Pretuning and adaptation of Pl controllers

A method is proposed for the closed-loop tuning of a PI controller in cascade with a plant having an unknown transfer function, based on adding a variable-frequency sinewave to the loop's set-point. It applies design-point methodology in the Nyquist diagram to a phase-frequency adaptor coupled with gain estimators that monitor the closed-loop signals. The approach is shown to give good results over a wide range of cases, using test transfer functions taken from the literature that represent typical process dynamics. By comparing its step responses with those of loops tuned by standard Ziegler-Nichols and Cohen-Coon rules (as applied by many autotuners), the approach is seen to give consistent transients that are characterised by a user-specified damping factor. Adaptive tuning can be attained, 'quietly in the background' during normal PI control of a slowly varying plant, as convergence and tracking are obtained even if the output signal:noise ratio is less than one.