中文摘要：

针对多个单输入欠驱动Lagrangian系统的同步控制问题，根据所定义的同步运动系统的同步误差信号，将各轴的位置误差与位置同步误差的比例耦合项作为新的状态变量，采用递阶滑模控制方法设计了一种交叉耦合位置同步控制器。采用该控制策略，对由两部一级倒立摆实际设备构成的同步运动装置的实时控制实验结果和4部一级倒立摆同步运动系统进行了仿真。仿真结果表明，在闭环系统精确跟踪指令信号的同时保证了各子系统间协调同步运动，而且该同步控制器的同步性能优于积分耦合同步控制器的性能。

英文摘要：

A synchronization stratege was proposed for multiple single-input underactuated Lagrangian systems. According to the defined synchronization errors of synchorinization motion system, the proportion coupling terms composed of position errors and position synchronization errors were constructed as new state variables. Then, a cross-coupling position synchronization controller was generated by using the hierarchical sliding mode control method. The real-time experiments on a real synchronization motion equipment with two single inverted pendulums and simulations on a synchronization motion control system with four single inverted pendulums illustrate that the proposed approach realizes a precise trajectorytracking control of the closed-loop systems, while they move synchronously. The effect of the proposed synchronization controller is better than the integral coupling synchronization controller.