Interfacing fast and slow subsystems in the real-time simulation of dynamic systems.

Abstract

The simulation of two-time-scale systems in real time normally excludes the powerful methods used in the non-real-time simulation of such systems. Available real-time methods either try to use a robust algorithm for the fast subsystem, or attempt to decrease the step size used to simulate the fast subsystem, while maintaining a larger step size for the slow subsystem (multi-rate integration). Proper interfacing of the two subsystems remains a problem, since an improper interface can affect the accuracy and stability of the overall closed-loop simulation. This dissertation provides a general methodology for analyzing the interface between slow and fast subsystems in two-time-scale problems. For example, there are various methods of generating the multi-rate data input for the fast subsystem from the slow subsystem outputs. Choosing an improper interface can make the difference between a simulation that will run in real-time and one that will not. The dissertation also provides an analysis of the theory and application of output averaging when using the fast subsystem output average as the slow subsystem input. By analyzing different combinations of inputs and outputs when using the State Transition Method to simulate the fast subsystem in the linear case, it is possible to determine the relative accuracy and stability merits of these interface methods. The results are generalized to multirate integration and function generation, as required in real-time simulation of nonlinear two-time-scale systems. Several specific examples of linear and nonlinear systems demonstrate the usefulness of the methodology.