Real-time digital simulation is a powerful means for engineers and scientists in government, industry, and academia to perform research and training as well as serving as a basis for many commercial applications. Due to the special constraints imposed by digitally simulating continuous systems in real time, however, many of these systems either require costly high-speed components or are unable to provide suitable performance characteristics using affordable computers.

This dissertation describes a new technique for the synthesis of numerical integrators specifically designed for the real-time digital simulation of continuous systems. This methodology is based upon the fact that the state derivatives in a simulation model typically have a significantly limited bandwidth. This information is exploited to improve the efficiency of numerical integrators by selecting the coefficients of a general-form integrator such that it approximates an ideal integrator over the limited frequency spectrum of the state derivative.

The specific constraints and performance characteristics necessitated by the real-time environment are first identified and addressed. A method for analyzing the frequency response of individual state variables in a system is presented together with frequency-domain gain and phase error metrics which characterize the performance of the numerical integrators within limited frequency spectra. The resulting technique for synthesizing numerical integrators based upon their required performance and nominal input signal characteristics is then presented. The method consists of varying parameter values of a general-form difference equation to minimize gain and phase errors over the limited frequency band of that particular integrator. These techniques are applied first to a simple example as a proof of concept; it is then used to improve the cost/performance ratio for the more complex case of an automobile vehicle dynamics model.

The results of this research provide a means for the evaluation and development of highly effective numerical integrators for real-time simulations. The improved efficiency of simulations using these techniques permits higher fidelity models to be implemented on lower cost platforms. This enables these simulators to be used in a broader range of applications where high fidelity is required while at the same time minimizing recurring costs.

Graduation Date





Klee, Harold


Doctor of Philosophy (Ph.D.)


College of Engineering


Department of Electrical and Computer Engineering

Degree Program

Electrical and Computer Engineering






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Access Status

Doctoral Dissertation (Open Access)



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