3-RPC并联机构微运动分析及控制仿真

Micro-Motion Analysis and Simulation for the 3-RPC Parallel Manipulator

采用微运动法求解并联机构的Jacobian矩阵,可避免传统螺旋法解超越方程组的难题,且得到的矩阵是非奇异方阵。基于3-RPC并联机构模型,运用微运动法求解机构的Jacobian矩阵,将其作为控制系统的输入输出理论参考值。建立机构的Solid Works三维模型,并转化为Matlab/Sim Mechanics仿真分析模型。基于比例切换控制律设计滑模变结构控制器(SMC),采用Lyapunov函数证明SMC控制器的稳定性,分别建立PID控制器和SMC控制器的Matlab/Simulink系统框图并进行仿真分析与对比,结果表明:SMC控制器的轨迹跟踪精度比PID控制器的高,且响应速度快,鲁棒性强,从而验证了SMC控制的有效性。

The Jacob ian matrix of 3-RPC parallel manipulator is solved by micro-motion method, which can avoid the problem of solving transcendental equations using traditional spiral method and the resulting matrix is non-singular square matrix. Based on the model of 3-RPC parallel manipulator, we solve its Jacobian matrix by micro-motion method and the Jacobian matrix is theoretical reference value for control system. The three-dimensional model of3-RPC/s established by SolidWorks soft and it is transformed to Matlab/SimMechanics model for simulation using Matlab soft. The sliding model controller （SMC） is designed by proportional switching control law, then we prove the stability of SMC controller based on the Lyapunov function. We compare the effect of PID controller with SMC controller, the results show that the trajectory travking precision of SMC controller is higher than that of PID controller, and the SMC controller has faster response speed and better robustness.