Estimation of a plant relay nonlinearity by nonlinear oscillations analysis

Relay-type nonlinearities are studied and applied since the beginning of the automatic control era. They can be used to control a plant or to identify points of the frequency characteristic of the plant. In this paper, the idea of applying a relay for the estimation of a hard nonlinearity in the plant is introduced. Precisely, if the plant contains a relay-type nonlinearity. its value can be measured by introducing another relay in the feedback with the plant. It is shown that a new characteristic can be derived, including both the plant and the identification relay, and that the first harmonic approximation of the self-oscillations in the system allows to estimate the plant relay amplitude. At the end. forced oscillations in the system with both relays are studied.