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April  2017, 13(2): 917-929. doi: 10.3934/jimo.2016053

## 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

Received  June 2015 Revised  June 2016 Published  August 2016

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

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.

Citation: Han Wu, Changfan Zhang, Jing He, Kaihui Zhao. Distributed fault-tolerant consensus tracking for networked non-identical motors. Journal of Industrial & Management Optimization, 2017, 13 (2) : 917-929. doi: 10.3934/jimo.2016053
##### References:

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##### References:
The system fault-tolerant control diagram for follower motor i
Communication topology for a group of four followers with a virtual leader
The unknown nonlinear failures estimation in both cases using sliding mode observer (7)
Angular speed estimation using observer (7) with ${\theta ^{d1}} = 2t$(rad)
Angular speed estimation using observer (7) with ${\theta ^{d2}} = 3\sin \left({\pi t/2}\right)$ (rad)
Consensus tracking for rotor position and angular speed with protocol (15) when ${\theta ^{d1}} = 2t$(rad)
Consensus tracking for rotor position and angular speed with protocol (15) when ${\theta ^{d2}} = 3\sin \left({\pi t/2}\right)$(rad)
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)
Angular speed estimation using observer (7) with ${\theta ^{d1}} = 2t$(rad) ($\omega$: 10rad/s/unit)
Angular speed estimation using observer (7) with ${\theta ^{d2}} = 3\sin \left( {\pi t} \right)$(rad) ($\omega$: 7.85rad/s/unit)
Consensus tracking for rotor position and angular speed with protocol (15) when ${\theta ^{d1}} = 2t$(rad) ($\theta$: 90rad/unit, $\omega$: 10rad/s/unit)
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)
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
 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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