Resonance Suppression of Flexible Manipulators Based on Pole Assignment Method

doi:10.12068/j.issn.1005-3026.2025.20230343

Abstract

Abstract:

In order to suppress the possible resonance of the servo drive system when flexible manipulators move， and reduce the speed fluctuation of the motor output end， a method of designing PI controllers by the pole assignment method is proposed. Based on the assumed mode method and Lagrange dynamic equation， a dynamic model of the flexible manipulator driven by the servo motor is established. The transfer function of the system is obtained by using its state equation， and the transfer characteristics of the servo drive system are analyzed. The parameters of the PI controller are designed by the pole assignment method with the same real part， and the influence of pole natural frequency ratio and damping coefficient on the system evaluation index is discussed. Finally， the simulation experiment is carried out. The results show that the appropriate increase of damping coefficient is beneficial to the stability of the system， but the length and rotational inertia of the flexible load should not be too large. Compared with the traditional Ziegler-Nichols method， the effectiveness of the proposed method is proved.

Key words: flexible manipulator, servo system, vibration suppression, pole assignment, PI controller

CLC Number:

TP 13

Xiao-peng LI, Quan LI, Chao-wei SHANGGUAN, Meng YIN. Resonance Suppression of Flexible Manipulators Based on Pole Assignment Method[J]. Journal of Northeastern University(Natural Science), 2025, 46(6): 86-92.

Figures/Tables 8

Fig.1 Flexible single-rod servo drive system

Fig.2 Speed loop control block diagram of the servo system’s driving flexible load

Fig.3 Bode diagram of the third-order modal system

Fig.4 System evaluation index cloud map

Fig.5 Experiment platform[14]

Table 1 System parameters under different working conditions

柔性负载参数	工况1	工况2	工况3	工况4
抗弯刚度EI/(N·m²)	395	395	395	395
长度l/m	1	1.5	2	2.5
质量m/kg	1	1	1	1
线密度μ/(kg·m^-1)	1	0.67	0.5	0.4
转动惯量I_a/(kg·m²)	0.333 3	0.75	1.333	2.083 3
刚柔耦合系数F_a1/(kg^1/2·m)	0.568 8	0.853 2	1.137 6	1.422 0
模态频率ω₁/(rad·s^-1)	69.871 7	38.033 3	24.703 4	17.676 3

Fig.6 Experimental results of the pole assignment method with equal real part

Fig.7 Comparison of the pole assignment method with equal real part and the Z-N method

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