基于μ综合的平面单臂柔性梁鲁棒振动控制研究

RESEARCH ON ROBUST VIBRATION CONTROL OF PLANE SINGLE ARM FLEXIBLE BEAM BASED ONμSYNTHESIS

针对平面单臂柔性梁轨迹跟踪及末端弹性振动问题,提出了基于μ综合的控制方法对其进行抑振控制。首先,采用假设模态法描述弹性变形,并基于Lagrange方程建立动力学模型;其次,考虑载荷质量和结构阻尼的参数不确定性及建模摄动,运用线性分式变换,选用加权函数建立混合不确定模型。通过引入理想模型改进μ综合的标准控制结构,提高了系统收敛性并改善了闭环系统性能。基于μ综合控制方法,设计了系统鲁棒控制器。仿真结果表明,控制器的结构奇异值上下界均小于1,表示系统具有良好的鲁棒稳定性及鲁棒性能。通过与PD控制器对比分析,表明在存在不确定性和干扰的情况下,所提出的控制策略能更高精度地进行轨迹跟踪,更有效地衰减末端振动,验证了该控制策略的有效性。

Aiming at the problem of trajectory tracking and end elastic vibration of plane single arm flexible beam,a method based onμsynthesis control method was used to suppress the vibration.Firstly,by hypothetical modal method described elastic deformation,and using Lagrange equation established the dynamic model.Secondly,considering the parameter uncertainty and modeling perturbation of load mass and structural damping,by using linear fractional transformation and weighting function established mixed uncertainty model.By introducing ideal model to improve the standard control structure ofμsynthesis,which improved system convergence and closed⁃loop system performance.Based onμsynthesis control method,the robust controller of the system was designed.The simulation results show that the upper and lower bounds of the structural singular value of the controller are less than 1,indicating that the system has good robust stability and robust performance.Through the comparative analysis with PD controller,it shows that in the presence of uncertainty and interference,the proposed control strategy can track the trajectory with higher accuracy and attenuate the end vibration more effectively,which verifies the effectiveness of the control strategy.