Event-triggered control of flexible manipulator constraint system modeled by PDE

Tongyu Wang; Yadong Chen; Tongyu Wang; Yadong Chen

doi:10.3934/mbe.2023441

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 10043-10062. doi: 10.3934/mbe.2023441

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Event-triggered control of flexible manipulator constraint system modeled by PDE

Tongyu Wang ,
Yadong Chen ^,

College of Medicine and Biological Information Engineering, Northeastern University, Shenyang 110169, China

Academic Editor:Xiaodi Li

Received: 03 February 2023 Revised: 04 March 2023 Accepted: 20 March 2023 Published: 28 March 2023

The vibration suppression control of a flexible manipulator system modeled by partial differential equation (PDE) with state constraints is studied in this paper. On the basis of the backstepping recursive design framework, the problem of the constraint of joint angle and boundary vibration deflection is solved by using the Barrier Lyapunov function (BLF). Moreover, based on the relative threshold strategy, an event-triggered mechanism is proposed to save the communication workload between controller and actuator, which not only deals with the state constraints of the partial differential flexible manipulator system, but also effectively improves the system work efficiency. Good damping effect on vibration and the elevated system performance can be seen under the proposed control strategy. At the same time, the state can meet the constraints given in advance, and all system signals are bounded. The proposed scheme is effective, which is proven by simulation results.
- state constraints,
- partial differential equations,
- event-triggered control,
- Barrier Lyapunov function
Citation: Tongyu Wang, Yadong Chen. Event-triggered control of flexible manipulator constraint system modeled by PDE[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 10043-10062. doi: 10.3934/mbe.2023441

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Abstract

The vibration suppression control of a flexible manipulator system modeled by partial differential equation (PDE) with state constraints is studied in this paper. On the basis of the backstepping recursive design framework, the problem of the constraint of joint angle and boundary vibration deflection is solved by using the Barrier Lyapunov function (BLF). Moreover, based on the relative threshold strategy, an event-triggered mechanism is proposed to save the communication workload between controller and actuator, which not only deals with the state constraints of the partial differential flexible manipulator system, but also effectively improves the system work efficiency. Good damping effect on vibration and the elevated system performance can be seen under the proposed control strategy. At the same time, the state can meet the constraints given in advance, and all system signals are bounded. The proposed scheme is effective, which is proven by simulation results.

References

[1]	W. Kim, F. Tendick, S. Ellis, L. Stark, A comparison of position and rate control for telemanipulations with consideration of manipulator system dynamics, IEEE J. Rob. Autom., 3 (1987), 426–436. https://doi.org/10.1109/JRA.1987.1087117 doi: 10.1109/JRA.1987.1087117
[2]	C. Fernandes, L. Gurvit, Z. X. Li, Attitude control of space platform/manipulator system using internal motion, Space Rob. Dyn. Control, 1993 (1993), 131–163. https://doi.org/10.1007/978-1-4615-3588-1_6 doi: 10.1007/978-1-4615-3588-1_6
[3]	Yun, D. Moon, J. Ha, S. Kang, W. Lee, Modman: An advanced reconfigurable manipulator system with genderless connector and automatic kinematic modeling algorithm, IEEE Rob. Autom. Lett., 5 (2020), 4225–4232. https://doi.org/10.1109/LRA.2020.2994486 doi: 10.1109/LRA.2020.2994486
[4]	M. Tognon, H. A. T. Chávez, E. Gasparin, Q. Sablé, D. Bicego, A truly-redundant aerial manipulator system with application to push-and-slide inspection in industrial plants, IEEE Rob. Autom. Lett., 4 (2019), 1846–1851. https://doi.org/10.1109/LRA.2019.2895880 doi: 10.1109/LRA.2019.2895880
[5]	J. Zhang, L. Jin, C. Yang, Distributed cooperative kinematic control of multiple robotic manipulators with an improved communication efficiency, IEEE/ASME Trans. Mechatron., 27 (2021), 149–158. https://doi.org/10.1109/TMECH.2021.3059441 doi: 10.1109/TMECH.2021.3059441
[6]	Y. Zhou, Y. Li, PLC control system of pneumatic manipulator automatic assembly line based on cloud computing platform, J. Phys. Conf. Ser., 1744 (2021), 022011. https://doi.org/10.1088/1742-6596/1744/2/022011 doi: 10.1088/1742-6596/1744/2/022011
[7]	Z. Xie, L. Jin, X. Luo, Z. Sun, M. Liu, RNN for repetitive motion generation of redundant robot manipulators: An orthogonal projection-based scheme, IEEE Trans. Neural Networks Learn. Syst., 33 (2020), 615–628. https://doi.org/10.1109/TNNLS.2020.3028304 doi: 10.1109/TNNLS.2020.3028304
[8]	S. K. Dwivedy, P. Eberhard, Dynamic analysis of flexible manipulators, a literature review, Mech. Mach. Theory, 41 (2006), 749–777. https://doi.org/10.1016/j.mechmachtheory.2006.01.014 doi: 10.1016/j.mechmachtheory.2006.01.014
[9]	Z. Mohamed, J. M. Martins, M. O.Tokhi, J. Sá Da Costa, M. A. Botto, Vibration control of a very flexible manipulator system, Control Eng. Prac., 13 (2005), 267–277. https://doi.org/10.1016/j.conengprac.2003.11.014 doi: 10.1016/j.conengprac.2003.11.014
[10]	L. Tian, C. Collins, A dynamic recurrent neural network-based controller for a rigid-flexible manipulator system, Mechatronics, 14 (2004), 471–490. https://doi.org/10.1016/j.mechatronics.2003.10.002 doi: 10.1016/j.mechatronics.2003.10.002
[11]	Y. Liu, W. Zhan, M. Xing, Y. Wu, R. Xu, X. Wu, Boundary control of a rotating and length-varying flexible robotic manipulator system, IEEE Trans. Syst. Man Cybern. Syst., 52 (2020), 377–386. https://doi.org/10.1109/TSMC.2020.2999485 doi: 10.1109/TSMC.2020.2999485
[12]	F. Cao, J. Liu, Three-dimensional modeling and input saturation control for a two-link flexible manipulator based on infinite dimensional model, J. Franklin Inst., 357 (2020), 1026–1042. https://doi.org/10.1016/j.jfranklin.2019.10.018 doi: 10.1016/j.jfranklin.2019.10.018
[13]	Y. Song, X. He, Z. Liu, W. He, C. Sun, F. Y. Wang, Parallel control of distributed parameter systems, IEEE Trans. Cybern., 48 (2018), 3291–3301. https://doi.org/10.1109/TCYB.2018.2849569 doi: 10.1109/TCYB.2018.2849569
[14]	F. Cao, J. Liu, Boundary control for PDE flexible manipulators: Accommodation to both actuator faults and sensor faults, Asian J. Control, 24 (2022), 1700–1712. https://doi.org/10.1002/asjc.2560 doi: 10.1002/asjc.2560
[15]	T. Jiang, J. Liu, W. He, Boundary control for a flexible manipulator based on infinite dimensional disturbance observer, J. Sound Vib., 348 (2015), 1–14. https://doi.org/10.1016/j.jsv.2015.02.044 doi: 10.1016/j.jsv.2015.02.044
[16]	M. Dogan, Y. Istefanopulos, Optimal nonlinear controller design for flexible robot manipulators with adaptive internal model, IET Control Theory Appl., 1 (2007), 770–778. https://doi.org/10.1049/iet-cta:20050272 doi: 10.1049/iet-cta:20050272
[17]	T. Wongratanaphisan, M. O. T. Cole, Robust impedance control of a flexible structure mounted manipulator performing contact tasks, IEEE Trans. Rob., 25 (2009), 445–451. https://doi.org/10.1109/TRO.2008.2012340 doi: 10.1109/TRO.2008.2012340
[18]	H. C. Shin, S. B. Choi, Position control of a two-link flexible manipulator featuring piezoelectric actuators and sensors, Mechatronics, 11 (2001), 707–729. https://doi.org/10.1016/S0957-4158(00)00045-3 doi: 10.1016/S0957-4158(00)00045-3
[19]	S. Tong, Y. Li, Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems, Sci. China Inf. Sci., 57 (2014), 1–14. https://doi.org/10.1007/s11432-013-5043-y doi: 10.1007/s11432-013-5043-y
[20]	W. He, X. He, M. Zou, H. Li, PDE model-based boundary control design for a flexible robotic manipulator with input backlash, IEEE Trans. Control Syst. Technol., 27 (2018), 790–797. https://doi.org/10.1109/TCST.2017.2780055 doi: 10.1109/TCST.2017.2780055
[21]	H. J. Yang, M. Tan, Sliding mode control for flexible-link manipulators based on adaptive neural networks, Int. J. Autom. Comput., 15 (2018), 239–248. https://doi.org/10.1007/s11633-018-1122-2 doi: 10.1007/s11633-018-1122-2
[22]	L. Li, J. Liu, Neural-network-based adaptive fault-tolerant vibration control of single-link flexible manipulator, Trans. Inst. Meas. Control, 42 (2020), 430–438. https://doi.org/10.1177/0142331219874157 doi: 10.1177/0142331219874157
[23]	M. B. Cheng, V. Radisavljevic, W. C. Su, Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties, Automatica, 47 (2011), 381–387. https://doi.org/10.1016/j.automatica.2010.10.045 doi: 10.1016/j.automatica.2010.10.045
[24]	Y. Zhao, H. Gao, J. Qiu, Fuzzy observer based control for nonlinear coupled hyperbolic PDE-ODE systems, IEEE Trans. Fuzzy Syst., 27 (2018), 1332–1346. https://doi.org/10.1109/TFUZZ.2018.2877635 doi: 10.1109/TFUZZ.2018.2877635
[25]	J. Qiu, S. X. Ding, H. Gao, S. Yin, Fuzzy-model-based reliable static output feedback control of nonlinear hyperbolic PDE systems, IEEE Trans. Fuzzy Syst., 24 (2015), 388–400. https://doi.org/10.1109/TFUZZ.2015.2457934 doi: 10.1109/TFUZZ.2015.2457934
[26]	J. W. Wang, S. H. Tsai, H. X. Li, H. Lam, Spatially piecewise fuzzy control design for sampled-data exponential stabilization of semilinear parabolic PDE systems, IEEE Trans. Fuzzy Syst., 26 (2018), 2967–2980. https://doi.org/10.1109/TFUZZ.2018.2809686 doi: 10.1109/TFUZZ.2018.2809686
[27]	X. Song, R. Zhang, C. K. Ahn, S. Song, Adaptive event-triggered control of networked fuzzy PDE systems under hybrid cyber-attacks, IEEE Trans. Fuzzy Syst., 30 (2022), 4211–4223. https://doi.org/10.1109/TFUZZ.2022.3145816 doi: 10.1109/TFUZZ.2022.3145816
[28]	S. Tong, S. Sui, Y. Li, Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained, IEEE Trans. Fuzzy Syst., 23 (2015), 729–742. https://doi.org/10.1109/TFUZZ.2014.2327987 doi: 10.1109/TFUZZ.2014.2327987
[29]	S. C. Tong, X. Min, Y. X. Li, Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions, IEEE Trans. Cybern., 50 (2020), 3903–3913. https://doi.org/10.1109/TCYB.2020.2977175 doi: 10.1109/TCYB.2020.2977175
[30]	Y. J. Liu, L. Ma, L. Liu, S. Tong, C. L. P. Chen, Adaptive neural network learning controller design for a class of nonlinear systems with time-varying state constraints, IEEE Trans. Neural Networks Learn. Syst., 31 (2019), 66–75. https://doi.org/10.1109/TNNLS.2019.2899589 doi: 10.1109/TNNLS.2019.2899589
[31]	Y. J. Liu, M. Gong, L. Liu, S. Tong, C. L. P. Chen, Fuzzy observer constraint based on adaptive control for uncertain nonlinear MIMO systems with time-varying state constraints, IEEE Trans. Cybern., 51 (2019), 1380–1389. https://doi.org/10.1109/TCYB.2019.2933700 doi: 10.1109/TCYB.2019.2933700
[32]	W. Wu, Y. Li, S. Tong, Fuzzy adaptive tracking control for state constraint switched stochastic nonlinear systems with unstable inverse dynamics, IEEE Trans. Syst. Man Cybern. Syst., 51 (2019), 5522–5534. https://doi.org/10.1109/TSMC.2019.2956263 doi: 10.1109/TSMC.2019.2956263
[33]	L. Tang, X. Y. Zhang, Y. J. Liu, S. Tong, PDE Based adaptive control of flexible riser system with input backlash and state constraints, IEEE Trans. Circuits Syst. I, 69 (2022), 2193–2202. https://doi.org/10.1109/TCSI.2022.3149290 doi: 10.1109/TCSI.2022.3149290
[34]	X. Xing, J. Liu, PDE model-based state-feedback control of constrained moving vehicle-mounted flexible manipulator with prescribed performance, J. Sound Vib., 441 (2019), 126–151. https://doi.org/10.1016/j.jsv.2018.10.023 doi: 10.1016/j.jsv.2018.10.023
[35]	F. Xu, L. Tang, Y. J. Liu, S. Tong, Tangent barrier Lyapunov function‐based constrained control of flexible manipulator system with actuator failure, Int. J. Robust Nonlinear Control, 31 (2021), 8523–8536. https://doi.org/10.1002/rnc.5735 doi: 10.1002/rnc.5735
[36]	L. Liu, X. Li, Y. J. Liu, S. Tong, Neural network based adaptive event trigger control for a class of electromagnetic suspension systems, Control Eng. Prac., 106 (2021), 104675. https://doi.org/10.1016/j.conengprac.2020.104675 doi: 10.1016/j.conengprac.2020.104675
[37]	Y. X. Li, G. H. Yang, S. Tong, Fuzzy adaptive distributed event-triggered consensus control of uncertain nonlinear multiagent systems, IEEE Trans. Syst. Man Cybern. Syst., 49 (2018), 1777–1786. https://doi.org/10.1109/TSMC.2018.2812216 doi: 10.1109/TSMC.2018.2812216
[38]	X. Li, H. Wu, J. Cao, Prescribed-time synchronization in networks of piecewise smooth systems via a nonlinear dynamic event-triggered control strategy, Math. Comput. Simul., 203 (2023), 647–668. https://doi.org/10.1016/j.matcom.2022.07.010 doi: 10.1016/j.matcom.2022.07.010
[39]	Z. Liu, J. Wang, C. L. P. Chen, Y. Zhang, Event trigger fuzzy adaptive compensation control of uncertain stochastic nonlinear systems with actuator failures, IEEE Trans. Fuzzy Syst., 26 (2018), 3770–3781. https://doi.org/10.1109/TFUZZ.2018.2848909 doi: 10.1109/TFUZZ.2018.2848909
[40]	J. Lian, C. Li, Event‐triggered adaptive tracking control of uncertain switched nonlinear systems, Int. J. Robust Nonlinear Control, 31 (2021), 4154–4169. https://doi.org/10.1002/rnc.5470 doi: 10.1002/rnc.5470
[41]	L. Xing, C. Wen, Z. Liu, H. Su, J. Cai, Event-triggered adaptive control for a class of uncertain nonlinear systems, IEEE Trans. Autom. Control, 62 (2016), 2071–2076. https://doi.org/10.1109/TAC.2016.2594204 doi: 10.1109/TAC.2016.2594204
[42]	X. Zhang, W. Xu, S. S. Nair, V. Chellaboina, PDE modeling and control of a flexible two-link manipulator, IEEE Trans. Control Syst. Technol., 13 (2005), 301–312. https://doi.org/10.1109/TCST.2004.842446 doi: 10.1109/TCST.2004.842446
[43]	F. Han, Y. Jia, Sliding mode boundary control for a planar two-link rigid-flexible manipulator with input disturbances, Int. J. Control Autom. Syst., 18 (2020), 351–362. https://doi.org/10.1007/s12555-019-0277-0 doi: 10.1007/s12555-019-0277-0
[44]	Z. Liu, J. Liu, Boundary control of a flexible robotic manipulator with output constraints, Asian J. Control, 19 (2017), 332–345. https://doi.org/10.1002/asjc.1342 doi: 10.1002/asjc.1342
[45]	L. Meirovitch, R. Parker, Fundamentals of Vibrations, Waveland Press, 2010.
[46]	T. Jiang, J. Liu, W. He, Adaptive boundary control for a flexible manipulator with state constraints using a barrier Lyapunov function, J. Dyn. Syst. Meas. Control, 140 (2018). https://doi.org/10.1115/1.4039364 doi: 10.1115/1.4039364
[47]	J. Bai, H. Wu, J. Cao, Secure synchronization and identification for fractional complex networks with multiple weight couplings under DoS attacks, Comput. Appl. Math., 41 (2022), 187. https://doi.org/10.1007/s40314-022-01895-2 doi: 10.1007/s40314-022-01895-2

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