Improved Technique for Frequency Limited Gramians based Model Order Reduction of 2D Systems

Abstract

Derivation of a mathematical system is a crucial parameter for design, analysis and simulation of dynamic system. Higher order complex models are obtained, while deriving from physical systems. These models are represented by partial differential equations, ordinary differential equations and Laplace etc. For simplification and ease in solving reduced order systems (ROS) are feasible that approaches the real system as strictly as possible. Considerable amount of research have been taken place on different features of model order reduction. Existing techniques have the drawbacks of lacking properties like stability, passivity, large approximation error and lack of a-priori bounds etc. In many applications the error should be less in definite frequency intervals. This inspires the idea model reduction in limited frequency interval model reduction. The interested frequency interval is calculated by using limited frequency interval Gramians. Many frequency limited interval model reduction techniques are proposed to guarantee less approximation error in the interested frequency range. The techniques with less error in interested frequency interval don’t guarantees stable ROS. Similarly, the stability preserving techniques introduces larger approximation error in interested frequency interval. A Cross Gramian based new frequency limited technique for model reduction of 2D discrete time systems was proposed in this research. Cross Gramian provides the combined information of controllability and observability Gramians. New generalized Sylvester equations for calculation of frequency interval cross Gramian were derived in order to obtain information regarding controllability and observability within a single matrix. The comparison of simulation time with previous technique is given to show the improvement in results. This thesis report concludes with some numerical examples and results of proposed technique.