Frequency weighted model order reduction techniques

This thesis investigates the frequency weighted balanced model order reduction problem for linear time invariant systems. First, two new frequency weighted balanced truncation techniques based on zero crossterms are proposed. Both methods are applicable for single-sided weighting, and are based on modifications to Sreeram and Sahlan’s technique. The first method uses the properties of all-pass function to transform the original frequency weighted model order reduction problem into an equivalent unweighted model reduction problem, while in the second method, the relationship between the final and the intermediate reduced order model used in Sreeram and Sahlan’s technique is derived. Numerical examples show that a significant error reduction can be achieved using both methods. Second, we present an improvement to frequency weighted balanced truncation technique based on well-known partial fraction expansion idea. The method yields stable reduced-order models for double-sided weightings. Two numerical examples including a practical application example, show a significant improvement over the other well-known techniques. Lastly, we present passivity preserving frequency-weighted model order reduction techniques for general large-scale RLC (resistor-inductor-capacitor) systems. Three well-known frequency weighted balanced truncation techniques (Enns’, Wang et al.’s and Lin and Chiu’s), which preserve only stability and not passivity are generalized to include passivity. Conditions under which the passivity is preserved are also derived. Four practical examples are given to show the validity and effectiveness of the proposed algorithms using different weighting functions.