PID autotuning using relay feedback

Abstract

PID autotuning algorithms based on relay feedback are used to identify different points of the process frequency response before performing the actual tuning procedure. These algorithms require minimal amount of priori information about the controlled process, they are also insensitive to modeling errirs and disturbances. In this paper, a PID autotuning procedure implementation based on Åström and Hägglund's method (1984) is presented. The procedure is based on the estimation of the ultimate gain and ultimate frequency using a relay test signal in closed loop. This signal, which is generated automatically, forces the controlled process variable to oscillate at the ultimate frequency with limited amplitude. The only design parameter to be set is the relay amplitude which is inherently relatively small. The PID parameters are calculated using the Ziegler-Nichols tuning rules. In the case where the system is completely unknown, an initial tuning is required before the system can reach the set point, afterwards, a more accurate estimation is made. In case of linear systems, the ultimate gain and the ultimate frequency extracted from the initial tuning are expected to be similar to those extracted from the fine tuning. In case of non-linear systems, estimation should be conducted for each change of the set point. Furthermore, the PID parameters extracted in the procedure can be used either for initialization of other advanced optimization algorithms or for calibrating complicated adaptive regulators.