Fast time domain simulation for large order hybrid systems

Abstract

Simulation is an important tool for the analysis and design of complex systems. As the models become more and more complex, more powerful simulation methods are desired. As an attempt to address this problem, a simulation scheme is proposed and developed in this thesis. The main objective of this work is to simulate continuous-time linear time-invariant (CT-LTI) systems efficiently with acceptable approximation and error. The method basically divides the original large order system into smaller subsystems, simulates them with state transition formula and superposes the responses by using the linearity property of LTI systems. A similarity transformation can first be employed to obtain the modal canonical form of the system. The modal form can then be divided into subsystems with manageable sizes. Discretization scheme specially developed for these subsystems can then be employed to get their discretized counterparts. At this stage, the original continuous-time IVP becomes a set of of smaller matrix vector multiplication routines. Special matrix vector product solver is chosen to exploit the sparsity resulted from the diagonalized structure of the A-matrix. Also, subsystems are considered in frequency domain to see if multiple sampling rate scheme is acceptable. Finally, the results of the simulations can be superposed to form the response of the original system. Next, the more advanced problem of simulating hybrid feedback control systems are studied.

(cont.) The algorithm has been compared with the standard MATLAB LTI system simulation routine lsim.m and is shown to be able to simulate large order systems even when isim. m fails. It is also shown that the new simulator is more efficient than lsim. m even for moderately large order systems simulations. Finally, the method is applied to SIM (Space Interferometry Mission, 2000 state variables) as an example of real world applications.