Model reduction of large scale systems using approximate component cost analysis

Abstract

State-space model reduction methods, such as the component cost analysis (CCA), requires the solution of Lyapunov equations of order equal to the order of the system. However, for many engineering applications, the storage requirements and computational time needed for the solution of such large Lyapunov equations is often prohibitive. In this work, the use of Krylov-subspace iterative methods is examined to obtain low-rank approximate solutions of Lyapunov equations for use in CCA model reduction of large space structures. The methods are applied to obtain reduced-order models of the International Space Station multi-body assembly stages for simulation and control purposes. In addition, closed-form expressions for cost equivalent and cost decoupled realizations are derived based on the approximate Lyapunov solutions. It is shown that using the proposed methods, approximate CCA reduced-order models can be obtained with a significant reduction in the computational effort and time.