PI Control Strategy for the Moving Speed of Flexible Robotic Arms

doi:10.12068/j.issn.1005-3026.2024.10.006

Abstract

Abstract:

A flexible robotic arm and its flexible load may result in changes to such specific parameters as rotational inertia as the arm’s posture changes， subsequently affecting the output speed of the servo drive system. By using a pole placement method with the same damping coefficient， the parameters of the proportional-integral （PI） controller in the drive system are adjusted， enabling the PI controller to automatically adjust its parameters in response to changes in the robotic arm’s posture， thereby dynamically stabilizing the motor’s output speed. A mathematical model is established based on the Lagrangian principles and continuum vibration theory， and the transfer function is obtained through state equations. The PI controller parameters are adjusted using the pole placement method with the same damping coefficient and applied to the speed loop control. The impact of the damping coefficient and natural frequency on the system’s resonance peak， resonance frequency， and bandwidth is analyzed. Numerical simulation demonstrates that appropriately adjusting the damping coefficient can reduce speed fluctuations in the servo drive system. A comparison with the Ziegler-Nichols self-tuning （Z-N） method shows that the pole placement method with the same damping coefficient achieves system stability in a shorter time.

Key words: flexible robotic arm, flexible load, PI controller, pole placement method with the same damping coefficient, servo drive system

CLC Number:

TH 113.1

Xiao-peng LI, Guo-wen CHEN, Meng YIN, Jia-xing FU. PI Control Strategy for the Moving Speed of Flexible Robotic Arms[J]. Journal of Northeastern University(Natural Science), 2024, 45(10): 1409-1416.

Figures/Tables 10

Fig.1 Model of the servo drive system with flexible load

Fig.2 Simplified flexible load servo drive system

Fig.3 Block diagram of the control of the rotational speed loop for flexible load

Fig.4 Block diagram of the control of the rotational speed loop for rigid load

Fig.5 Bode diagram of the servo drive system

Fig.6 Schematic diagram of the pole placement method with the same damping coefficient

Fig.7 System evaluation index diagram of the pole

Table 1 Different pose system parameters

参数	位姿1	位姿2	位姿3
抗弯刚度EI/（N·m²）	400	400	400
线密度ρ_l/（kg·m^-1）	0.800	0.636	0.574
长度l/m	1.1	1.7	2.2
体密度ρ/（kg·m^-3）	7 760	6 120	5 450
厚度b/m	0.015	0.015	0.015
高度h/m	0.015	0.015	0.015
负载转动惯量I_a/（kg·m²）	0.322	0.612	0.926
一阶模态柔性耦合系数F_a1/（kg^1/2·m）	0.500	0.614	0.718
一阶模态角频率ω₁/（rad·s^-1）	68.13	39.77	28.44

Fig.8 Simulation results of the pole configuration

Fig.9 Comparison diagram of the servo system’s

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[3]	Xiao-peng LI, Sai-nan ZHOU, Jia-qi LIU, Meng YIN. Vibration Suppression of Dual-Flexible Manipulator with Fuzzy Tuning PI Parameters [J]. Journal of Northeastern University(Natural Science), 2024, 45(2): 217-225.
[4]	LI Xiao-peng， ZHOU Sai-nan， YIN Meng， FAN Xing. PI Control Strategy of Double-Flexible Manipulator’s Servo System [J]. Journal of Northeastern University(Natural Science), 2023, 44(5): 642-651.