Structure preserving model order reduction of large sparse second-order index-1 systems and application to a mechatronics model

Structure preserving model reduction of large-scale second-order linear dynamical systems

Second-order linear dynamical systems appear in many physical systems of interests such as electrical, mechanical, electromechanically coupled, and thermomechanically coupled systems. When continuous systems of these types are discretized by a numerical method they lead to a large-scale system of equations which one must solve to obtain either the transient or steadystate behavior. In many case...

Accuracy Enhanced Stability and Structure Preserving Model Reduction Technique for Dynamical Systems with Second Order Structure

A method for model reduction of dynamical systems with the second order structure is proposed in this paper. The proposed technique preserves the second order structure of the system, and also preserves the stability of the original systems. The method uses the controllability and observability gramians within the time interval to build the appropriate Petrov-Galerkin projection for dynamical s...

6 Model Reduction of Second - Order Systems

Model reduction of second order systems

where the matrix M ∈ RN×N is assumed to be invertible. Models of mechanical systems are often of this type since (1.1) then represents the equation of motion of the system. For such a system M = MT , C = CT and K = KT are respectively the mass, damping and stiffness matrices, f(t) ∈ RN×1 is the vector of external forces, and x(t) ∈ RN×1 is the vector of internal generalized coordinates (see [4]...

Structure-Preserving Model Order Reduction of RCL Circuit Equations

In recent years, order-reduction techniques based on Krylov subspaces have become the methods of choice for generating macromodels of large multi-port RLC circuits. Despite the success of these techniques and the extensive research efforts in this area, for general RCL circuits, the existing Krylov subspace-based reduction algorithms do not fully preserve all essential structures of the given l...