Complete and exact identification of self-sustained oscillations in relay sampled-data systems

A simple and systematic approach is presented to obtain the complete, exact, and exhaustive description of limit cycles that may exist in a relay sampled-data control system. The final expression in its closed form is obtained by simple substitution. There is no restriction on the order of the plant, nor does the feedback have to be unity. The period of the oscillation poses no problem in the approach presented. Clear and explicit relations between the self-sustained oscillations and system parameters have been established.