Tuning and robustness analysis of event-based PID controllers under different event generation strategies

Abstract

In this article, we propose practical rules for tuning event-based PID controllers with two sampling strategies: symmetric send-on-delta (SSOD) and regular quantification (RQ). We present a detailed analysis about the effect of the derivative term of the controller when using SSOD or RQ and some guide lines are given to select the derivative filter coefficient. The two sampling strategies are compared, showing that, even when both of them lead to similar controlled output response, systems with RQ have better robustness properties than those with SSOD. The study is based on the describing function and the results are applicable to process with dynamic responses of different types: with time delays, non-minimum phase, under-damped response, etc. The rules presented here are given in terms of phase and gain margins that are measures of robustness used in the design of continuous PID controllers. This allows the application of conventional PID tuning methods to the case of event-based PID. The tuning rules are very simple and can be used for tuning PID, PI, PD and other controller structures.