# 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] Frank Sottile. The special Schubert calculus is real. Electronic Research Announcements, 1999, 5: 35-39. [2] 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 [3] 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 - A, 2021  doi: 10.3934/dcds.2021035 [4] 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 [5] Cécile Carrère, Grégoire Nadin. Influence of mutations in phenotypically-structured populations in time periodic environment. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3609-3630. doi: 10.3934/dcdsb.2020075 [6] Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183 [7] Guillermo Reyes, Juan-Luis Vázquez. Long time behavior for the inhomogeneous PME in a medium with slowly decaying density. Communications on Pure & Applied Analysis, 2009, 8 (2) : 493-508. doi: 10.3934/cpaa.2009.8.493 [8] Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189 [9] Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258 [10] Linlin Li, Bedreddine Ainseba. Large-time behavior of matured population in an age-structured model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2561-2580. doi: 10.3934/dcdsb.2020195 [11] Tomáš Roubíček. An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 867-893. doi: 10.3934/dcdss.2017044 [12] Xiaomao Deng, Xiao-Chuan Cai, Jun Zou. A parallel space-time domain decomposition method for unsteady source inversion problems. Inverse Problems & Imaging, 2015, 9 (4) : 1069-1091. doi: 10.3934/ipi.2015.9.1069 [13] Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2677-2692. doi: 10.3934/dcdsb.2020200 [14] Elena K. Kostousova. External polyhedral estimates of reachable sets of discrete-time systems with integral bounds on additive terms. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021015 [15] Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021014

2019 Impact Factor: 1.366