Reduced Order Model Based on Dominant and Non-Dominant State Of Discrete Time Control Systems

Abstract

Analysis and implementation of large scale linear control systems are both tedious and costly and too complicated to be used in real problems. Therefore, to analyze such large scale linear control systems, it is necessary to reduce it to a lower order system, which is a sufficient representation of the higher order system. In this paper, we propose a model order reduction of large scale linear control systems. First, identify the dominant and non-dominant states for a linear system using modal approach. Develop a reduced order model for reduction of large-scale linear discrete-time control system using dominant and non-dominant state of a system. The reduced order model is used for control applications like reduced order controller, reduced order observer and observer-based reduced order controller for the linear control system. Lyapunov stability theory is the methodology used for establishing the reduced order controllers and observers for the large-scale discrete-time linear systems. Reduced order control is used to stabilize the system and observers are used to determine the system is observable or not. Observer-based and functional observer strategies for the large scale discrete-time linear control systems will be investigated, which shall enhance their performance in industrial applications. Reduced order functional observers will also be derived for large scale linear control systems, which have important applications in implementing controllers for the linear systems.