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Fast time‐domain simulation for large‐order linear time‐invariant state space systems
Author(s) -
Cheong Sou Kin,
de Weck Olivier L.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1294
Subject(s) - computer science , lti system theory , linear system , algorithm , computation , discretization , solver , control theory (sociology) , mathematics , mathematical analysis , control (management) , artificial intelligence , programming language
Time‐domain simulation is essential for both analysis and design of complex systems. Unfortunately, high model fidelity leads to large system size and bandwidths, often causing excessive computation and memory saturation. In response we develop an efficient scheme for large‐order linear time‐invariant systems. First, the A matrix is block diagonalized. Then, subsystems of manageable dimensions and bandwidth are formed, allowing multiple sampling rates. Each subsystem is then discretized using a O ( n s ) scheme, where n s is the number of states. Subsequently, a sparse matrix O ( n s ) discrete‐time system solver is employed to compute the history of the state and output. Finally, the response of the original system is obtained by superposition. In practical engineering applications, closing feedback loops and cascading filters can hinder the efficient use of the simulation scheme. Solutions to these problems are addressed in the paper. The simulation scheme, implemented as a MATLAB function fastlsim, is benchmarked against the standard LTI system simulator lsim and is shown to be superior for medium to large systems. The algorithm scales close to O ( n 2 s ) for a set of benchmarked systems. Simulation of a high‐fidelity model of ( n s ≈ 2200) the Space Interferometry Mission spacecraft illustrates real world application of the method. Copyright © 2005 John Wiley & Sons, Ltd.