MODEL ORDER REDUCTION FOR LINEAR DYNAMIC SYSTEMS AND ITS APPLICATION

Abstract

The aim of this thesis is to develop some new model reduction methods for the simplification of large scale linear time-invariant (LTI) systems and the controller design. The new model reduction methods are proposed in the frequency domain as well as in the time domain. The proposed methods guarantee the stability of the reduced order models if the original large scale systems are stable. The proposed methods are compared with the well-known and recently proposed model order reduction techniques and found comparable in quality. These methods circumvent some of the inherent shortcomings associated with some existing standard model order reduction methods. Some of the proposed methods are applied for the design of controllers and compensators. Time moments and Markov parameters are the pivotal parameters in the model order reduction. The time moments and Markov parameters are used for the matching of steady-state responses and transient responses of the original system and reduced order model respectively. In this thesis, it is shown that the without matching of Markov parameters, the transient responses of the reduced and original systems can be matched closely and the time moments can be used for the matching of transient responses. Some mixed model reduction methods are proposed in the frequency domain using the advantages of Routh approximation and factor division methods. In this method, the denominator coefficients of the reduced model are obtained by using Routh approximation method and the numerator coefficients are determined by using factor division algorithm. Another model reduction method is based on the Routh approximation method and a simple mathematical algorithm. A new method referred to as “Improved Routh stability method” is proposed for the LTI systems. In this method, Routh stability method is used for obtaining the denominator polynomial and a simple mathematical algorithm is used for computing the numerator polynomial. An improved stability equation method is also proposed, in which stability equation method is used for the evaluation of the denominator coefficients and the numerator coefficients are evaluated by using a simple mathematical algorithm. Two mixed model reduction methods based on modal method are proposed. In the first method, the model method is used for obtaining the denominator polynomial and the factor division algorithm is used for obtaining the numerator polynomial. In the second method, the numerator polynomial ii is determined by using a simple mathematical algorithm. Two new model reduction methods based on Mihailov stability criterion are proposed for the simplification of large scale systems. A new model reduction method referred to as “generalized pole clustering method” similar to pole clustering method is proposed. The generalized pole clustering method is a special case of pole clustering method. Further, three mixed methods based on generalized pole clustering method and some other existing methods are proposed for the large scale linear time invariant single as well as multivariable systems. Three model order reduction methods in the time domain are also proposed for the LTI systems. These methods are proposed to overcome the steady-state gain problem of balanced truncation method. The first method is based on the balanced truncation and factor division methods. In this method, the balanced truncation method is used for obtaining the denominator polynomial of the reduced model and the factor division algorithm is applied for the determination of the numerator polynomial. The second method is based on the Padé approximation and balanced truncation methods. In this method, the Padé approximation method is utilized for obtaining the numerator polynomial of the reduced model and the denominator polynomial is determined by using balanced truncation method. In the third method, the balanced truncation technique is used for computing the denominator polynomial and the numerator polynomial is obtained by using a simple mathematical algorithm. The controller is designed on the basis of the reduced order model using the convention method based proposed model reduction methods. This design procedure is carried out with the help of reference model. The desired performance specifications of the plant are translated into a reference model transfer function. In this approach, a reduced model is obtained from the large scale original system and the controller is design by using the reduced order model. The obtained controller is applied to the original higher order system. The performance comparison of various models has been carried out using MATLAB software package.