球杆系统基于二阶滑模的分级滑模控制

Hierarchical sliding mode control of a ball and beam system based on second order sliding mode

为解决球杆系统的稳定控制问题,提出一种基于二阶滑模的分级滑模控制方法。与基于传统滑模的分级滑模控制方法相比,该文方法能够应用连续、无抖振的分级滑模控制器实现球杆系统的有效控制。分别定义刚性球和连杆两个子系统的第一级滑动变量,然后采用两者的线性组合来构造第二级滑动变量。所提出的分级滑模控制律包含第二级滑动面的等效控制律和一个待确定的切换控制律。基于球杆系统的动力学模型推得控制器的等效控制律,然后借助状态反馈和二阶滑模控制算法得出控制器的切换控制律。在该文控制器作用下球杆系统能够快速、准确地收敛至期望的平衡点,仿真实验结果表明该文方法的有效性和该文控制器的鲁棒性。

A hierarchical sliding mode control method based on second order sliding mode is proposed to solve the stable control problem of a ball and beam system.Compared with the hierarchical sliding mode control methods based on traditional sliding mode control,the proposed control method can realize effective control of the ball and beam system by using a continuous and chattering-free hierarchical sliding mode controller.The first level sliding variables of the rigid ball subsystem and the link subsystem are defined,and then the second level sliding variable is constructed by linearly combining the two first level sliding variables.The proposed hierarchical sliding mode control law consists of the equivalent control law of the second level sliding surface and a switching control law to be determined.The equivalent control law of the proposed controller is derived based on the dynamic model of the ball and beam system,and then the switching control law is obtained by means of state feedback and a second order sliding mode control algorithm.The ball and beam system can be driven by the proposed controller to converge to the desired equilibrium quickly and accurately.The simulation results show the effectiveness of the proposed control method and the robustness of the proposed controller.