Modeling and Identification of Electromechanical Systems Using Orthonormal Jacobi Functions

Solving parameter identification and structure identification in electromechanical systems is relevant in applications for diagnostics of the technical condition of technical systems, as well as in the development of algorithms for controlling machines and mechanisms. Impulse response functions, correlation and autocorrelation coordinate functions are used as dynamic characteristics. The correspondent models unambiguously give an idea of the mathematical description of a linear or linearized electromechanical system. The methods of spectral description of the dynamic characteristics, based on Fourier transforms, are quite effective in relation to physically realizable systems under normal operating conditions. The paper aims to present new approaches to the development of algorithms for identifying electromechanical systems based on the study of the properties of synthesized transformed orthonormal Jacobi functions and the design of spectral models of the impulse response functions of electromechanical systems. The methods of the theory of spectral and operator transformations, as well as functional analysis, are used in the study. The results demonstrate the success of algorithms for nonparametric identification of linear or linearized electromechanical systems based on spectral models of their impulse response functions in the basis of synthesized generalized orthonormal Jacobi functions. The results of the study can be used in practice for the diagnostics and development of control systems for electric drives of machines and installations with changing parameters or structures.