Formulation Of Lower Order Model For Linear Time In Variant Discrete Systems Employing Modern Table And Genetic Algorithm

The model reduction is the process of approximating, as closely as possible, the dynamics of higher order linear time invariant system by a reduced order model. This paper presents a simple scheme for deriving a second order model for a given absolutely stable higher order Linear Time Invariant Discrete System (LTIDS). The proposed scheme uses a Marden Table to formulate the numerator and the denominator of an initial second order model. The coefficient of the z-term of the numerator polynomial is fixed by maintaining the transient gain ratio of the given original higher order system. The integral square error is computed by constructing the unit step responses of the original higher order system and the formulated second order model derived from Marden Table. To minimize the integral square error, so that the characteristics of the second order model closely matches the given higher order system, the genetic algorithm is applied to tune the remaining parameters of the model. The performance of the proposed method is compared with that of the other existing model reduction methods and the results are tabulated. The proposed scheme is illustrated through numerical examples.