Multi-loop periodic event-triggered actuation: applications to PID, cascade, and decoupling control

Abstract

This paper studies periodic event-triggered actuation applied to PID, cascade, and decoupling control. We propose an event-triggered output feedback controller, in which the control command is actuated only when it exceeds its previous value by a certain threshold. An exponential stability condition is derived in the form of LMIs using a Lyapunov–Krasovskii functional based on Wirtinger's inequality. It is shown that an observer-based controller can reject an unknown step disturbance. Using this result, we propose a way to tune the event threshold subject to a given stability margin. We apply the proposed framework to PID, cascade, and decoupling control to illustrate how the event thresholds can be tuned in practice. Numerical examples show for these three control architectures how controller–actuator communication can be reduced without performance degradation.