An Algebraic Procedure for the Design of Linear Time Invariant Discrete and Continuous Systems Employing Lower Order Model
N. Malathi1, N. Devarajan2

1N.Malathi, Research Scholar, Department of Electrical Engineering, Centre for Research, Anna University, Chennai (TamilNadu), India.

2N. Devarajan, Dean Research, Sri Ramakrishna Institute of Technology, Coimbatore (TamilNadu), India.

Manuscript received on 05 March 2019 | Revised Manuscript received on 17 March 2019 | Manuscript Published on 22 March 2019 | PP: 491-496 | Volume-8 Issue-5S April 2019 | Retrieval Number: ES3470018319/19©BEIESP

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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.

Keywords: Model Order Reduction, Identification, step Response, Laurent Series, Amplitude Matching, Sample Time, LTIDS, LTICS, PID.
Scope of the Article: Computer Architecture and VLSI