具有极点配置的不确定性机器人鲁棒H_∞控制

Robust H_∞ Control with Pole Placement for an Uncertain Robotic Manipulator

针对具有时变负载和参数不确定的n关节机器人 ,提出利用线性矩阵不等式技术来设计具有极点配置的鲁棒H∞ 控制器的新方法 .通过非线性补偿将机器人系统化为一具有不确定摄动的线性系统 ,利用线性矩阵不等式技术对此线性系统设计满足闭环极点配置要求的状态反馈H∞ 控制器 ,并将控制器的设计归结为求解一包含矩阵不等式约束的优化问题 ,且提出了一种获得此优化问题可行解的迭代方法 .最后利用DDR -Ⅱ型直接驱动机器人进行了仿算 ,验证了所提出的方法可保证机器人在存在时变负载和参数不确定情况下随关节位置变化始终具有很好的鲁棒控制性能 .

A new approach was presented to design a robust H∞ controller with pole placement based on linear matrix inequality (LMI) technique for an n-joint rigid robotic manipulator with time varying payload and parameter uncertainty. With the use of nonlinear compensation, the robotic system was translated into a linear system with uncertainty terms. A state-feedback H∞ controller satisfying the closed-loop pole placement demand for the linear system was designed via LMI technique. The controller design then comes into a convex optimization problem including LMIs. An iterative method to acquire the feasible solution of the above optimization problem was presented. The effectiveness of the proposed controller is demonstrated by simulation for a self-designed direct drive 2-joint planar robotic manipulator.