Graduate Thesis Or Dissertation
 

A study of the stability of a third-order system with saturation

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/gf06g6499

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  • The stability of a third-order, nonlinear system with a saturation characteristic was studied by applying the second method of Liapunov, which is the most general approach currently used for dynamic systems. This thesis presents (1) the analysis of a third-order, nonlinear system, (2) a suitable Liapunov function, generated by the variable-gradient method, for determining the stability regions of the system, and, (3) a hybrid simulation to study the conditions obtained by using Liapunov's second method. Because the Liapunov functions generated by the variable-gradient method give only sufficient conditions for asymptotic stability, some additional assumptions may be necessary to find a larger stable region than the stable region determined by only one assumption relative to the variable-gradient function. The main purpose of the hybrid simulation was to find an asymptotically stable region which could be compared with the region determined by Liapunov theory. Also, under certain limitations, changes in the stable regions were observed for several different saturation characteristics, even though asymptotic stability did not always exist. The hybrid computer is well suited for this simulation primarily because of the decision-making elements available and the plotting equipment for displaying trajectories used to observe stability characteristics. The simulation program was written in the Hytran Operations Interpreter, and was implemented on an Electronics Associates, Inc. , EAI 690 Hybrid Computing System. As an example of a third-order, nonlinear system, a field-controlled, d-c motor with constant armature current and a controller with the saturation characteristics, was used.
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