EFFICIENT COMPUTATION OF CLOSED-LOOP FREQUENCY-RESPONSE FOR LARGE-ORDER FLEXIBLE SYSTEMS

An efficient and robust computational scheme is given for the calculat ion of the frequency response function of a large-order, flexible syst em implemented with a linear, time-invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of th e plant based on a model of the structure using normal mode coordinate s. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, full-matrix techniques whose computational times pe r frequency point range from quadratic to cubic functions of system si ze. This permits the practical frequency-domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formul ations are given for both open- and closed-loop systems. Numerical exa mples are presented showing the advantages of tile present formulation over traditional approaches, both in speed and in accuracy. Using a m odel with 703 structural modes, a speed-up of almost two orders of mag nitude was observed, while accuracy improved by up to 5 decimal places .