柔性机械臂非线性动力学模型及控制的研究

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，利用变形约束方程和小变形假设条件，对带有末端荷载的柔性机械臂，推导出考虑动力刚化（ＤｙｎｍａｉｃＳｔｉｆ－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。

Study of Dynamic Model and Control of a Flexible Beam

According to the consistent energy principle and the deformation constraint equations, the consistent linear dynamic model in finite dimensions of a horizontally slewing inextensible Euler Bernouli beam with a tip payload is derived with Dynamic Stiffening effect being considered by using assumptive modes method. To trace the joint angle trajectory precisely, the input output partial linearing control method is used to decouple the nonlinear model and to generate the desired control input for ideal joint angle trajectory. To suppress the simultaneous elastic vibratios in movement, an elastic stabilization is designed by using the LQR control method. Numerical simulation results are presented to show the effectiveness of the proposed control strategy.