中文摘要：

研究了Acrobot这一垂直平面欠驱动机械臂的动态伺服控制问题.该问题期望驱动Acrobot到达构形空间中任意目标位置.由于Acrobot不能稳定在除平衡点外的位置,因此考虑将系统镇定到经过目标点的周期轨道上.利用虚约束来描述这样的轨道,进而给出了在所选虚约束作用下系统的零动态和积分曲线.接着设计了级联形式的控制器,内环控制器基于改进的反馈线性化方法,引入了一个使内环呈现二阶系统特性的虚拟输入,在该虚拟输入的基础上,设计了基于Lyapunov稳定性理论的外环控制器.最后通过数字仿真证明所提出的方法合理有效,并且获得比基于能量的动态伺服方法更优的结果.

英文摘要：

The dynamical servo control problem of a vertical planar underactuated manipulator acrobot is studied in this paper. This problem aims to drive acrobot to any position in the construction space. Since the acrobot cannot be stabilized at any position except the equilibrium points,we consider to stabilize the system to a periodic orbit which passes through the target position. The virtual constraint is used to describe these periodic orbits,and then the zero dynamics and the relative integral curve under the selected virtual constraint are given. A cascade form controller is designed. The inner loop controller is based on the improved feedback linearization method and a virtual input which makes the inner loop like a second-order system is introduced. With this virtual input,an outer loop controller is designed based on Lyapunov stabilizing theory. The simulation results show the effectiveness of the designed control law,and that this method is better than the energy based method.