Abstract
An adaptive Fourier neural network sliding mode controller with H ∞ tracking performance (AFNN-SMC+ H ∞) is applied for a Pneumatic actuator system (PAS) to overcome time-varying nonlinear dynamics and external disturbances. Benefiting from the use of orthogonal Fourier basis function, the proposed AFNN has fast estimated convergence speed; also, because AFNN has unique solution, it can avoid falling into the local minimum. The architecture of AFNN can also easily be determined by its clear physical meaning of the neurons. To attenuate the vibration of proportional directional control valve and the adaptive approximation error, the H ∞ tracking design technique is incorporated into the proposed AFNN-SMC. Finally, practical experiments are successfully implemented in position regulation, trajectory tracking, and velocity control of the PAS, which illustrates the effectiveness of the proposed controller.
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C. H. Lu, Y. R. Hwang and Y. T. Shen, Backstepping slidingmode control for a pneumatic control system, Proc. Inst. Mech. Eng., Part I J. Syst. and Control Eng., 224 (6) (2010) 763–770.
J. E. Bobrow and F. Jabbari, Adaptive pneumatic force actuator and position control, J. Dyn. Syst. Meas., Control, 113 (1991) 267–272.
B. W. McDonell and J. E. Bobrow, Adaptive tracking control of an air powered robot actuator, J. Dyn. Syst. Meas., Control, 115 (3) (1993) 427–433.
R. Richardson, A. R. Plummer and M. D. Brown, Self-tuning control of a pneumatic actuator under the influence of gravity, IEEE Trans. Control Syst. Technol., 9 (2) (2001) 330–334.
J. Yao, Z. Jiao, D. Ma and L. Yan, High-accuracy tracking control of hydraulic rotary actuators with modeling uncertainties, IEEE/ASME Trans. Mechatronics, 19 (2) (2014) 633–641.
J. Yao, Z. Jiao and D. Ma, A practical nonlinear adaptive control of hydraulic servomechanisms with periodic-like disturbances, IEEE/ASME Trans. Mechatronics, DOI: 10.1109/TMECH.2015. 2409893 (2015).
J. Yao, Z. Jiao and B. Yao, Nonlinear adaptive robust backstepping force control of hydraulic load simulator: Theory and experiments, Journal of Mechanical Science and Technology, 28 (4) (2014) 1499–1507.
S. Drakunov, G. D. Hanchin, W. C. Su and Ü. Özgüner, Nonlinear control of rodless pneumatic servo actuator, or sliding modes versus Coulomb friction, Automatica, 33 (3) (1997) 1401–1408.
R. B. van Varseveld and G. M. Bone, Accurate position control of a pneumatic actuator using on/off solenoid valves, IEEE Trans. Mechatronics, 2 (3) (1997) 195–204.
J. Wang, J. Pu, P. R. Moore and Z. Zhang, Modeling study and servo-control of air motor systems, Int. J. Contr., 71 (3) (1998) 459–476.
C. H Lu, Y. R. Hwang and Y. T. Shen, Backstepping sliding mode tracking control of a vane-type air motor X-Y table motion system, ISA Trans., 50 (2) (2011) 278–286.
J. Wang, Ü. Kotta and J. Ke, Tracking control of nonlinear pneumatic actuator systems using static state feedback linearization of the input–output map, Proc. Estonian Acad. Sci. Phys. Math., 56 (1) (2007) 47–66.
J. E. Slotin and W. Li, Applied nonlinear control, Prentice-Hall Inc, New Jersey (1991).
H. I. Ali, S. B. Noor and B. M. M. H. Marhaban, A review of pneumatic actuators (Modeling and control), Australian Journal of Basic and Applied Sciences, 3 (2) (2009) 440–454.
H. Lee, E. Kim, H.-J. Kang and M. Park, Design of a sliding mode controller with fuzzy sliding surfaces, Proc. Inst. Elect. Eng., 145 (5) (1998) 411–418.
Y. S. Lu and J. S. Chen, A self-organizing fuzzy sliding-mode controller design for a class of nonlinear servo systems, IEEE Trans. Ind. Electron., 41 (5) (1994) 492–502.
Q. P. Ha, D. C. Rye and H. F. Durrant-Whyte, Fuzzy moving sliding mode control with application to robotic manipulators, Automatica, 35 (1999) 607–616.
S. B. Choi and J. S. Kim, A fuzzy-sliding mode controller for robust tracking of robotic manipulators, Mechatronics, 7 (2) (1997) 199–216.
G. C. Hwang and S. C. Lin, A stability approach to fuzzy control design for nonlinear systems, Fuzzy Sets Syst., 48 (3) (1992) 279–287.
E. Richer and Y. Hurmuzlu, A high performance pneumatic force actuator system: Part І-Nonlinear mathematical model, J. Dyn. Syst. Meas., Control, 122 (2000) 416–425.
E. Richer and Y. Hurmuzlu, A high performance pneumatic force actuator system: Part II-Nonlinear controller design, J. Dyn. Syst. Meas., Control, 122 (2000) 426–434.
J. E. Bobrow and B. W. McDonell, Modeling, identification, and control of a pneumatically actuated, force controllable robot, IEEE Trans. Robotics and Automation, 14 (5) (1998) 732–742.
F. C. Chen and C. C. Liu, Adaptively controlling nonlinear continuous-time systems using multilayer neural networks, IEEE Trans. Autom. Control, 39 (10) (1994) 1306–1310.
F. C. Chen and H. K. Khalil, Adaptive control of a class of nonlinear discrete-time systems using neural networks, IEEE Trans. Autom. Control, 40 (5) (1995) 791–801.
F. L. Lewis, A. Yesildirek and K. Liu, Multilayer neural-net robot controller with guaranteed tracking performance, IEEE Trans. Neural Networks, 7 (2) (1996) 388–398.
S. Jagannathan and F. L. Lewis, Discrete-time neural net controller for a class of nonlinear dynamical systems, IEEE Trans. Automatic Control, 41 (10) (1996) 1693–1699.
S. Jagannathan, Control of a class of nonlinear discrete-time system using multilayer neural networks, IEEE Trans. Neural Networks, 12 (5) (2008) 1113–1120.
S. Jagannathan and P. He, Neural-network-based statefeedback control of a nonlinear discrete-time system in nonstrict feedback form, IEEE Trans. Neural Networks, 19 (12) (2008) 2073–2087.
C. Yang, S. S. Ge, C. Xiang, T. Y. Chai and T. H. Lee, Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach, IEEE Trans. Neural Networks, 19 (11) (2008) 1873–1886.
Y. C. Tsai and A. C. Huang, FAT-based adaptive control for pneumatic servo systems with mismatched uncertainties, Mechanical Systems and Signal Processing, 22 (2008) 1263–1273.
T. Zhang, S. S. Ge and C. C. Hang, Adaptive neural network control for strict-feedback nonlinear systems using backstepping design, Automatica, 36 (12) (2000) 835–1846.
W. Y. Wang, M. L. Chan, C. C. J. Hsu and T. T. Lee, H¥ tracking-based sliding mode control for uncertain nonlinear systems via an adaptive fuzzy-neural approach, IEEE Trans. Systems, Man, Cybernetics B, 32 (4) (2002) 483–492.
W. S. Chen and Z. Q. Zhang, Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign, Fuzzy Sets and Systems, 161 (6) (2010) 821–836.
C. F. Hsu, C. M. Lin and T. T. Lee, Wavelet adaptive backstepping control for a class of nonlinear systems, IEEE Trans. Neural Networks, 17 (5) (2006) 1175–1183.
J. Li, W. S. Chen and J. M. Li, Adaptive NN output-feedback stabilization for a class of strict-feedback stochastic nonlinear systems, ISA Trans., 48 (4) (2009) 468–475.
M. M. Polycarpou, Stable adaptive neural control scheme for nonlinear systems, IEEE Trans. Automatic Control, 41 (3) (1996) 447–451.
W. Zuo and L. Cai, Adaptive-Fourier-neural-network-based control for a class of uncertain nonlinear systems, IEEE Trans. Neural Networks, 19 (10) (2008) 1689–1701.
B. S. Chen, C. H. Lee and Y. C. Chang, H¥ tracking design of uncertain nonlinear SISO systems: Adaptive fuzzy approach, IEEE Trans. Fuzzy Systems, 4 (1) (1996) 32–43.
W. Zuo and L. Cai, Adaptive-Fourier-neural-network-based control for a class of uncertain nonlinear systems, IEEE Trans. Neural Networks, 19 (10) (2008) 1689–1701.
W. Zuo, Y. Zhu and L. Cai, Fourier-neural-network-based learning control for a class of uncertain nonlinear systems with flexible components, IEEE Trans. Neural Networks, 20 (1) (2009) 139–151.
Z. Yang, Z. Wei and L. Cai, Tracking control of a belt-driving system using improved Fourier series based learning controller, Proc. of IEEE International Conference on Intelligent Robots and Systems (2008) 881–886.
B. W. Andersen, The analysis and design of pneumatic systems, Krieger Publishing Co., New York, USA (1976).
J. F. Blackburn, G. Reethof and J. L. Shearer, Fluid power control, The Technology Press and Wiley, New York (1960).
S. Armstrong-Helouvry, P. Dupont and C. Canudas De Wit, Friction in servo machines: Analysis and control methods, Transactions of the ASME, J. of Application, Mechanics, and Reverend, 47 (7) (1994) 275–306.
S. Armstrong-Helouvry, P. Dupont and C. Canudas De Wit, A survey of models, analysis tools and compensation methods for the control of machines with friction, Automatica, 30 (1994) 1083–1183.
W. Rudin, Principles of mathematical analysis, 3rd ed., McGraw-Hill Inc., New York, USA (1976).
J. Huang and F. L. Lewis, Neural-network predictive control for nonlinear dynamic systems with time-delay, IEEE Trans. Neural Networks, 14 (2) (2003) 377–389.
S. Lin and A. A. Goldenberg, Neural-network control of mobile manipulators, IEEE Trans. Neural Networks, 12 (5) (2001) 1121–113.
J. Slotine and W. Li, Applied nonlinear control, Prentice Hall, Englewood Cliffs, N.J. (1991).
W. Jihong, K. Ülle and K. Jia, Tracking control of nonlinear pneumatic actuator systems using static state feedback linearization of the input-output map, Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 56 (1) (2007) 47–66.
W. Perruquetti, T. Floquet and P. Borne, A note on sliding observer and controller for generalized canonical forms, Proc. of the 37th IEEE Conference on Decision and Control (1998) 1920–1925.
S. W. Kim and J. J. Lee, Design of a fuzzy controller with fuzzy sliding surface, Fuzzy Sets and Systems, 117 (3) (1995) 359–367.
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Lian-Wang Lee received the M.S. in automation and control and the Ph.D. from National Taiwan University of Science and Technology, Taipei, in 2000 and 2009, respectively. He is an Assistant Professor with the Department of Mechanical Engineering, Lunghwa University of Science and Technology, Guishan, Taiwan. His research interests include fluid power control, nonlinear control, mechatronics, intelligent control, adaptive control, and sliding mode control.
I-Hsum Li received the M.S. in electronic engineering form Fu-Jen Catholic University, Taipei, Taiwan, in 2001, and the Ph.D. at National Taiwan University of Science and Technology, Taipei, Taiwan, in 2007. He is an Associate Professor in the Department of Computer Science and Information Engineering in Lee-Ming Institute of Technology, Taiwan. His research interests include genetic algorithms, fuzzy logic systems, adaptive control, system identification and antilock braking system.
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Lee, LW., Li, IH. Design and implementation of a robust FNN-based adaptive sliding-mode controller for pneumatic actuator systems. J Mech Sci Technol 30, 381–396 (2016). https://doi.org/10.1007/s12206-015-1243-2
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DOI: https://doi.org/10.1007/s12206-015-1243-2