Some Insights on Data-Based Frequency-Weighted Model Reduction

A well-known and effective frequency-weighted model reduction method is the so-called frequency-weighted balanced model truncation. However, all existing frequency weighted balanced reduction methods require that the weighting functions must have analytic transfer function representations. In view of this, we have presented some preliminary research of a frequency weighted order reduction method based on numerical integration in our previous study. This numerical integration method does not limit the weighting functions to have analytic transfer functions. This paper tries to gain some further insights on the frequency weighted model reduction method with numerical integration. First of all, the numerical integration (or data-based) frequency weighted model reduction is further illustrated through some examples, and the method is also compared with the (standard) balanced truncation, balanced stochastic truncation and the standard frequency weighted balanced truncation when analytic weighting functions or analytic approximations are available. It is found that the desired approximation (or model reduction) effects can be achieved by numerically adjusting the weighting in the desired frequency ranges. This provides a tremendous flexibility in practical applications. This flexibility indicates many possibilities in model reduction, system identification, low complex controller design, and many other areas of applications that are to be explored.