Vibration Control for Flexible Manipulators With Event-Triggering Mechanism and Actuator Failures

This article focuses on flexible single-link manipulators (FSLMs) under boundary control and in-domain control. The actuators of the system include the dc motor at the end of the joint and $m$ piezoelectric controllers installed at the flexible link, which is regarded as an Euler–Bernoulli beam. The problem of the infinite number of actuator failures, including the partial loss of the effectiveness and total loss of effectiveness, is solved by the adaptive compensation method. By introducing the relative threshold strategy, the event-triggered control (ETC) scheme is proposed to achieve angle regulation and vibration suppression while reducing the communication burden between the controllers and the actuators. The Lyapunov direct method is utilized to prove that the system is uniformly ultimately bounded and both the angular tracking error and elastic displacement converge to a neighborhood of zero. Numerical simulation results are provided to demonstrate the effectiveness of the proposed control law.