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

摘要/Abstract

摘要：

针对超声电机强非线性和时变性，提出一种基于改进鲸鱼优化算法（whale optimization algorithm, WOA）的自抗扰控制（active disturbance rejection control, ADRC）方法。首先，将改进线性ADRC与Smith预估器结合，设计三阶ADRC器。然后，采用WOA对控制器参数进行优化，并对传统WOA进行改进。将tent混沌映射应用于种群初始化并引入K-means++聚类算法实现种群分类，对不同类别种群采用相应收敛因子，同时设计非线性惯性权重，进一步提高算法的优化效果。最后，在考虑摩擦的情况下用粒子群优化算法、蜻蜓算法、改进前后的WOA分别优化所设计的控制器，并通过仿真验证了所提方法的有效性。

关键词: 超声电机, 自抗扰控制, 鲸鱼优化算法, 参数优化

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

中图分类号:

TP 273

冯建鑫, 李昊阳, 巩建雄, 龚柏春. 基于改进鲸鱼优化算法的超声电机自抗扰控制[J]. 系统工程与电子技术, 2025, 47(12): 4166-4173.

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.

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参考文献 30

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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