Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
Stability of multi-rate simulation algorithms
Proceedings of the 2007 Summer Computer Simulation Conference
Simulation of an unmanned underwater vehicle (UUV): a multi-rate simulation
Proceedings of the 2007 Summer Computer Simulation Conference
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State-transition methods have proved effective in the real-time simulation of power electronic systems based on piecewise continuous linear differential equation models. They offer excellent stability, accuracy, and efficiency compared to other commonly used methods, which makes them especially suitable for the microsecond frame times that are often required in many real-time power-electronic system simulations. The state-transition approach is based on the evaluation of sums of infinite series that produce exact solutions to systems of linear differential equations. In practice the series are truncated, producing approximate solutions that still perform well. Research at Chico has made extensive use of a method in which the two series on which the state-transition approach is based are truncated to the first 3 and 2 terms respectively; a method designated as the ST(3,2) method. The question arises as to whether this approach also offers advantages when applied to non-linear differential equations. The non-linear equations must first be linearized in piecewise fashion to permit use of ST(3,2) and other ST methods. Simple non-linear examples are used in the paper to compare the performance of ST(3,2) with other methods. Pros and cons of the use of ST(3,2) for non-linear systems are discussed.