Truncation and residualization with weighted balanced coordinates

Abstract

Frequency-weighted internally balanced (FWIB) truncation is briefly reviewed. A previous frequency response error analysis for FWIB truncation is extended, and an exact error bound for the special case of order reduction by one state is presented in terms of the controllability-observability measure used in selecting the coordinate to truncate, as well as two additional frequency-dependent variables. An approximate error bound for the general case of order reduction by more than one state is also developed, under the assumption that only states with small controllability-observability measures are truncated. The error bound is shown to give justification for the FWIB truncation technique based only upon consideration of the controllability-observability measures. However, the presence of the two additional variables suggests a new technique based upon the derived criterion. FWIB residualization is presented, and a frequency response error analysis yields results similar to that found for FWIB truncation. Numerical examples are given to support the error analysis results, as well as to stress that FWIB truncation and residualization can be used in a coordinated manner to achieve higher accuracy than that achievable from either technique used alone.