Model Order Reduction for System with Negative Imaginary property: Structure-Preserving Approach

Abstract

Model order reduction (MOR) is a set of methods used to simplify the analysis and design of complex dynamical systems by reducing their size and complexity. However, these techniques often struggle to maintain important structural properties of the original system, such as stability, passivity, and negative imaginary (NI) behavior. NI systems are a type of dissipative system commonly found in applications like flexible structure dynamics and nanopositioning systems, where high-order models are often used. This research introduces a novel MOR approach specifically designed for NI systems that preserves the NI property while improving accuracy. The method uses a parameter optimization framework, where the reduced-order model (ROM) is created by systematically adjusting its matrix elements to minimize the difference between the original system and the ROM. To ensure the NI property is maintained, structural constraints are placed on the ROM parameterization. The effectiveness of this new approach is evaluated using several examples of NI systems and compared with current MOR techniques. Results show that the proposed method can significantly reduce model order while successfully preserving the NI property and improving the ROM’s accuracy.