The modeling and vibration analysis of a flexible manipulator considering a nonlinearity and effect from the gravity imply a singular problem. In order to avoid the singularity, the dynamic equation is decomposed into two subsystems, including flexible dynamic subsystem and rigid dynamic subsystem. A combined feed-forward and feedback control scheme is presented to design the controller of the flexible manipulator. In the combined control, an optimization is applied to obtain the desired trajectory based on the flexible dynamic subsystem. As we know, the optimization is dependent on the accuracy of model but there are inevitably errors of model and external disturbances. The feedback control is expected with high robustness and fast convergence to overcome the problem. In order to improve the performance of control, a hybrid sliding mode control (HySMC) is proposed to track the desired trajectory and further suppress the residual vibration. This paper presents the theoretical derivation and experimental verification of the proposed controller.

Proportional-Integral-Derivative (PID) control is widely used to control mechanical systems. In PID control technique, however, there are limits to the accuracy of the resulting movement because of the influence of gravity, friction, and interaction of joints caused by modeling errors. Digital acceleration control has robustness for the modeling errors. But it requires position, velocity, and acceleration of a controlled object to construct a controller. In this paper, we use the novel digital differentiator, ESDS. It enables digital acceleration control without increasing the number of sensors. Furthermore, the proposed method works effectively for quantized sensor data. The validity of the proposed method is confirmed by simulations and experiments using 2-link manipulator.