机器人手臂轨迹跟踪的变增益LPV鲁棒H∞控制器设计

摘要

According to the dynamic uncertainties and external disturbance uncertainties of robot manipulator model,a kind of robust H∞ controller design method with the variable gain linear parameter varying is introduced,and Robot manipulators trajectory tracking con-trollers are designed. Dynamic equations of the Robot manipulators trajectory tracking are established by Lagrange method,which adopts the variable gain linear parameter varying and convex decomposition technique,and the variable parameter models of dynamic models are transformed,the variable parameter models of the dynamic models are transformed into the linear parameter varying models with the convex polyhedron structure. Based on robust control theory and linear matrix inequality theory,the feedback controller at each vertex of the convex polyhedron is designed. Then,linear parameter varying controller is obtained by using each vertex controller. Simulation results show that robot manipulators have good tracking performance for the joint position change.%针对机器人手臂模型中存在动态不确定性和外部干扰的不确定性,引入变增益线性变参数的鲁棒H∞控制方法,设计了手臂轨迹跟踪控制器.采用拉格朗日法建立机器人手臂轨迹跟踪动态方程;利用变增益线性变参数凸分解技术,将这一动态模型转化为具有凸多面体结构的线性变参数模型;根据鲁棒控制理论和线性矩阵不等式理论,在凸多面体的各个顶点设计反馈控制器,然后利用各个顶点控制器综合得到线性变参数控制器.仿真结果表明,机器人手臂对于关节位置的变化始终具有良好的跟踪性能.