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.