Certain Algebraic Schemes For Second Order Model Formulation And Applications In Linear Time Invariant Systems

Abstract

The systems present in industrial processes of today are newlinecharacterized by complex dynamic models and are represented by newlinemathematical equations of higher order The complexity of verifying newlineanalyzing and assessing the general properties designing controllers and newlineimplementation is very high which leads to the use of reduced order models newlineThe original large scale model is reduced to a smaller model which newlineapproximates the transfer function of the original model by retaining the newlineimportant characteristics newlineThe thesis presents a simplified method of model reduction applied newlinefor Linear Time Invariant Systems LTICS The proposed method of model newlinereduction focuses on the advantages of Routh approximation and Particle newlineSwarm Optimisation PSO The cumulative error index J is used for the newlinecomparison of step responses of original and reduced systems Moreover the newlineproposed method is extended for the reduction of Linear Time Invariant newlineDiscrete Systems LTIDS The proposed method is explained with illustrative newlineexamples and the reduced model obtained for various stable systems newlineguaranteed stable reduced models The obtained results are compared with the newlinevarious existing methods in terms of cumulative error value newlineBy using the reduced models obtained from the proposed method newlinevarious applications like the design of PID controller design of state feedback newlinecontroller and observer design of optimal Controller and design of filters are newlinediscussed They proved that the reduced model reduces the complexity in newlinedesign newline newline