Improved Frequency Weighted Model Reduction Technique

Abstract

In today’s era, having a simpler mathematical model is very necessary to analyze and understand a system. “Model Order Reduction” (MOR) is the technique which helps reducing our efforts and computational complexities of the mathematical model which is to be analyzed to understand a system’s behavior. It helps us in complex numerical simulation by reducing the order of the system, without bringing a change in its basic properties. MOR is actually the procedure of transforming a higher order complex system into a lower order and non complex system with a reasonable accuracy so we may design the system easily and model and simulate a large complex system doing less effort. Balanced truncation is most commonly used MOR technique that ensures stability and yields an error bound for full frequency range. Sometimes we desire to reduce the system over a specific frequency band, so it motivates the use of frequency weightings in MOR. This thesis focuses on model reduction techniques using frequency weightings. First a full order system is considered and then frequency weighted model order reduction is carried out on that system using proposed techniques, hence yielding a stable reduced order model (ROM). Stability will be guaranteed by having positive/ semidefinite input and output matrices hence assuring the positive semi-definiteness of observability and controllability Gramians. These Gramians will help us formulate a transformation matrix by the help of which we will find new state space realizations of the ROM (internally balanced realizations) which will be stable and gives computable error bounds and approximation error. Existing MOR techniques do preserve stability along with relatively large approximation errors and error bounds but proposed research aim is to develope techniques that yield low approximation error and computable error bound as compared to existing stability preserving techniques.