Design of repetitive control system based on advanced periodic event-triggered scheme for linear systems

Handling unknown disturbances and tracking periodic signals with limited communication is a persistent challenge in practical control applications. Performance degradation and potential instability may arise due to factors such as time-varying delays, unknown exogenous disturbances, structural uncertainties, and the intensive data exchange between sensors and controllers. These challenges can impair system performance and, in severe cases, compromise stability. To overcome them, this work introduces a control framework that integrates an adaptive periodic event-triggered mechanism (APETM), an equivalent-input-disturbance (EID) estimator, and a modified repetitive controller (MRC), thereby ensuring closed-loop stability while enhancing overall performance. The developed scheme is tailored for linear systems influenced by unknown external disturbances and required to function under limited communication resources. The EID-based MRC improves signal tracking and disturbance rejection, while the APETM reduces unnecessary transmissions and communication resources. The complete design is formulated as a time-delay system, and its stability is rigorously established using a Lyapunov approach in conjunction with linear matrix inequalities. Simulations on a rotational speed control and rotary servo motor confirm the method’s effectiveness and reliability over the exciting approach.