Oscillations in relay systems

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Abstract
This paper surveys the application of a frequency-domain method, initially presented by Tsypkin, and its extensions for the evaluation of free and forced oscillations in relay systems. It is shown that in a single-loop system containing a relay with no dead zone, the solution for a limit cycle is obtained from a single, nonlinear algebraic equation which can be solved graphically in a similar manner to the approximate describing function approach. For a relay with dead zone or other more complicated situations, such as multi-pulse oscillations or systems with multiple relays, more than one nonlinear algebraic equation must be solved to obtain the free or forced oscillation solutions. Details of general computer programs for obtaining these solutions are given. Several solutions can exist, which may correspond to stable or unstable limit cycles, and a necessary and sufficient condition for determining the stability of the oscillations is given.
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