## 1 Introduction  
With lower power consumption, lighter weight and higher flexibility, flexible manipulators have been largely used in industrial production, and aerospace, search in some complex environments, thereby expanding the use of manipulators [1,2]. However, because flexible manipulators use flexible materials, the rigidity of the whole system is poor, and it is easy to produce vibration. Therefore, how to suppress the vibration of flexible manipulators has become one of the hottest issues now. The vibration suppression of the flexible manipulator is divided into passive suppression in the early stage and active suppression in the present stage. In early passive suppression, accurate dynamic models were established, and the structure of the manipulator was optimized using the finite element method [3,4]. This method has a long development cycle and cannot guarantee a good vibration suppression effect. Active suppression is to control manipulators through the control algorithm [5,6] to achieve vibration suppression of flexible manipulators. With the emergence of intelligent control algorithms, neural networks have also been applied to the vibration suppression of flexible manipulators. [PERSON] et al. [7] used the Particle Swarm Optimization (PSO) intelligent search algorithm and back propagation neural networks (BPNNs) to suppress the vibration of flexible manipulators. [PERSON] et al. [8] proposed a neural network based adaptive integral sliding mode observer to suppress the vibration of flexible space manipulators. Based on rigid-flexible manipulators, [PERSON] et al. [9] proposed an adaptive neural network sliding mode control strategy to estimate unknown disturbances and uncertain parameters. [PERSON] et al. [10] introduced radial basis neural network functions (RBNNFs) to cope with system parameter uncertainties and input saturations. As a common control method, the boundary control method is often used to sup-press the vibration of manipulators. [PERSON] et al. [11] devised a boundary control approach to suppress distributed elastic deformation and vibration. However, there are still large errors in angle tracking. [PERSON] et al. [12] proposed an adaptive boundary iterative learning vibration control for a class of rigid-flexible manipulator systems under distributed disturbances and input constraints. However, the design of the control law is complicated. [PERSON] et al. [13] proposed a novel boundary control strategy for a vibrating single-link flexible manipulator system modeled using partial differential equations. In the design of the control law, the expression is still complicated, and there are some small high-frequency vibrations in the control input of the simulation results. [PERSON] et al. [14] proposed two boundary control laws to manage vibration suppression and angular position tracking of manipulator systems. However, there are some problems in that the suppression effect of some parameters is not good. As an intelligent control method, the fuzzy backstepping control method does not need an accurate mathematical model and has good adaptability to complex systems. [PERSON] et al. [15] proposed an adaptive fuzzy backstepping method that reflected the effect of vibration suppression mainly through the parameters of velocity and displacement tracking. However, the specific type of external interference is not clearly pointed out in the paper, and the parameters and state of the motor when the manipulator is running are not considered. [PERSON] et al. [16] proposed an adaptive fuzzy backstepping control method for uncertain nonlinear systems. The paper still fails to consider the influence of specific external interference on the system in the simulation and does not consider the parameter setting of the motor. If the parameters of the motor are not considered, the reliability and authenticity of the simulation will be slightly reduced.