Area methods for relay feedback tests

The amplitude and period of the relay feedback oscillation are used to obtain the ultimate parameter of a dynamic process and to tune a proportional-integral-derivative (PID) controller automatically. Equations for the ultimate gain and period are based on ignoring higher harmonic terms in the relay feedback response. The integral of the relay feedback response can suppress the higher harmonic terms, and the amplitude of this integral has been found to be better for estimating the ultimate gain of a process. As extensions, simpler methods that use several area calculations of the relay feedback response are proposed and shown to provide more accurate frequency responses, ultimate gain and period, and parametric models.