Getting More Information from Relay-Feedback Tests

Abstract

The relay-feedback test is a simple and widely used identification tool for obtaining dynamic information that is useful for tuning feedback controllers. The height of the change in the manipulated variable h is specified, the test is run, and two parameters are normally obtained: the amplitude of the periodic output curve a (from which the ultimate gain Ku can be calculated) and the ultimate period Pu. These two parameters provide important information, but they are not sufficient for determining controller tuning for some processes, the most important being processes with large deadtimes. Many authors have suggested methods for extending this type of test in order to obtain additional information: run an additional step test, run a second relay-feedback test with a known dynamic element inserted in the loop, etc. This paper discusses the idea of avoiding these additional tests by simply looking at the shape of the output curve. First-order processes with small deadtime-to-time constant ratios (D/τ) give output curves that are triangular in shape. Large ratios yield curves that are a series of rectangular pulses. A simple characterization factor is proposed for quantifying the curve shape. This additional shape information can be used to determine all three parameters of a first-order/deadtime process (gain, deadtime, and time constant) from one relay-feedback test.