Vibration Suppression of a High-Speed Flexible Parallel Manipulator Based on Its Inverse Dynamics

For a novel 2-DoF flexible parallel manipulator, its kinematic and vibration control was investigated based on the inverse dynamic model by using sliding mode control. Taking into account the complexity of rigid-flexible coupling effect of the flexible manipulator, the assumed mode method and Lagrange multiplier method were applied to derive the dynamic equations of the system. It is a differential algebraic equation. In order to design conveniently the controller based on the model, the coordinate-partitioned method was used to convert the differential algebraic equations into a second-order differential one. According to the demand of motion and vibration control, the sliding mode control method was applied to design the controller in order to obtain the desired trajectory and attenuate the elastic deformation of flexible manipulator. The numerical simulation results showed the proposed controller can eliminate the deflections of the midpoint of the flexible part and have a good trajectory track performance.