Adaptive fuzzy backstepping super-twisting sliding mode control of nonlinear systems with unknown hysteresis. (English) Zbl 07887090
Summary: In this paper, an adaptive fuzzy backstepping super-twisting sliding mode control (AFBSTSMC) scheme is proposed for a class of nonlinear systems with unknown hysteresis, unmeasured states, and external disturbances. First, fuzzy logic systems are employed to approximate the unknown nonlinear functions of the controlled systems, and a fuzzy state observer is designed to estimate the unmeasured states. Then, combining the backstepping technique and adaptive sliding mode control with super-twisting algorithm, the AFBSTSMC scheme is proposed without constructing the hysteresis inverse. The problem of “explosion of complexity” inherent in the conventional backstepping design method is eliminated by utilizing the dynamic surface control technique. Moreover, the chattering phenomenon is significantly reduced by using the developed adaptive fuzzy super-twisting controller. It is proved that the proposed control scheme can guarantee that all the signals in the closed-loop system are semi-globally ultimately uniformly bounded and the observer and tracking errors can converge to a small domain of the origin. Finally, the effectiveness of the presented control scheme is confirmed in two examples including a numerical simulation and an inverted pendulum with unknown hysteresis actuator.
© 2021 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
© 2021 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
MSC:
| 93-XX | Systems theory; control |
Keywords:
backstepping; dynamic surface control; fuzzy logic systems; hysteresis; super-twisting sliding mode controlReferences:
| [1] | Z.Chen, B.Yao, and Q.Wang, Adaptive robust precision motion control of linear motors with integrated compensation of nonlinearities and bearing flexible modes, IEEE Trans. Indust. Inform.9 (2012), no. 2, 965-973. |
| [2] | H.Wang et al., Adaptive neural tracking control for a class of nonstrict‐feedback stochastic nonlinear systems with unknown backlash‐like hysteresis, IEEE Trans. Neural Netw.25 (2014), no. 5, 947-958. |
| [3] | C.Su et al., Robust adaptive control of a class of nonlinear systems with unknown backlash‐like hysteresis, IEEE Trans. Autom. Control45 (2000), no. 12, 2427-2432. · Zbl 0990.93118 |
| [4] | G.Bertotti, Dynamic generalization of the scalar preisach model of hysteresis, IEEE Trans. Magnet.28 (1992), no. 5, 2599-2601. |
| [5] | M. A.Janaideh and O.Aljanaideh, Further results on open‐loop compensation of rate‐dependent hysteresis in a magnetostrictive actuator with the prandtl‐ishlinskii model, Mech. Syst. Signal Process.104(2018), 835-850. |
| [6] | Y. X.Wen et al., Method for random vibration of hysteretic systems, J. Eng. Mech. Div.102(1976), no. 2, 249-263. |
| [7] | S.Bi et al., Operator‐based robust control for nonlinear uncertain systems with unknown backlash‐like hysteresis, Int J. Control Autom. Syst.14 (2016), no. 2, 469-477. |
| [8] | M.Ming et al., Hysteresis modelling and feedforward compensation of piezoelectric nanopositioning stage with a modified Bouc‐Wen model, Micro Nano Lett.13 (2018), no. 8, 1170-1174. |
| [9] | Z.Yu et al., Adaptive neural output feedback control for nonstrict‐feedback stochastic nonlinear systems with unknown backlash‐like hysteresis and unknown control directions, IEEE Trans. Neural Netw. Learn. Syst.29 (2018), no. 4, 1147-1160. |
| [10] | G.Gu and L.Zhu, Comparative experiments regarding approaches to feedforward hysteresis compensation for piezoceramic actuators, Smart Mater. Struct.23 (2014), no. 9, 95029. |
| [11] | M.Ruderman and T.Bertram, Control of magnetic shape memory actuators using observer‐based inverse hysteresis approach, IEEE Trans. Control Syst. Technol.22 (2014), no. 3, 1181-1189. |
| [12] | S.Xie et al., Modeling and compensation of asymmetric hysteresis for pneumatic artificial muscles with a modified generalized prandtl-ishlinskii model, Mechatronics52 (2018), 49-57. |
| [13] | S.Xie et al., Hysteresis modeling and trajectory tracking control of the pneumatic muscle actuator using modified Prandtlishlinskii model, Mech. Machine Theory120 (2018), 213-224. |
| [14] | X.Zhang et al., Output feedback adaptive motion control and its experimental verification for time‐delay nonlinear systems with asymmetric hysteresis, IEEE Trans. Indust. Electron.67 (2020), no. 8, 6824-6834. |
| [15] | L.Cheng et al., Neural‐network‐based nonlinear model predictive control for piezoelectric actuators, IEEE Trans. Indust. Electron.62 (2015), no. 12, 7717-7727. |
| [16] | H.Ma, Y.Li, and Z.Xiong, A generalized input‐output‐based digital sliding‐mode control for piezoelectric actuators with non‐minimum phase property, Int. J. Control Autom. Syst.17 (2018), no. 3, 773-782. |
| [17] | W.He et al., Adaptive neural network control of a robotic manipulator with unknown backlash‐like hysteresis, Iet Control Theory Appl.11 (2017), no. 4, 567-575. |
| [18] | H. A.Yousef et al., Enhanced adaptive control for a benchmark piezoelectric‐actuated system via fuzzy approximation, Int. J. Adapt. Control Signal Process.33 (2019), no. 9, 1329-1343. · Zbl 1425.93167 |
| [19] | W.Lv, F.Wang, and YLi, Finite‐time adaptive fuzzy output‐feedback control of mimo nonlinear systems with hysteresis, Neurocomputing296 (2018), 74-81. |
| [20] | H.Liang et al., Neural‐network‐based event‐triggered adaptive control of nonaffine nonlinear multiagent systems with dynamic uncertainties, IEEE Trans. Neural Netw. Learn. Syst. (2020), 1-12. https://doi.org/10.1109/TNNLS.2020.3003950 · doi:10.1109/TNNLS.2020.3003950 |
| [21] | Y.Pan et al., Singularity‐free fixed‐time fuzzy control for robotic systems with user‐defined performance, IEEE Trans. Fuzzy Syst. (2020), 1-11. https://doi.org/10.1109/TFUZZ.2020.2999746 · doi:10.1109/TFUZZ.2020.2999746 |
| [22] | L.Bai et al., Observer‐based adaptive control for stochastic nonstrict‐feedback systems with unknown backlash‐like hysteresis, Int. J. Adapt. Control Signal Process31 (2017), no. 10, 1481-1490. · Zbl 1376.93058 |
| [23] | Z.Namadchian and M.Rouhani, Adaptive neural tracking control of switched stochastic pure‐feedback nonlinear systems with unknown Bouc‐Wen hysteresis input, IEEE Trans. Neural Netw. Learn. Syst.29(2018), no. 12, 5859-5869. |
| [24] | Y.Li, S.Tong, and T.Li, Adaptive fuzzy output feedback control of uncertain nonlinear systems with unknown backlash‐like hysteresis, Inform. Sci.198 (2012), 130-146. · Zbl 1248.93101 |
| [25] | Y.Liu et al., Global adaptive control for uncertain nonaffine nonlinear hysteretic systems, Isa Trans.58 (2015), 255-261. |
| [26] | L.Ma et al., Adaptive neural control for switched nonlinear systems with unknown backlash‐like hysteresis and output dead‐zone, Neurocomputing357 (2019), 203-214. |
| [27] | H.Wang et al., Robust adaptive neural control for pure‐feedback stochastic nonlinear systems with prandtl‐ishlinskii hysteresis, Neurocomputing314 (2018), 169-176. |
| [28] | Y.Wu and Y.Dong, Robust adaptive neural network control for a class of multiple‐input multiple‐output nonlinear time delay system with hysteresis inputs and dynamic uncertainties, Asian J. Control21 (2019), no. 5, 2330-2339. · Zbl 1432.93082 |
| [29] | D.Swaroop et al., Dynamic surface control for a class of nonlinear systems, IEEE Trans. Autom. Control45 (2000), no. 10, 1893-1899. · Zbl 0991.93041 |
| [30] | M.Xia and T.Zhang, Adaptive neural dynamic surface control for full state constrained stochastic nonlinear systems with unmodeled dynamics, J. Franklin Inst.356 (2019), no. 1, 129-146. · Zbl 1405.93138 |
| [31] | S.Song et al., Adaptive hybrid fuzzy output feedback control for fractional‐order nonlinear systems with time‐varying delays and input saturation, Appl. Math. Comput.364 (2020), 124662. · Zbl 1433.93059 |
| [32] | Y.Shu, Y.Tong, and C.Yu, Robust neural tracking control for switched nonaffine stochastic nonlinear systems with unknown control directions and backlash‐like hysteresis, J. Franklin Inst.357 (2020), no. 5, 2791-2812. · Zbl 1451.93074 |
| [33] | X.Wang et al., Neural network based adaptive dynamic surface control of nonaffine nonlinear systems with time delay and input hysteresis nonlinearities, Neurocomputing333 (2019), 53-63. |
| [34] | X.Zhang and Y.Lin, An adaptive output feedback dynamic surface control for a class of nonlinear systems with unknown backlash‐like hysteresis, Asian J. Control15 (2013), no. 2, 489-500. · Zbl 1327.93249 |
| [35] | H.Yue et al., Adaptive fuzzy dynamic surface tracking control for a class of nonlinear systems with unknown distributed time delays and backlash‐like hysteresis, Int. J. Adv. Robot. Syst.14 (2017), no. 5, 1729881417733886. |
| [36] | L.Liu, Z.Wang, and H.Zhang, Adaptive dynamic surface error constrained control for mimo systems with backlash‐like hysteresis via prediction error technique, Nonlin. Dyn.84 (2016), no. 4, 1989-2002. · Zbl 1355.93074 |
| [37] | B.Niu, T.Qin, and X.Fan, Adaptive neural network tracking control for a class of switched stochastic pure‐feedback nonlinear systems with backlash‐like hysteresis, Int. J. Syst. Sci.47 (2016), no. 14, 3378-3393. · Zbl 1346.93221 |
| [38] | B.Cong, X.Liu, and C.Zhen, Backstepping based adaptive sliding mode control for spacecraft attitude maneuvers, Aerosp. Sci. Technol.30 (2013), no. 1, 1-7. |
| [39] | A. A.Khalili, Z.Mohamed, and M. A. M.Basri, Enhanced backstepping sliding mode controller for motion tracking of a nonlinear 2‐DOF Piezo‐actuated micromanipulation system, Microsyst. Technol.‐Micro‐Nanosyst.‐Inform. Storage Process. Syst.25 (2019), no. 10, 3765-3777. |
| [40] | F.Lin, S.Lee, and P.Chou, Intelligent integral backstepping sliding‐mode control using recurrent neural network for Piezo‐flexural nanopositioning stage, Asian J. Control18 (2016), no. 2, 456-472. · Zbl 1346.93108 |
| [41] | V. I.Utkin, Sliding modes in control and optimization, Germany, Springer Berlin Heidelberg, 1992. · Zbl 0748.93044 |
| [42] | H.Lee and V. I.Utkin, Chattering suppression methods in sliding mode control systems, Ann. Rev. Control31 (2007), no. 2, 179-188. |
| [43] | T.Gonzalez, J. A.Moreno, and L.Fridman, Variable gain super‐twisting sliding mode control, IEEE Trans. Autom. Control57 (2011), no. 8, 2100-2105. · Zbl 1369.93124 |
| [44] | C. E.Hall and Y. B.Shtessel, Sliding mode disturbance observer‐based control for a reusable launch vehicle, J. Guidance Control Dyn.29 (2006), no. 6, 1315-1328. |
| [45] | S.Park et al., Adaptive fuzzy super‐twisting backstepping control design for MIMO nonlinear strict feedback systems, Int. J. Control Autom. Syst.16 (2018), no. 3, 1165-1178. |
| [46] | C.Li and X.Yang, Adaptive neural output feedback control for a class of switched non‐linear systems with unknown backlash‐like hysteresis of the actuator, Trans. Inst. Measurement Control41 (2019), no. 4, 900-910. |
| [47] | M.Chen and S. S.Ge, Adaptive neural output feedback control of uncertain nonlinear systems with unknown hysteresis using disturbance observer, IEEE Trans. Indust. Electron.62 (2015), no. 12, 7706-7716. |
| [48] | Y.Li, T.Li, and S.Tong, Adaptive neural networks output feedback dynamic surface control design for MIMO pure‐feedback nonlinear systems with hysteresis, Neurocomputing198 (2016), 58-68. |
| [49] | P.Ming‐Chang, Adaptive observerâĂŘbased global sliding mode control for uncertain discrete‐time nonlinear systems with timeâĂŘdelays and input nonlinearity, Asian J. Control21 (2019), no. 5, 2290-2300. · Zbl 1432.93057 |
| [50] | S.Ahmed, H.Wang, and Y.Tian, Adaptive high‐order terminal sliding mode control based on time delay estimation for the robotic manipulators with backlash hysteresis, IEEE Trans. Syst. Man Cybern.51 (2021), no. 2, 1128-1137. |
| [51] | L.Tang and D.Li, Time‐varying barrier Lyapunov function based adaptive neural controller design for nonlinear pure‐feedback systems with unknown hysteresis, Int. J. Control Autom. Syst.17 (2019), no. 7, 1642-1654. |
| [52] | J.Peng and R.Dubay, Adaptive fuzzy backstepping control for a class of uncertain nonlinear strict‐feedback systems based on dynamic surface control approach, Expert Syst. Appl.120 (2019), 239-252. |
| [53] | D.Wang and J.Huang, Neural network‐based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict‐feedback form, IEEE Trans. Neural Netw.16 (2005), no. 1, 195-202. |
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