PID output-feedback control under event-triggered protocol

Abstract

This paper is concerned with the $H_{\infty }$ proportional-integral-derivative (PID) output-feedback control problem for a class of linear discrete-time systems under event-triggered protocols. The controller and the actuators are connected through a communication network of limited bandwidth, and an event-triggered communication mechanism is adopted to decide when a certain control signal should be transmitted to the respective actuator. Furthermore, a novel PID output-feedback controller is designed where the accumulative sum-loop (the counterpart to the integral-loop in the continues-time setting) operates on a limited time-window with hope to mitigate the effect from the past measurement data. The main objective of the problem under consideration is to design a desired PID controller such that the closed-loop system is exponentially stable and the prescribed $H_{\infty }$ disturbance rejection attenuation level is guaranteed under event-triggered protocols. By means of the Lyapunov stability theory combined with the orthogonal decomposition, sufficient conditions are established under which the addressed PID controller design problem is recast into a linear convex optimization one that can be easily solved via available software packages. Finally, a simulation example is exploited to illustrate the usefulness and effectiveness of the established control scheme.

Keywords:

• PID control
• $H_{\infty }$ control
• event-triggered mechanism
• orthogonal decomposition
• output feedback

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the Royal Society of the UK, the National Natural Science Foundation of China [grant number 61573246]; the Shanghai Rising-Star Programme of China [grant number 16QA1403000]; the Hujiang Foundation of China [grant number C14002], [grant number D15009]; the Alexander von Humboldt Foundation of Germany.