Reduced order modeling of delta operator systems by optimal frequency fitting approach

The delta operator modeling provides a unified framework for both continuous-time and discrete-time modeling in system theory. At high sampling rate, the shift operator fails to provide meaningful information whereas, the delta operator parameterized system provides the same results as of continuous time systems. In this paper reduced order modeling of delta operator parameterized systems is considered. A complex domain ($\delta$) optimal frequency matching (OFM) technique is proposed and frequency points are optimized using Particle Swarm Optimization (PSO) algorithm. This OFM is then utilized to find the reduced order model of the higher order system. PSO algorithm is a robust, global optimization technique, used to find these OFMs and thereby used to find the coefficients of the reduced order model by minimizing a cost function developed based on the responses of the higher order model and that of the reduced order model when both are excited by pseudo random binary sequences (PRBS). The performance characteristics are evaluated in software simulation using MATLAB considering example of higher order system in delta domain and time & frequency responses of the corresponding reduced model.