COMPARATIVE ANALYSIS OF POSITIVE REAL BALANCING AND MODAL TRUNCATION TECHNIQUES FOR MODEL REDUCTION IN ELECTRICAL AND ELECTRONIC SYSTEMS

Abstract

The complexity in modern electrical and electronic circuits has necessitated the need for efficient methods to manage behavior, simulate, and analyze them. Reduced-order modeling techniques are effective tools to address these challenges by simplifying systems while retaining essential characteristics. This research presents an analysis and comparison of two model reduction methods: Positive Real Balanced Truncation (PRR) and Modal Truncation Reduction (MTR). The characteristics of PRR and MTR are examined through an assessment of eighth-order electrical and electronic circuits. These techniques are implemented using Matlab to reduce the systems to second-order. Phase angle frequency response plots are generated to compare the original and reduced-order systems. Significant phase angle discrepancies between the reduced-order and original systems are observed at frequencies below 10⁴ rad/s for both algorithms, beyond this frequency, the response matches that of the original system. Through a meticulous comparison of performance metrics, including absolute error, transient time, settling time, overshoot, and peak value, PRR demonstrates stability, precision during the transition phase, and more effective control capabilities compared to MTR.