Data-driven balanced truncation for second-order systems with generalized proportional damping
For engineers designing control systems, this provides a structured model reduction technique that maintains physical interpretability, though the improvement over existing methods is not quantified.
This work develops a data-driven balanced truncation method for second-order linear dynamical systems that preserves a generalized proportional damping structure. Numerical examples demonstrate the method's effectiveness in producing low-dimensional surrogate models.
Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop a new approach for the structured data-driven surrogate modeling of linear dynamical systems described by second-order time derivatives via balanced truncation model-order reduction. The proposed method is a data-driven reformulation of position-velocity balanced truncation for second-order systems and generalizes the quadrature-based balanced truncation for unstructured first-order systems to the second-order case. The computed surrogates encode a generalized proportional damping structure, and we propose a computational procedure for inferring the damping coefficients from data by minimizing a least-squares error over the coefficients. Several numerical examples demonstrate the effectiveness of the proposed method.