A comparative study of model reduction methods

Model reduction techniques are grouped into four approaches according to their underlying principle, which are (1) Continued fraction expansion approach, (2) Dominant mode approach, (3) Optimum fitting approach, (4) Singular value decomposition approach.

Based on the simulation of the step response and the least sum of the squares of the sample errors, the simplified models are evaluated. In practical application, the quality of approximation and the ease of hand calculation are considered. Some complicated techniques can be replaced by a simple calculation in the single variable case so that they are seen to be equivalent.

A new generalized Cauer form of continued fraction expansion method is developed, which provides a general algorithm to match different numbers of time moments or Markov parameters so that different Cauer forms can be a special case of the new method.

For the discrete-time transfer function obtained by the least square method, a new transform approach is presented to find the equivalent continuous-time transfer function. The denominator of the transfer function shows that the simplified low-order models need "optimum poles" instead of "dominant poles" in order to approximate the original model.