平面3-RRR柔性并联机器人残余振动主动控制

Active Residual Vibration Control of Planar 3-RRR Flexible Parallel Robots

摘要:

对平面3-RRR柔性并联机器人残余振动主动控制问题进行了研究。基于有限元法和拉格朗日方程，建立了带压电陶瓷制动器和传感器的智能梁单元的运动方程。考虑刚体运动和弹性变形运动的约束关系，通过组装，形成了3-RRR柔性并联机器人系统的运动学方程，基于模态理论把物理空间下描述的高阶运动方程变换到模态空间下的低阶模态方程。根据导出的低阶模态方程，设计了应变速度反馈控制器和最优状态反馈控制器，数值仿真结果表明：两种控制器都能有效地抑制系统的残余振动。同时，相对于应变速度反馈控制，最优状态反馈控制能以更低的控制输入电压取得更好的控制效果。

Abstract:

A research concerning active residual vibration control of planar 3-RRR flexible parallel robots was presented. First, based on the finite element method and the Lagrange’s equation, the equations of motion of the smart beam bonded lead zirconate titanate (PZT) actuators and sensors were modeled. Considering constraint equations of rigid motion and elastic motion, the general motion equations of planar 3-RRR flexible parallel robots were determined by the compatibility. The high-order equations of the system in physical space were transformed into modal space through the modal theory. According to the low-order modal equations, both the strain rate feedback controler and the optimal state feedback controler were designed for suppressing residual vibration of the system. The numerical simulation results revealed that two kinds of controllers could effectively suppress residual vibration of the system. Moreover, comparing the strain rate feedback control, the optimal state feedback control could obtain better control results in a lower control voltage.