考虑误差补偿的柔性机械臂命令滤波滑模控制

Command-filtered backstepping sliding mode control of a flexible robotic arm considering error compensation

针对单关节柔性机械臂控制中存在参数摄动、外部干扰及滤波误差等导致轨迹跟踪精度性能变差的问题,提出一种考虑误差补偿的命令滤波滑模控制方法。首先,给出含不确定项的单关节柔性机械臂动力学方程,设计反步滑模控制;然后,引入二阶命令滤波器获得虚拟控制量的导数,避免传统反步控制引起的“计算爆炸”问题;最后,基于李雅普诺夫理论设计误差补偿机制用以消除命令滤波器所产生的滤波误差。仿真结果表明,当系统存在参数摄动和外部干扰时,所提出的误差补偿命令滤波滑模控制与未加误差补偿的命令滤波滑模控制和误差补偿命令滤波控制方法相比,其轨迹跟踪精度分别提升了19.8%和74.0%,滤波误差分别减少了44.4%和31.4%。

In response to the issues of parameter perturbations,external disturbances,and filtering errors affecting trajectory tracking accuracy in single-joint flexible robotic arm control,a command-filtered sliding mode control method with error compensation was proposed.Firstly,the dynamic equation of the single-joint flexible robotic arm with uncertainties was presented and a backstepping sliding mode control was designed.Then,a second-order command filter was introduced to obtain the derivative of the virtual control signal,thereby avoiding the″computational explosion″issue associated with traditional backstepping control.Finally,an error compensation mechanism based on Lyapunov theory was used to eliminate filtering errors generated by the command filter.Simulation results demonstrate that when the system experiences parameter perturbations and external disturbances,the proposed error compensation command-filtered sliding mode control achieves trajectory tracking accuracy improvements of 19.8%and 74%compared to command-filtered sliding mode control without error compensation and error compensation command-filtered control methods,respectively.Filtering errors are reduced by 44.4%and 31.4%,respectively.