Measurement of multivariable frequency response functions in the presence of non-linear distortions - Some practical aspects

The aim of this paper is the design of optimal multi-input periodic excitations (i.e. sets of multisines) that allow accurate calculation of a non-parametric multivariable frequency response function (MFRF) of a multiple input multiple output (MIMO) system in the presence of non-linear distortions. Due to the presence of non-linear distortions it is essential that the different experiments necessary to determine the MFRF are performed at the same operating point. It will be shown that, in order to reduce the noise on the measured MFRF, one has to consider the class of excitation signals for which the matrix formed by the input Fourier vectors used in the different experiments has a condition number close to one for all the considered frequencies (modified E-optimality). Within this selected class of excitations with condition number close to one, the uncertainty on the measured MFRFs can further be minimized by maximizing the determinant of the Fisher information matrix. This is achieved by using crest factor optimized excitation signals. The theoretical results are experimentally verified in the field of electric machinery. Finally, a precompensation technique is proposed that further improves the signal-to-noise ratio (SNR) of the measurements.