Fast Time Domain Simulation for Large-order Linear Time Invariant Systems

K.C. Sou and O.L. de Weck (USA)


Time Domain, Simulation, State Transition, Linear Time Invariant Systems


Time domain simulation can be time consuming and cause memory saturation problems when systems get large, sampling rates are high and input time histories are long. In this paper, an efficient simulation scheme is presented to simulate large order continuous-time linear time-invariant (LTI) systems. The A matrix (assumed to be block-diagonalizable) of the system is first diagonalized. Then, subsystems of manageable dimensions and bandwidth are formed and multiple sampling rates can be chosen to associate with the subsystems. Each subsystem is then discretized using a O(ns) discretization scheme, where ns is the number of state variables. Next, a sparse matrix recognizable O(ns) discrete-time system solver (i.e. matrix-vector product solver) is employed to compute the history of the state and the output. Finally, the response of the original system is obtained by superposition and interpolation of the subsystem responses. The simulation scheme is shown to be superior in the case of medium and large order systems.

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