A simple rule for tuning Event-Based PID controllers with Symmetric Send-On-Delta sampling strategy

In this paper we analyse the conditions that produce oscillations in event based PID controllers. A Symmetric Send-On-Delta scheme (SSOD) is assumed, and the describing function is the tool used to address the problem. Once the conditions for oscillations are established, a new robustness to oscillations performance measure is introduced. Then a very simple and intuitive rule of thumb is given about how to tune PID controllers to avoid the limit cycles. The rule presented here entails with the classical concept of phase margin, providing the key to design SSOD based PID by using continuous PID tuning methods. The proposed ideas are tested in simulations with a batch of models widely used in PID design methods testing.