Linear System of Order Reduction Using a Modified Balanced Truncation Method

Abstract

Most of the physical structures may be described in terms of mathematical models. The mathematical methods of system modelling also lead to a thorough explanation of the mechanism in the form of mathematical equations, which are often difficult to use for both analysis and controller synthesis. Consequently, it is useful and very important to determine the likelihood of different calculations of the same type, but in a lower-order representation, which can be assumed to correctly represent almost all the basic features of the system under examination. In this article, the proposed method is based on the modified balanced truncation method (BTM) by which the steady-state value from the problem of the BTM has been circumvented. This weakness has been eliminated by using a modified BTM to narrow the deviations by incorporating a gain factor into the response transfer matrix of the reduced-order model (ROM) to adjust the steady-state value of the ROM, without affecting the variations in dynamical behaviour as compared to the original system. To illustrate the proposed method, a real-time application model has been reduced where the ROM retains all the essential characteristics of the original system. In order to analyse the effectiveness, accuracy and validation with the other existing reduction methods, two standard numerical test systems have been taken from the literature and been tested also.