基于改进鲸鱼优化算法的超声电机自抗扰控制

doi:10.12305/j.issn.1001-506X.2025.12.28

Abstract

Abstract:

Aiming at the strong nonlinearity and time-varying nature of ultrasonic motor, an active disturbance rejection control （ADRC） method based on the improved whale optimization algorithm （WOA） is proposed. Firstly, the improved linear ADRC is combined with the Smith predictor to design a third-order active disturbance rejection controller. Then, the WOA is used to optimize the controller parameters, and the traditional WOA is improved. The tent chaotic map is applied to population initialization and the K-means++ clustering algorithm is introduced to realize population classification. The corresponding convergence factors are used for different types of populations, and the nonlinear inertia weight is designed to further improve the optimization effect of the algorithm. Finally, the designed controller is optimized by using the particle swarm optimization algorithm, the dragonfly algorithm, and the WOA before and after the improvement under the condition of friction, and the effectiveness of the proposed method is verified by simulation.

Key words: ultrasonic motor, active disturbance rejection controll (ADRC), whale optimization algorithm (WOA), parameter optimization

CLC Number:

TP 273

Jianxin FENG, Haoyang LI, Jianxiong GONG, Baichun GONG. Ultrasonic motor ADRC based on improved whale optimization algorithm[J]. Systems Engineering and Electronics, 2025, 47(12): 4166-4173.

Figures/Tables 14

Fig.1

Table 1

Table 2

Table 3

Table 4

Fig.2

Fig.3

Table 5

Fig.4

Fig.5

Table 6

Fig.6

Fig.7

Fig.8

References 30

1	STORCK H, LITTMANN W, WALLASCHEK J, et al. The effect of friction reduction in presence of ultrasonic vibrations and its relevance to travelling wave ultrasonic motors[J]. Ultrasonics, 2002, 40 (1/8): 379- 383.
2	OLOFSSON J, LINDBERG F, JOHANSSON S, et al. On the role of tribofilm formation on the alumina drive components of an ultrasonic motor[J]. Wear, 2009, 267 (5/8): 1295- 1300.
3	ZHANG Y H, FU Y H, HUA X J, et al. Wear debris of friction materials for linear standing-wave ultrasonic motors: theory and experiments[J]. Wear, 2020, 448-449: 203216.
4	LI X N, WEN Z Y, JIA B T, et al. A review of application and development trends in ultrasonic motors[J]. ES Materials & Manufacturing, 2020, 12, 3- 16.
5	XU D M, ZHANG B J, YU S M, et al. Review on single-phase driven ultrasonic motors[J]. Journal of Intelligent Material Systems and Structures, 2023, 34 (5): 525- 535. doi: 10.1177/1045389X221121911
6	LIU Z, FU Q W, YANG P, et al. Design and performance evaluation of a miniature I-shaped linear ultrasonic motor with two vibrators[J]. Ultraso-nics, 2023, 131, 106965. doi: 10.1016/j.ultras.2023.106965
7	WANG G Q, SONG J F, ZHAO G, et al. Improving output performance of ultrasonic motor by coating MoS2 on the stator[J]. Tribology International, 2023, 186, 108608. doi: 10.1016/j.triboint.2023.108608
8	MUSTAFA A, SASAMURA T, MORITA T. Robust speed control of ultrasonic motors based on deep reinforcement learning of a Lyapunov function[J]. IEEE Access, 2022, 10, 46895- 46910. doi: 10.1109/ACCESS.2022.3170995
9	GARRIDO R, LUNA L. Robust ultra-precision motion control of linear ultrasonic motors: a combined ADRC-Luenberger observer approach[J]. Control Engineering Practice, 2021, 111, 104812. doi: 10.1016/j.conengprac.2021.104812
10	MING M, LIANG W Y, FENG Z, et al. PID-type sliding mode-based adaptive motion control of a 2-DOF piezoelectric ultrasonicmotor driven stage[J]. Mechatronics, 2021, 76: 102543.
11	SONG L, SHI J Z. Adaptive PI control of ultrasonic motor using iterative learning methods[J]. ISA Transactions, 2023, 139, 499- 509. doi: 10.1016/j.isatra.2023.03.032
12	KEBBAB F Z, JABRI D, BELKHIAT D E C, et al. Frequency speed control of rotary travelling wave ultrasonic motor using fuzzy controller[J]. Engineering, Technology & Applied Science Research, 2018, 8(4): 3276−3281.
13	SHI J Z, HUANG W W, ZHOU Y. T–S fuzzy control of travelling-wave ultrasonic motor[J]. Journal of Control, Automation and Electrical Systems, 2020, 31 (2): 319- 328.
14	MUSTAFA A, SASAMURA T, MORITA T. Sensorless speed control of ultrasonic motors using deep reinforcement learning[J]. IEEE Sensors Journal, 2023, 24(3): 4023−4035.
15	JIANG Y, WANG F, SASAMURA T, et al. Dynamic characteristics and deep reinforcement learning of proportional-integral-differential controller for quadruped stator-based ultrasonic linear motor[J]. Japanese Journal of Applied Physics, 2024, 63 (4): 04SP38. doi: 10.35848/1347-4065/ad2f18
16	韩京清. 自抗扰控制器及其应用[J]. 控制与决策, 1998, 13 (1): 19- 23. doi: 10.3321/j.issn:1001-0920.1998.01.005
	HAN J Q. Active disturbance rejection controller and its applications[J]. Control and Decision, 1998, 13 (1): 19- 23. doi: 10.3321/j.issn:1001-0920.1998.01.005
17	HAN J Q. From PID to active disturbancerejection control[J]. IEEE Trans. On Dustrial Electronics, 2009, 56 (3): 900- 906. doi: 10.1109/TIE.2008.2011621
18	ZHANG D Y, YAO X L, WU Q H, et al. ADR-C based control for a class of input time delay systems[J]. Journal of Systems Engineering and Electronics, 2017, 28 (6): 1210- 1220. doi: 10.21629/JSEE.2017.06.19
19	GAO Z Q. Scaling and bandwidth-parameterization based controller tuning[C]//Proc. of the American Control Conference, 2003: 4989−4996.
20	GAO Z Q. Active disturbance rejection control: a paradigm shift in feedback control system design[C]//Proc. of the American Control Confe-rence, 2006: 2399−2405.
21	王鑫. 线性自抗扰控制器参数整定及其应用研究[D]. 合肥: 安徽大学, 2022.
	WANG X. Parameter tuning and application of linear active disturbance rejection controller[D]. Hefei: Anhui University, 2022.
22	李广强, 董文超, 朱大庆, 等. 基于改进鲸鱼优化算法的AUV三维路径规划[J]. 系统工程与电子技术, 2023, 45 (7): 2170- 2182.
	LI G Q, DONG W C, ZHU D Q, et al. 3D path planning for AUV based on improved whale optimization algorithm[J]. Systems Engineering and Electronics, 2023, 45 (7): 2170- 2182.
23	NADIMI-SHAHRAKI M, ZAMANI H, ASGHARI V Z, et al. A systematic review of the whale optimization algorithm: theoretical foundation, improvements, and hybridizations[J]. Archives of Computational Methods in Engineering, 2023, 30 (7): 4113- 4159. doi: 10.1007/s11831-023-09928-7
24	AKRAAM M, RASHID T, ZAFAR S. An image encryption scheme proposed by modifying chaotic tent map using fuzzy numbers[J]. Multimedia Tools and Applications, 2023, 82 (11): 16861- 16879. doi: 10.1007/s11042-022-13941-6
25	KOPETS E, VYACHESLAV R, OLEG V, et al. Fractal tent map with application to surrogate testing[J]. Fractal and Fractional, 2024, 8 (6): 344. doi: 10.3390/fractalfract8060344
26	LI H Z, WANG J. Collaborative annealing power k-means++ clustering[J]. Knowledge- Based Systems, 2022, 255, 109593. doi: 10.1016/j.knosys.2022.109593
27	高程, 都延丽, 步雨浓, 等. 面向复杂多任务的异构无人机集群分组调配[J]. 系统工程与电子技术, 2024, 46 (3): 972- 981.
	GAO C, DU Y L, BU Y N, et al. Heterogeneous UAV swarm grouping deployment for complex multiple tasks[J]. Systems Engineering and Electronics, 2024, 46 (3): 972- 981.
28	CHATTERJEE A, SIARRY P. Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization[J]. Computers & Operations Research, 2006, 33 (3): 859- 871.
29	YU H, GAO Y, WANG L, et al. A hybrid particle swarm optimization algorithm enhanced with nonlinear inertial weight and gaussian mutation for job shop scheduling problems[J]. Mathematics, 2020, 8, 1355. doi: 10.3390/math8081355
30	冯建鑫, 王强, 王雅雷, 等. 基于改进量子遗传算法的超声电机模糊PID控制[J]. 吉林大学学报（工学版）, 2021, 51 (6): 1990- 1996.
	FENG J X, WANG Q, WANG Y L, et al. Fuzzy PID control of ultrasonic motor based on improved quantum genetic algorithm[J]. Journal of Jilin University （Engineering and Technology Edition）, 2021, 51 (6): 1990- 1996.

函数	维数	取值范围	理论极值
${f_1} = \displaystyle\sum\limits_{i = 1}^n {x_i^2} $	30	[−100,100]	0
${f_2} = \displaystyle\sum\limits_{i = 1}^n {\left\| {{x_i}} \right\|} + \displaystyle\prod\limits_{i = 1}^n {\left\| {{x_i}} \right\|} $	30	[−10,10]	0
$ {f_3} = {\max _i}\left\{ {\left\| {{x_i}} \right\|,1 \leqslant i \leqslant 30} \right\} $	30	[−100,100]	0
${f_4} = \displaystyle\sum\limits_{i = 1}^{30} {[x_i^2 - 10\cos (2\text{π} {x_i}) + 10]} $	30	[−5.12,5.12]	0
$\begin{gathered} {f_5}(x) = - 20\exp \left( - 0.2\sqrt {\frac{1}{{30}}\sum\limits_{i = 1}^{30} {x_i^2} } \right)- \exp\left(\frac{1}{{30}}\sum\limits_{i = 1}^{30} \cos (2\text{π} {x_i})\right) + 20 + {\rm{e}}\end{gathered} $	30	[−32,32]	0
$ f_6=\dfrac{1}{4\; 000}\displaystyle\sum\limits_{i=1}^nx_i^2-\displaystyle\prod\limits_{i=1}^n\cos\dfrac{x_i}{\sqrt{2}}+1 $	30	[−600,600]	0

函数	算法	最优值	平均值	最差值	标准差
${f_1}$	PSO	3.03e-08	2.24e-07	1.05e-06	2.30e-07
	DA	1.99e+03	6.67e+03	1.42e+04	2.82e+03
	WOA	4.43e-29	3.37e-22	8.59e-21	1.57e-21
	IWOA	1.48e-96	1.14e-90	2.04e-89	3.78e-90
${f_2}$	PSO	2.10e-06	3.45e-05	1.89e-04	3.82e-05
	DA	5.854	31.988	1.14e+02	21.883
	WOA	4.97e-22	4.22e-18	6.59e-17	1.27e-17
	IWOA	1.07e-54	8.95e-50	2.54e-48	4.63e-49
${f_3}$	PSO	0.378	1.109	2.894	0.555
	DA	27.766	45.619	63.310	10.540
	WOA	2.947	64.288	89.807	23.532
	IWOA	8.27e-34	4.40e-31	2.71e-30	6.36e-31
${f_4}$	PSO	16.141	35.717	1.42e+02	22.838
	DA	1.22e+02	2.08e+02	3.14e+02	49.175
	WOA	0	16.167	2.51e+02	60.753
	IWOA	0	0	0	0
${f_5}$	PSO	6.41e-05	11.976	19.967	9.945
	DA	8.665	14.713	18.182	1.955
	WOA	1.47e-14	1.84e-12	3.66e-11	6.70e-12
	IWOA	4.44e-16	2.69e-15	4.00e-15	1.74e-15
${f_6}$	PSO	5.42e-08	0.012	0.042	0.013
	DA	18.519	60.228	1.23e+02	23.219
	WOA	0	1.48e-17	1.11e-16	3.84e-17
	IWOA	0	0	0	0

${F_c}$/N	${F_s}$/N	${w_s}$/（m/s）	${\sigma _0}$	$ {\sigma _1} $	${\sigma _2}$
2.444	0.599	0.010	0.477	0.270	0.005

参数	WOA	DA	IWOA	PSO
$ {\omega _{\text{c}}} $	3 028.663	2 054.116	8 175.719	9 910.667
$ {b_0} $	1 262 280	1 200 767	922 164.9	663 146.6
$ {\omega _{\text{o}}} $	317.715	393.607	294.318	400
$ {\omega _{{\text{o1}}}} $	100.837	144.513	300.293	171.269
$ {\omega _{{\text{o2}}}} $	283.867	295.213	302.659	205.391
$ \alpha $	1 419.399	1998.327	671.389	401.082
$\hat \tau $	0.003	0.002 85	0.002 317	0.001 554
最小适应度值	0.000 228	0.000 256	0.000 146	0.000 178

参数	WOA	DA	IWOA	PSO
$ {\omega _{\text{c}}} $	5 440.736	17 365.56	18 637.47	18 907.12
$ {b_0} $	1 186 601	2 000 000	1 923 256	1 361 394
$ {\omega _{\text{o}}} $	124.408	122.927	146.170	71.383
$ {\omega _{{\text{o1}}}} $	272.092	57.556	50	71.383
$ {\omega _{{\text{o2}}}} $	247.850	256.410	50	72.712
$ \alpha $	5 647.49	8 136.524	10 000	8 934.579
$\hat \tau $	0.000 778	0.000 541	0.000 11	0.000 18
最小适应度值	1.488	0.934	0.196	0.349

Ultrasonic motor ADRC based on improved whale optimization algorithm

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 14

References 30

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Caiyun WANG, Yifan JIA, Xiaofei LI, Jianing WANG, Yida WU. Ballistic target HRRP recognition method based on improved whale algorithm and BiGRU [J]. Systems Engineering and Electronics, 2025, 47(6): 1824-1832.
[2]	Bo GUO, Ming TIE, Wenhui FAN, Chuanxu LI. Cooperative guidance method of high lift-to-drag ratio aircraft based on sliding mode control [J]. Systems Engineering and Electronics, 2025, 47(2): 580-590.
[3]	Zhihao CAI, Shiqi XING, Xinyuan SU, Junpeng WANG, Weize MENG, Hao WANG. Multi-point source spatial arraying method based on triplet antenna [J]. Systems Engineering and Electronics, 2025, 47(11): 3574-3585.
[4]	Xuehao LIU, Wenxue LIU, Chaosan YANG, Wenjing ZHU, Yu SONG, Jinhai LI. Optimization method of user quantity prediction based on GPR model [J]. Systems Engineering and Electronics, 2024, 46(8): 2721-2729.
[5]	Caiyun WANG, Yun CHANG, Xiaofei LI, Jianing WANG, Yida WU, Huiwen ZHANG. Infrared spatial cone-shaped target recognition based on improved MKELM [J]. Systems Engineering and Electronics, 2024, 46(10): 3257-3264.
[6]	Guangqiang LI, Wenchao DONG, Daqing ZHU, Yue YU, Hao CHEN, Shuanghe YU. 3D path planning for AUV based on improved whaleoptimization algorithm [J]. Systems Engineering and Electronics, 2023, 45(7): 2170-2182.
[7]	Wenqi YANG, Jianhua LU, Xu JIANG, Yuanxin WANG. Design of quadrotor attitude active disturbance rejection controller based on improved ESO [J]. Systems Engineering and Electronics, 2022, 44(12): 3792-3799.
[8]	Chi HAN, Wei XIONG. Operational effectiveness evaluation of space reconnaissance equipment based on SVR optimized by improved grey wolf optimizer [J]. Systems Engineering and Electronics, 2021, 43(10): 2902-2910.
[9]	Zilong WU, Hong CHEN, Yingke LEI, Xin LI, Hao XIONG. Communication emitter individual identification based on stacked LSTM network [J]. Systems Engineering and Electronics, 2020, 42(12): 2915-2923.
[10]	Weiguo SHI, Ming GUO. Variable sampling period scheduling of networked control system based on whale optimization algorithm relevance vector machine [J]. Systems Engineering and Electronics, 2020, 42(10): 2348-2355.
[11]	HUANG Wei, XU Jiancheng, WU Huaxing, LI Junbing. Missile formation consensus control algorithm based on parameter optimization [J]. Systems Engineering and Electronics, 2018, 40(11): 2528-.
[12]	YANG Yingjie1, YU Yongli1, ZHANG Liu1, ZHANG Wei2. Sensitivity analysis and parameters optimization for equipment maintenance support simulation system [J]. Systems Engineering and Electronics, 2016, 38(3): 575-581.
[13]	WANG Jing-cheng1, CAO Hui2, ZHANG Yan-bin2, REN Zhi-wen1. Parameter optimization algorithm of SVDD based on minimizing the density outside [J]. Systems Engineering and Electronics, 2015, 37(6): 1446-1451.
[14]	LIU Zhong, ZHAO Yan hui. Fractional order missile controller design with optimum structure [J]. Systems Engineering and Electronics, 2014, 36(12): 2490-2495.
[15]	CHANG Zhi-peng，CHENG Long-sheng. Automatic optimization algorithm of multiple parameters for kernel Fisher discriminant analysis [J]. Journal of Systems Engineering and Electronics, 2013, 35(1): 212-217.

参数	WOA	DA	IWOA	PSO
$ {\omega _{\text{c}}} $	4 326.858	1 915.435	3 962.961	1 968.237
$ {b_0} $	1 887 034	2 000 000	1 958 052	1 904 391
$ {\omega _{\text{o}}} $	356.406	245.044	279.786	394.016
$ {\omega _{{\text{o1}}}} $	112.821	370.728	127.205	50
$ {\omega _{{\text{o2}}}} $	301.659	147.956	223.953	378.960
$ \alpha $	737.748	2 978.886	2 967.428	2 116.098
$\hat \tau $	0.000 186	0.000 02	0.000 016	0.000 089
最小适应度值	0.000 128	0.000 044	0.000 037	0.000 062