BALANCED REDUCED ORDER MODELS OF LARGE SCALE SYSTEMS

Abstract

The core problem of model reduction is to find a simpler conceptual model that is still valid, with respect to the Simulation Requirements. There could be two approaches to reach to a simpler model: a constructive or an evolutive. For the "constructive" approach, a simpler model would emerge directly from scratch. For the "evolutive" one, a simpler model should be derived from an initial one. For this last case, still there are two possibilities: (1) The initial model is more complex, and an attempt is made to simplify it. This approach is called as Evolutive/Reductionist approach. (2) Initially an over-simplified model is produced and then necessary details are added. This approach is called as Evolutive/Expansionist approach. The work presented in the thesis focuses on the first technique that is Evolutive/Rductionist technique. It deals within the framework of continuous-time, linear time invariant state space control systems. By control system it means a dynamical system with inputs e.g. controls, disturbances and outputs e.g. measurements of variables of interest. The dimension of a state-space model, also known as the model order, is the number of independent variables needed to characterize the "state" of the system, which, roughly speaking, represents the memory that the system has of its past. The two best available techniques of model reduction have some disjoint set of drawbacks. Singular Value Decomposition based approximation methods has a global error bound and the preserved stability but the drawback is, that applicability is restricted to relatively low dimensions. Whereas Krylov-based methods remedied the matter of applicability but lack in guaranteed stability preservation and a global error bound. So this dissertation is an attempt to get rid of these anomalies by combining the two methods in order to get the best features of both the methods to get the reduced model more closely to the original higher order model. The proposed technique results in a stable and passive reduced order model of a fairly high order original system with a preserved steady state response.