Abstract: This paper discusses the control problem of a flexible manipulator under varying end-effector load. The dual-link flexible manipulator system is decomposed into two subsystems: a slowly varying subsystem and a rapidly varying subsystem, using singular perturbations. A hybrid control method is proposed, employing adaptive fuzzy sliding mode control for the slowly varying subsystem and optimal control for the rapidly varying subsystem. Simulation results show that this method not only achieves fast and accurate tracking of the flexible manipulator's trajectory and effectively suppresses elastic vibrations, but also exhibits strong robustness to load variations. Keywords: Two-link; Flexible manipulator; Singular perturbation; Adaptive fuzzy sliding mode control; Optimal control Abstract: A composite controller is designed based on the singular perturbation model of a two-link flexible manipulator. An adaptive fuzzy sliding mode control is designed for the slow subsystem, and an optimal control is designed to stabilize the fast subsystem. Numerical simulation results confirm that the proposed controller can not only perform fast and accurate tracking, but also effectively suppress tip vibration and has strong robustness to varying loads. Keywords: Two-link; Flexible manipulator; Singular perturbation; Adaptive fuzzy sliding mode control; Optimal control Controlling a flexible manipulator aims to achieve two goals: first, to achieve precise positioning or force control; and second, to eliminate elastic vibration as quickly as possible during the positioning or force control process. The presence of elastic vibration in a flexible manipulator makes its dynamics nonlinear, infinite-dimensional, and distributed-parameter, which makes the control problem of the flexible manipulator a major challenge. There are generally two types of methods for controlling flexible manipulators. The two main control methods are: 1) traditional control theories, including PID control, robust control, H-infinity control, and singular perturbation control; and 2) intelligent control methods such as neural networks, fuzzy control, and genetic algorithms. Fuzzy control, for objects difficult to handle using traditional methods, such as strongly coupled, nonlinear, and uncertain objects, can readily derive control strategies, and its algorithms are simple and have good real-time performance. For the position control problem of a dual-link flexible manipulator under varying load, this paper decomposes the system into two subsystems, a slowly changing subsystem and a rapidly changing subsystem, based on the hypothetical modal method and singular perturbation theory [1,2]. When designing the controller for the slowly changing subsystem, considering the system's strong nonlinearity, strong coupling, and uncertainty, an adaptive fuzzy sliding mode control (AFS) method is adopted. The rapidly changing subsystem becomes a linear system after transformation, so simple optimal control can quickly and effectively suppress vibration. Finally, simulation calculations verify the effectiveness of the proposed method. For details, please click: Adaptive Fuzzy Sliding Mode Control of Dual-Link Flexible Manipulator under Load.