PADE APPROXIMATION AND ITS APPLICATIONS IN CONTROL SYSTEM DESIGN

Abstract

Model reduction is the technique to reduce a higher order model into a low order model without loss of its original characteristics. Because of more complexity of mathematical term, a higher order model is difficult to use. So to work better with less complexity; a low order model is preferred to solve the practical life problems. To achieve this goal different methods for model reduction have been designed and developed by researchers This dissertation report aims at mentioning some model reduction techniques such as mixed method used to reduced a higher order model into a lower order model and to design a controller. All these techniques have some losses since the reconstructed model is not an exact replica of the original model. In this report our aim is to explain Pade approximation and some mixed methods for model reduction and used these methods for controller design. It can be .seen that the Pade approximation method does not always give a reliable approximation of a high order system. If Pade approximation gives a stable reduced order model then it is the best reduced order model among all other reduced order models as concern the performance specification. Hence, it is generally recommended to combine the classical Pade method with other approximation methods. Here some mixed methods are used for controller design with a problem in which numerator with Pade approximation and denominator with other methods as Routh Hurwitz array, Routh approximation, Stability equation method, Differentiation equation and Truncation method has solved. Finally the report conclude with the fact that the many possible reduction techniques to be used to achieve better approximation and specification for controller design.