Model reduction and control of linear discrete time control systems thesis

Abstract

Deriving reduced-order models for large-scale linear systems has been an active area of research in the control systems literature. Mathematical modelling and scientific computing are active areas of research in the control systems literature. In the analysis and design of algorithms for complex systems, it is often necessary to derive low order models simplifying high order system models. The use of a reduced order model makes it easier to implement analysis, simulations and control system designs. Also, there is a great demand from the industry to use low order models rather than high order models for physical or industrial systems because it is easy to work with low order models and design controllers, observers, etc. Some important reasons for using reduced order models of large scale linear systems are: 1) To have a better understanding of the large scale linear system. 2) To reduce the computational complexity of the system. newline3) To reduce the hardware complexity. 4) To make feasible controller and observer designs The methods available in the literature for reduced order model reduction for continuoustime and discrete-time linear control systems can be broadly classified into two areas: A) Classical control methods using the transfer-functions of the linear systems B) Modern control methods using the state-space models of the linear systems This dissertation is a modern control study, which derives new results for the model reduction of large-scale discrete-time control systems using the state-space models of the newlinesystems. There are many advantages of using modern control theory for linear control systems because the state space analysis is applicable to any types of linear control systems. The state space analysis can be performed with initial conditions and the variables used to represent the system can be any variables in the system. Using the modern control analysis, the internal states of the system at any time instant can be predicted.