Closed-loop Tuning of PID Controllers

A method for automatic tuning of PID controllers in 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 cross-over frequency and the critical frequency for the feedbck loop. A discrete parametric transfer function model is estimated from the experiment data. Important parameters concerning the estimation such as prefilter cut-off frequency and sampling interval are determined automatically from the experiment data. The PID parameters are determined from a constrained optimization in the frequency domain. The constraints are classical control system properties such as maximum amplitudes of the sensitivity and the complementary sensitivity functions. Other constraints can also be specified. 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.