The two-inertia system with variable-length flexible load (TSVFL) is a typical dynamic model uncertain system. It is affected by transmission flexibility, flexible load length variation, and inaccurate friction torque, in which the flexible load will vibrate during rotation. In this study, a neural network compensation sliding mode control (SMC) strategy mixed with the angle-independent method (AIM) is proposed to suppress the vibration of the TSVFL. Among them, the AIM is proposed to design the fluctuating desired input of the motor. The vibration of the flexible load is offset by the speed fluctuation of the motor. The RBF neural networks are proposed to recognize the uncertain term in the TSVFL's dynamic model. First, the nonlinear mathematical model of the TSVFL is deduced based on the assumed mode method. Then, the Lyapunov stability theorem is proposed to design the weight coefficients’ adaptive law in neural networks and the robust term in the control law. Finally, simulation and physical experiments on output speed control are implemented. The results show that the proposed strategy is able to effectively decrease the error and weaken the vibration.

Gravity and flexibility will cause fluctuations of the rotation angle in the servo system for flexible manipulators. The fluctuation will seriously affect the motion accuracy of end-effectors. Therefore, this paper adopts a control method combining the RBF (Radial Basis Function) neural network and pole placement strategy to suppress the rotation angle fluctuations. The RBF neural network is used to identify uncertain items caused by the manipulator’s flexibility and the time-varying characteristics of dynamic parameters. Besides, the pole placement strategy is used to optimize the PD (Proportional Differential) controller’s parameters to improve the response speed and stability. Firstly, a dynamic model of flexible manipulators considering gravity is established based on the assumed mode method and Lagrange’s principle. Then, the system’s control characteristics are analyzed, and the pole placement strategy optimizes the parameters of the PD controllers. Next, the control method based on the RBF neural network is proposed, and the Lyapunov stability theory demonstrates stability. Finally, numerical analysis and control experiments prove the effectiveness of the control method proposed in this paper. The means and standard deviations of rotation angle error are reduced by the control method. The results show that the control method can effectively reduce the rotation angle error and improve motion accuracy.