In this paper, a hierarchical sliding mode controller is proposed for a single-link flexible manipulator positioning with active vibration suppression. The derived model is highly nonlinear, and the manipulator is affected by unknown, matched, and bounded model uncertainties and/or external disturbances. First, the dynamic equations of the system are derived using the Hamilton’s principle, and the elastic movement is approximated using the assumed mode method. System equations are then formulated in the state space form and adapted to the control algorithm via suitable decomposition into two interconnected lower-order subsystems associated with the rigid body motion and the flexible one respectively. Next, an integral sliding mode control is proposed to tackle the matched uncertainties and/or disturbances. Lyapunov’s theory has been applied to prove the asymptotic stability of the sliding surface. Simulation results showed that the proposed controller can effectively reduce the residual vibration while positioning the flexible manipulator.

本文提出了一种分层滑模控制器，用于具有主动振动抑制的单连杆柔性机械臂定位。导出的模型是高度非线性的，并且操纵器受到未知的、匹配的和有界的模型不确定性和/或外部干扰的影响。首先，利用哈密顿原理推导了系统的动力学方程，并利用假定模态法对弹性运动进行了近似。然后以状态空间形式制定系统方程，并通过适当分解为分别与刚体运动和柔性运动相关的两个互连的低阶子系统来适应控制算法。接下来，提出了积分滑模控制来解决匹配的不确定性和/或干扰。李雅普诺夫理论已被应用来证明滑动面的渐近稳定性。仿真结果表明，所提出的控制器能够有效降低柔性机械臂定位时的残余振动。