Development and study of a polyharmonic autointegration method for calculating amplitude-phase-frequency characteristics of dynamic objects and control systems

The paper discusses the development and study the efficiency of a new polyharmonic autointegration method with full averaging of Fourier coefficient for calculating amplitude-phase-frequency characteristics of non-linear dynamic objects and control systems within a specified computational error and a minimum amount of time. The proposed version of the polyharmonic autointegration method is based on numerical integration of systems of non-linear differential equations of the math models of the objects and control systems with monoharmonic inputs at fixed frequencies and analysis of periodic responses to these inputs using Fourier method. According to the proposed method the process of integrating differential equations of the math model at each of the fixed frequencies continues until the average values of Fourier coefficients of the harmonic under study and the additional harmonics of the output periodic response of a dynamic object or a control system to a monoharmonic input over the elapsed number of periods of the input signal become sufficiently constant.