A new method for tuning PI controllers with symmetric send-on-delta sampling strategy

- We analyze the conditions that produce limit cycle in event based systems.
- Then a new tuning method is developed to tune PI controllers to avoid the limit cycles.
- Because the method is based on the Describing Function, the effect of higher order harmonics has been studied.
- The feasibility of the tuning method is corroborated by symulations and experiments.

In this paper we present a new method for tuning PI controllers with symmetric send-on-delta (SSOD) sampling strategy. First we analyze the conditions that produce oscillations in event based systems considering SSOD sampling strategy. The Describing Function is the tool used to address the problem. Once the conditions for oscillations are established, a new robustness to oscillation performance measure is introduced which entails with the concept of phase margin, one of the most traditional measures of relative stability in closed-loop control systems. Therefore, the application of the proposed robustness measure is easy and intuitive. The method is tested by both simulations and experiments. Additionally, a Java application has been developed to aid in the design according to the results presented in the paper.