Abstract
In this paper, a finite-time neural funnel control (FTNFC) scheme is proposed for motor servo systems with unknown input constraint. To deal with the non-smooth input saturation constraint problem, a smooth non-affine function of the control input signal is employed to approximate the saturation constraint, which is further transformed into an affine form according to the mean-value theorem. A fast terminal sliding mode manifold is constructed by using a novel funnel error variable to force the tracking error falling into a prescribe boundary within a finite time. Then, a simple sigmoid neural network is utilized to approximate the unknown system nonlinearity including the saturation. Different from the prescribed performance control (PPC), the proposed finite-time neural funnel control avoids using the inverse transformed function in the controller design, and could guarantee the prescribed tracking performance without knowing the saturation bounds in prior. The effectiveness and superior performance of the proposed method are verified by comparative simulation results.
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Li S and Liu Z, Adaptive speed control for permanent-magnet synchronous motor system with variations of load inertia, IEEE Transactions on Industrial Electronics, 2009, 56(8): 3050–3059.
Na J, Mahyuddin M N, Herrmann G, et al., Robust adaptive finite-time parameter estimation and control for robotic systems, International Journal of Robust and Nonlinear Control, 2015, 25(16): 3045–3071.
Chen Q, Tao L, Nan Y R, et al., Adaptive nonlinear sliding mode control of mechanical servo system with LuGre friction compensation. Journal of Dynamic Systems, Measurement and Control, 2016, 138(2): 021003-1-9.
Perez-Arancibia N, Tsao T, and Gibson J, Saturation-induced instability and its avoidance in adaptive control of hard disk drives, IEEE Transactions on Control Systems Technology, 2010, 18(2): 368–382.
Chen Q and Tang X Q, Nonsingular terminal sliding-mode funnel control for prescribed performance of motor servo systems with unknown input saturation, Control Theory and Applications, 2015, 32(8): 1064–1071.
Hu Q L, Ma G F, and Xie L H, Robust and adaptive variable structure output feedback control of uncertain systems with input nonlinearity, Automatica, 2008, 44(4): 552–559.
Chen M, Ge S S, and How B, Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities, IEEE Transactions on Neural Networks, 2010, 21(5): 796–812.
Chen M, Ge S S, and Ren B B, Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints, Automatica, 2011, 47(3): 452–455.
Wen C Y, Zhou J, Liu Z T, et al., Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance, IEEE Transactions on Automatic Control, 2011, 56(7): 1672–1678.
Wang H, Chen B, Liu X, et al., Adaptive neural tracking control for stochastic nonlinear strictfeedback systems with unknown input saturation, Information Sciences, 2014, 269(11): 300–315.
Tee K P, Ren B B, and Ge S S, Control of nonlinear systems with time-varying output constraints, Automatica, 2011, 47(11): 2511–2516.
Niu B and Zhao J, Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems, Systems and Control Letters, 2013, 62(10): 963–971.
Li Y, Li T, and Jing X, Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function, International Journal of Adaptive Control and Signal Processing, 2014, 28(2): 184–199.
Bechlioulis C P and Rovithakis G A, Robust partial-state feedback prescribed performance control of cascade systems with unknown nonlinearities, IEEE Transactions on Automatic Control, 2011, 56(9): 2224–2230.
Na J, Adaptive prescribed performance control of nonlinear systems with unknown dead zone, International Journal of Adaptive Control and Signal Processing, 2013, 27(5): 426–446.
Na J, Chen Q, Ren X M, et al., Adaptive prescribed performance motion control of servo mechanisms with friction compensation, IEEE Transactions on Industrial Electronics, 2014, 61(1): 486–494.
Huang Y B, Na J, Wu X, et al., Adaptive control of nonlinear uncertain active suspension systems with prescribed performance, ISA Transactions, 2015, 54: 145–155.
Ilchman A, Ryan E P, and Trenn S, PI-funnel control for two mass systems, IEEE Transactions on Automatic Control, 2009, 54(4): 981–923.
Hackl C M, Endisch C, and Schroder D, Contribution to non-identifier based adaptive control in mechatronics, Robotics and Autonomous Systems, 2009, 57(10): 996–1005.
Hackl C M, High-gain adaptive position control, International Journal of Control, 2011, 84(10): 1695–1716.
Han S I and Lee J M, Recurrent fuzzy neural network backstepping control for the prescribed output tracking performance of nonlinear dynamic systems, ISA transactions, 2014, 53(1): 33–43.
Han S I and Lee J M, Fuzzy echo state neural networks and funnel dynamic surface control for prescribed performance of a nonlinear dynamic system, IEEE Transactions on Industrial Electronics, 2014, 61(2): 1099–1112.
Man Z H, Paplinski A P, and Wu H R, A robust MIMO terminal sliding mode control scheme for rigid robotic manipulator, IEEE Transactions on Automatic Control, 1994, 39(12): 2464–2469.
Yu X H and Man Z H, Fast terminal sliding-mode control design for nonlinear dynamical systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2002, 49(2): 261–264.
Hong Y, Huang J, and Xu Y, On an output feedback finite-time stabilization problem, IEEE Transactions on Automatic Control, 2001, 46(2): 305–309.
Wang L Y, Chai T Y, and Zhai L F, Neural-network-based terminal sliding-mode control of robotic manipulators including actuator dynamics, IEEE Transactions on Industrial Electronics, 2009, 56(9): 3296–3304.
Zou A M, Kumar K D, Hou Z G, et al., Finite-time attitude tracking control for spacecraft using terminal sliding mode and chebyshev neural network, IEEE Transactions on Systems, Man, and Cybernetics — Part B: Cybernetics, 2011, 41(4): 950–963.
Lee M J and Choi Y K, An adaptive neurocontroller using RBFN for robot manipulators, IEEE Transactions on Industrial Electronics, 2004, 51(3): 711–717.
Chen Q, Yu L, and Nan Y R, Finite-time tracking control for motor servo systems with unknown dead-zones, Journal of Systems Science and Complexity, 2013, 26(6): 940–956.
Chen M, Wu Q X, and Cui R X, Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems, ISA Transactions, 2013, 52(2): 198–206.
Yu S, Yu X H, and Shirinzadehc B, Continuous finite-time control for robotic manipulators with terminal sliding mode, Automatica, 2005, 41(11): 1957–1964.
Huang S N and Tan K K, Intelligent friction modeling and compensation using neural network approximations, IEEE Transactions on Industrial Electronics, 2012, 59(8): 3342–3349.
Liu H and Zhang T, Neural network-based robust finite-time control for robotic manipulators considering actuator dynamics, Robotics and Computer-Integrated Manufacturing, 2013, 29(2): 301–308.
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This research was supported by the National Natural Science Foundation of China under Grant Nos. 61403343 and 61433003, Zhejiang Provincial Natural Science Foundation of China under Grant No. Y17F030063, and the China Postdoctoral Science Foundation Funded Project under Grant No. 2015M580521.
This paper was recommended for publication by Editor LIU Yungang.
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Chen, Q., Tang, X., Nan, Y. et al. Finite-time neural funnel control for motor servo systems with unknown input constraint. J Syst Sci Complex 30, 579–594 (2017). https://doi.org/10.1007/s11424-017-6028-5
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DOI: https://doi.org/10.1007/s11424-017-6028-5