具有自适应非线性增益的开环PD型迭代学习控制

doi:10.3969/j.issn.1001-506X.2020.03.021

系统工程与电子技术 ›› 2020, Vol. 42 ›› Issue (3): 660-666.doi: 10.3969/j.issn.1001-506X.2020.03.021

具有自适应非线性增益的开环PD型迭代学习控制

代明光(), 齐蓉(), 李兵强(), 赵逸云()

西北工业大学自动化学院, 陕西西安 710129

收稿日期:2019-07-11 出版日期:2020-03-01 发布日期:2020-02-28
作者简介:代明光 (1990-),男,博士研究生,主要研究方向为电机伺服控制、迭代学习控制。E-mail:dmg.nwpu@qq.com|齐蓉 (1962-),女,教授,博士,主要研究方向为电机智能控制及测试技术、运动控制技术、控制理论与应用。E-mail:lhqr@nwpu.edu.cn|李兵强 (1982-),男,副教授,博士,主要研究方向为现代电机控制技术、迭代学习控制。E-mail:libingqiang@nwpu.edu.cn|赵逸云 (1995-),男,博士研究生,主要研究方向为伺服驱动控制、非线性系统控制、迭代学习控制。E-mail:zhaoyiyun@mail.nwpu.edu.cn
基金资助:
国家自然科学基金(51777170);陕西省重点研究开发计划(2018ZDCXL-GY-05-07-01)

Open-loop PD-type iterative learning control with adaptive nonlinear gain

Mingguang DAI(), Rong QI(), Bingqiang LI(), Yiyun ZHAO()

School of Automation, Northwestern Polytechnical University, Xi'an 710129, China

Received:2019-07-11 Online:2020-03-01 Published:2020-02-28
Supported by:
国家自然科学基金(51777170);陕西省重点研究开发计划(2018ZDCXL-GY-05-07-01)

摘要/Abstract

摘要：

针对同时存在周期性干扰和随机测量噪声的一类非线性系统,提出一种基于误差幅值和误差变化率的开环PD型迭代学习非线性增益自适应算法,分别给出了比例和微分的增益调整规则,并对所提算法进行了严格的理论分析,同时推导出收敛条件。结果表明,与传统学习增益固定的开环PD型迭代学习律相比,当非线性系统同时存在周期性扰动和幅值较大测量噪声时,自适应非线性增益学习律能根据误差幅值和误差变化率在线调整比例和微分学习增益,抑制扰动和噪声,使得在学习收敛速度和收敛精度之间在某种程度上得以折中,在学习初始阶段高增益下保证了迭代学习的收敛速度,学习末了阶段小增益下具有较强的鲁棒性和收敛精度,得到的误差跟踪曲线更加平滑。

关键词: 迭代学习控制, 开环PD型学习律, 非线性增益, 周期性干扰, 随机测量噪声

Abstract:

An open-loop PD-type iterative learning nonlinear gain adaptive algorithm based on the error amplitude and error rate of change is proposed for a class of nonlinear systems with both periodic disturbance and random measurement noise. The adjustment rules of the proportional and differential nonlinear gain are given respectively, and the proposed algorithm is analyzed theoretically and the convergence conditions are given. The results show that compared with the traditional open-loop PD-type iterative learning law with the fixed learning gain, when the nonlinear system has both periodic disturbance and measurement noise with large amplitude, the adaptive learning law of the nonlinear gain can regulate the proportional and differential learning gain online according to the error amplitude and error change rate, and suppress the disturbance and noise. Using this algorithm, the convergence speed of iterative learning is guaranteed under the high gain in the initial stage of learning, and the convergence precision and robustness are stronger under the small gain in the final stage of learning, and the error tracking curve obtained is smoother.

Key words: iterative learning control, open-loop PD learning law, nonlinear gain, periodic disturbance, random measurement noise

中图分类号:

TP273

代明光, 齐蓉, 李兵强, 赵逸云. 具有自适应非线性增益的开环PD型迭代学习控制[J]. 系统工程与电子技术, 2020, 42(3): 660-666.

Mingguang DAI, Rong QI, Bingqiang LI, Yiyun ZHAO. Open-loop PD-type iterative learning control with adaptive nonlinear gain[J]. Systems Engineering and Electronics, 2020, 42(3): 660-666.

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参考文献 19

1	AHN H S , CHEN Y Q , MOORE K L . Iterative learning control: brief survey and categorization[J]. IEEE Trans. on Systems, Man, and Cybernetics, 2007, 37 (6): 1099- 1121.
2	BRISTOW D A , THARAYIL M , ALLEYNE A G . A survey of iterative learning control[J]. IEEE Control Systems Magazine, 2006, 26 (3): 96- 114. doi: 10.1109/MCS.2006.1636313
3	李建成, 席涛. 基于滑模迭代学习律的航天器姿态控制[J]. 系统工程与电子技术, 2012, 34 (9): 1895- 1899.
	LI J C , XI T . Spacecraft attitude control scheme based on sliding mode controller with iterative learning law[J]. Systems Engineering and Electronics, 2012, 34 (9): 1895- 1899.
4	STEINHAUSER A , SWEVERS J . An efficient iterative learning approach to time-optimal path tracking for industrial robots[J]. IEEE Trans. on Industrial Informatics, 2018, 14 (11): 5200- 5207. doi: 10.1109/TII.2018.2851963
5	姜晓明, 王岩, 王程, 等. 鲁棒迭代学习控制及在高精密平台中的应用[J]. 系统工程与电子技术, 2013, 35 (3): 601- 608.
	JIANG X M , WANG Y , WANG C , et al. Robust iterative learning control and its application to high precision test bench[J]. Systems Engineering and Electronics, 2013, 35 (3): 601- 608.
6	刘京, 李洪文, 邓永停. 基于鲁棒迭代学习控制的永磁同步电机转矩脉动抑制[J]. 光学精密工程, 2017, 25 (10): 2645- 2660.
	LIU J , LI H W , DENG Y T . Torque ripple minimization of PMSM based on robust iterative learning control[J]. Optics and Precision Engineering, 2017, 25 (10): 2645- 2660.
7	周颖, 何磊, 郑凤. 具有时延和数据丢失的直线电机迭代学习控制[J]. 控制理论与应用, 2017, 34 (12): 1631- 1636.
	ZHOU Y , HE L , ZHENG F . Iterative learning control for linear motor system with time delay and data dropout[J]. Control Theory and Applications, 2017, 34 (12): 1631- 1636.
8	LIU T , GAO F R , WANG Y Q . IMC-based iterative learning control for batch processes with uncertain time delay[J]. Journal of Process Control, 2010, 20 (2): 173- 180. doi: 10.1016/j.jprocont.2009.10.008
9	AHN H S, MOORE K L, CHEN Y Q.Iterative learning control: robustness and monotonic convergence for interval systems[M]. Springer Publishing Company, Incorporated, 2007.
10	MADADY A . An extended PID type iterative learning control[J]. International Journal of Control, Automation and Systems, 2013, 11 (3): 470- 481. doi: 10.1007/s12555-012-0350-4
11	ZHENG M , WANG C , SUN L , et al. Design of arbitrary-order robust iterative learning control based on robust control theory[J]. Mechatronics, 2017, 47, 67- 76. doi: 10.1016/j.mechatronics.2017.08.009
12	SHEN D , HAN J , WANG Y . Stochastic point-to-point iterative learning tracking without prior information on system matrices[J]. IEEE Trans.on Automation Science and Engineering, 2017, 14 (1): 376- 382. doi: 10.1109/TASE.2016.2617868
13	MENG D Y , MOORE K L . Robust iterative learning control for nonrepetitive uncertain systems[J]. IEEE Trans.on Automatic Control, 2017, 62 (2): 907- 913. doi: 10.1109/TAC.2016.2560961
14	魏燕定. 提高迭代自学习控制算法收敛速度初探[J]. 控制理论与应用, 2001, 18 (2): 314- 316.
	WEI Y D . Research on convergent speed of iterative learning control[J]. Control Theory and Applications. Control Theory and Applications, 2001, 18 (2): 314- 316.
15	赵希梅, 金鸿雁. 永磁直线同步电机伺服系统的分段变论域模糊迭代学习控制[J]. 电工技术学报, 2017, 32 (23): 9- 15.
	ZHAO X M , JING H Y . Segmented variable universe fuzzy iterative learning control for permanent magnet linear synchronous motor servo system[J]. Transactions of China Electrotechnical Society, 2017, 32 (23): 9- 15.
16	LI B Q , LIN H , XING H L . Adaptive adjustment of iterative learning control gain matrix in harsh noise environment[J]. Journal of Systems Engineering and Electronics, 2013, 24 (1): 128- 134. doi: 10.1109/JSEE.2013.00016
17	赵希梅, 马志军, 朱国昕. 永磁直线同步电机自适应PD型迭代学习控制[J]. 沈阳工业大学学报, 2016, 38 (1): 7- 12.
	ZHAO X M , MA Z J , ZHU G X . Adaptive PD-type iterative learning control for permanent magnet linear synchronous motor[J]. Journal of Shenyang University of Technology, 2016, 38 (1): 7- 12.
18	PUCHTA E D P, SIQUEIRA H V, MAURICIO D S K.Optimization tools based on metaheuristics for performance enhancement in a Gaussian adaptive PID controller[J]. IEEE Trans.on Cybernetics, 2019. DOI: 10.1109/TCYB.2019.2895319.
19	ISAYED B M, HAWWA M A.A nonlinear PID control scheme for hard disk drive servos systems[C]//Proc.of the 15th Mediterranean Conference on Control and Automation, 2007: 550-555.

参数类型	数值	参数类型	数值
K_P	3.57	K_D	2.1
k_P0	0.1	k_D0	0.1
k_P1	1	k_D1	1
ω_P	200	ω_D	100
		γ	0.75

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[2]	张克军, 彭国华. PD^α-型分数阶迭代学习控制在L^p范数意义下的收敛性分析[J]. 系统工程与电子技术, 2017, 39(10): 2285-2290.
[3]	尹艳玲1, 王泰华1, 曾旗2. 基于2D模型的网络系统迭代学习控制设计方法[J]. 系统工程与电子技术, 2015, 37(5): 1157-1162.
[4]	孙秀霞, 刘希, 徐嵩, 蔡鸣, 高杨军, 唐强. 无人机航迹角的非线性增益递归滑模控制[J]. 系统工程与电子技术, 2015, 37(2): 379-384.
[5]	李向阳. 基于等效控制的迭代学习控制[J]. 系统工程与电子技术, 2014, 36(7): 1397-1404.
[6]	黄立勋，方勇. 包含数据丢失的迭代学习控制系统收敛性分析[J]. 系统工程与电子技术, 2014, 36(2): 361-367.
[7]	兰永红，何吕君，黄辉先，罗毅平. 分数阶非线性时滞系统的P型迭代学习控制[J]. Journal of Systems Engineering and Electronics, 2013, 35(5): 1070-1074.
[8]	姜晓明，王岩，王程，陈兴林. 鲁棒迭代学习控制及在高精密平台中的应用[J]. Journal of Systems Engineering and Electronics, 2013, 35(3): 601-608.
[9]	曹伟，丛望，孙明. 带有初态学习的指数变增益迭代学习控制[J]. Journal of Systems Engineering and Electronics, 2012, 34(4): 773-777.
[10]	戴喜生, 田森平. 具有控制时滞的不确定分布参数系统迭代学习控制[J]. Journal of Systems Engineering and Electronics, 2012, 34(10): 2117-2120.
[11]	李静, 胡云安. 时变非线性系统直接自适应迭代学习控制[J]. Journal of Systems Engineering and Electronics, 2012, 34(1): 154-159.
[12]	孙瑜, 夏鹏, 林辉. 含状态时滞的非线性间歇过程迭代学习控制研究[J]. Journal of Systems Engineering and Electronics, 2011, 33(2): 380-384.
[13]	孙云平, 李俊民, 王江安. 目标轨线迭代可变的非线性系统自适应学习控制[J]. Journal of Systems Engineering and Electronics, 2009, 31(7): 1715-1719.

具有自适应非线性增益的开环PD型迭代学习控制

Open-loop PD-type iterative learning control with adaptive nonlinear gain

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