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

Abstract

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

CLC Number:

TP273

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.

Figures/Tables 7

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References 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

[1]	LAN Tianyi, LIN Hui. Accelerated iterative learning control algorithm with variable gain and adjustment of learning interval [J]. Systems Engineering and Electronics, 2017, 39(4): 883-887.
[2]	ZHANG Kejun, PENG Guohua. Convergence analysis of PD^α-type fractional-order iterative learning control in the sense of L^pnorm [J]. Systems Engineering and Electronics, 2017, 39(10): 2285-2290.
[3]	YIN Yanling1, WANG Taihua1, ZENG Qi2. Networkbased iterative learning control design based on 2D model [J]. Systems Engineering and Electronics, 2015, 37(5): 1157-1162.
[4]	SUN Xiu-xia, LIU Xi, XU Song, CAI Ming, GAO Yang-jun, TANG Qiang. Nonlinear gains recursive sliding mode control for flight-path angle of UAVs [J]. Systems Engineering and Electronics, 2015, 37(2): 379-384.
[5]	LI Xiangyang. Iterative learning control based on equivalent control [J]. Systems Engineering and Electronics, 2014, 36(7): 1397-1404.
[6]	HUANG Li-xun， FANG Yong. Convergence analysis of iterative learning control system in the presence of data dropouts [J]. Systems Engineering and Electronics, 2014, 36(2): 361-367.
[7]	LAN Yong-hong，HE Lü-jun，HUANG Hui-xian, LUO Yi-ping. P-type iterative learning control of fractional order nonlinear time-delay system [J]. Journal of Systems Engineering and Electronics, 2013, 35(5): 1070-1074.
[8]	JIANG Xiao-ming， WANG Yan， WANG Cheng， CHEN Xing-lin. Robust iterative learning control and its application to high precision test bench [J]. Journal of Systems Engineering and Electronics, 2013, 35(3): 601-608.
[9]	CAO Wei， CONG Wang， SUN Ming. Iterative learning control of variable index gain with initial state study [J]. Journal of Systems Engineering and Electronics, 2012, 34(4): 773-777.
[10]	DAI Xi-sheng, TIAN Sen-ping. Iterative learning control for uncertain linear distributed parameter systems with control delay [J]. Journal of Systems Engineering and Electronics, 2012, 34(10): 2117-2120.
[11]	LI Jing, HU Yunan. Direct adaptive iterative learning control of timevarying nonlinear systems [J]. Journal of Systems Engineering and Electronics, 2012, 34(1): 154-159.
[12]	SUN Yu, XIA Peng, LIN Hui. Iterative learning control for a class of nonlinear batch processes with state delay [J]. Journal of Systems Engineering and Electronics, 2011, 33(2): 380-384.
[13]	SUN Yun-ping, LI Jun-min, WANG Jiang-an. Adaptive learning control of nonlinear systems with iteration-varying trajectory [J]. Journal of Systems Engineering and Electronics, 2009, 31(7): 1715-1719.

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

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