Drives power reduction procedure to fill in the multiple-input multiple-output random control reference matrix

In Multiple-Input Multiple-Output (MIMO) random control testing, one of the challenges is related to the MIMO definition of the target in case where a full set of field measurements are unavailable and the specifications are therefore retrieved from standards. For multi-axis control tests in fact, although the target is a fully Spectral Density Matrix (SDM) in the frequency band of interest, the test specifications are often provided as multiple PSDs, coming from the single-axis practice. Therefore, additional information about the cross-correlation between pairs of control channels needs to be included, defining the Cross Spectral Densities (CSDs) as off-diagonal terms of the reference SDM. This paper proposes an innovative fully automatic target definition procedure to fill in the MIMO random reference matrix in cases where no information about the CSD terms is available. The developed method yields a set of coherences and phases of the CSD terms that is able to minimize the drives power needed to reach the test specifications. Additionally, the retrieved target complies with the required property of the spectral density matrix being positive semi-definite and with the constraint imposed on the PSDs, considered as test specifications. A series of tests with a three-axial electrodynamic shaker is carried out comparing the proposed target definition procedure with respect to other state-of-the-art solutions.