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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

Han Wu 1,2, , Changfan Zhang 1,, , Jing He 1,3, and  Kaihui Zhao 1,

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.

Keywords: Fault-tolerant, consensus tracking, unmeasurable angular speed, multiple unknown failures, sliding mode observer, RT-LAB real-time simulator.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Han Wu, Changfan Zhang, Jing He, Kaihui Zhao. Distributed fault-tolerant consensus tracking for networked non-identical motors. Journal of Industrial and Management Optimization, 2017, 13 (2) : 917-929. doi: 10.3934/jimo.2016053
References:
[1]

A. A. Ahmadi, F. R. Salmasi and M. Noori-Manzar, Speed sensorless and sensor-fault tolerant optimal pi regulator for networked dc motor system with unknown time-delay and packet dropout, IEEE Trans. Industrial Electronics, 61 (2014), 708-717.  doi: 10.1109/TIE.2013.2253073.

[2]

F. Aghili, Fault-tolerant torque control of BLDC motors, IEEE Trans. Power Electronics, 26 (2011), 355-363.  doi: 10.1109/TPEL.2010.2060361.

[3]

S. Abourida, C. Dufour and J. Belanger, Hardware-in-the-loop simulation of finite-element based motor drives with RT-Lab and JMAG, IEEE International Symposium on Industrial Electronics, 3 (2006), 2462-2466.  doi: 10.1109/ISIE.2006.295959.

[4]

B. Jiang, M. Staroswiecki and V. Cocquempot, Fault accommodation for nonlinear dynamic systems, IEEE Trans. Autom. Control, 51 (2006), 1578-1583.  doi: 10.1109/TAC.2006.878732.

[5] H. K. Khalil, Nonlinear Systems, 3 edition, Prentice hall, Upper Saddle River, 2002. 
[6]

M. Karimadini and H. Lin, Fault-tolerant cooperative tasking for multi-agent systems, Int. J. Control, 84 (2011), 2092-2107.  doi: 10.1080/00207179.2011.631149.

[7]

E. Semsar-Kazerooni and K. Khorasani, Team consensus for a network of unmanned vehicles in presence of actuator faults, IEEE Trans. Control Syst. Technol., 18 (2010), 1155-1161.  doi: 10.1109/TCST.2009.2032921.

[8]

H. Su and M. Z. Q. Chen, Multi-agent containment control with input saturation on switching topologies, IET Control Theory Appli., 9 (2015), 399-409.  doi: 10.1049/iet-cta.2014.0393.

[9]

H. Su, M. Z. Q. Chen and X. Wang, Global coordinated tracking of multi-agent systems with disturbance uncertainties via bounded control inputs, Nonlinear Dynamics, 82 (2015), 2059-2068.  doi: 10.1007/s11071-015-2299-3.

[10]

H. Su, M. Z. Q. Chen and G. Chen, Robust semi-global coordinated tracking of linear multi-agent systems with input saturation, Int. J. Robust Nonlinear Control, 14 (2015), 2375-2390.  doi: 10.1002/rnc.3210.

[11]

H. Su, G. Jia and M. Z. Q. Chen, Semi-global containment control of multi-agent systems with intermittent input saturation, Journal of the Franklin Institute, 352 (2015), 3504-3525.  doi: 10.1016/j.jfranklin.2014.09.006.

[12]

I. Shames, A. M. H. Teixeira and H. Sandberg, Distributed fault detection for interconnected second-order systems, Automatica, 47 (2011), 2757-2764.  doi: 10.1016/j.automatica.2011.09.011.

[13]

Q. Shen, B. Jiang and P. Shi, Cooperative adaptive fuzzy tracking control for networked unknown nonlinear multi-agent systems with time-varying actuator faults, IEEE Trans. Fuzzy Systems, 22 (2013), 494-504.  doi: 10.1109/TFUZZ.2013.2260757.

[14]

Y. Shtessel, C. Edwards and L. Fridman, et al., Sliding Mode Control and Observation, Birkhauser, New York, 2014.

[15]

P. Tichy, P. Slechta and R. J. Staron, Multi-agent technology for fault tolerance and flexible control, IEEE Trans. Syst. Man Cybern. C, 36 (2006), 700-704.  doi: 10.1109/TSMCC.2006.879381.

[16]

C. Xu, Y. Zheng and H. Su, Containment Control for Coupled Harmonic Oscillators with Multiple Leaders under Directed Topology, Int. J. Control, 88 (2015), 248-255.  doi: 10.1080/00207179.2014.944873.

[17]

H. Yang, M. Staroswiecki and B. Jiang, Fault tolerant cooperative control for a class of nonlinear multi-agent systems, Syst. Control Lett., 60 (2011), 271-277.  doi: 10.1016/j.sysconle.2011.02.004.

[18]

J. Zhang, A. K. Swain and S. K. Nguang, Robust sliding mode observer based fault estimation for certain class of uncertain nonlinear systems, Asian J. Control, 17 (2015), 1296-1309.  doi: 10.1002/asjc.987.

[19]

Z. Zuo, J. Zhang and Y. Wang, Distributed consensus of linear multi-agent systems with fault tolerant control protocols, Proc. 33th IEEE Chinese Control Conf., (2014), 1656-1661.  doi: 10.1109/ChiCC.2014.6896877.

show all references

References:
[1]

A. A. Ahmadi, F. R. Salmasi and M. Noori-Manzar, Speed sensorless and sensor-fault tolerant optimal pi regulator for networked dc motor system with unknown time-delay and packet dropout, IEEE Trans. Industrial Electronics, 61 (2014), 708-717.  doi: 10.1109/TIE.2013.2253073.

[2]

F. Aghili, Fault-tolerant torque control of BLDC motors, IEEE Trans. Power Electronics, 26 (2011), 355-363.  doi: 10.1109/TPEL.2010.2060361.

[3]

S. Abourida, C. Dufour and J. Belanger, Hardware-in-the-loop simulation of finite-element based motor drives with RT-Lab and JMAG, IEEE International Symposium on Industrial Electronics, 3 (2006), 2462-2466.  doi: 10.1109/ISIE.2006.295959.

[4]

B. Jiang, M. Staroswiecki and V. Cocquempot, Fault accommodation for nonlinear dynamic systems, IEEE Trans. Autom. Control, 51 (2006), 1578-1583.  doi: 10.1109/TAC.2006.878732.

[5] H. K. Khalil, Nonlinear Systems, 3 edition, Prentice hall, Upper Saddle River, 2002. 
[6]

M. Karimadini and H. Lin, Fault-tolerant cooperative tasking for multi-agent systems, Int. J. Control, 84 (2011), 2092-2107.  doi: 10.1080/00207179.2011.631149.

[7]

E. Semsar-Kazerooni and K. Khorasani, Team consensus for a network of unmanned vehicles in presence of actuator faults, IEEE Trans. Control Syst. Technol., 18 (2010), 1155-1161.  doi: 10.1109/TCST.2009.2032921.

[8]

H. Su and M. Z. Q. Chen, Multi-agent containment control with input saturation on switching topologies, IET Control Theory Appli., 9 (2015), 399-409.  doi: 10.1049/iet-cta.2014.0393.

[9]

H. Su, M. Z. Q. Chen and X. Wang, Global coordinated tracking of multi-agent systems with disturbance uncertainties via bounded control inputs, Nonlinear Dynamics, 82 (2015), 2059-2068.  doi: 10.1007/s11071-015-2299-3.

[10]

H. Su, M. Z. Q. Chen and G. Chen, Robust semi-global coordinated tracking of linear multi-agent systems with input saturation, Int. J. Robust Nonlinear Control, 14 (2015), 2375-2390.  doi: 10.1002/rnc.3210.

[11]

H. Su, G. Jia and M. Z. Q. Chen, Semi-global containment control of multi-agent systems with intermittent input saturation, Journal of the Franklin Institute, 352 (2015), 3504-3525.  doi: 10.1016/j.jfranklin.2014.09.006.

[12]

I. Shames, A. M. H. Teixeira and H. Sandberg, Distributed fault detection for interconnected second-order systems, Automatica, 47 (2011), 2757-2764.  doi: 10.1016/j.automatica.2011.09.011.

[13]

Q. Shen, B. Jiang and P. Shi, Cooperative adaptive fuzzy tracking control for networked unknown nonlinear multi-agent systems with time-varying actuator faults, IEEE Trans. Fuzzy Systems, 22 (2013), 494-504.  doi: 10.1109/TFUZZ.2013.2260757.

[14]

Y. Shtessel, C. Edwards and L. Fridman, et al., Sliding Mode Control and Observation, Birkhauser, New York, 2014.

[15]

P. Tichy, P. Slechta and R. J. Staron, Multi-agent technology for fault tolerance and flexible control, IEEE Trans. Syst. Man Cybern. C, 36 (2006), 700-704.  doi: 10.1109/TSMCC.2006.879381.

[16]

C. Xu, Y. Zheng and H. Su, Containment Control for Coupled Harmonic Oscillators with Multiple Leaders under Directed Topology, Int. J. Control, 88 (2015), 248-255.  doi: 10.1080/00207179.2014.944873.

[17]

H. Yang, M. Staroswiecki and B. Jiang, Fault tolerant cooperative control for a class of nonlinear multi-agent systems, Syst. Control Lett., 60 (2011), 271-277.  doi: 10.1016/j.sysconle.2011.02.004.

[18]

J. Zhang, A. K. Swain and S. K. Nguang, Robust sliding mode observer based fault estimation for certain class of uncertain nonlinear systems, Asian J. Control, 17 (2015), 1296-1309.  doi: 10.1002/asjc.987.

[19]

Z. Zuo, J. Zhang and Y. Wang, Distributed consensus of linear multi-agent systems with fault tolerant control protocols, Proc. 33th IEEE Chinese Control Conf., (2014), 1656-1661.  doi: 10.1109/ChiCC.2014.6896877.

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 1Motor 2Motor 3Motor 4
R$(\Omega)$0.20.50.40.60.7
$K_t$0.0050.010.0080.0150.02
J$(k_g\cdot m^2)$0.020.030.0250.050.04
$K_e$0.10.20.20.180.25
Initial $\theta {\kern 1pt} {\kern 1pt} {\kern 1pt} \left( {rad} \right)$0.5-0.81.3-2.0-2.4
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Motor.Motor 0(L)Motor 1Motor 2Motor 3Motor 4
R$(\Omega)$0.20.50.40.60.7
$K_t$0.0050.010.0080.0150.02
J$(k_g\cdot m^2)$0.020.030.0250.050.04
$K_e$0.10.20.20.180.25
Initial $\theta {\kern 1pt} {\kern 1pt} {\kern 1pt} \left( {rad} \right)$0.5-0.81.3-2.0-2.4
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