基于MATLAB的3-RPS并联机构控制系统仿真

Simulation for control system of 3-RPS parallel mechanism based on MATLAB

针对传统螺旋法求解并联机构Jacobian矩阵的缺陷,提出了一种基于并联机构微运动分析的微位移法.该微位移法在求解过程中可避免求解超越方程组的难题,且得到的Jacobian矩阵为非奇异方阵.同时,针对并联机构传统控制器轨迹跟踪精度低的问题,设计了一种基于并联机构动力学方程和比例切换控制律的滑模变结构控制器(SMC).首先,建立机构的MATLAB/SimMechanics仿真分析模型,采用微位移法求解并联机构的Jacobian矩阵,为控制系统提供理论参考输入值.其次,设计SMC控制器,运用Lyapunov函数证明控制器的稳定性;最后,分别建立机构PID控制和SMC控制系统的MATLAB/Simulink框图,对其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控制器的精度高,稳态误差小,且鲁棒性强,响应速度快,从而验证了SMC控制的有效性.

Owing to the defects of traditional spiral method to solve Jacobian matrix of parallel mechanism,a micro-displacement method was put forward based on micro-motion analysis of 3- RPS parallel mechanism. The method could avoid the problem of transcendental equation group in the solving process, and the Jacobian matrix acquired was a non singular matrix. At the same time,aiming at the low trajectory tracking precision of conventional controller of parallel mecha- nism,the sliding model controller （SMC） was designed by the dynamic equation of 3-RPS parallel mechanism and proportional switching control law. Firstly, the MATLAB/SimMechanics simulation analysis model of 3-RPS parallel mechanism was presented and the Jacobian matrix of 3-RPS parallel manipulator was solved by micro-displacement method, which was the theoretical reference value for control system. Secondly, the SMC controller was designed, then the stability of SMC controller was proven based on the Lyapunov function. Finally, the MATLAB/Simulink model of PID controller and SMC controller were respectively established,and the simulation analysis and comparison were performed. The results show that the SMC controller has higher trajectory tracking precision, smaller steady-state error, faster response speed and better robustness than that of PID controller,so the effectiveness of SMC controller is verified.