ABSTRACT
In this chapter we look at constructing a reduced order model from a dynamical system. This represents the practical application of the open loop balanced representation studied in the previous chapter. In fact, there are various ways of obtaining a reduced order model and in the chapter we discuss the method based on the open loop balanced realization. Here, we first calculate a system representation where the state variables are ordered according to a particular system characteristic (controllability or observability or by both properties as in the open-loop balanced realization). The next step is to eliminate the less important state variables from the original system so as to obtain a reduced order model with a lower number of state variables. This can be done by direct truncation or by singular perturbation approximation. Both techniques will be examined. Another general aspect of the methods for constructing reduced order models is the requirement to obtain a small error, the error being a certain norm between the original model and the reduced order one (the chosen norm helps classify the approximation methods). The two techniques for constructing a reduced order model will be examined from the point of view of the errors they produce (so at the quality of the model). This chapter deals with reduced order models with an open-loop balanced form, but other chapters will deal with reduced order models based on other techniques.
Finally, this chapter also includes a few results regarding symmetric systems. The links between dynamical systems and electrical networks are presented. The dichotomy between circuits and systems is emphasized in several aspects. The discussion regards both continuous and discrete time systems. The various subjects of this chapter are complemented by several MATLAB problems that are critically discussed.
