An algebraic procedure for the design of linear time invariant discrete and continuous systems employing lower order model

Abstract

A simple algebraic procedure for model reduction of Linear Time Invariant Discrete Systems (LTIDS) is formulated. For the given original higher order system, a second order reduced model is assumed with unknown parameters. These parameters are determined by matching the selected amplitudes (including the steady state and dominant dynamics) from the plot of original system response with the Laurent series terms of reduced second order unit step response, which are the expressions in terms of unknown parameters. The responses of original and the determined second order systems are compared. The proposed reduced order system can retain the stability, steady state and the peak amplitudes of the original higher order system response. However, if the dynamics of resultant reduced order system response diverge, then the sample time is tuned to an appropriate value to attain the time match. The proposed model reduction method is extended for Linear Time Invariant Continuous Systems (LTICS). By employing the proposed second order reduced order model, the Proportional Integral Derivative (PID) controller is designed and then attached to the original higher order system for stabilization of the output response. The results for LTIDS and LTICS are shown with few examples.