Abstract
This paper presents a new passivity-preserving order reduction method for linear time-invariant passive systems, which are also called positive real (PR) systems, with the aid of the balanced truncation (BT) method. The proposed method stems from the conic positive real balanced truncation (CPRBT) method, which is a modification of the BT method for PR systems. CPRBT presents an algorithm in which the reduced models are obtained from some Riccati equations in which the phase angle of the transfer function has been taken into consideration. Although CPRBT is a powerful algorithm for obtaining accurate PR reduced-order models, it cannot guarantee that the phase diagram of the reduced model remains inside the same interval as that of the original full-order system. We aim to address such a problem by modifying CPRBT in the way that the phase angle of the reduced transfer function always remains inside the conic and homolographic phase interval of the original system. This is proven through some matrix manipulations, which has added mathematical value to the paper. Finally, in order to assess the efficacy of the proposed method, two numerical examples are simulated.
Highlights
Model order reduction (MOR) plays a fundamental role in the analysis, control, and simulation of real-world systems
This paper proposes a new passivity-preserving order reduction method for positive real (PR) systems whose phase angle is inside the interval (−θ, θ)
The proposed method is a modification to the conic positive real balanced truncation (CPRBT) method
Summary
Model order reduction (MOR) plays a fundamental role in the analysis, control, and simulation of real-world systems. BT is so popular for reducing the order of linear time-invariant (LTI) systems, and it has a great reputation for preserving stability and offering an error bound This method, cannot preserve some other features of the system such as passivity, bounded realness, and the negative imaginary property. We focus on the order reduction of PR systems whose transfer function lies inside a conic sector with an inner angle 2θ, as indicated, based on balancing methods. The CPRBT method is a passivity-preserving balancing-based method which has used the phase angle of the transfer function in order reduction for the first time [23] A > 0 (A ≥ 0) means that matrix A is positive (semi) definite
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