Robust order reduction using system balancing with respect of the method of singular perturbation

Abstract

Several techniques for system order reduction are presented here, known from literature, all of them based on system balancing and some of them employing the method of singular perturbation. These techniques are compared with the two techniques known as the direct truncation and the balancing residualization method for efficiency in approximating the model in two cases: when the system is in the open loop and when the system is working in the closed loop with negative unity gain. All of these techniques for order reduction have the same robustness accuracy evaluated with respect to the H-infinity norm of the reduced-order system. A modification of these techniques preserves the exact DC gain as the original system, and produce from very good to excellent accuracy at low and medium frequencies. To illustrate the efficiency of the order-reduction techniques here presented, a real simulation example is given. The closed loop case simulation shows that high frequency dynamics of the original system can be of more importance for more accurate approximation of the system behaviour in the closed loop even if the high frequency modes appear to be of less significance in the open loop.