柔性机械臂的状态观测及跟踪控制研究
Research on State Observation and Tracking Control of Flexible Manipulators

提出一种基于非线性状态观测器的输入输出控制策略，实现了平面运动多连杆柔性机械臂的关节角跟踪控制和弹性振动的抑制。应用拉格朗日法建立柔性机械臂的动力学模型。基于欧拉-伯努利梁理论，采用有限维度的假设模态描述机械臂的弹性振动。通过重新定义机械臂末端处的输出变量，运用输入输出线性化方法，设计反馈控制器实现了对关节角的控制；以非线性观测器获得弹性振动幅值的变化率，以此构建了振动抑制控制器。通过李雅普诺夫定理证明了设计的非线性观测器的稳定性和误差一致收敛性，引入遗传算法对振动抑制控制器的增益实现了整定，仿真结果证明了提出的控制方法的有效性。
An observer-based input-output control strategy is presented to track the joint angle and to eliminate the flexible vibration for planar multi-link flexible manipulators. The Lagrangian approach is applied to build the dynamic model of the flexible manipulator. Based on Euler-Bernoulli beam theory, the finite-dimensional assumed modes method is used to describe the elastic vibration of the flexible manipulator. The control strategy presented is developed based on input-output feedback linearization theory. The feedback controller is designed to control the joint angle by redefining output variables near the end point of the arm. A non-linear observer is design to estimate the amplitude variation of elastic vibration. The observed values are used to build a vibration-suppressed controller. The nonlinear stability of dynamic system and the uniform convergence of the error are proved by Lyapunov theorem. Genetic algorithms is introduced to optimize the gains of vibration-suppressed controller. Simulation results have proved the effectiveness of the control strategy