Adaptive actuator fault-tolerant control for a three-dimensional Euler–Bernoulli beam with output constraints and uncertain end load

Abstract

This paper studied an adaptive actuator fault-tolerant control scheme for the flexible Euler–Bernoulli beam in the three-dimensional space with output constraints and uncertain end load. The dynamic models are represented by partial differential equations (PDEs) and ordinary differential equations (ODEs). When part of the actuator fails, an adaptive control scheme is designed to regulate the vibration and stabilize the flexible three-dimensional Euler–Bernoulli beam. Barrier Lyapunov Function (BLF) is adopted to realize output constraints of the system. Adaptive control law with projection mapping operator is designed to compensate for the end load which is uncertain and bounded. The goal of this paper is to suppress the displacement of the flexible three-dimensional Euler–Bernoulli beam which can be constrained in given bounds under actuator fault and uncertain, bounded end load. It is confirmed that the proposed control scheme can deal with the vibration, adaptive actuator fault-tolerant control, uncertain and bounded end load and output constraints of the system simultaneously. Finally, numerical simulations illustrate the effectiveness and feasibility of the method.