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July  2022, 15(7): 1699-1712. doi: 10.3934/dcdss.2021167

Finite-time sliding mode control for UVMS via T-S fuzzy approach

1. 

School of Electrical Engineering and Automation, Anhui University, 111 Jiulong Road, Hefei 230601, Anhui, China

2. 

State Key Laboratory for Control and Management of Complex Systems, Institute of Automation, Chinese Academy of Sciences, 95 Zhongguancun Road, Beijing 100190, China

*Corresponding author: Shuping He

Received  September 2021 Revised  October 2021 Published  July 2022 Early access  December 2021

In order to solve the control problem of Underwater Vehicle with Manipulator System (UVMS), this paper proposes a finite-time sliding mode control strategy via T-S fuzzy approach. From the general dynamic model of UVMS and considering the influence between the manipulator and the underwater vehicle, hydrodynamic damping, buoyancy and gravity as the fuzzy items, we establish global fuzzy dynamic model and design a closed-loop fuzzy sliding mode controller. We prove the model in theory from two aspects: the reachability of sliding domain and the finite-time boundedness. We also give the solution of the controller gain. A simulation on the actual four joint dynamic model of UVMS with two fuzzy subsystems is carried out to verify the effectiveness of this method.

Citation: Xiang Dong, Chengcheng Ren, Shuping He, Long Cheng, Shuo Wang. Finite-time sliding mode control for UVMS via T-S fuzzy approach. Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1699-1712. doi: 10.3934/dcdss.2021167
References:
[1]

F. AmatoM. Ariola and C. Cosentino, Finite-time stability of linear time-varying systems: Analysis and controller design, IEEE Trans. Automat. Control, 55 (2010), 1003-1008.  doi: 10.1109/TAC.2010.2041680.

[2]

Z. CaoY. Niu and J. Song, Finite-time sliding mode control of Markovian jump cyber-physical systems against randomly occurring injection attacks, IEEE Trans. Automat. Control, 65 (2020), 1264-1271.  doi: 10.1109/TAC.2019.2926156.

[3]

B. ChenY. Niu and Y. Zou, Security control for Markov jump system with adversarial attacks and unknown transition rates via adaptive sliding mode technique, Journal of the Franklin Institute, 356 (2019), 3333-3352.  doi: 10.1016/j.jfranklin.2019.01.045.

[4]

L. ChenH. Wang and Y. Huang et al., Robust hierarchical sliding mode control of a two-wheeled self-balancing vehicle using perturbation estimation, Mechanical Systems and Signal Processing, 139 (2020), 106584.  doi: 10.1016/j.ymssp.2019.106584.

[5]

Z. ChenZ. Li and C. L. P. Chen, Disturbance observer-based fuzzy control of uncertain MIMO mechanical systems with input nonlinearities and its application to robotic exoskeleton, IEEE Transactions on Cybernetics, 47 (2016), 984-994.  doi: 10.1109/TCYB.2016.2536149.

[6]

Y. Dai and S. Yu, Design of an indirect adaptive controller for the trajectory tracking of UVMS, Ocean Engineering, 151 (2018), 234-245.  doi: 10.1016/j.oceaneng.2017.12.070.

[7]

X. Fan and Z. Wang, Event-triggered sliding-mode control for a class of T-S fuzzy systems, IEEE Transactions on Fuzzy Systems, 28 (2020), 2656-2664.  doi: 10.1109/TFUZZ.2019.2940867.

[8]

G. GarciaS. Tarbouriech and J. Bernussou, Finite-time stabilization of linear time-varying continuous systems, IEEE Trans. Automat. Control, 54 (2009), 364-369.  doi: 10.1109/TAC.2008.2008325.

[9]

Y. HuH. Wang and Z. Cao et al., Extreme-learning-machine-based FNTSM control strategy for electronic throttle, Neural Computing and Applications, 32 (2020), 14507-14518.  doi: 10.1007/s00521-019-04446-9.

[10]

Y. HuH. Wang and S. He et al., Adaptive tracking control of an electronic throttle valve based on recursive terminal sliding mode, IEEE Transactions on Vehicular Technology, 70 (2021), 251-262.  doi: 10.1109/TVT.2020.3045778.

[11]

J. JiangH. R. KarimiY. Kao and C. Gao, Adaptive control of nonlinear semi-markovian jump T-S fuzzy systems with immeasurable premise variables via sliding mode observer, IEEE Transactions on Cybernetics, 50 (2020), 810-820.  doi: 10.1109/TCYB.2018.2874166.

[12]

S. Kuppusamy and Y. H. Joo, Nonfragile retarded sampled-data switched control of T-S fuzzy systems and its applications, IEEE Transactions on Fuzzy Systems, 28 (2020), 2523-2532.  doi: 10.1109/TFUZZ.2019.2940432.

[13]

J. LiY. Niu and J. Song, Finite-time boundedness of sliding mode control under periodic event-triggered strategy, Internat. J. Robust Nonlinear Control, 31 (2021), 623-639.  doi: 10.1002/rnc.5298.

[14]

G. MaraniK. C. Song and J. Yuh, Underwater autonomous manipulation for intervention missions AUVs, Ocean Engineering, 36 (2009), 15-23.  doi: 10.1016/j.oceaneng.2008.08.007.

[15]

S. PengY. XiaG. P. Liu and D. Rees, On designing of sliding-mode control for stochastic jump systems, IEEE Trans. Automat. Control, 51 (2006), 97-103.  doi: 10.1109/TAC.2005.861716.

[16]

C. Ren and S. He, Sliding mode control for a class of nonlinear positive Markov jumping systems with uncertainties in a finite-time interval, International Journal of Control, Automation and Systems, 17 (2019), 1634-1641. 

[17]

C. RenS. He and X. Luan et al., Finite-time L$_2$-gain asynchronous control for continuous-time positive hidden markov jump systems via T-S fuzzy model approach, IEEE Transactions on Cybernetics, 51 (2021), 77-87.  doi: 10.1109/TCYB.2020.2996743.

[18]

C. RenR. Nie and S. He, Finite-time positiveness and distributed control of Lipschitz nonlinear multi-agent systems, J. Franklin Inst., 356 (2019), 8080-8092.  doi: 10.1016/j.jfranklin.2019.06.044.

[19]

M. R. SoltanpourP. Otadolajam and M. H. Khooban, Robust control strategy for electrically driven robot manipulators: Adaptive fuzzy sliding mode, IET Science, Measurement & Technology, 9 (2015), 322-334.  doi: 10.1049/iet-smt.2013.0265.

[20]

J. SongY. NiuH. K. Lam and Y. Zou, Asynchronous sliding mode control of singularly perturbed semi-Markovian jump systems: Application to an operational amplifier circuit, Automatica, 118 (2020), 109026.  doi: 10.1016/j.automatica.2020.109026.

[21]

J. SongY. Niu and Y. Zou, Finite-time stabilization via sliding mode control, IEEE Trans. Automat. Control, 62 (2017), 1478-1483.  doi: 10.1109/TAC.2016.2578300.

[22]

T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man and Cybernetics, 15 (1985), 116-132.  doi: 10.1109/TSMC.1985.6313399.

[23]

H. WangL. ShiZ. Man and et al., Continuous fast nonsingular terminal sliding mode control of automotive electronic throttle systems using finite-time exact observer, IEEE Transactions on Industrial Electronics, 65 (2018), 7160-7172.  doi: 10.1109/TIE.2018.2795591.

[24]

M. Ye and H. Wang, Robust adaptive integral terminal sliding mode control for steer-by-wire systems based on extreme learning machine, Computers and Electrical Engineering, 86 (2020), 106756.  doi: 10.1016/j.compeleceng.2020.106756.

[25]

M. Ye and H. Wang, A robust adaptive chattering-free sliding mode control strategy for automotive electronic throttle system via genetic algorithm, IEEE Access, 8 (2020), 68-80.  doi: 10.1109/ACCESS.2019.2934232.

[26]

J. ZhangH. Wang and Z. Cao et al., Fast nonsingular terminal sliding mode control for permanent-magnet linear motor via ELM, Neural Computing and Applications, 32 (2020), 14447-14457.  doi: 10.1007/s00521-019-04502-4.

[27]

J. ZhangH. Wang and J. Zheng et al., Adaptive sliding mode-based lateral stability control of steer-by-wire vehicles with experimental validations, IEEE Transactions on Vehicular Technology, 69 (2020), 9589-9600.  doi: 10.1109/TVT.2020.3003326.

[28]

J. ZhangF. ZhuH. R. Karimi and F. Wang, Observer-based sliding mode control for T-S fuzzy descriptor systems with time delay, IEEE Transactions on Fuzzy Systems, 27 (2019), 2009-2023.  doi: 10.1109/TFUZZ.2019.2893220.

[29]

Z. ZhangY. NiuZ. Cao and J. Song, Security sliding mode control of interval type-2 fuzzy systems subject to cyber attacks: The stochastic communication protocol case, IEEE Transactions on Fuzzy Systems, 29 (2021), 240-251.  doi: 10.1109/TFUZZ.2020.2972785.

show all references

References:
[1]

F. AmatoM. Ariola and C. Cosentino, Finite-time stability of linear time-varying systems: Analysis and controller design, IEEE Trans. Automat. Control, 55 (2010), 1003-1008.  doi: 10.1109/TAC.2010.2041680.

[2]

Z. CaoY. Niu and J. Song, Finite-time sliding mode control of Markovian jump cyber-physical systems against randomly occurring injection attacks, IEEE Trans. Automat. Control, 65 (2020), 1264-1271.  doi: 10.1109/TAC.2019.2926156.

[3]

B. ChenY. Niu and Y. Zou, Security control for Markov jump system with adversarial attacks and unknown transition rates via adaptive sliding mode technique, Journal of the Franklin Institute, 356 (2019), 3333-3352.  doi: 10.1016/j.jfranklin.2019.01.045.

[4]

L. ChenH. Wang and Y. Huang et al., Robust hierarchical sliding mode control of a two-wheeled self-balancing vehicle using perturbation estimation, Mechanical Systems and Signal Processing, 139 (2020), 106584.  doi: 10.1016/j.ymssp.2019.106584.

[5]

Z. ChenZ. Li and C. L. P. Chen, Disturbance observer-based fuzzy control of uncertain MIMO mechanical systems with input nonlinearities and its application to robotic exoskeleton, IEEE Transactions on Cybernetics, 47 (2016), 984-994.  doi: 10.1109/TCYB.2016.2536149.

[6]

Y. Dai and S. Yu, Design of an indirect adaptive controller for the trajectory tracking of UVMS, Ocean Engineering, 151 (2018), 234-245.  doi: 10.1016/j.oceaneng.2017.12.070.

[7]

X. Fan and Z. Wang, Event-triggered sliding-mode control for a class of T-S fuzzy systems, IEEE Transactions on Fuzzy Systems, 28 (2020), 2656-2664.  doi: 10.1109/TFUZZ.2019.2940867.

[8]

G. GarciaS. Tarbouriech and J. Bernussou, Finite-time stabilization of linear time-varying continuous systems, IEEE Trans. Automat. Control, 54 (2009), 364-369.  doi: 10.1109/TAC.2008.2008325.

[9]

Y. HuH. Wang and Z. Cao et al., Extreme-learning-machine-based FNTSM control strategy for electronic throttle, Neural Computing and Applications, 32 (2020), 14507-14518.  doi: 10.1007/s00521-019-04446-9.

[10]

Y. HuH. Wang and S. He et al., Adaptive tracking control of an electronic throttle valve based on recursive terminal sliding mode, IEEE Transactions on Vehicular Technology, 70 (2021), 251-262.  doi: 10.1109/TVT.2020.3045778.

[11]

J. JiangH. R. KarimiY. Kao and C. Gao, Adaptive control of nonlinear semi-markovian jump T-S fuzzy systems with immeasurable premise variables via sliding mode observer, IEEE Transactions on Cybernetics, 50 (2020), 810-820.  doi: 10.1109/TCYB.2018.2874166.

[12]

S. Kuppusamy and Y. H. Joo, Nonfragile retarded sampled-data switched control of T-S fuzzy systems and its applications, IEEE Transactions on Fuzzy Systems, 28 (2020), 2523-2532.  doi: 10.1109/TFUZZ.2019.2940432.

[13]

J. LiY. Niu and J. Song, Finite-time boundedness of sliding mode control under periodic event-triggered strategy, Internat. J. Robust Nonlinear Control, 31 (2021), 623-639.  doi: 10.1002/rnc.5298.

[14]

G. MaraniK. C. Song and J. Yuh, Underwater autonomous manipulation for intervention missions AUVs, Ocean Engineering, 36 (2009), 15-23.  doi: 10.1016/j.oceaneng.2008.08.007.

[15]

S. PengY. XiaG. P. Liu and D. Rees, On designing of sliding-mode control for stochastic jump systems, IEEE Trans. Automat. Control, 51 (2006), 97-103.  doi: 10.1109/TAC.2005.861716.

[16]

C. Ren and S. He, Sliding mode control for a class of nonlinear positive Markov jumping systems with uncertainties in a finite-time interval, International Journal of Control, Automation and Systems, 17 (2019), 1634-1641. 

[17]

C. RenS. He and X. Luan et al., Finite-time L$_2$-gain asynchronous control for continuous-time positive hidden markov jump systems via T-S fuzzy model approach, IEEE Transactions on Cybernetics, 51 (2021), 77-87.  doi: 10.1109/TCYB.2020.2996743.

[18]

C. RenR. Nie and S. He, Finite-time positiveness and distributed control of Lipschitz nonlinear multi-agent systems, J. Franklin Inst., 356 (2019), 8080-8092.  doi: 10.1016/j.jfranklin.2019.06.044.

[19]

M. R. SoltanpourP. Otadolajam and M. H. Khooban, Robust control strategy for electrically driven robot manipulators: Adaptive fuzzy sliding mode, IET Science, Measurement & Technology, 9 (2015), 322-334.  doi: 10.1049/iet-smt.2013.0265.

[20]

J. SongY. NiuH. K. Lam and Y. Zou, Asynchronous sliding mode control of singularly perturbed semi-Markovian jump systems: Application to an operational amplifier circuit, Automatica, 118 (2020), 109026.  doi: 10.1016/j.automatica.2020.109026.

[21]

J. SongY. Niu and Y. Zou, Finite-time stabilization via sliding mode control, IEEE Trans. Automat. Control, 62 (2017), 1478-1483.  doi: 10.1109/TAC.2016.2578300.

[22]

T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man and Cybernetics, 15 (1985), 116-132.  doi: 10.1109/TSMC.1985.6313399.

[23]

H. WangL. ShiZ. Man and et al., Continuous fast nonsingular terminal sliding mode control of automotive electronic throttle systems using finite-time exact observer, IEEE Transactions on Industrial Electronics, 65 (2018), 7160-7172.  doi: 10.1109/TIE.2018.2795591.

[24]

M. Ye and H. Wang, Robust adaptive integral terminal sliding mode control for steer-by-wire systems based on extreme learning machine, Computers and Electrical Engineering, 86 (2020), 106756.  doi: 10.1016/j.compeleceng.2020.106756.

[25]

M. Ye and H. Wang, A robust adaptive chattering-free sliding mode control strategy for automotive electronic throttle system via genetic algorithm, IEEE Access, 8 (2020), 68-80.  doi: 10.1109/ACCESS.2019.2934232.

[26]

J. ZhangH. Wang and Z. Cao et al., Fast nonsingular terminal sliding mode control for permanent-magnet linear motor via ELM, Neural Computing and Applications, 32 (2020), 14447-14457.  doi: 10.1007/s00521-019-04502-4.

[27]

J. ZhangH. Wang and J. Zheng et al., Adaptive sliding mode-based lateral stability control of steer-by-wire vehicles with experimental validations, IEEE Transactions on Vehicular Technology, 69 (2020), 9589-9600.  doi: 10.1109/TVT.2020.3003326.

[28]

J. ZhangF. ZhuH. R. Karimi and F. Wang, Observer-based sliding mode control for T-S fuzzy descriptor systems with time delay, IEEE Transactions on Fuzzy Systems, 27 (2019), 2009-2023.  doi: 10.1109/TFUZZ.2019.2893220.

[29]

Z. ZhangY. NiuZ. Cao and J. Song, Security sliding mode control of interval type-2 fuzzy systems subject to cyber attacks: The stochastic communication protocol case, IEEE Transactions on Fuzzy Systems, 29 (2021), 240-251.  doi: 10.1109/TFUZZ.2020.2972785.

Figure 1.  The global fuzzy sliding mode variable
Figure 2.  The system state trajectory of open-loop and closed-loop
Table 1.  The main parameters of UVMS model
Parameter Value
$ l_1 $ $ 1.12m $
$ l_2 $ $ 0.89m $
$ m_1 $ $ 4.32kg $
$ m_2 $ $ 3.43kg $
$ g $ $ 9.8m/s^2 $
Parameter Value
$ l_1 $ $ 1.12m $
$ l_2 $ $ 0.89m $
$ m_1 $ $ 4.32kg $
$ m_2 $ $ 3.43kg $
$ g $ $ 9.8m/s^2 $
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