Reduced Order Sampled – Data Controller

Abstract

The accurate mathematical models of most real-world systems are very large-scale models which are quite hard to investigate, analyze and simulate due to hardware and memory constraints. In such scenarios, the aim is to approximate the original system with a reduced order model which preserves the essential properties of the original system like stability, passivity and closed-loop dynamics etc. The course taken for the achievement of a reduced order model of the original system is termed as Model order reduction. Over the whole frequency spectrum, low approximation error is expected but sometimes it is desired to have low approximation error in specific band of frequencies. This provoked the idea of the model reduction technique by using frequency weights which highlights the certain frequency interval for low approximation error. Several frequency weighted model order reduction procedures can be found in literature which certifies less approximation error in anticipated frequency band but are unable to promise the stability of the reduced order models and vice versa. Also, the reduction techniques are controllability and observability Gramians based which are computationally expensive. As an alternative, cross Gramian based model reduction is used which is comparatively efficient in terms of execution time and results in comparable approximation error. The usual situations, where plant is continuous and controller is discrete, is sampled-data or hybrid systems. The controller order reduction can be accomplished by using model order reduction techniques while keeping the closed loop dynamics preserved. ix In this research work, a novel model order reduction routine by using frequency weights is presented for non-symmetric MIMO continuous, discrete time systems. For nonsymmetric MIMO hybrid systems, where a continuous time plant is controlled by sampled-data controller, frequency weighted sampled-data controller reduction using cross Gramian is proposed. The proposed techniques are modifications of frequency weighted controllability and observability Gramian based model reduction and an extension of unweighted non-symmetric model reduction technique based on cross Gramian. The proposed techniques retain the low error in certain frequency band while consumes lesser execution time.