Event-based discrete PI controllers robustness analysis through sampled describing function technique

In this work, the robustness of discrete PI controllers when used with a Symmetric-Send-On-Delta (SSOD) sampling law is addressed. Hitherto, the continuous Describing Function has been employed as a suitable tool to evaluate the robustness of such systems to limit cycle oscillations induced by the SSOD. However, due to the discrete implementation of the controllers in most of the actual applications, the Sampled Describing Function technique is used in this work to provide a more realistic approach, which takes into account the effect of both the SSOD and sampling period of the discrete controller on inducing such oscillation. A simple measure has been developed to characterise the robustness of these systems and it has been tested through several examples, showing its validity in predicting the apparition or avoidance of limit cycles. This measure has been used to evaluate the robustness of some spread tuning rules applied to a wide batch of systems reflecting the dynamics of most processes in the industry