模糊整定PI参数的双柔性机械臂振动抑制

doi:10.12068/j.issn.1005-3026.2024.02.009

摘要/Abstract

摘要：

机械臂伺服驱动系统中柔性因素的存在易导致机械臂输出转速波动，甚至引发系统谐振.为抑制系统转速波动，使机械臂传动系统性能稳定，使用模糊理论整定PI控制器参数的控制策略.根据假设模态法和拉格朗日动力学方程建立了考虑LuGre摩擦模型的双柔性机械臂传动系统动力学方程，并分析了动力学方程中耦合非线性项对系统传动特性的影响.使用极点配置策略确定PI控制器参数的取值范围，后根据模糊规则实时调整控制器参数，以减小伺服系统输出转速的波动，进而抑制系统谐振.最后，借助数值仿真分析和机械臂控制实验，与传统PI控制策略对比，发现本文所述控制策略可使电机端转角跟踪误差绝对值的平均值降低43.066%，柔性负载转角误差的标准差降低46.506%，更加验证了所提模糊规则整定PI控制器参数抑振方法的有效性.

关键词: 双柔性机械臂, 柔性关节, 柔性负载, 模糊整定, PI控制

Abstract:

The existence of flexible factors in the manipulator servo drive system can easily lead to the fluctuation of the output speed of the manipulator， and even lead to system resonance. In order to suppress the speed fluctuation of the system and stabilize the performance of the manipulator’s transmission system， the fuzzy theory is used to set the control strategy of PI controller parameters. According to the assumed mode method and Lagrange dynamic equation， the dynamic equation of the dual-flexible manipulator’s transmission system considering LuGre friction model is established， and the influence of the coupling nonlinear terms in the dynamic equation on the transmission characteristics of the system is analyzed. The pole assignment strategy is used to determine the value range of the PI controller parameters， and then the controller parameters are adjusted in real time according to the fuzzy rules to reduce the fluctuation of the servo system output speed and further suppress the system resonance. Finally， by means of numerical simulation analysis and manipulators’ control experiment， compared with the traditional PI control strategy， it is found that the control strategy taken in this study can reduce the average value of the absolute value of the motor end angle tracking error by 43.066%， and the standard deviation of the flexible load angle error by 46.506%， which further verifies the effectiveness of the proposed vibration suppression method with fuzzy tuning PI controller parameters.

Key words: dual-flexible manipulator, flexible joint, flexible load, fuzzy tuning, PI control

中图分类号:

TH 113.1

李小彭, 周赛男, 刘佳琪, 尹猛. 模糊整定PI参数的双柔性机械臂振动抑制[J]. 东北大学学报（自然科学版）, 2024, 45(2): 217-225.

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.

图/表 14

图1 具有柔性负载的柔性关节伺服驱动系统模型图

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

表1 系统参数

Table 1 System parameters

参数	名称	参数	名称
J_m/（kg·m²）	电机转动惯量	θ_m/rad	电机转角
I_a/（kg·m²）	负载转动惯量	θ_l/rad	负载转角
T_m/（N·m）	电机电磁转矩	ω_m/（rad·s^-1）	电机角速度
T_l/（N·m）	负载转矩	ω_l/（rad·s^-1）	负载角速度
K_s/ （N·m·rad^-1）	传动系统扭转刚度	y（x，t）/m	负载变形量

图2 柔性负载的末端变形（a）—柔性负载的末端变形分布图；（b）—（a）的局部放大图；（c）—一维变形和忽略耦合非线性项之间的偏差.

Fig. 2 End deformation of flexible load

图3 PI控制策略系统框图

Fig. 3 Block diagram of PI control strategy system

图4 模糊PI控制器结构图

Fig. 4 Structure diagram of the fuzzy PI controller

表2 控制器输出参数KP模糊规则

Table 2 Fuzzy rules for controller output parameter KP

ΔK_P		EC
ΔK_P		NB	NM	NS	ZO	PS	PM	PB
E	NB	PB	PB	PM	PM	PS	ZO	ZO
	NM	PB	PB	PM	PS	PS	ZO	NS
	NS	PM	PM	PM	PS	ZO	NS	NS
	ZO	PM	PM	PS	ZO	NS	NM	NM
	PS	PS	PS	ZO	NS	NS	NM	NM
	PM	PS	ZO	NS	NM	NM	NM	NB
	PB	ZO	ZO	NM	NM	NM	NB	NB

表3 控制器输出参数KI模糊规则

Table 3 Fuzzy rules for controller output parameter KI

ΔK_I		EC
ΔK_I		NB	NM	NS	ZO	PS	PM	PB
E	NB	NB	NB	NM	NM	NS	ZO	ZO
	NM	NB	NB	NM	NS	NS	ZO	ZO
	NS	NB	NM	NS	NS	ZO	PS	PS
	ZO	NM	NM	NS	ZO	PS	PM	PM
	PS	NM	NS	ZO	PS	PS	PM	PB
	PM	ZO	ZO	PS	PS	PM	PB	PB
	PB	ZO	ZO	PS	PS	PM	PB	PB

图5 模糊推理关系（a）—KP模糊推理关系；（b）—KI模糊推理关系.

Fig. 5 Fuzzy reasoning relationship

表4 双柔性机械臂系统参数

Table 4 Parameters of the dual‐flexible manipulator system

参数	长度1	长度2
l/m	1	4
m/kg	1	1
EI/（N·m²）	80	80
ρA/（kg·m^-2）	1	0.25
J_l/（kg·m²）	0.333	5.333
ω₁/（rad·s^-1）	17.116	11.117
β₁	1.25	0.937 5
J_m/（kg·m²）	2
K_s/（N·m·rad^-1）	500
初始控制器参数	K_P1=15，K_I1=20
终止控制器参数	K_P2=20，K_I2=30

图6 耦合非线性项和负载长度对柔性负载变形的影响

Fig. 6 Effect of coupling nonlinearity and load length

图7 不同控制策略下柔性负载的变形

Fig. 7 Deformation of flexible load under different control strategies

图8 不同控制策略的仿真结果（a）—电机端输出转速；（b）—电机端转速误差；（c）—柔性负载输出转速；（d）—柔性负载输出转角.

Fig. 8 Simulation results of different control strategies

图9 双柔性机械臂实验平台

Fig. 9 Dual‐flexible manipulator experiment platform

图10 控制实验结果（a）—长度1时电机的输入输出曲线；（b）—长度1时柔性负载转角误差曲线；（c）—长度2时电机的输入输出曲线；（d）—长度2时柔性负载转角误差曲线.

Fig. 10 Results of the control experimen

参考文献 14

1	Shang D， Li X， Yin M，et al.Speed control method for dual‐flexible manipulator with a telescopic arm considering bearing friction based on adaptive PI controller with DOB［J］.Alexandria Engineering Journal，2022，61（6）：4741-4756.
2	Oh S， Kong K.High‐precision robust force control of a series elastic actuator［J］.IEEE/ASME Transactions on Mechatronics，2016，22（1）：71-80.
3	Spong M.Modeling and control of elastic joint robots［J］.Journal of Dynamic Systems，Measurement，and Control，1987，109（1）：310-319.
4	李小彭，尚东阳，李凡杰，等.输电线巡检机器人位姿变化的柔性关节控制策略［J］.东北大学学报（自然科学版），2020，41（11）：1577-1583.
	Li Xiao‐peng， Shang Dong‐yang， Li Fan‐jie，et al.Flexible joint control strategy based on posture change of transmission line inspection robots［J］.Journal of Northeastern University（Natural Science），2020，41（11）：1577-1583.
5	Katsura S， Ohnishi K.Force servoing by flexible manipulator based on resonance ratio control［J］.IEEE Transactions on Industrial Electronics，2007，54（1）：539-547.
6	Rezaei V， Shafei A.Dynamic analysis of flexible robotic manipulators constructed of functionally graded materials［J］.Iranian Journal of Science and Technology：Transactions of Mechanical Engineering，2018，43（1）：327-342.
7	Shang D， Li X， Yin M，et al.Speed control strategy of dual flexible servo system considering time‐varying parameters for flexible manipulator with an axially translating arm［J］.Asian Journal of Control，2022，25：1-15.
8	丁有爽，肖曦.基于极点配置的永磁同步电机驱动柔性负载PI调节器参数确定方法［J］.中国电机工程学报，2017，37（4）：1225-1239.
	Ding You‐shuang， Xiao Xi. Parameter tuning methods based on pole placement for PI controllers of flexible loads driven by PMSM［J］.Proceedings of the CSEE，2017，37（4）：1225-1239.
9	Shang D， Li X， Yin M，et al.Vibration suppression method based on PI fuzzy controller containing disturbance observe for dual‐flexible manipulator with an axially translating arm［J］.International Journal of Control，Automation and Systems，2022，20（5）：1682-1694.
10	Yin M， Shang D， Huang B，et al.Modeling and control strategy of flexible joint servo system in humanoid manipulator driven by tendon‐sheath［J］.Journal of Mechanical Science and Technology，2022，36（5）：2585-2595.
11	Wu X， Huang Y. Adaptive fractional‐order non‐singular terminal sliding mode control based on fuzzy wavelet neural networks for omnidirectional mobile robot manipulator［J］.ISA Transactions，2022，121：258-267.
12	Shang D， Li X， Yin M，et al.Dynamic modeling and fuzzy compensation sliding mode control for flexible manipulator servo system［J］.Applied Mathematical Modelling，2022，107：530-556.
13	Astrom K， Canudas‐De‐Wit C.Revisiting the LuGre friction model［J］.IEEE Control Systems Magazine，2008，28（6）：101-114.
14	Damaren C， Sharf I.Simulation of flexible‐link manipulators with inertial and geometric nonlinearities［J］.Journal of Dynamic Systems Measurement & Control，1995，117（1）：74-87.

[1]	李小彭，周赛男，尹猛，樊星. 双柔性机械臂伺服系统PI控制策略[J]. 东北大学学报（自然科学版）, 2023, 44(5): 642-651.
[2]	李小彭，尚东阳，李凡杰，闻邦椿. 输电线巡检机器人位姿变化的柔性关节控制策略[J]. 东北大学学报:自然科学版, 2020, 41(11): 1577-1583.
[3]	李明杰，周平. 机械制浆过程磨机负荷内模PI控制[J]. 东北大学学报:自然科学版, 2017, 38(6): 783-788.
[4]	尹凤杰;井元伟;岳晓宁;. 基于模糊变结构控制设计一种鲁棒主动队列管理算法[J]. 东北大学学报(自然科学版), 2006, 27(3): 240-243.