基于新型趋近率的含齿隙随动系统鲁棒控制

doi:10.12305/j.issn.1001-506X.2023.04.26

Abstract

Abstract:

Aiming at the requirements with high precision, fast response and strong robustness of the servo system includes backlash, a control strategy based on the new sliding mode reaching law is proposed. Firstly, an integral nonsingular terminal sliding mode controller is introduced in the design of position loop, which can effectively overcome the changes of structural parameters and improve the response ability. Secondly, the linear extended state observer is used to compensate the backlash factor in the transmission structure which increases the stability and robustness of the system. Finally, based on the designed new sliding mode reaching law, the jitter problem of controller output is overcome. The joint simulation experiments prove the effectiveness of the proposed method.

Key words: servo system with backlash, integral nonsingular terminal sliding mode (INTSM), linear extended state observer (LESO), sliding mode reaching law

CLC Number:

TJ765.2

Fangjun LI, Shengjie WANG, Junfeng LI, Hao LI, Chenjun CUI. Robust control of servo system with backlash based on new reaching law[J]. Systems Engineering and Electronics, 2023, 45(4): 1177-1184.

Figures/Tables 15

Fig.1

Fig.2

Fig.3

Table 1

Table 2

Table 3

Table 4

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Table 5

Table 6

References 31

1	付东学, 赵希梅. 永磁直线同步电机自适应反推全局快速终端滑模控制[J]. 电工技术学报, 2020, 35 (8): 1634- 1641.
	FU D X , ZHAO X M . Adaptive backstepping global fast terminal sliding mode control for permanent magnet linear synchronous motor[J]. Transactions of China Electrotechnical Society, 2020, 35 (8): 1634- 1641.
2	李玉霞, 王帅, 王建立, 等. 地平主焦点式大视场望远镜的双电机消旋系统[J]. 光学精密工程, 2021, 29 (4): 749- 762.
	LI Y X , WANG S , WANG J L , et al. Dual-motor de-rotator system of prime focus alt-azimuth telescope with large field of view[J]. Optics and Precision Engineering, 2021, 29 (4): 749- 762.
3	WANG Q W , WANG G L , ZHAO N N , et al. An impedance model-based multiparameter identification method of PMSM for both offline and online conditions[J]. IEEE Trans.on Power Electronics, 2021, 36 (1): 727- 738. doi: 10.1109/TPEL.2020.3000896
4	QU L Z , QIAO W , QU L Y . An enhanced linear active disturbance rejection rotor position sensorless control for permanent magnet synchronous motors[J]. IEEE Trans.on Power Electronics, 2020, 35 (6): 6175- 6184. doi: 10.1109/TPEL.2019.2953162
5	YANG Q C , LIU T , WU X , et al. A planetary gear reducer backlash identification based on servo motor current signal and optimized fisher discriminant analysis[J]. ISA Transactions, 2021, 112, 350- 362. doi: 10.1016/j.isatra.2020.12.016
6	GHANNADI B , SHARIF R R , MCPHEE J . A modified homotopy optimization for parameter identification in dynamic systems with backlash discontinuity[J]. Nonlinear Dynamics, 2019, 95, 57- 72. doi: 10.1007/s11071-018-4550-1
7	LYU W S , WANG F . Adaptive fuzzy finite-time control for uncertain nonlinear systems with asymmetric actuator backlash[J]. International Journal of Fuzzy Systems, 2019, 21, 50- 59. doi: 10.1007/s40815-018-0532-1
8	田福庆, 姜尚, 梁伟阁. 含齿隙弹载舵机的全局反步模糊自适应控制[J]. 自动化学报, 2019, 45 (6): 1177- 1185.
	TIAN F Q , JIANG S , LIANG W G . Global backstepping fuzzy adaptive control for ammunition actuator with backlash[J]. ACTA Automatica Sinica, 2019, 45 (6): 1177- 1185.
9	SEBASTIAN V , MARIO P . Time-domain identification method for detecting mechanical backlash in electrical drives[J]. IEEE Trans.on Industrial Electronics, 2009, 56 (2): 568- 573. doi: 10.1109/TIE.2008.2003498
10	HAN Y , LIU C , WU J H . Backlash identification for PMSM servo system based on relay feedback[J]. Nonlinear Dynamics, 2016, 84, 2363- 2375. doi: 10.1007/s11071-016-2650-3
11	RUDERMAN M , FRIDMAN L . Model-free sliding-mode-based detection and estimation of backlash in drives with single encoder[J]. IEEE Trans.on Control Systems Technology, 2021, 29 (2): 812- 817. doi: 10.1109/TCST.2019.2956914
12	MARGIELEWICZ J , GSKA D , LITAK G . Modelling of gear backlash[J]. Nonlinear Dynamics, 2019, 97, 355- 368. doi: 10.1007/s11071-019-04973-z
13	DIMITRIOS P , MOGENS B , HANS H N , et al. Robust backlash estimation for industrial drive-train systems-theory and validation[J]. IEEE Trans.on Control Systems Technology, 2019, 27 (5): 1847- 1861. doi: 10.1109/TCST.2018.2837642
14	韩崇伟, 彭超, 石志翔, 等. 基于干扰抑制的含齿隙伺服系统鲁棒控制方法[J]. 系统仿真学报, 2018, 30 (2): 691- 698.
	HAN C W , PENG C , SHI Z X , et al. Disturbance rejection based robust control approach for servo system with backlash[J]. Journal of System Simulation, 2018, 30 (2): 691- 698.
15	ZHU P K , CHEN Y , LI M , et al. Fractional-order sliding mode position tracking control for servo system with disturbance[J]. ISA Transactions, 2020, 105, 269- 277. doi: 10.1016/j.isatra.2020.05.032
16	XIE Y L , ZHANG X L , MENG W , et al. Coupled fractional-order sliding mode control and obstacle avoidance of a four-wheeled steerable mobile robot[J]. ISA Transactions, 2021, 108, 282- 294. doi: 10.1016/j.isatra.2020.08.025
17	MA H F , LIU C , LIU Y , et al. Sliding mode control for uncertain discrete time systems based on fractional order reaching law[J]. IET Control Theory & Applications, 2019, 13 (13): 1963- 1970.
18	XU W , DIAN R J , LIU Y , et al. Robust flux estimation method for linear induction motors based on improved extended state observers[J]. IEEE Trans.on Power Electronics, 2019, 34 (5): 4628- 4640. doi: 10.1109/TPEL.2018.2865800
19	LIU C Q , LUO G Z , DUAN X L , et al. Adaptive LADRC-based disturbance rejection method for electromechanical servo system[J]. IEEE Trans.on Industry Applications, 2020, 56 (1): 876- 889. doi: 10.1109/TIA.2019.2955664
20	LIU Z G , WANG Y Q , LIU S , et al. An approach to suppress low-frequency oscillation by combining extended state observer with model predictive control of EMUS rectifier[J]. IEEE Trans.on Power Electronics, 2019, 34 (10): 10282- 10297. doi: 10.1109/TPEL.2019.2893491
21	LI G F , WU Y J , XU P Y . An observer-based fixed-time position tracking strategy for DC torque motor systems[J]. Mechanical Systems and Signal Processing, 2020, 142 (1): 106774.
22	孟思华, 王尧尧, 陈柏, 等. 基于时延估计的绳驱动飞行机械臂模糊非奇异终端滑模飞行控制[J]. 中南大学学报(自然科学版), 2021, 52 (10): 3465- 3474.
	MENG S H , WANG Y Y , CHEN B , et al. Fuzzy nonsingular terminal sliding mode flying control of cable-driven flying manipulators based on time-delay estimation[J]. Journal of Central South University, 2021, 52 (10): 3465- 3474.
23	ABADI A , AMRAOUI A E , MEKKI H , et al. Robust tracking control of quadrotor based on flatness and active disturbance rejection control[J]. IET Control Theory and Applications, 2020, 14 (8): 1057- 1068. doi: 10.1049/iet-cta.2019.1363
24	XU Z , ZHANG T R , BAO Y L , et al. A nonlinear extended state observer for rotor position and speed estimation for sensorless IPMSM drives[J]. IEEE Trans.on Power Electronics, 2020, 35 (1): 733- 743. doi: 10.1109/TPEL.2019.2914119
25	WANG C W , ZHANG Z Y , WANG H , et al. Disturbance observer-based output feedback control of hydraulic servo system considering mismatched uncertainties and internal pressure dynamics stability[J]. IET Control Theory and Applications, 2020, 14 (8): 1046- 1056. doi: 10.1049/iet-cta.2019.0346
26	QU L Z , QIAO W , QU L Y . Active-disturbance-rejection-based sliding-mode current control for permanent-magnet synchronous motors[J]. IEEE Trans.on Power Electronics, 2021, 36 (1): 751- 760.
27	LIU X D , YU H S . Continuous adaptive integral-type sliding mode control based on disturbance observer for PMSM drives[J]. Nonlinear Dynamics, 2021, 104, 1429- 1441.
28	WANG Y Q , FENG Y T , ZHANG X G , et al. A new reaching law for antidisturbance sliding-mode control of PMSM speed regulation system[J]. IEEE Trans.on Power Electronics, 2020, 35 (4): 4117- 4126.
29	李思远, 陈子坤, 梁曦, 等. 带有齿隙的空间机械臂动力学仿真与试验设计[J]. 测试技术学报, 2017, 31 (1): 17- 23.
	LI S Y , CHEN Z K , LIANG X , et al. Dynamical simulation and experimental design of space manipulator with backlashes[J]. Journal of Test and Measurement Technology, 2017, 31 (1): 17- 23.
30	蒋潇蓉, 郁家耀, 周君涛, 等. 基于ADAMS的某无后坐炮发射动态仿真分析[J]. 兵器装备工程学报, 2020, 41 (8): 17- 21.
	JIANG X R , YU J Y , ZHOU J T , et al. Dynamic simulation analysis of a recoilless gun launching based on ADAMS[J]. Journal of Ordnance Equipment Engineering, 2020, 41 (8): 17- 21.
31	周凯红, 郭玉田, 黄思敏. 基于Adams和Matlab的非圆锥齿轮传动机构仿真研究[J]. 机电工程, 2022, 39 (1): 40- 46.
	ZHOU K H , GUO Y T , HUANG S M . Simulation of non-bevel gear transmission mechanism based on Adams and Matlab[J]. Journal of Mechanical & Electrical Engineering, 2022, 39 (1): 40- 46.

参数	数值
定子电感L/mH	4.25
定子电阻R/Ω	0.26
力矩系数K_t/(N·m·A^－1)	1.066
反电势系数C_e/(V/(rad·s^－1))	0.8
减速器减速比i_r	10
齿轮结构传动比i_m	5
负载转动惯量J_m/(kg·m²)	22.776
摩擦系数B_m/(N·m·s·rad^－1)	0.01

参数	数值
位置环比例系数	70
速度环比例系数	14
速度环积分系数	0.1
电流环比例系数	0.212
电流环积分系数	13

参数	数值
位置环比例系数	1.65
LESO系数λ₁	12
LESO系数λ₂	800
INTSM系数β	1
INTSM系数p/q	5/3
INTSM系数D	1 000
INTSM系数k	1 000

参数	数值
位置环比例系数	1.65
LESO系数λ₁	12
LESO系数λ₂	800
INTSM系数β	1
INTSM系数p/q	5/3
INTSM系数D	1 000
INTSM系数k	1 000
INTSM系数α	7

控制策略	加载过程位置偏差最大值/rad	撤去时位置偏差最大值/rad	误差减小至0.1%所用时间/s
PID方法	0.005 1	0.002	3.92
指数趋近率控制策略	0.002 8	0.003	0.50
新型趋近率控制策略	0.003 7	0.004	0.69

Robust control of servo system with backlash based on new reaching law

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 15

References 31

Related Articles 1

Recommended Articles

Metrics

Comments

控制策略	位置偏差最大值/rad	误差减小至0.1%所用时间/s
PID方法	0.012	1.040
指数趋近率控制策略	0.013	0.335
新型趋近率控制策略	0.015	0.459