  The relay autotuning method identifies plant parameters, from oscillations of
the plant under relay feedback. To predict the presence and nature of such
oscillations, we apply the following two approaches: (a) analysis of the
switching dynamics, while using an ideal relay, and (b) bifurcation analysis,
while using a smooth approximation of the relay. For stable plants with
positive DC gains, our analyses predict that: (i) a periodic orbit is
guaranteed, for a class of non-minimum phase plants of relative degree one,
whose step response starts with an inverse response, and (ii) for a wider class
of plants, whose root locus diagrams cross the imaginary axis at complex
conjugate values, limit cycles are merely suggested.
