# American Institute of Mathematical Sciences

• Previous Article
New structural properties of inventory models with Polya frequency distributed demand and fixed setup cost
• JIMO Home
• This Issue
• Next Article
Throughput of flow lines with unreliable parallel-machine workstations and blocking
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:

show all references

##### 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
 [1] Peng Zhang, Yongquan Zeng, Guotai Chi. Time-consistent multiperiod mean semivariance portfolio selection with the real constraints. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1663-1680. doi: 10.3934/jimo.2020039 [2] Xiaochen Mao, Weijie Ding, Xiangyu Zhou, Song Wang, Xingyong Li. Complexity in time-delay networks of multiple interacting neural groups. Electronic Research Archive, , () : -. doi: 10.3934/era.2021022 [3] Chris Guiver, Nathan Poppelreiter, Richard Rebarber, Brigitte Tenhumberg, Stuart Townley. Dynamic observers for unknown populations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3279-3302. doi: 10.3934/dcdsb.2020232 [4] Frank Sottile. The special Schubert calculus is real. Electronic Research Announcements, 1999, 5: 35-39. [5] Mayte Pérez-Llanos, Juan Pablo Pinasco, Nicolas Saintier. Opinion fitness and convergence to consensus in homogeneous and heterogeneous populations. Networks & Heterogeneous Media, 2021, 16 (2) : 257-281. doi: 10.3934/nhm.2021006 [6] Nikolai Botkin, Varvara Turova, Barzin Hosseini, Johannes Diepolder, Florian Holzapfel. Tracking aircraft trajectories in the presence of wind disturbances. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021010 [7] Rafael López, Óscar Perdomo. Constant-speed ramps for a central force field. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3447-3464. doi: 10.3934/dcds.2021003 [8] Yi Gao, Rui Li, Yingjing Shi, Li Xiao. Design of path planning and tracking control of quadrotor. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021063 [9] Christian Meyer, Stephan Walther. Optimal control of perfect plasticity part I: Stress tracking. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021022 [10] Lara Abi Rizk, Jean-Baptiste Burie, Arnaud Ducrot. Asymptotic speed of spread for a nonlocal evolutionary-epidemic system. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021064 [11] Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim, Doo Seok Lee. Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021035 [12] Claudianor O. Alves, Giovany M. Figueiredo, Riccardo Molle. Multiple positive bound state solutions for a critical Choquard equation. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021061 [13] Kai Cai, Guangyue Han. An optimization approach to the Langberg-Médard multiple unicast conjecture. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021001 [14] Qiang Lin, Yang Xiao, Jingju Zheng. Selecting the supply chain financing mode under price-sensitive demand: Confirmed warehouse financing vs. trade credit. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2031-2049. doi: 10.3934/jimo.2020057 [15] Yohei Yamazaki. Center stable manifolds around line solitary waves of the Zakharov–Kuznetsov equation with critical speed. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3579-3614. doi: 10.3934/dcds.2021008 [16] Guanwei Chen, Martin Schechter. Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021124 [17] Jianping Gao, Shangjiang Guo, Wenxian Shen. Persistence and time periodic positive solutions of doubly nonlocal Fisher-KPP equations in time periodic and space heterogeneous media. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2645-2676. doi: 10.3934/dcdsb.2020199 [18] Qiwei Wu, Liping Luan. Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping. Communications on Pure & Applied Analysis, 2021, 20 (3) : 995-1023. doi: 10.3934/cpaa.2021003 [19] Elimhan N. Mahmudov. Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021010 [20] Olivier Ley, Erwin Topp, Miguel Yangari. Some results for the large time behavior of Hamilton-Jacobi equations with Caputo time derivative. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3555-3577. doi: 10.3934/dcds.2021007

2019 Impact Factor: 1.366