A REAL-TIME SOLUTION TECHNIQUE FOR STIFF LINEAR DIFFERENTIAL SYSTEMS.

摘要

A very common engineering problem encountered in the performance analysis of hardware for guidance and control purposes is the "closing of the loop" around such hardware with appropriate differential models. Solutions to such models, using inputs from the hardware and sending the outputs from the model to the hardware, must be performed in real-time.;This dissertation addresses the problem of obtaining real-time solutions via digital computational hardware for stiff, linear, time-invariant system models, suitable for hardware-in-the-loop application. This is accomplished by developing a solution technique that is A-stable and suitable to real-time processing, requiring very few sequential arithmetic steps. The method is capable of handling arbitrary stiffness within the numerical capacity of the hardware employed and requires no model scaling.;The solution technique is a considerable departure from conventional differential equation solvers in that it lays the theoretical foundation for taking advantage of desk-top-type general purpose computers in conjunction with a special purpose digital processor implementing algorithms based on the trapezoidal rule.;As part of the solution method development, a critique of digital differential equation solvers and numerical integration techniques is presented in terms of their ability to provide real-time solutions to stiff differential system models.;At present, there exist very few differential equation solvers and only analog computers capable of this task, and none are capable of handling stiff differential system models.