A one-step procedure for frequency response estimation based on a Switch-Mode Transfer Function Analyzer

Abstract

Frequency response analysis is a well established system identification method. In this paper, a simple and efficient method based on the classical Transfer Function Analyzer (TFA) technique is implemented for system identification. The novel algorithm has been called SwitchMode-TFA. The originality of the proposed approach consists of: i) using a chirp TFA test input instead of a pure sine function, ii) using a variable sampling period instead of the traditional fixed sampling period and iii) a simplified implementation using switched electric circuits. The advantage of our approach is thus threefold: i) the frequency response of the system is obtained for the entire range of frequencies by means of only one identification test; ii) the number of samples per cycle remains constant, independent of the excited frequencies and iii) it can be easily implemented in hardware platforms. The results in both simulation and real-life examples indicate that the proposed Switch-Mode-TFA method can be reliably used for frequency response analysis in many other applications.

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“…To determine experimentally the frequency response in (10), a robust procedure is needed to evaluate correctly, even in the presence of severe disturbances, the amplitude A y and phase ϕ y of the output signal y(t). Such a procedure is based on the transfer function analyzer-discrete Fourier transform (TFA-DFT) [29,30].…”

“…Consider the multiplication of the measured output y(t) by sine and cosine functions of the frequency of the system input ω and then integrated over the measurement period T m = k 2π ω , with k an integer value [29,30]. Then, the following results are obtained:…”

“…In this case, the contribution of the last terms can be neglected compared to the first term, which is growing with T m . Furthermore, it is assumed that for a long integration time, the noise n(t) will be filtered out (i.e., zero average) [30]. In this case, (12) reduces to:…”

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