平面并联机构的残余振动控制

RESIDUAL VIBRATION CONTROL OF PLANAR PARALLEL MECHANISM

针对残余振动限制并联机构高速、高精度应用必须抑制残余振动的特点,以一个2自由度平面并联机构为研究对象,研究抑制其残余振动的方法。采用矢量法进行运动学分析,推导出动平台和各支链的速度和加速度,进而利用虚功原理建立动力学模型。为减少电动机动态对整个动力学系统的影响,每个输入轴分别单独设计一个PD(比例一微分)控制器,整个动力学系统包括这些PD控制器。根据试验测得的系统固有频率和阻尼比设计ZV(零振动)整形控制器。为验证ZV整形控制器的效果,对动平台单步移动情况下并联机构的响应进行仿真。仿真表明,输入整形控制可以显著减小并联机构中的残余振动,这种控制方法同样适用于其他类型的并联机构。

Residual vibration limits the use of parallel mechanisms for high-speed and high-precision operations. Residual vibration must be reduced. Parallel mechanisms using a planar parallel mechanism with two degrees of freedom are presented as an example. The kinematics of the planar parallel mechanism is analyzed by vector method. Based on the kinematics, the linear and angular accelerations of the moving platform and links are derived, respectively. Then virtual work principle is employed to deal with the dynamics of the parallel mechanism. To minimize the effect of the dynamics of the motor to the dynamics of the parallel mechanism, each real axis is controlled by a PD（proportional-derivative） controller, respectively. These PD controllers are included in the dynamic system of the parallel mechanism. According to the natural frequency and damping ratio of dynamics system obtained by experiment, a ZV shaper is designed. The step move of the parallel mechanism is simulated, and the results show that input shaping can reduce the residual vibration of the parallel mechanism. The control method can be applied to various kinds of parallel mechanisms.