Multiple switching relays for the estimation of ultimate data

Sustained oscillations are obtained by putting relays in the feedback loop, which provide ultimate periods and gains of processes that can be used to tune PID controllers. The ultimate periods obtained by conventional relay autotuning have relative errors up to 5% for first order plus time delay processes. To improve the estimation of ultimate periods, modified relays such as a saturation relay and a relay with preload have been available. However, these modifications lose the binary (on-off) property of the conventional relay. Here relays with multiple switching which produce pulse-widthmodulation (PWM) signals are proposed. They retain the binary property and show improved identification accuracies of ultimate parameters.