A scheme for theoretical and experimental evaluation of multivariable system stability robustness

A scheme for theoretical and experimental evaluation of multivariable system stability robustness measures is described. The experimental scheme is based on the estimation of frequency responses from power-spectra analyses of a set of time responses due to sine-sweep excitation at each input and then computation of the appropriate singular values. The procedure can also be used on an open-loop stable system to predict the closed-loop stability before closing the loop. Classical Nyquist diagrams can also be constructed to determine one-loop-at-a-time gain or phase margins. The scheme has been implemented in a wind tunnel test for singular-value evaluation of digital flutter suppression control laws and compared with theory. The singular values at the plant input and output of the actual system and the theoretical model are qualitatively similar but have some discrepancies.