Tip position control of single flexible manipulators based on LQR with the Mamdani model

Flexible manipulators have been actively used in various fields, such as aerospace, industry and medical treatment. It remains that the tip of the flexible manipulator should accurately trail the target trajectory without vibration. This paper proposes a novel method of the tip position control of a single flexible manipulator based on LQR with the Mamdani model. Firstly, using the assumed mode method and the Lagrange equations, the dynamic model of the single flexible manipulator is established. Then, the state equations are derived by the dynamic model. Based on the Mamdani model, the fuzzy algorithm is added to the traditional LQR control, and the self-adaptive adjustment of the LQR control variable R is conducted, which improves the adaptability of the control system. Finally, numerical simulations and experiments are presented. The results demonstrate that the novel control method presented in this paper can rapidly achieve the location in the position control and effectively suppress the elastic vibration of the single flexible manipulator, which has more considerable effect compared with the traditional LQR control method.