Abstract: A novel sliding mode variable structure control scheme is proposed for a class of underactuated systems with two degrees of freedom. The whole system is decomposed into two subsystems, and the sliding surfaces of both subsystems are defined. The equivalent control of the first sub-sliding surface is utilized to construct the control input of the controlled system, and the sliding surface of the second subsystem is incorporated into the switching control law. The switching control of the controller is derived based on the sliding surface of the first subsystem, and then the ultimate sliding mode control law is obtained. The derived control law, which guarantees that both sub-sliding surfaces are asymptotically stable, can dynamically adjust its switching gain according to the variation of the second sub-sliding surface. The simulation results of an overhead crane system confirm the effectiveness and robustness of the proposed control scheme.

Key words:  Underactuated system, sliding mode control, subsystem, time-varying switching gain

摘要： 针对一类二自由度欠驱动系统的控制问题，提出了一种新型的滑模变结构控制策略。将整个系统分解为2个子系统，并分别定义2个子系统的滑动面。利用第1个子系统滑动面的等效控制来构造系统的控制输入，并将第2个子系统的滑动面引入到切换控制律的设计中。基于第1个子系统的滑动面设计了控制器的切换控制部分，从而得出最终的滑模控制律。所得控制律能够根据第2个子系统滑动面的变化动态地调整其切换增益，并保证2个子系统的滑动面都是渐近稳定的。桥式吊车系统的仿真实验结果表明了所提出的控制策略的有效性和鲁棒性。

关键词:

欠驱动系统, 滑模控制, 子系统, 时变切换增益