Abstract
Conventional guidance law designs can only guarantee steady-state performance. However, transient performance is also the key performance index in practical guidance applications. In this paper, a novel terminal guidance law is presented for missile intercepting maneuvering target with impact angle constraints, which can strictly guarantee the prescribed steady-state and transient performances of interception. By utilizing the prescribed performance control technique, the prescribed performance tracking control problem is transformed into an equivalent unconstrained form such that the tracking error can be limit to the prescribed performance bound. Then, on the basis of transferred the tracking error, a novel nonsingular terminal sliding mode control-based guidance law is proposed with impact angle constraint, and the extended state observer is incorporated to online estimate the external disturbances and unknown target maneuver. The closed-loop system stability and the convergence characteristic are rigorously proved. Finally, extensive contrast simulations are conducted to demonstrate the efficiency and superiority of the proposed guidance law for different engagement scenarios.
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H. B. Zhou, S. M. Song, and J. H. Song, “Design of sliding mode guidance law with dynamic delay and impact angle constraint,” International Journal of Control, Automation, and Systems, vol. 15, no. 1, pp. 239–247, January 2017.
V. Rajasekhar and A. G. Sreenatha, “Fuzzy logic implementation of proportional navigation guidance,” Acta Astronautica, vol. 46, no. 1, pp. 17–24, January 2000.
X. Hu, S. X. Yang, F. F. Xiong, and G. Q. Zhang, “Stability of spinning missile with homing proportional guidance law,” Aerospace Science and Technology, vol. 71, pp. 546–555, December 2017.
K. S. Erer and O. Merttopçuoğlu, “Indirect impact-angle-control against stationary targets using biased pure proportional navigation,” Journal of Guidance, Control, and Dynamics, vol. 35, no. 2, pp. 700–704, August 2012.
J. W. Zhu, D. L. Su, Y. Xie, and H. F. Sun, “Impact time and angle control guidance independent of time-to-go prediction,” Aerospace Science and Technology, vol. 86, pp. 818–825, March 2019.
C. L. Lin, Y. P. Lin, and K. M. Chen, “On the design of fuzzified trajectory shaping guidance law,” ISA Transactions, vol. 48, no. 2, pp. 148–155, April 2009.
G. Weiss and I. Rusnak, “All-aspect three-dimensional guidance law based on feedback linearization,” Journal of Guidance, Control, and Dynamics, vol. 38, no. 12, pp. 2421–2428, December 2015.
B. S. Chen, Y. Y. Chen, and C. L. Lin, “Nonlinear fuzzy H∞ guidance law with saturation of actuators against maneuvering targets,” IEEE Transactions on Control Systems Technology, vol. 10, no. 6, pp. 769–779, December 2002.
K. Z. Meng, D. Zhou, and R. L. Du, “L2 gain-based guidance law with acceleration saturation,” Proc. of the 54th Annual Conf. Society of Instrument and Control Engineers of Japan, pp. 800–805, July 2015.
J. W. Zhu and S. X. Zhang, “Adaptive optimal gliding guidance independent of QEGC,” Aerospace Science and Technology, vol. 71, pp. 373–381, December 2017.
G. Y. Li, Z. G. Yu, and Z. X. Wang, “Three-dimensional adaptive sliding mode guidance law for missile with autopilot lag and actuator fault,” International Journal of Control, Automation, and Systems, vol. 17, no. 6, pp. 1369–1377, May 2019.
N. Harl and S. N. Balakrishnan, “Impact time and angle guidance with sliding mode control,” IEEE Transactions on Control Systems Technology, vol. 20, no. 6, 1436–1449, December 2012.
Y. Zhao, Y. Z. Sheng, and X. D. Liu, “Sliding mode control-based guidance law with impact angle constraint,” Chinese Journal of Aeronautics, vol. 27, no. 1, pp. 145–152, 2014.
O. Mofid, M. Momeni, S. Mobayen, and A. Fekih, “A disturbance-observer-based sliding mode control for the robust synchronization of uncertain delayed chaotic systems: Application to data security,” IEEE Access, vol. 9, pp. 16546–16555, January 2021.
Y. N. Yang and Y. Yan, “Neural network approximation-based nonsingular terminal sliding mode control for trajectory tracking of robotic airships,” Aerospace Science and Technology, vol. 54, pp. 192–197, April 2016.
O. Mofid and S. Mobayen, “Sliding mode disturbance observer control based on adaptive synchronization in a class of fractional-order chaotic systems,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 3, pp. 462–474, December 2018.
Z. H. Zhao, C. T. Li, J. Yang, and S. H. Li, “Output feedback continuous terminal sliding mode guidance law for missile-target interception with autopilot dynamics,” Aerospace Science and Technology, vol. 86, pp. 256–267, March 2019.
J. H. Song, S. M. Song, Y. Guo, and H. B. Zhou, “Nonlinear disturbance observer-based fast terminal sliding mode guidance law with impact angle constraints,” International Journal of Innovative Computing Information and Control, vol. 11, no. 3, pp. 787–802, January 2015.
S. R. Kumar, S. Rao, and D. Ghose, “Sliding-mode guidance and control for all-aspect interceptors with terminal angle constraints,” Journal of Guidance, Control, and Dynamics, vol. 35, no. 4, pp. 1230–1246, July 2012.
B. C. Zhou and W. H. Wang, “An improved nonsingular fast terminal sliding mode guidance law with impact angle constraints,” Proc. of the 8th International Conference on Intelligent Control and Information Processing, pp. 8–15, November 2017.
S. R. Kumar, S. Rao, and D. Ghose, “Nonsingular terminal sliding mode control with terminal angle constraints for non-manuievering targets,” Proc. of the 12th IEEE Workshop on Variable Structure Systems, pp. 291–296, January 2012.
S. R. Kumar, S. Rao, and D. Ghose, “Nonsingular terminal sliding mode guidance with impact angle constraints,” Journal of Guidance, Control, and Dynamics, vol. 37, no. 4, pp. 1114–1130, July 2014.
J. L. Zhao and J. Zhou, “Strictly convergent nonsingular terminal sliding mode guidance law with impact angle constraints,” Optik, vol. 127, no. 22, pp. 10971–10980, November 2016.
C. P. Bechlioulis and G. A. Rovithakis, “Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems,” Automatica, vol. 45, no. 2, pp. 532–538, February 2009.
C. P. Bechlioulis and G. A. Rovithakis, “Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2090–2099, November 2008.
A. K. Kostarigka, Z. Doulgeri, and G. A. Rovithakis, “Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity,” Automatica, vol. 49, no. 5, pp. 1137–1147, May 2013.
M. Wang and A. L. Yang, “Dynamic learning from adaptive neural control of robot manipulators with prescribed performance,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 2244–2255, January 2017.
J. Na, Q. Chen, X. M. Ren, and Y. Guo, “Adaptive prescribed performance motion control of servo mechanisms with friction compensation,” IEEE Transactions on Industrial Electronics, vol. 61, no. 1, pp. 486–494, January 2014.
Q. Y. Yang and M. Chen, “Adaptive neural prescribed performance tracking control for near space vehicles with input nonlinearity,” Neurocomputing, vol. 174, pp. 780–789, October 2015.
Y. B. Huang, J. Na, X. Wu, X. Q. Liu, and Y. Guo, “Adaptive control of nonlinear uncertain active suspension systems with prescribed performance,” ISA Transactions, vol. 54, pp. 145–155, January 2015.
J. Na, Y. B. Huang, X. Wu, G. B. Gao, G. Herrmann, and J. Z. Jiang, “Active adaptive estimation and control for vehicle suspensions with prescribed performance,” IEEE Transactions on Control Systems Technology, vol. 26, no. 6, pp. 2063–2077, November 2018.
C. Ming, R. S. Sun, and B. Zhu, “Nonlinear fault-tolerant control with prescribed performance for air-breathing supersonic missiles,” Journal of Spacecraft and Rockets, vol. 54, no. 5, pp. 1092–1099, August 2017.
S. F. Xiong, W. H. Wang, X. D. Liu, S. Wang, and Z. Q. Chen, “Guidance law against maneuvering targets with intercept angle constraint,” ISA Transactions, vol. 53, no. 4, pp. 1332–1342, July 2014.
J. Q. Han, “From PID to active disturbance rejection control,” IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900–906, March 2009.
Z. Zhu, D. Xu, J. M. Liu, and Y. Q. Xia, “Missile guidance law based on extended state observer,” IEEE Transactions on Industrial Electronics, vol. 60, no. 12, pp. 5882–5891, December 2013.
M. R. Mokhtari, A. C. Braham, and B. Cherki, “Extended state observer-based control for coaxial-rotor UAV,” ISA Transactions, vol. 61, pp. 1–14, March 2016.
J. X. Liu, S. Vazquez, L. Wu, A. Marquez, H. J. Gao, and L. G. Franquelo, “Extended state observer-based sliding-mode control for three-phase power converters,” IEEE Transactions on Industrial Electronics, vol. 64, no. 1, pp. 22–31, September 2016.
S. E. Talole, J. P. Kolhe, and S. B. Phadke, “Extended-state-observer-based control of flexible-joint system with experimental validation,” IEEE Transactions on Industrial Electronics, vol. 57, no. 4, pp. 1411–1419, May 2010.
S. M. He, D. F. Lin, and J. Wang, “Chattering-free adaptive fast convergent terminal sliding mode controllers for position tracking of robotic manipulators,” Proc. of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, vol. 230, no. 4, pp. 514–526, March 2015.
J. Q. Han and R. Zhang, “Error analysis of the second order ESO,” Journal of system Science and Mathematical Science, vol. 19, no. 4, pp. 465–471, October 1999.
J. H. Song, S. M. Song, and H. B. Zhou, “Adaptive nonsingular fast terminal sliding mode guidance law with impact angle constraints,” International Journal of Control, Automation, and Systems, vol. 14, no. 1, pp. 99–114, February 2016.
Funding
This project was supported by National Natural Science Foundation of China (52002185). The authors are grateful for the projects supported by the National Natural Science Foundation of China (Grant No. 52002185).
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Chao Ming received his Ph.D. degree in the School of Energy and Power Engineering from Nanjing University of Science and Technology in 2017. He is currently a lecturer at the School of Mechanical Engineering, Nanjing University of Science and Technology. His research interests include the guidance and control design of aircraft.
Xiaoming Wang is currently a professor at the School of Mechanical Engineering, Nanjing University of Science and Technology. His research interests include the system technology of the intelligent ammunition.
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Ming, C., Wang, X. Nonsingular Terminal Sliding Mode Control-based Prescribed Performance Guidance Law with Impact Angle Constraints. Int. J. Control Autom. Syst. 20, 715–726 (2022). https://doi.org/10.1007/s12555-020-0806-x
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DOI: https://doi.org/10.1007/s12555-020-0806-x