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

doi:10.21629/JSEE.2020.01.18

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

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.

Figures/Tables 6

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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

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