基于变幂次趋近律的滚珠丝杠进给系统滑模控制
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摘要
为了解决滚珠丝杠进给系统滑模控制的抖振问题并提高系统跟踪性能,提出了一种基于变幂次趋近律的滑模控制方法.所设计的非线性干扰观测器能精确地观测出是否满足匹配条件的干扰.采用改进的变幂次趋近律提高了滑模函数的收敛速度,改善了运动品质.在控制律中设计积分补偿项消除了匀速段的稳态误差.仿真及实验结果表明:基于指数趋近律方法的最大跟踪误差仿真值与实验值分别为3.40和17.77μm,基于改进的变幂次趋近律方法的最大跟踪误差仿真值与实验值降低至2.79和11.00μm.控制电压信号中的抖振明显削弱,且增加外部干扰后仍能维持高精度.仿真及实验结果证明了基于变幂次趋近律的滚珠丝杠进给系统滑模控制方法能够有效消除抖振及匀速段的稳态误差,提高跟踪精度,且对外部干扰具有强鲁棒性.
To solve the chattering problem of sliding mode control for ball screw drives and improve the tracking performance of the system, a sliding mode control method based on variable power reaching law was proposed. The matched and mismatched disturbance could be accurately observed by the designed nonlinear disturbance observer. The improved variable power reaching law was adopted to increase the convergence speed of the sliding mode function and improve the motion quality. The integral compensation term of the control law was designed to eliminate the steady-state error at the uniform speed stage. The results show that the simulation value and experimental value of the maximum tracking error with the exponential reaching law method are 3.40 and 17.77 μm, the above values decrease to 2.79 and 11.00 μm with the improved variable power reaching law method. The chattering in the control voltage signal is obviously weakened and the tracking accuracy can still be maintained after adding external disturbance. It is proved that sliding mode control for ball screw drives based on the proposed variable power reaching law can effectively eliminate the chattering and the steady-state error at the uniform speed stage and improve the tracking accuracy meanwhile, it has strong robustness to external disturbance.
To solve the chattering problem of sliding mode control for ball screw drives and improve the tracking performance of the system, a sliding mode control method based on variable power reaching law was proposed. The matched and mismatched disturbance could be accurately observed by the designed nonlinear disturbance observer. The improved variable power reaching law was adopted to increase the convergence speed of the sliding mode function and improve the motion quality. The integral compensation term of the control law was designed to eliminate the steady-state error at the uniform speed stage. The results show that the simulation value and experimental value of the maximum tracking error with the exponential reaching law method are 3.40 and 17.77 μm, the above values decrease to 2.79 and 11.00 μm with the improved variable power reaching law method. The chattering in the control voltage signal is obviously weakened and the tracking accuracy can still be maintained after adding external disturbance. It is proved that sliding mode control for ball screw drives based on the proposed variable power reaching law can effectively eliminate the chattering and the steady-state error at the uniform speed stage and improve the tracking accuracy meanwhile, it has strong robustness to external disturbance.
引文
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[6] 包达飞, 汤文成, 董亮. 带摩擦补偿的滚珠丝杠副进给系统自适应滑模控制[J]. 东南大学学报(自然科学版), 2015, 45(3): 455-460. DOI:10.3969/j.issn.1001-0505.2015.03.008.Bao D F, Tang W C, Dong L. Adaptive sliding mode control of ball screw drives with friction compensation[J]. Journal of Southeast University (Natural Science Edition), 2015, 45(3): 455-460. DOI:10.3969/j.issn.1001-0505.2015.03.008.(in Chinese)
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[10] Ginoya D, Shendge P D, Phadke S B. Sliding mode control for mismatched uncertain systems using an extended disturbance observer[J]. IEEE Transactions on Industrial Electronics, 2014, 61(4): 1983-1992. DOI:10.1109/tie.2013.2271597.
[11] Rajabi N, Abolmasoumi A H, Soleymani M. Sliding mode trajectory tracking control of a ball-screw-driven shake table based on online state estimations using EKF/UKF[J]. Structural Control and Health Monitoring, 2018, 25(4): e2133. DOI:10.1002/stc.2133.
[12] 张合新, 范金锁, 孟飞, 等. 一种新型滑模控制双幂次趋近律[J]. 控制与决策, 2013, 28(2): 289-293.Zhang H X, Fan J S, Meng F, et al. A new double power reaching law for sliding mode control[J]. Control and Decision, 2013, 28(2): 289-293.(in Chinese)
[13] 李慧洁, 蔡远利. 基于双幂次趋近律的滑模控制方法[J]. 控制与决策, 2016, 31(3): 498-502. DOI:10.13195/j.kzyjc.2014.1908.Li H J, Cai Y L. Sliding mode control with double power reaching law[J]. Control and Decision, 2016, 31(3): 498-502. DOI:10.13195/j.kzyjc.2014.1908.(in Chinese)
[14] Chen Y Q, Wei Y H, Zhong H, et al. Sliding mode control with a second-order switching law for a class of nonlinear fractional order systems[J]. Nonlinear Dynamics, 2016, 85(1): 633-643. DOI:10.1007/s11071-016-2712-6.
[15] Chen Y Q, Wei Y H, Wang Y. On 2 types of robust reaching laws[J]. International Journal of Robust and Nonlinear Control, 2018, 28(6): 2651-2667. DOI:10.1002/rnc.4042.
[16] 岳才成, 钱林方, 陈龙淼, 等. 基于双幂次趋近律火炮链传动药仓自适应控制[J]. 东南大学学报(自然科学版), 2017, 47(6): 1135-1140.Yue C C, Qian L F, Chen L M, et al. Adaptive control for artillery chain driving powder based on double power reaching law[J]. Journal of Southeast University(Natural Science Edition), 2017, 47(6): 1135-1140.(in Chinese)
[17] 佃松宜, 李银锋, 蒲明, 等. 一类非匹配不确定纯反馈非线性系统新型变幂次趋近律滑模控制[J]. 工程科学与技术, 2017, 49(5): 164-170. DOI:10.15961/j.jsuese.201601152.Dian S Y, Li Y F, Pu M, et al. New exponential reaching law sliding mode control for the pure feedback nonlinear systems with mismatched uncertainties[J]. Advanced Engineering Sciences, 2017, 49(5): 164-170. DOI:10.15961/j.jsuese.201601152.(in Chinese)
[18] Dong L, Tang W C. Hybrid modeling and analysis of structural dynamic of a ball screw feed drive system[J]. Mechanika, 2013, 19(3): 316-323. DOI:10.5755/j01.mech.19.3.4662.
[19] 蒋书运, 祝书龙. 带滚珠丝杠副的直线导轨结合部动态刚度特性[J]. 机械工程学报, 2010, 46(1): 92-99. DOI:10.3901/JME.2010.01.092.Jiang S Y, Zhu S L. Dynamic characteristic parameters of linear guideway joint with ball screw[J]. Journal of Mechanical Engineering, 2010, 46(1): 92-99. DOI:10.3901/JME.2010.01.092.(in Chinese)
[20] 董亮. 高速滚珠丝杠进给系统动态特性与控制技术研究[D]. 南京: 东南大学, 2015.Dong L. System dynamics and precision control of high speed ball screw drives[D]. Nanjing: Southeast University, 2015.(in Chinese)
[2] 刘金琨. 滑模变结构控制MATLAB仿真:基本理论与设计方法[M]. 北京: 清华大学出版社, 2015: 1-16.
[3] Erkorkmaz K, Kamalzadeh A. High bandwidth control of ball screw drives[J]. CIRP Annals, 2006, 55(1): 393-398. DOI:10.1016/s0007-8506(07)60443-0.
[4] Kamalzadeh A, Erkorkmaz K. Compensation of axial vibrations in ball screw drives[J]. CIRP Annals, 2007, 56(1): 373-378. DOI:10.1016/j.cirp.2007.05.087.
[5] Dong L, Tang W C. Adaptive backstepping sliding mode control of flexible ball screw drives with time-varying parametric uncertainties and disturbances[J]. ISA Transactions, 2014, 53(1): 110-116. DOI:10.1016/j.isatra.2013.08.009.
[6] 包达飞, 汤文成, 董亮. 带摩擦补偿的滚珠丝杠副进给系统自适应滑模控制[J]. 东南大学学报(自然科学版), 2015, 45(3): 455-460. DOI:10.3969/j.issn.1001-0505.2015.03.008.Bao D F, Tang W C, Dong L. Adaptive sliding mode control of ball screw drives with friction compensation[J]. Journal of Southeast University (Natural Science Edition), 2015, 45(3): 455-460. DOI:10.3969/j.issn.1001-0505.2015.03.008.(in Chinese)
[7] Yang J, Chen W H, Li S. Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties[J]. IET Control Theory & Applications, 2011, 5(18): 2053-2062. DOI:10.1049/iet-cta.2010.0616.
[8] Li S H, Yang J, Chen W H, et al. Generalized extended state observer based control for systems with mismatched uncertainties[J]. IEEE Transactions on Industrial Electronics, 2012, 59(12): 4792-4802. DOI:10.1109/tie.2011.2182011.
[9] Yang J, Li S H, Yu X H. Sliding-mode control for systems with mismatched uncertainties via a disturbance observer[J]. IEEE Transactions on Industrial Electronics, 2013, 60(1): 160-169. DOI:10.1109/tie.2012.2183841.
[10] Ginoya D, Shendge P D, Phadke S B. Sliding mode control for mismatched uncertain systems using an extended disturbance observer[J]. IEEE Transactions on Industrial Electronics, 2014, 61(4): 1983-1992. DOI:10.1109/tie.2013.2271597.
[11] Rajabi N, Abolmasoumi A H, Soleymani M. Sliding mode trajectory tracking control of a ball-screw-driven shake table based on online state estimations using EKF/UKF[J]. Structural Control and Health Monitoring, 2018, 25(4): e2133. DOI:10.1002/stc.2133.
[12] 张合新, 范金锁, 孟飞, 等. 一种新型滑模控制双幂次趋近律[J]. 控制与决策, 2013, 28(2): 289-293.Zhang H X, Fan J S, Meng F, et al. A new double power reaching law for sliding mode control[J]. Control and Decision, 2013, 28(2): 289-293.(in Chinese)
[13] 李慧洁, 蔡远利. 基于双幂次趋近律的滑模控制方法[J]. 控制与决策, 2016, 31(3): 498-502. DOI:10.13195/j.kzyjc.2014.1908.Li H J, Cai Y L. Sliding mode control with double power reaching law[J]. Control and Decision, 2016, 31(3): 498-502. DOI:10.13195/j.kzyjc.2014.1908.(in Chinese)
[14] Chen Y Q, Wei Y H, Zhong H, et al. Sliding mode control with a second-order switching law for a class of nonlinear fractional order systems[J]. Nonlinear Dynamics, 2016, 85(1): 633-643. DOI:10.1007/s11071-016-2712-6.
[15] Chen Y Q, Wei Y H, Wang Y. On 2 types of robust reaching laws[J]. International Journal of Robust and Nonlinear Control, 2018, 28(6): 2651-2667. DOI:10.1002/rnc.4042.
[16] 岳才成, 钱林方, 陈龙淼, 等. 基于双幂次趋近律火炮链传动药仓自适应控制[J]. 东南大学学报(自然科学版), 2017, 47(6): 1135-1140.Yue C C, Qian L F, Chen L M, et al. Adaptive control for artillery chain driving powder based on double power reaching law[J]. Journal of Southeast University(Natural Science Edition), 2017, 47(6): 1135-1140.(in Chinese)
[17] 佃松宜, 李银锋, 蒲明, 等. 一类非匹配不确定纯反馈非线性系统新型变幂次趋近律滑模控制[J]. 工程科学与技术, 2017, 49(5): 164-170. DOI:10.15961/j.jsuese.201601152.Dian S Y, Li Y F, Pu M, et al. New exponential reaching law sliding mode control for the pure feedback nonlinear systems with mismatched uncertainties[J]. Advanced Engineering Sciences, 2017, 49(5): 164-170. DOI:10.15961/j.jsuese.201601152.(in Chinese)
[18] Dong L, Tang W C. Hybrid modeling and analysis of structural dynamic of a ball screw feed drive system[J]. Mechanika, 2013, 19(3): 316-323. DOI:10.5755/j01.mech.19.3.4662.
[19] 蒋书运, 祝书龙. 带滚珠丝杠副的直线导轨结合部动态刚度特性[J]. 机械工程学报, 2010, 46(1): 92-99. DOI:10.3901/JME.2010.01.092.Jiang S Y, Zhu S L. Dynamic characteristic parameters of linear guideway joint with ball screw[J]. Journal of Mechanical Engineering, 2010, 46(1): 92-99. DOI:10.3901/JME.2010.01.092.(in Chinese)
[20] 董亮. 高速滚珠丝杠进给系统动态特性与控制技术研究[D]. 南京: 东南大学, 2015.Dong L. System dynamics and precision control of high speed ball screw drives[D]. Nanjing: Southeast University, 2015.(in Chinese)