Fast FRF measurement of multivariable systems using periodic excitations

Classical methods for measuring the frequency response function (FRF) of a multi-variable system with n_u inputs and n_y outputs using periodic excitation signals, either put special conditions on the spectral content of the inputs (no common excited frequencies between each pair of inputs), or require n_u experiments with uncorrela-ted sets of inputs. Since at least 2 consecutive periods should be measured to quantify the noise level on the FRF measurement, the loss in frequency resolution of these classical solutions w.r.t. to random excitations with the same experiment duration is 2n_u. To quantify the level of the nonlinear distortions, the FRF measurements should be repeated at least 2 times with independent random phase realisations of the periodic inputs. This increases the loss in frequency resolution further to a factor 4n_u. For the same frequency resolution of the FRF measurement, the experiment duration of the classical methods using periodic excitations is 2n_u (linear systems) or 4n_u (nonlinear systems) larger than that for random excitations. In this paper we present a method for measuring the FRF, the noise level, and the level of the nonlinear distortions with a loss in frequency resolution or an increase in measurement time of only a factor 2 compared with random excitations, and this, irrespective of the number of inputs n_u and outputs n_y.