PDE‐Based Prescribed Performance Tracking and Vibration Control of Flexible Manipulators With Unknown Control Directions and Dead Zones

Abstract

This article investigates the prescribed performance tracking and vibration control of flexible manipulators with unknown control directions and dead zones, which are governed by partial differential equations. To this end, we initially applied a state transformation to convert the tracking error in angular position as constrained by the prescribed performance function into an equivalent unconstrained form. Subsequently, with the aid of variable frequency Nussbaum function, an event‐triggered adaptive boundary control scheme is developed to handle the complexities of the control inputs, while ensuring that the transformed error and structural vibrations were bounded. The results of a Lyapunov stability analysis demonstrated that all closed‐loop signals, including those of the transformed error, were bounded, indicating that the tracking error in angular position satisfied the prescribed performance‐related constraint. Moreover, by using Barbalat's lemma, it is proved that the structural vibrations eventually converges to zero. Finally, numerical simulations are conducted to validate the effectiveness of the proposed boundary control scheme.