A New Technique of Model Reduction: Modified L-K Transformation

A two-time-scale system can be reduced to a lower order system, slow mode subsystem, by the technique of singular perturbation, in which the quasi- steady state approximation and the L-K transformation are used. However, as pointed out in [4], the quasi-steady state approximation is good only for the sufficiently singularly perturbed systems and the L-K transformation always loses some steady state component of the full order system. A new technique, modified L-K transformation, is proposed here to transform A system into weak and strong subsystems representing different modes of the full order system respectively. The singular value decomposition is employed in minimizing the weakness indices. The reduced system is obtained by keeping the strong subsystem. By using the formulas of constructing L and K matrices [4], this technique is very easy to be applied.