Model Order Reduction by Balanced Truncation Method

Abstract

In this thesis, we focus our attention on one of the most important method for the model order reduction called balanced truncation method for continuous linear time invariant systems. Balancing system is equivalent to finding the controllability and observability Gramian of the system in diagonal form which is equal to the Hankel singular values. As a result of the balanced truncation method, we find an approximation error which is norm of transfer functions (in frequency domain) and norm of the outputs. Numerical results for the mass spring damper system have shown that balanced truncation method is one of the most efficient methods for model order reduction, since the reduced system maintains the properties and simulates the behavior of the original system.