Validity of continuous tuning rules in event-based PI controllers using symmetric send-on-delta sampling: An experimental approach

One of the difficulties encountered in the tuning of event-based proportional-integral (PI) controllers using symmetric send-on-delta sampling (SSOD) is the possible appearance of a stable limit cycle, especially when tuning rules designed for continuous control loops are applied. This oscillation is a consequence of the intersection in the Nyquist map of the open loop transfer function (process + controller) with the negative reciprocal of the describing function (DF) of the SSOD sampler. As the DF-based approach is an approximated method and therefore it introduces errors in the locations of the intersections in the Nyquist map, a set of oscillation-free PI controller parameters regions generated by an experimental approach are presented in this paper. The relevant aspect of these regions is that any parameters’ couple located inside them implies a controller that can be applied for the control of first order or integrating processes without generating stable limit cycles. As these regions constitute a resource to check whether a continuous tuning rule can be safely applied in an event-based control loop, a study of the validity of some PI tuning rules is provided in the paper. Also, the regions provide a framework for the design of tuning rules specifically formulated for event-based PI controllers and an example of that is presented in the paper. Finally, it is analyzed whether the classical sensitivity functions can be used as a tool to check and design tuning rules for SSOD-PI controllers instead of the experimental regions.