Study On Applications Of The Typical Methods For Analyzing Nonlinear Systems

Approximation analysis of the nonlinear systems is difficult in interdisciplinary research. Also, a lot of existing analyses of the nonlinear system mainly concentrate on quantitative analysis. So it’s hard to choose the right methods. The research going deep into the nonlinear approximation seems to be important. Besides, the switching converters are the typical nonlinear circuits and usually adopt the state-space averaging method. Because of the averaging process and the assumption of the waveform linearity, the results are inaccurate and have a lot of limitations. So it is urgent to analyze the applicability of nonlinear approximation methods. Also, it is very important to analyze the methods which can be used in the switching converters.In this paper, we discuss several common nonlinear analysis methods of strong applicability and theirs characteristics. And we study the switching converters deeply using the equivalent small parameter method. It is studied in the following aspects:(1) Several typical analytical methods principles are introduced. There are slowly varying amplitude method, singular perturbation method, phase plane method, describing function method, equivalent small parameter method(ESP). And combined with the van der Pol oscillator, the features and the range of application have been comparatively analyzed.(2) Focused on the equivalent small parameter method, we use it to analyze the DC-DC switching converter in the state of open loop and closed loop. First, the nonlinear mathematical model based on the switching converter is established. Then through the theoretical derivation, the steady-state solution of the system state variables can be obtained. Compared with the state space averaging, the ESP method considers the system harmonic and can reflect the impact of the switching period on the steady-state.(3) Based on the study of the steady-state in the switching converter, the further study is focused on the ESP method. The ESP method is put into the solution of the transient solution in DC-DC switching converter. First, the solving process is deduced. And combined with the steady-state solution, the transient solution computing process can be simplified. Then, along with it, the system stability is discussed. Finally, the effectiveness can be verified through the specific Boost converter.(4) The ESP method is generalized into the study of the open-loop fractional switching converters. First of all, the nonlinear mathematical model is established based on the fractional switching converters. Secondly, the steady-state solution and the transient solution can be approximately solved by the ESP method. And combined with specific circuit, the significance of this method can be validated.