MODEL ORDER REDUCTION USING GENETIC ALGORITHM AND ITS CONTROL

Abstract

This project involves the study of techniques of Reduced Order Modeling (ROM) of Higher Order Systems, a branch of systems and control theory, which aims at studying the dynamical properties of systems and reducing the complexity of the system, while preserving the input output characteristics to the maximum extent possible. The study involved model order reduction of linear time invariant (LTI), single input single output (SISO) systems using unorthodox optimization technique ‘Genetic Algorithm’. The same reduction is previously done for comparison by more conventional techniques ‘Routh Pade approximation’ and ‘Routh approximation’. “Routh Pade approximation” is a mixed method for finding stable reduced-order models using the Pade approximation technique and the Routh-Hurwitz array. This method guarantees stability of the reduced model when the original system is stable. “Routh approximation method” is based on an expansion that uses the Routh table of the original transfer function, the method has a number of useful properties: if the original transfer function is stable, then all approximants are stable; the sequence of approximants converge monotonically to the original in terms of ‘‘impulse response” energy; and poles and zeros of the approximants move toward the poles and zeros of the original as the order of the approximation is increased. In the “Genetic algorithm” based reduction method lower order transfer function are determined by minimizing the integral square error between the transient responses of original and reduced order models using Genetic algorithm in MATLAB. The reduction procedure is simple and computer oriented. It is shown that the algorithm has advantage that the reduced order models retain the steady-state value and stability of the original system. The problem of controller design for higher order system via reduced model is also investigated. The project describes a technique for designing a stabilizing controller for the stable higher order system via its reduced order model. The method uses the parameterization of all compensators that stabilize a given plant. It is shown that the Compensator, which is obtained from reduced model, not only stabilizes reduced Model but also the higher order system. The developed methods are illustrated with numerical examples.