Use of the Modified EPSILON Decomposition for the LTI Models Reduction

Abstract

For the purposes of representing the characteristics of physical systems, the LTI (Linear Time Invariant) models are often used. Even in the case where the physical system is described by a set of nonlinear differential equations, the linearization process is able to determine a set of linear differential equations e.g. at the working point. The main problem that arises when designing the system model is the order of the resulting matrices. The model order reduction of the LTI models is a common operation which led to obtain a model of smaller size. The large system size issue often make impossible to perform real-time simulation or designate the control system - for example, determining the LQG control system is possible only for relatively small models. In order to achieve high accuracy of the reduced model with the original model, it is necessary to perform a reduction in the specified range of frequency. The problem arises when the resulting model has to match both - low and high frequencies. In addition, models that describe the slow and fast phenomenon are difficult to numerical analyze. The authors propose the use of a methodology, which bases on separating the model into two parts - the fast part and the slow part. The modified Epsilon decomposition is proposed do achieve this goal. The obtained results confirm that the presented methodology is correct.