A Study of Tunable Integration and Control Theory for the Analysis of Differential Equation Solvers.
Final rept. Jan 75-Dec 76,
FRANK J SEILER RESEARCH LAB UNITED STATES AIR FORCE ACADEMY COLO
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Tunable integration is an approach to the numerical solution of ordinary differential equations that is conceived, developed, and employed based upon the principles of linear control theory. The properties of the zero-order-hold tunable integrator and the control-theory methods used to analyze those properties are equally important in the context of this report. Beginning with a discussion of numerical error from a control-theory perspective, the concept is presented of an ideal integrator having no error but that due to finite computer word length. The lack of adaptability of the ideal integrator motivates the tunable integrator, which possesses the requisite flexibility. The majority of the report covers the analytic development of tunable integration, the frequency response of the zero-order-hold tunable integrator, and a root-locus analysis of that integrator as employed in a first-order, linear system. Throughout the presentation, emphasis is placed on the use of these control-theory techniques to determine stability and to tune the integrator for improved performance.
- Numerical Mathematics
- Operations Research