Parameter estimation for dual-rate sampled Hammerstein systems with dead-zone nonlinearity

doi:10.21629/JSEE.2020.01.18

Journal of Systems Engineering and Electronics ›› 2020, Vol. 31 ›› Issue (1): 185-193.doi: 10.21629/JSEE.2020.01.18

收稿日期:2019-04-08 出版日期:2020-02-20 发布日期:2020-02-25

Parameter estimation for dual-rate sampled Hammerstein systems with dead-zone nonlinearity

Hongwei WANG^1,^2,*(), Yuxiao CHEN¹()

¹ School of Electrical Engineering, Xinjiang University, Urumqi 830047, China
² School of Control Science and Engineering, Dalian University of Technology, Dalian 110024, China

Received:2019-04-08 Online:2020-02-20 Published:2020-02-25
Contact: Hongwei WANG E-mail:1195201627@qq.com;cyxling@126.com
About author:WANG Hongwei was born in 1969. He is a Ph.D. and a professor. He is sent to help Xinjiang University by Dalian University of Technology. His research interests are switched system identification, nonlinear system identification and fuzzy modeling. E-mail: 1195201627@qq.com|CHEN Yuxiao was born in 1995. She is now pursuing her M.S. degree at School of Electrical Engineering, Xinjiang University. Her research interests are nonlinear system modeling and system identification. E-mail: cyxling@126.com
Supported by:
the National Natural Science Foundation of China(61863034);This work was supported by the National Natural Science Foundation of China (61863034)

摘要/Abstract

Abstract:

The identification of nonlinear systems with multiple sampled rates is a difficult task. The motivation of our paper is to study the parameter estimation problem of Hammerstein systems with dead-zone characteristics by using the dual-rate sampled data. Firstly, the auxiliary model identification principle is used to estimate the unmeasurable variables, and the recursive estimation algorithm is proposed to identify the parameters of the static nonlinear model with the dead-zone function and the parameters of the dynamic linear system model. Then, the convergence of the proposed identification algorithm is analyzed by using the martingale convergence theorem. It is proved theoretically that the estimated parameters can converge to the real values under the condition of continuous excitation. Finally, the validity of the proposed algorithm is proved by the identification of the dual-rate sampled nonlinear systems.

Key words: dual-rate sampled data, dead-zone nonlinearity, Hammerstein model, system identification, convergence analysis

. [J]. Journal of Systems Engineering and Electronics, 2020, 31(1): 185-193.

Hongwei WANG, Yuxiao CHEN. Parameter estimation for dual-rate sampled Hammerstein systems with dead-zone nonlinearity[J]. Journal of Systems Engineering and Electronics, 2020, 31(1): 185-193.

图/表 6

参考文献 30

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$t$	$\alpha _1 $	$\alpha _2 $	$\beta _1 $	$\beta _2 $	$m_1 $	$m_1 d_1 $	$m_2 $	$m_2 d_2 $	$m_1 $	$m_2 $	$\delta$ /(%)
100	0.398 1	0.304 7	0.523 9	0.618 7	0.443 5	0.154 9	0.729 1	-0.240 1	0.474 1	0.922 5	15.479 9
1 000	0.399 4	0.302 1	0.498 4	0.601 4	0.499 5	0.206 7	0.701 4	-0.221 0	0.519 0	0.802 2	6.729 3
2 000	0.399 2	0.302 2	0.501 6	0.603 3	0.501 2	0.202 2	0.708 3	-0.221 3	0.509 3	0.774 3	4.902 4
3 000	0.398 9	0.302 8	0.503 8	0.607 5	0.500 7	0.201 4	0.708 0	-0.220 5	0.504 1	0.765 0	4.307 0
4 000	0.398 7	0.303 1	0.503 9	0.605 9	0.502 4	0.202 2	0.703 9	-0.217 4	0.501 7	0.749 2	3.252 7
5 000	0.398 8	0.303 0	0.500 8	0.604 7	0.501 0	0.200 8	0.704 3	-0.216 0	0.502 0	0.727 4	1.867 5
True value	0.400	0.300	0.500	0.600	0.500	0.200	0.700	-0.210	0.500	0.700	0.000 0

$t$	$\alpha _1 $	$\alpha _2 $	$\beta _1 $	$\beta _2 $	$m_1$	$m_1 d_1 $	$m_2 $	$m_2 d_2 $	$m_1 $	$m_2 $	$\delta/(\%) $
100	0.365 6	0.331 4	0.467 0	0.636 8	0.436 1	0.127 6	0.695 9	-0.206 5	0.303 0	0.612 2	15.795 9
1 000	0.461 2	0.298 6	0.548 9	0.600 8	0.489 9	0.191 9	0.712 1	-0.220 9	0.395 0	0.739 5	8.886 2
2 000	0.445 4	0.298 6	0.533 4	0.602 5	0.509 8	0.219 4	0.711 4	-0.216 1	0.528 0	0.670 2	4.760 6
3 000	0.442 5	0.302 9	0.522 5	0.609 8	0.501 0	0.205 6	0.709 2	-0.211 5	0.505 1	0.642 6	4.916 1
4 000	0.426 9	0.297 0	0.514 4	0.600 5	0.501 0	0.203 5	0.700 8	-0.205 3	0.505 9	0.655 0	3.541 0
5 000	0.425 7	0.292 9	0.515 8	0.598 4	0.504 1	0.207 0	0.705 6	-0.211 8	0.524 7	0.702 5	2.633 0
True value	0.400	0.300	0.500	0.600	0.500	0.200	0.700	-0.210	0.500	0.700	0.000 0

$t$	$\alpha _1 $	$\alpha _2 $	$\beta _1 $	$\beta _2 $	$m_1 $	$m_1 d_1 $	$m_2 $	$m_2 d_2 $	$m_1 $	$m_2 $	$\delta /(\%)$
100	0.544 6	0.292 3	0.601 4	0.688 0	0.480 4	0.243 6	0.712 4	-0.217 1	0.639 9	0.594 3	17.263 2
1 000	0.402 2	0.263 8	0.494 6	0.574 9	0.494 3	0.185 2	0.685 3	-0.213 5	0.363 1	0.567 7	12.632 8
2 000	0.399 1	0.282 3	0.480 7	0.580 4	0.514 7	0.224 0	0.699 8	-0.214 7	0.561 8	0.554 6	10.523 0
3 000	0.395 8	0.277 9	0.476 3	0.575 5	0.506 1	0.219 2	0.699 0	-0.211 6	0.533 8	0.567 8	9.239 7
4 000	0.422 1	0.294 2	0.508 6	0.595 5	0.509 9	0.220 1	0.699 6	-0.210 2	0.524 1	0.606 0	6.594 0
5 000	0.410 3	0.282 7	0.494 3	0.580 2	0.505 9	0.214 5	0.701 4	-0.216 1	0.510 8	0.621 3	5.535 2
True value	0.400	0.300	0.500	0.600	0.500	0.200	0.700	-0.210	0.500	0.700	0.000 0

Parameter estimation for dual-rate sampled Hammerstein systems with dead-zone nonlinearity

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