Dimension reduction and controller design for large scale systems using balanced truncation

Abstract

Modeling of physical systems with high accuracy results into a complex model with higher-order dynamics. This creates intricacy in analysis, simulation and controller design. So one needs to find an approximate simpler representation of such complex systems while preserving the characteristic properties of the higher order system. Reduced lower order representations provide facility in easy analysis of such systems by reduction in computational complexity and faster simulation. In the present paper, a numerically efficient approximation method such as balanced truncation has been applied to obtain the small scale linear time invariant system. Here results of approximation are then evaluated through integral square error. Finally controller has also been designed for the reduced dimension representation of large scale systems. Few numerical problems have been tested to show the effectiveness of the approach.