Two Algorithms for Fast and Accurate Passivity-Preserving Model Order Reduction

Abstract

This paper presents two recently developed algorithms for efficient model order reduction. Both algorithms enable the fast solution of continuous-time algebraic Riccati equations (CAREs) that constitute the bottleneck in the passivity-preserving balanced stochastic truncation (BST). The first algorithm is a Smith-method-based Newton algorithm, called Newton/Smith CARE, that exploits low-rank matrices commonly found in physical system modeling. The second algorithm is a projectand-balance scheme that utilizes dominant eigenspace projection, followed by a simultaneous solution of a pair of dual CAREs through completely separating the stable and unstable invariant subspaces of a Hamiltonian matrix. The algorithms can be applied individually or together. Numerical examples show the proposed algorithms offer significant computational savings and better accuracy in reduced-order models over those from conventional schemes.

A Passivity-Preserving Frequency-Weighted Model Order Reduction Technique

“…However, the ROMs yielded by Krylov methods are not compact. Therefore, in the next stage TBR [6] is used to obtain a compact ROM [7], [23]. Inspired by this staging concept, it is proposed to consider the double-sided weighted problem as a sequence of two single-sided weighted problems.…”

“…In this section, two passive models of a wire comprising of 100 and 150 repeated RLC sections are considered which produce a 200 th and 300 th order system respectively [23]. The input and output weighting systems considered are V (s) = 10 (s + 10)…”

Passivity-Preserving Parameterized Model Order Reduction Using Singular Values and Matrix Interpolation

“…The fast and efficient modified Smith technique [18], [19] enables us to find the controllability grammian (W c ) and the observability grammian (W o ) of a large system. For the statespace model described in (1), the generalized grammians are defined as the unique solutions of the linear equations…”

Robust Passivity Preserving Parametric Model Order Reduction using Matrix Interpolation

“…The fast and efficient modified Smith technique, Gugercin et al [2001], Wong et al [2006] is used in this paper to find the controllability grammian (W c ) and the observability grammian (W o ) of a large scale system. For the state-space model (1), the generalized grammians are defined as the unique solutions of the linear equations…”

“…This paper proposes a novel PMOR technique that enhances and improves the method of Panzer et al [2010], Eid et al [2011] by using common projection matrices over the entire design space and passivity preserving parameterization schemes. The modified Smith technique, Gugercin et al [2001], Wong et al [2006], is used to compute efficiently the grammians of the large system and then similarity transformation matrices are generated using the projection-based passive truncated balanced realization (TBR), Yan et al [2007]. The estimation grid and validation grid are chosen for the design space and transformation matrices are computed over the estimation points in the design space.…”