中文摘要：

建立了三维吊车系统的数学模型,采用分离变量法建立了三维吊车的时变线性模型,并讨论了系统的可控性.针对变绳长吊车系统的防摆问题,设计了变增益LQR控制器,有效地实现了三维吊车的防摆控制.对比仿真实验结果证明变增益LQR控制方法具有较强的自适应性和稳定性,显著提高了控制性能.

英文摘要：

The dynamic model of three dimension （3D） crane system is built. Then the linear time-varying system is obtained by using the method of separating variables, and the controllability is discussed. As to the anti-swing control problem for the 3D crane under the condition of variable length of the rope, the variable gain LQR controller is designed, and the good control performance is obtained. The comparative simulation results demonstrate that the variable gain LQR controller has higher adaptability and stability, and the effectiveness is improved obviously.