Observer-Based PID Control under an Event-Triggered Protocol

This paper is concerned with the observer-based proportional-integral-derivative (PID) control problem for a class of linear discrete-time systems. An event-triggered communication scheme is employed with hope to reduce the communication burden and save network resources. Such a scheme is based on the relative error with respect to the measurement signal in order to determine whether the measurement output should be transmitted to the observer or not. A novel PID controller is designed where the integral-loop is with limited time-window whose length is adjustable according to engineering practice. The purpose of the problem under investigation is to design an observer-based PID controller such that the closed-loop system is exponentially stable under the event-triggered protocol. A sufficient condition is given for the existence of the desired controller by means of the linear matrix inequality technique combined with the orthogonal decomposition method. Finally, the effectiveness of the developed observer-based PID control strategy is demonstrated in the numerical simulation.