Comparison of order reduction methods for control applications

Abstract

The quality of a reduced order model can only be assessed if the reduction goal is clearly defined. When e.g. using reduced order models for simulation studies, the input output behaviours of the original system and of the reduced order model should match as closely as possible. Here, however, the problem of compensator order reduction is adressed, and the best reduced order compensator model is clearly the one, which gives approximately the same closed loop behaviour as the full order compensator. Such a compensator model does not necessarily reproduce the input output behaviour of the original compensator best, so that an application of the various existing reduction methods will not give a good reduced order compensator model in general. Better results should be obtained when closed loop properties directly enter the reduction process. This is e.g. the case in the frequency weighted balancing of Enns, and in the LQG balancing of Jonckheere and Silverman. Using three nontrivial examples taken from literature, these two methods are compared with results obtained from an unweighted balancing.

Keywords:

• balanced realizations
• compensator order reduction
• frequency weighted balancing
• LQG balancing