Hybrid sliding mode control with optimization for flexible manipulator under fast motion

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.