Spectral Method of Identification of Peltier Thermoelectric Elements Based on Piecewise Linear Approximation

The functioning of a thermoelectric system in a stationary mode is often inefficient because it does not allow flexible control of the temperature regime. The design of thermoelectric devices and systems in transient modes requires identifying their dynamic models, first of all, the control object – the Peltier thermoelectric module. As a rule, well-known identification techniques involve calculating the parameters of a fractional-rational transfer function (or, equivalently, an autoregressive model) of the object of control. At the same time, the increase in the accuracy of identification requirements is associated with significant computational costs. The proposed identification technique requires the determination of the time dependencies of the control current and temperature deviation, the calculation of their spectra based on piecewise linear approximation, and the calculation of the transfer coefficient as the ratio of the spectra of the output and input signals. The calculated relations of piecewise linear approximating functions, spectral densities, and time forms of input and output parameters of the model under study are presented. The amplitude and phase frequency response of the Peltier module are calculated. The low RMS error in the identification of the amplitude-frequency characteristic and phase-frequency characteristic showed the effectiveness of the proposed identification technique.

Keywords:

Peltier element , transition mode , piecewise linear function , Spectral method