Analysis of a System Controlled by a Relay with Dead Zone, Hysteresis and Integral Feedback

The applicability of the describing function method of analysis to a plant/controller system containing a nonlinear relay with feedback is investigated. A second order plant model is employed, with system parameters based on a ship steering system application. Analytical predictions of limit-cycle behavior are made and are found to be in disagreement with time-domain results. It is hypothesized that the theory fails due to insufficient filtering of harmonics in the relay feedback loop. The system is theoretically modified to include additional filtering in the feedback loop to test this hypothesis, and good correlation between theory and time-domain results is observed. Implications for plant/controller design and the ship steering problem are discussed.