Fuzzy modeling of multirate sampled nonlinear systems based on multi-model method

doi:10.23919/JSEE.2020.000051

Abstract

Abstract:

Based on the multi-model principle, the fuzzy identification for nonlinear systems with multirate sampled data is studied. Firstly, the nonlinear system with multirate sampled data can be shown as the nonlinear weighted combination of some linear models at multiple local working points. On this basis, the fuzzy model of the multirate sampled nonlinear system is built. The premise structure of the fuzzy model is confirmed by using fuzzy competitive learning, and the conclusion parameters of the fuzzy model are estimated by the random gradient descent algorithm. The convergence of the proposed identification algorithm is given by using the martingale theorem and lemmas. The fuzzy model of the PH neutralization process of acid-base titration for hair quality detection is constructed to demonstrate the effectiveness of the proposed method.

Key words: multirate sampled data, nonlinear system, fuzzy model, multi-model

Hongwei WANG, Penglong FENG. Fuzzy modeling of multirate sampled nonlinear systems based on multi-model method[J]. Journal of Systems Engineering and Electronics, 2020, 31(4): 761-769.

Figures/Tables 5

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Parameter	Setting value	Parameter	Setting value
$A$/cm$^{2}$	207	$W_{a3}$/(moL$\cdot$L$^{ - 1}$)	-3.06$\times 10^{ - 3}$
$H$/cm	14.0	$W_{b1}$/(moL$\cdot$L$^{ - 1}$)	0
$C_{0}$/(mL$\cdot$cm$^{ - 0.5}$$\cdot$s)	8.75	$W_{b2}$/(moL$\cdot$L$^{ - 1}$)	3$\times 10^{ - 2}$
$q_{1}$/(mL$\cdot$S$^{ - 1}$)	16.6	$W_{b3}$/(moL$\cdot$L$^{ - 1}$)	5$\times 10^{ - 5}$
$q_{2}$/(mL$\cdot$S$^{ - 1}$)	0.55	$pK_{1}$	6.35
$q_{3}$/(mL$\cdot$S$^{ - 1}$)	16.2	$pK_{2}$	10.25
$W_{a1}$/(moL$\cdot$L$^{ - 1}$)	3$\times 10^{ - 3}$	$\tau $	0.5
$W_{a2}$/(moL$\cdot$L$^{ - 1}$)	-3$\times 10^{ - 2}$	${{{\rm{P}}}}{{{\rm{H}}}}_{4}$	7

Modeling method	Number of rules	MSE
FCM	6	0.217 0
WFCM	6	0.105 0
Our method	6	0.063 2

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