×

Dynamic modeling and neural network compensation for dual-flexible servo system with an underactuated hand. (English) Zbl 1521.93027

Summary: This paper investigates a difficult problem of nonlinear dynamics and motion control of a dual-flexible servo system with an underactuated hand (DFSS-UH). Variation in grasping mass and nonlinear factors of the DFSS-UH including complex flexible deformation and friction torque aggravate the output speed fluctuation, leading to modeling errors in the dynamics, which in turn affects the underactuated hand motion accuracy. A novel neural network sliding mode control (NNSMC) method is designed to control the DFSS-UH. The strategy utilizes neural networks to compensate for dynamics modeling errors, which takes into account neglected nonlinear factors and inaccurate friction torque. The reaching law with the hyperbolic tangent function is proposed to improve sliding mode control, thereby weakening the chattering phenomenon. First of all, the DFSS-UH mechanical model considering many nonlinear factors is established and a dynamic simplification model which ignores higher-order modes is proposed. Secondly, the adaptive law of weighted coefficients is proposed according to the stability of the DFSS-UH. Finally, the physical control platform of the DFSS-UH is built, and simulation and control experiments are conducted. Experimental results show that the improved NNSMC strategy decreases the tracking error of flexible load, thereby enhancing the control accuracy of the DFSS-UH.

MSC:

93B12 Variable structure systems
93C10 Nonlinear systems in control theory
Full Text: DOI

References:

[1] Li, F.; Li, X.; Guo, Y.; Shang, D., Analysis of contact mechanical characteristics of flexible parts in harmonic gear reducer, Shock Vib., Article 5521320 pp. (2021), (2021)
[2] Li, X.; Song, C.; Zhu, C.; Song, H., Load analysis of thin-walled flexible bearing in harmonic reducer considering assembly with flexspline and cam, Mech. Mach. Theory., 180, Article 105154 pp. (2023)
[3] Saupe, F.; Knoblach, A., Experimental determination of frequency response function estimates for flexible joint industrial manipulators with serial kinematics, Mech. Syst. Sig. Process., 52, 60-72 (2015)
[4] Sharifi, M.; Swikir, A.; Noroozi, N.; Zamani, M., Compositional construction of abstractions for infinite networks of discrete-time switched systems, Nonlinear Anal., 44, 101173 (2022) · Zbl 1485.93035
[5] Wei, J.; Cao, D.; Wang, L.; Huang, H.; Huang, W., Dynamic modeling and simulation for flexible spacecraft with flexible jointed solar panels, Int. J. Mech. Sci., 130, 558-570 (2017)
[6] Liu, F.; Wang, L.; Jin, D.; Liu, X.; Lu, P., Equivalent micropolar beam model for spatial vibration analysis of planar repetitive truss structure with flexible joints, Int. J. Mech. Sci., 165, Article 105202 pp. (2020)
[7] Do, T. T.; Vu, V. H.; Liu, Z., Linearization of dynamic equations for vibration and modal analysis of flexible joint manipulators, Mech. Mach. Theory., 167, Article 104516 pp. (2022)
[8] Ahn, J. G.; Kim, J. G.; Yang, H. L., Interpolation multipoint constraints with selection criteria of degree of freedoms for flexible multibody dynamics, Appl. Math. Comput., 409, 15, Article 126361 pp. (2021) · Zbl 1510.70016
[9] Zhao, Z.; He, X.; An, C. K., Boundary disturbance observer-based control of a vibrating single-link flexible manipulator, IEEE Trans. Syst. Man Cybern. -Syst., 51, 4, 2382-2390 (2021)
[10] Zhou, X.; Tian, Yang.; Wang, H., Neural network state observer-based robust adaptive fault-tolerant quantized iterative learning control for the rigid-flexible coupled robotic systems with unknown time delays, Appl. Math. Comput., 430, Article 127286 pp. (2022) · Zbl 1510.93090
[11] Kumar, P.; Pratiher, B., Nonlinear dynamic analysis of a multi-link manipulator with flexible links-joints mounted on a mobile platform, Adv. Space Res., 71, 5, 2095-2127 (2023)
[12] Chen, B.; Huang, J.; Ji, J. C., Control of flexible single-link manipulators having Duffing oscillator dynamics, Mech. Syst. Sig. Process., 121, 44-57 (2019)
[13] Shang, D.; Li, X.; Yin, M.; Li, F., Dynamic modeling and control for dual-flexible servo system considering two-dimensional deformation based on neural network compensation, Mech. Mach. Theory., 175, Article 104954 pp. (2022), none
[14] KorayeM, M. H.; Dehkordi, S. F., Dynamic modeling of flexible cooperative mobile manipulator with revolute-prismatic joints for the purpose of moving common object with closed kinematic chain using the recursive Gibbs-Appell formulation, Mech. Mach. Theory., 137, none, 254-279 (2019)
[15] Liu, Y.; Chen, X.; Wu, Y.; Cai, H.; Yokoi, H., Adaptive neural network control of a flexible spacecraft subject to input nonlinearity and asymmetric output constraint, IEEE Trans. Neural Networks Learn. Syst., 33, 11, 6226-6234 (2022)
[16] Gargiulo, L.; Cordier, J. J.; Friconneau, J. P.; Grisolia, C.; Palmer, J. D.; Perrot, Y.; Samaille, F., Towards operations on Tore Supra of an ITER relevant inspection robot and associated processes, Fusion Eng. Des., 82, 15-24, 1996-2000 (2007)
[17] Wang, L.; Wang, D.; Wu, J., Dynamic performance analysis of parallel manipulators based on two-inertia-system, Mech. Mach. Theory., 137, 237-253 (2019)
[18] Chen, Y.; Yang, M.; Long, J.; Hu, K.; Xu, D.; Blaabjerg, F., Analysis of oscillation frequency deviation in elastic coupling digital drive system and robust notch filter strategy, IEEE Trans. Ind. Electron., 66, 1, 90-101 (2019)
[19] Oh, S.; Kong, K., High-precision robust force control of a series elastic actuator, IEEE-ASME Trans. Mechatron., 22, 1, 71-80 (2017)
[20] Yang, Z.; Li, X.; Chen, R.; Shang, D.; Xu, J.; Yang, H., Dynamic performance analysis of the variable stiffness actuator considering gap and friction characteristics based on two-inertia-system, Mech. Mach. Theory., 168, none, Article 104584 pp. (2022)
[21] Gao, H.; He, W.; Zhou, C.; Sun, C., Neural network control of a two-link flexible robotic manipulator using assumed mode method, IEEE-ASME Trans. Mechatron., 15, 2, 755-765 (2019)
[22] Zhao, Z.; Liu, Z., Finite-time convergence disturbance rejection control for a flexible Timoshenko manipulator, IEEE-CAA J. Automatica Sin., 8, 1, 157-168 (2021)
[23] Kayastha, S.; Katupitiya, J.; Pearce, G.; Rao, A., Comparative study of post-impact motion control of a flexible arm space robot, Eur. J. Control, 69, Article 100738 pp. (2023) · Zbl 1507.93160
[24] Yang, S.; Zhang, Y.; Wen, H.; Jin, D., Coordinated control of dual-arm robot on space structure for capturing space targets, Adv. Space Res., 71, 5, 2437-2448 (2023)
[25] Chalhob, N. G.; Gordaninejad, F.; Lin, Q.; Ghazavi, A., Dynamic modeling of a laminated composite-material flexible robot arm made of short beams, Math. Comput. Model., 14, 468-473 (1990)
[26] Shang, D.; Li, X.; Yin, M.; Li, F., Vibration suppression method based on PI fuzzy controller containing disturbance observe for dual-flexible manipulator with an axially translating arm, Int. J. Control Autom. Syst., 20, 5, 1682-1694 (2022)
[27] He, W.; Ge, S. S., Vibration control of a flexible beam with output constraint, IEEE Trans. Ind. Electron., 62, 8, 5023-5030 (2015)
[28] Halim, D.; Luo, X.; Trivailo, P. M., Decentralized vibration control of a multi-link flexible robotic manipulator using smart piezoelectric transducers, Acta Astronaut., 104, 1, 186-196 (2014)
[29] Ji, N.; Liu, J., Adaptive boundary control for flexible three-dimensional Euler-Bernoulli beam with input signal quantization, Int. J. Adapt. Control Signal Process., 32, 8, 1162-1181 (2018) · Zbl 1398.93158
[30] Al-Bedoor, B. O.; Hamdan, M. N., Geometrically non-linear dynamic model of a rotating flexible arm, J. Sound Vibr., 240, 1, 59-72 (2001) · Zbl 1237.74108
[31] Vierira, L.; Goncalves, R.; Camotim, D.; Pedro, J., . O., Generalized Beam Theory deformation modes for steel-concrete composite bridge decks including shear connection flexibility, Thin-Walled Struct., 169, Article 108408 pp. (2021)
[32] Du, Z.; Ding, Z.; Liu, Y.; Chan, S., Advanced flexibility-based beam-column element allowing for shear deformation and initial imperfection for direct analysis, Eng. Struct., 199, Article 109586 pp. (2019)
[33] Shang, D.; Li, X.; Yin, M.; Li, F., Control method of flexible manipulator servo system based on a combination of RBF neural network and pole placement strategy, Mathematics, 9, 8, 896 (2021)
[34] Liu, Y.; Guo, F.; He, X.; Hui, Q., Boundary control for an axially moving system with input restriction based on disturbance observers, IEEE Trans. Syst. Man Cybern., 49, 11, 2242-2253 (2019)
[35] Kim, S., Moment of inertia and friction torque coefficient identification in a servo drive system, IEEE Trans. Ind. Electron., 66, 1, 60-70 (2018)
[36] Xie, W., Sliding-mode-observer-based adaptive control for servo actuator with friction, IEEE Trans. Ind. Electron., 54, 3, 1517-1527 (2007)
[37] Astrom, K. J.; Canudas-de-wit, C., Revisiting the LuGre friction model stick-slip motion and rate, IEEE Control Syst. Mag., 28, 6, 101-114 (2008) · Zbl 1395.74065
[38] Liang, H.; Chong, K. T.; No, T. S.; Yi, S. Y., Vehicle longitudinal brake control using variable parameter sliding control, Control Eng. Pract., 11, 4, 403-411 (2003)
[39] Li, Y. Y.; Yam, L. H., Robust vibration control of uncertain systems using variable parameter feedback and model-based fuzzy strategies, Comput. Struct., 79, 11, 1109-1119 (2001)
[40] Chen, T.; Shan, J. J., Distributed tracking of a class of underactuated lagrangian systems with uncertain parameters and actuator faults, IEEE Trans. Ind. Electron., 67, 5, 4244-4253 (2020)
[41] Du, Z.; Yun, W.; Hu, S., Discrete-time event-triggered H-infinity stabilization for networked cascade control systems with uncertain delay, J. Frankl. Inst.-Eng. Appl. Math., 356, 16, 9524-9544 (2019) · Zbl 1423.93337
[42] Li, D.; Chen, C. L.P.; Liu, Y.; Tong, S., Neural network controller design for a class of nonlinear delayed systems with time-varying full-state constraints, IEEE Trans. Neural Networks Learn. Syst., 30, 9, 2625-2636 (2019)
[43] Sun, J.; Yi, J.; Pu, Z., Fixed-time adaptive fuzzy control for uncertain nonstrict-feedback systems with time-varying constraints and input saturations, IEEE Trans. Fuzzy Syst., 30, 4, 1114-1128 (2022)
[44] Xiao, B.; Yin, S.; Kaynak, O., Tracking control of robotic manipulators with uncertain kinematics and dynamics, IEEE Trans. Ind. Electron., 63, 10, 6439-6449 (2016)
[45] Chen, T.; Shan, J. J., Distributed control of multiple flexible manipulators with unknown disturbances and dead-zone input, IEEE Trans. Ind. Electron., 67, 11, 9937-9947 (2020)
[46] Finite-time adaptive dynamic surface synchronization control for dual-motor servo systems with backlash and time-varying uncertainties, ISA Trans (2022)
[47] Liu, W.; Du, J.; Lin, J.; Li, Z., Stabilization control of 3-DOF parallel vessel-borne platform with dynamic uncertainties and unknown disturbances, Appl. Ocean Res., 126, Article 103271 pp. (2022)
[48] Ruan, X.; Xu, C.; J, Feng; Wang, J.; Zhao, Y., Adaptive dynamic event-triggered control for multi-agent systems with matched uncertainties under directed topologies, Physica A, 586, Article 126450 pp. (2022) · Zbl 1531.93213
[49] Ma, L.; Xu, N.; Zhao, X.; Zong, G.; Huo, X., Small-gain technique-based adaptive neural output-feedback fault-tolerant control of switched nonlinear systems with unmodeled dynamics, IEEE Trans. Syst. Man Cybern. -Syst., 51, 11, 7051-7062 (2021)
[50] Yao, Q., Adaptive fuzzy neural network control for a space manipulator in the presence of output constraints and input nonlinearities, Adv. Space Res., 67, 6, 1830-1843 (2021)
[51] Wang, S.; Tao, L.; Chen, Q.; Na, J.; Ren, X., USDE-Based sliding mode control for servo mechanisms with unknown system dynamics, IEEE-ASME Trans. Mechatron., 25, 2, 1056-1066 (2020)
[52] Fei, J. T.; Wang, Z.; Pan, Q., Self-constructing fuzzy neural fractional-order sliding mode control of active power filter, IEEE Trans. Neural Networks Learn. Syst. (2022), Early Access
[53] Fei, J. T.; Wang, Z.; Fang, Y. M., Self-evolving recurrent chebyshev fuzzy neural sliding mode control for active power filter, IEEE Trans. Ind. Inf., 19, 3, 2729-2739 (2023)
[54] Fei, J. T.; Chen, Y.; Liu, L. H.J.; Fang, Y. M., Fuzzy multiple hidden layer recurrent neural control of nonlinear system using terminal sliding-mode controller, IEEE Trans. Cybern., 52, 9, 9519-9534 (2022)
[55] Wang, J.; Zhao, L.; Yu, L., Adaptive terminal sliding mode control for magnetic levitation systems with enhanced disturbance compensation, IEEE Trans. Ind. Electron., 68, 1, 756-766 (2020)
[56] Majumder, T.; Mishra, R. K.; Singh, S. S.; Sahu, P. K., Robust congestion control in cognitive radio network using event-triggered sliding mode based on reaching laws, J. Franklin. Inst., 357, 11, 7399-7422 (2020) · Zbl 1447.93070
[57] Han, S. M.; Benaroya, H.; Wei, T., Dynamics of transversely vibrating beams using four engineering theories, J. Sound Vibr., 225, 5, 935-988 (1999) · Zbl 1235.74075
[58] Abe, A., Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation, Mech. Mach. Theory., 44, 9, 1627-1639 (2009) · Zbl 1178.70002
[59] Shafei, A. M.; Shafei, H. R., Considering link flexibility in the dynamic synthesis of closed-loop mechanisms: a general approach, J. Vib. Acoust., 142, 2, Article 021004 pp. (2020)
[60] Ahmadizadeh, M.; Shafei, A. M.; Jafari, R., Frictional impact-contacts in multiple flexible links, Int. J. Struct. Stab. Dyn., 21, 06, Article 2150075 pp. (2021) · Zbl 1535.74558
[61] Damaren, C.; Sharf, I., Simulation of flexible-link manipulators with inertial and geometric nonlinearities, J. Dyn. Syst. Meas. Control-Trans. ASME., 117, 1, 74-87 (1995) · Zbl 0825.93507
[62] Aghababa, M. P.; Akbari, M. E., A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic system with unknown uncertainties and external disturbances, Appl. Math. Comput., 218, 9, 5757-5768 (2012) · Zbl 1238.93026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.