Relay-based gain and phase margins PI controller design

In this paper, an iterative procedure for achieving gain and phase margin specifications for a PI controller is presented. The iteration scheme is based on the use of two relay tests applied to the closed-loop system. The first relay test is standard, and it is used here to obtain the gain margin of the closed-loop system at each iteration step. The second one is applied to the closed-loop system such that a limit cycle is developed at the loop gain crossover frequency. Under this condition, it is possible to obtain an estimate of the phase margin of the loop transfer function. The procedure is used for PI controller tuning in a vanadium-dioxide (VO₂) thin-film characterization experiment, with desired gain and phase margin specifications.