BIASED MODEL ORDER REDUCTION AND CONTROLLER DESIGN

Abstract

In this dissertation four different methods of obtaining biased reduced models are explained and PID controller design is done using these methods. Biased means a number of different reduced models of the same order may be obtained by varying the Markov parameters and time moments. The dissertation is organized as follows: Chapter 1 includes introduction to model order reduction techniques. In Chapter 2, introduce classification of different techniques of model order reduction. Chapter 3 tells how the high order system is reduced by Simplified Routh Approximation Method. Model reduction by Simplified Routh Approximation Method (SRAM) is presented for both frequency as well as time domain. In the frequency domain this method is extended to produce biased models. The method uses only one Routh-type array to generate both numerator and denominator of the kth order model.. Computation of the time moments and Markov parameters of the -retained system beforehand' and: solving the Pade equation for the reduced numerator are not, necessary. In the time - domain' (State space form), it avoids the necessity for matrix inversion and multiplication-of the system matrices and the use of recursive formulas. Chapter 4,Continued fraction algorithm is used to produce biased models. Reduced model is calculated from the coefficients of the full transfer function using the cauer continued fraction expansions of the first and the second form. Chapter 5, Improved Pade Approximants Using Stability Equation Method. A combined method making use of the advantages of stability equation- method and Pade Approximation method- is used to produce biased models. Chapter 6, biased model reduction by the -factor division method-- isextendedto. produce biased models. A simple Routh-type algorithm avoids the necessity to calculate the retained system timemoments and Markov parameters -beforehand and _ solvingthe Pade equations for the reduced numerator Chapter 7, out of the four two methods Improved Pade Approximation Using Stability Equation and SRAM are applied to excitation system of single machine connected to the infinite bus system. It has been shown in this example that reduced models of the respected systems can be successfully used in place of higher order models for optimal design of PID controller to improve their performance according to the requirements. Chapter 8, contains conclusion and references.