Modeling and neural network control of a flexible beam with unknown spatiotemporally varying disturbance using assumed mode method

In this paper, based on the Lagrange equation, and considering the nth order elastic mode, the dynamics of a flexible beam equation with unknown spatiotemporally varying disturbance are derived in tangent coordinates system using assumed mode method (AMM). Subsequently, a disturbance observer is developed to solve the unknown spatiotemporally varying disturbance. And neural network (NN) control with full-state feedback and output feedback is proposed to approximate the dynamic uncertainty of the flexible beam system and achieve vibration suppression. It is proved by Lyapunov's stability that the elastic vibration of the flexible beam system can be effectively suppressed. Extensive numerical simulation results verify the performance of the compounded disturbance observer-based adaptive neural network strategy from the perspective of practice.