain range of the controller and a detailed proof of stability are given.The other is the backstep controller,which can control the system to track the expected value given.Finally,a new method of using chaotic system to detect the frequencies of power harmonic signals is proposed,and the frequency of each harmonic is successfully obtained through this method.(2)The state feedback control method is used to construct a new four-dimensional hyperchaotic system on the basis of the three-dimensional chaotic system introduced above.Then analyze the nonlinear dynamic behavior of the system according to the numerical simulation,including time-domain waveform diagram,symmetry,dissipation,equilibrium point,eigenvalue,Lyapunov exponent,Poincaré cross section and 0-1 test.Finally,a simulation circuit is designed for the four-dimensional hyperchaotic system according to the chaotic circuit design principle,and the phase diagram of the hyperchaotic attractor is obtained from the simulation to verify the correctness of the theoretical derivation and numerical simulation.(3)First,a controller is designed to control the new four-dimensional hyperchaotic system.Design linear state feedback controller based on Barbashin-Krasovskii theory,the new four-dimensional hyperchaotic system can be controlled to the origin by using a linear state feedback controller.And the gain range of the controller and detailed stability proof are given.Then use the Lyapunov stability theory to design a backstepping controller,and give detailed derivation steps.Finally,the frequency of power harmonic signal is detected by the new four-dimensional hyperchaotic system.This detection method provides a new idea for power harmonic signals based on non-Duffing oscillators. |
