Automatic tuning of PID controllers based on transfer function estimation

Abstract

A method for the automatic tuning of PID controllers in a closed loop, based on the estimation of a parametric ‘black-box’ transfer function model, is proposed. The system is excited by generating limit cycle oscillations at two different frequencies, which are approximately the crossover frequency and the critical frequency for the feedback loop. A discrete parametric transfer function model is estimated from the experimental data. Important parameters concerning the estimation, such as the prefilter cut-off frequency and the sampling interval, are determined automatically from the experimental data. The PID parameters are determined from a constrained optimization in the frequency domain. The constraints are classical control system properties, such as the maximum amplitudes of the sensitivity and the complementary sensitivity functions. Given these constraints, the PID parameters are determined such that the low frequency amplitude characteristic for the controller is maximized. Simulation experiments show that the tuning procedure has low sensitivity to disturbances and noise during the tuning experiment.