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针对轴向不伸长的Ｅｕｌｅｒ－Ｂｅｒｎｏｕｌｉ梁，采用假设模态法，根据能量一致性原理，利用变形约束方程的小变形假设条件，对带有末端荷载的柔性机械臂，推导出考虑动力刚化（ｄｙｎａｍｉｃｓｔｉｆ－ｅｎｉｎｇ）影响的柔性机械臂有限维一致线性化动力学方程。为实现柔性机械臂关节转角运动轨迹的精确跟踪，采用基于输入输出部分线性化的控制方法设计非线性控制器，对该非线性动力学模型进行解耦并产生理想关节转角运动轨迹的控制输入。采用线性系统最优状态反馈控制规律设计弹性模态稳态器抑制弹性体的振动。数值仿真验证了该控制策略的有效性。
Aiming at the Euler-Bernouli beam with no axial elongation, the assumption of dynamic stiffening was deduced for the flexible manipulator with terminal load by using the modal method and the small deformation assumption of the deformation constraint equation according to the energy consistency principle. (Dynamicstif-ening) of the flexible manipulator finite dimensional uniform linear dynamic equations. In order to realize accurate tracking of flexible manipulator’s joint rotation trajectory, a nonlinear controller based on input-output partial linearization is designed to decouple the nonlinear dynamics model and generate the control input of ideal articulation path. Elastic modal steady-state suppressor is used to suppress the vibration of the elastomer by using the law of linear system optimal state feedback control. Numerical simulation verifies the effectiveness of this control strategy.