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Aiming at the problem of trajectory tracking and end elastic vibration of plane single arm flexible beam, a method based on μ synthesis 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 andmodeling 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 of μ synthesis, which improved system convergence and closed-loop system performance. Based on μ synthesis 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.