Distributed fault-tolerant consensus tracking for networked non-identical motors

Han Wu; Changfan Zhang; Jing He; Kaihui Zhao

doi:10.3934/jimo.2016053

Article Contents

2017, Volume 13, Issue 2: 917-929. Doi: 10.3934/jimo.2016053

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Distributed fault-tolerant consensus tracking for networked non-identical motors

1.
College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, Hunan, China
2.
School of Automation, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China
3.
College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha 410073, Hunan, China

* Corresponding author: Changfan Zhang, zhangchangfan@263.net
* Corresponding author: Changfan Zhang, zhangchangfan@263.net

Received: June 2015

Revised: June 2016

Published: August 2017

The first author is supported by NSF grants 61273157 and 61473117.

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Abstract

This paper investigates a distributed fault-tolerant consensus tracking algorithm for a group non-identical motors with unmeasured angular speed and unknown failures. First, the failures are modeled by nonlinear functions, and sliding mode observer is designed to estimate the angular speed and nonlinear failures. Then, in order to achieve the desired results, a novel distributed fault-tolerant algorithm is constructed based on the estimated angular speed and reconstructed failures. Theoretical analysis illustrates the stability and globally exponentially asymptotically convergence of the proposed observer and controller. The numerical simulations verify the high estimation accuracy, effectiveness and robustness of the proposed methods. The semi-physical experiments based on RT-LAB real-time simulator further test the system and controller with accurate performance in real-time.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. The system fault-tolerant control diagram for follower motor i

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Figure 2. Communication topology for a group of four followers with a virtual leader

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Figure 3. The unknown nonlinear failures estimation in both cases using sliding mode observer (7)

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Figure 4. Angular speed estimation using observer (7) with ${\theta ^{d1}} = 2t$(rad)

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Figure 5. Angular speed estimation using observer (7) with ${\theta ^{d2}} = 3\sin \left({\pi t/2}\right) $ (rad)

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Figure 6. Consensus tracking for rotor position and angular speed with protocol (15) when ${\theta ^{d1}} = 2t$(rad)

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Figure 7. Consensus tracking for rotor position and angular speed with protocol (15) when ${\theta ^{d2}} = 3\sin \left({\pi t/2}\right) $(rad)

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Figure 8. The unknown nonlinear failures estimation in both cases using sliding mode observer (7) (${F_{a1}},{\hat F_{a1}}$: 2/unit; ${F_{a2}},{\hat F_{a2}}$: 10/unit; ${F_{a3}},{\hat F_{a3}}$: 14.2/unit; ${F_{a4}},{\hat F_{a4}}$: 19/unit)

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Figure 9. Angular speed estimation using observer (7) with ${\theta ^{d1}} = 2t$(rad) ($\omega$: 10rad/s/unit)

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Figure 10. Angular speed estimation using observer (7) with ${\theta ^{d2}} = 3\sin \left( {\pi t} \right)$(rad) ($\omega$: 7.85rad/s/unit)

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Figure 11. Consensus tracking for rotor position and angular speed with protocol (15) when ${\theta ^{d1}} = 2t$(rad) ($\theta$: 90rad/unit, $\omega$: 10rad/s/unit)

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Figure 12. Consensus tracking for rotor position and angular speed with protocol (15) when ${\theta ^{d2}} = 3\sin \left( {\pi t} \right)$(rad) ($\theta$: 3.75rad/unit, $\omega$: 7.85rad/s/unit)

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Table 1. Parameters of Five Driven Motors

Motor.	Motor 0(L)	Motor 1	Motor 2	Motor 3	Motor 4
R$(\Omega)$	0.2	0.5	0.4	0.6	0.7
$K_t$	0.005	0.01	0.008	0.015	0.02
J$(k_g\cdot m^2)$	0.02	0.03	0.025	0.05	0.04
$K_e$	0.1	0.2	0.2	0.18	0.25
Initial $\theta {\kern 1pt} {\kern 1pt} {\kern 1pt} \left( {rad} \right)$	0.5	-0.8	1.3	-2.0	-2.4

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