Sampled SSOD Analysis with DF Method

In this chapter, it is explored the robustness of discrete PI controllers when paired with a Symmetric-Send-On-Delta (SSOD) sampling law. While the continuous Describing Function has traditionally been utilized to assess the robustness against limit cycle oscillations induced by SSOD, it does not encompass the implications of the discrete implementation of the controller. Sampled Describing Function technique offers a more realistic approach, considering both the SSOD behavior and the sampling period of the discrete controller. Through this approach, a measure to characterize the robustness of these systems is developed, which is validated across several examples, in which its effectiveness has been demonstrated in predicting the induction or avoidance of limit cycles. Furthermore, this measure is applied to assess the robustness of various widely-used tuning rules across a batch of systems representative of industrial dynamics.