Model reduction of large-scale systems using perturbed frequency domain balanced structure

The technique described in this paper uses singular perturbation and balanced structure to reduce the order of a large-scale plant model over a finite frequency range of operations pre-specified by the designer. This method reduces error rate in model reduction of real equipment that has to operate within a finite frequency range. The outcome of reducing the model within a specified frequency range of operation provides a better estimate of the full order plant model. To illustrate the effectiveness of the technique, a fourth order open-loop plant model is reduced to a second order over several different frequency ranges of operation. Also a sixth and a seventh order controller is designed using H∞ and reduced to a third order while maintaining a robust stability for the closed loop system. A singular value Bode diagram and a Nyquist diagram comparing the original and the reduced order system illustrate the effectiveness of the model reduction technique both in the open-loop and closed-loop sense.