含边界层的机械臂分数阶滑模控制

针对含扰动的机械臂系统，在经典滑模控制基础上引入分数阶微积分构造分数阶滑模面，同时在趋近律中设置边界层，用饱和函数替代符号函数以削弱滑模面的抖振现象，从而获得一种含边界层的机械臂分数阶滑模控制，并通过李雅普诺夫直接法证明其收敛性. 算例以两自由度机械臂系统为被控对象，仿真结果表明，相比于经典的滑模控制，含边界层的机械臂分数阶滑模控制可通过调节微分阶次获得更好的收敛性，实现精确的轨迹跟踪.

Fractional-order sliding mode control of robotic arms with boundary layer

For the robotic arm system with perturbation, the fractional-order calculus was introduced to construct a fractional-order sliding mode surface based on classical sliding mode control. While a boundary layer had set in the reaching law, and the sign function was replaced with the saturation function to weaken chattering phenomenon of the sliding mode surface to obtain a fractional-order sliding mode control of robotic arms with boundary layer, and its convergence had proved by the direct method of Lyapunov. Example with a two-degree-of-freedom robotic arm system as the controlled object, the simulation result shows that the fractional-order sliding mode control of robotic arms with boundary layer can achieve better convergence and accurate trajectory tracking by adjusting the differential order compared with the classical sliding mode control.