Time-variant frequency response function measurement of multivariate time-variant systems operating in feedback

The classical time-invariance assumption is often not (exactly) met in real-life applications. As a natural extension of the frequency response function (FRF), the time-variant FRF (TV-FRF) provides quick insight into the complex dynamics of time-variant systems. Recently, a procedure has been proposed to estimate nonparametrically the TV-FRF from known input, noisy output measurements of time-variant systems operating in open loop. However, in many applications, feedback is present either due to an explicit control action or due to the interaction between a nonideal actuator and the system under test. The extension of the open-loop approach to noisy input, noisy output measurements of time-variant systems operating in closed loop requires the deconvolution of the time-variant impulse response of the cascade of two time-variant systems. In this paper, this nontrivial problem is solved for a particular class of time-variant systems. The robustness of the approach with respect to the system assumption is demonstrated via simulations and measurements on an electronic circuit.