Model Reduction Techniques for Circuits: Positive Real Balancing and Stochastic Balancing Comparison

Abstract

In the domain of electrical engineering, model reduction and data dimensionality reduction play a pivotal role in addressing the complexities inherent to electronic circuits and systems. The challenges posed by high-dimensional models and extensive datasets necessitate efficient approaches for system analysis, simulation, and control. This paper investigates the efficacy of two model reduction techniques—Positive Real Balancing-based Reduction (PRR) and Stochastic Balancing-based Reduction (SBR)—in the context of preserving system attributes. The research focuses on maintaining stability, passivity, and minimum phase behavior while reducing model order. PRR and SBR algorithms, grounded in Gramians balancing, were implemented and evaluated using MATLAB. The study gradually reduced the order of the original system from 8 to 1 and examined the absolute errors between the reduced-order systems and the original system. The findings showcase distinctive trends. PRR exhibited higher accuracy as the order increased, while SBR balanced accuracy and computational efficiency. Both techniques displayed consistent error reduction as the order rose. The comparison of absolute errors across reduced orders highlighted the trade-off between precision and efficiency. This investigation contributes to the understanding of the trade-offs between accuracy and efficiency in model reduction techniques. The results offer insights into choosing suitable methods based on specific application requirements, thereby advancing the field of efficient model reduction in electrical systems.