Abstract
This paper considers the terminal guidance problem of missiles intercepting maneuvering targets with impact angle constraints. Based on an advanced nonsingular fast terminal sliding mode control scheme and adaptive control, an adaptive nonsingular fast terminal sliding mode guidance law is proposed in the presence of the target acceleration as an unknown bounded external disturbance. In the design procedure, an adaptive law is presented to estimate the unknown upper bound of the external disturbance. Theoretical analysis shows that the proposed guidance law can guarantee the finite-time convergence in both the reaching phase and the sliding phase by applying a Lyapunov-based approach. Numerical simulations are presented to demonstrate the effectiveness of the proposed guidance law. Although the proposed guidance law is developed for the constant speed missiles, by the extensive numerical simulations with a realistic missile model, the performance is shown to be equally good for the varying speed missiles.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- a m , a t :
-
lateral accelerations of the missile and target
- r, ṙ :
-
relative distance and relative velocity between the missile and target
- V m , V t :
-
velocities of the missile and target
- q, \(\dot q\) :
-
line-of-sight (LOS) angle and its rate
- φ m , φ t :
-
flight-path angles of the missile and target
- t f :
-
guidance terminal time
- φ d :
-
desired impact angle
- q d :
-
desired terminal LOS angle
- s :
-
variable for the sliding surface
- d :
-
term of the lumped disturbance
- Δ:
-
unknown upper bound of the lumped disturbance
- \(\hat \Delta \) :
-
estimated value of Δ
References
S. Rogers, “Missile guidance comparison,” Proc. of the AIAA Conference on Guidance, Navigation, and Control, pp. 1–4, 2004. [click]
A. Ratnoo and D. Ghose, “Impact angle constrained interception of stationary targets,” Journal of Guidance, Control, and Dynamics, vol. 31, no. 6, pp. 1817–1822, November-December 2008.[click]
K. S. Erer and O. Merttopcuoglu, “Indirect impact-anglecontrol against stationary targets using biased pure proportional navigation,” Journal of Guidance, Control, and Dynamics, vol. 35, no. 2, pp. 700–704, March-April 2012. [click]
C. H. Lee, T. H. Kim, and M. J. Tahk, “Interception angle control guidance using proportional navigation with error feedback,” Journal of Guidance, Control, and Dynamics, vol. 36, no. 5, pp. 1556–1561, September-October 2013. [click]
D. Zhou, S. Sun, and K. L. Teo, “Guidance laws with finite time convergence,” Journal of Guidance, Control, and Dynamics, vol. 32, no. 6, pp. 1838–1846, November-December 2009. [click]
C. D. Yang and H. Y. Chen, “Nonlinear H ∞ robust guidance law for homing missiles,” Journal of Guidance, Control, and Dynamics, vol. 21, no. 6, pp. 882–890, November-December 1998. [click]
D. Zhou, C. D. Mu, and T. L. Shen, “Robust guidance law with L2 gain performance,” Transactions of the Japan Society for Aeronautical and Space Sciences, vol. 44, no. 144, pp. 82–88, August 2001. [click]
W. H. Chen, J. L. Speyer, and D. Lianos, “Optimal intercept missile guidance strategies with autopilot lag,” Journal of Guidance, Control, and Dynamics, vol. 33, no. 4, pp. 1264–1272, July-August 2010. [click]
V. Shaferman and T. Shima, “Linear quadratic guidance law for imposing a terminal intercept angle,” Journal of Guidance, Control, and Dynamics, vol. 31, no. 5, pp. 1400–1412, September-October 2008. [click]
S. Sun, D. Zhou, and W. T. Hou, “A guidance law with finite time convergence accounting for autopilot lag,” Aerospace Science and Technology, vol. 25, pp. 132–137, March 2013. [click]
S. D. Brierley and R. Longchamp, “Application of slidingmode control to air-air interception problem,” IEEE Transactions on Aerospace and Electronic Systems, vol. 26, no. 2, pp. 306–325, March 1990. [click]
Y. X. Zhang, M.W. Sun, and Z. Q. Chen, “Finite-time convergent guidance law with impact angle constraint based on sliding-mode control,” Nonlinear Dynamics, vol. 70, no. 1, pp. 619–625, October 2012. [click]
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, pp. 1436–1449, November 2012. [click]
T. Yamasaki, S. N. Balakrishnan, and H. Takano, “Second order sliding mode-based intercept guidance with uncertainty and disturbance compensation,” Proc. of the AIAA Conference on Gudiance, Navigation, and Control, pp. 19–22, 2013. [click]
S. Rao and D. Ghose, “Sliding mode control based terminal impact angle constrained guidance laws using dual sliding surfaces,” Proc. of IEEE Workshop on Variable Structure Systems, pp. 325–330, January 2012. [click]
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-August 2012. [click]
Y. B. Shtessel, I. A. Shkolnikov, and A. Levant, “Guidance and control of missile interceptor using second-order sliding modes,” IEEE Transactions on Aerospace and Electronic Systems, vol. 45, no. 1, pp. 110–124, January 2009. [click]
Z. Man, A. P. Paplinski, and H. R. Wu, “A robust MIMO terminal sliding mode control scheme for rigid robotic manipulatiors,” IEEE Transactions on Automatic Control, vol. 39, no. 12, pp. 2464–2469, December 1994. [click]
Y. Feng, X. H. Yu, and Z. H. Man, “Non-singular terminal sliding mode control of rigid manipulators,” Automatica, vol. 38, no. 12, pp. 2159–2167, December 2002. [click]
L. Y. Wang, T. Y. Chai, and L. F. Zhai, “Neural-networkbased terminal sliding mode control of robotic manipulators including actuator dynamics,” IEEE Transactions on Industrial Electronics, vol. 56, no. 9, pp. 3296–3304, September 2009. [click]
S. R. Kumar, S. Rao, and D. Ghose, “Non-singular terminal sliding mode guidance and control with terminal angle constraints for non-maneuvering targets,” Proc. of IEEE Workshop on Variable Structure Systems, pp. 291–296, January 2012. [click]
Q. Z. Song, X. Y. Meng, “Design and simulation of guidance law with angular constraint based on non-singular terminal sliding mode,” Physics Procedia, vol. 25, pp. 1197–1204, April 2012. [click]
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-August 2014. [click]
S. F. Xiong,W. H.Wang, X. D. Liu, S.Wang, and Z. Chen, “Guidance law against maneuvering targets with intercept angle constraint,” ISA Transactions, vol. 53, no. 4, July 2014. [click]
X. H. Yu and Z. H. Man, “Fast terminal sliding mode control design for nonlinear dynamical systems,” IEEE Transactions on Circuits Systems Part I, vol. 39, no. 2, pp. 261–264, February 2002. [click]
S. H. Yu, X. H. Yu, and B. Shirinzadeh, “Continuous finitetime control for robotic manipulators with terminal sliding mode,” Automatica, vol. 41, no. 11, pp. 1957–1964, November 2005. [click]
Y. J. Huang, T. C. Kuo, and S. H. Chang, “Adaptive slidingmode control for nonlinear systems with uncertain parameters,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 38, no. 2, pp. 534–539, April 2008. [click]
B. L. Cong, C. Zhen, and X. D. Liu, “Disturbance observerbased adaptive integral sliding mode control for rigid spacecraft attitude maneuvers,” Proc. of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 227, no. 10, pp. 1660–1671, September 2013. [click]
Z. Zhu, Y. Q. Xia, and M. Y. Fu, “Adaptive sliding mode control for attitude stabilization with actuator saturation,” IEEE Transactions on Industrial Electronics, vol. 58, no. 10, pp. 4898–4907, 2011. [click]
M. C. Pai, “Observer-based adaptive sliding mode control for robust tracking and model following,” International Journal of Control, Automation and Systems, vol. 11, no. 2, pp. 225–232, October 2013. [click]
C. Lu, X. Q. Chen, and S. Tao, “Fault tolerant small satellite attitude control using adaptive non-singular terminal sliding mode,” Advances in Space Research, vol. 51, no. 12, pp. 2374–2393, June 2013. [click]
B. Xiao, Q. L. Hu, and Y. M. Zhang, “Adaptive sliding mode fault tolerant attitude tracking control for flexible spacecraft under actuator saturation,” IEEE Transactions on Control Systems Technology, vol. 20, no. 6, pp. 1605–1612, November 2012. [click]
X. D. Liu, Y. J. Wu, and B. T. Liu, “The research of adaptive sliding mode controller for motor servo system using fuzzy upper bound on disturbances,” International Journal of Control, Automation and Systems, vol. 10, no. 5, pp. 1064–1069, October 2012. [click]
S. Frikha, M. Djemel, and N. Derbel, “Observer based adaptive neuro-sliding mode control for MIMO nonlinear systems,” International Journal of Control, Automation and Systems, vol. 8, no.2, pp. 257-265, April 2010. [click]
B. S. Kim, J. G. Lee, and H. S. Han, “Biased PNC law for impact with angular constraint,” IEEE Transactions on Aerospace and Electronic Systems, vol. 34, no. 1, pp. 277–288, January1998. [click]
T. Yamasaki, S. N. Balakrishnan, H. Takano, et al, “Second order sliding mode-based intercept guidance with uncertainty and disturbance compensation,” Proc. of AIAA Guidance, Navigation, and Control (GNC) Conference, August 2013. [click]
X. H. Wang, J. A. Wang, “Partial integrated guidance and control for missiles with three-dimensional impact angle constraints,” Journal of Guidance, Control, and Dynamics, vol. 37, no. 2, pp. 644–657, March-April 2014. [click]
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Chang Kyung Ryoo under the direction of Editor Duk-Sun Shim. This paper was supported by the Foundation for Creative Research Groups of the National Natural Science Foundation of China under Grant No.61021002.
Junhong Song received her M.S. degree in Applied Mathematics from Harbin Institute of Technology in 2012. She is pursuing her Ph.D. degree at the School of Astronautics, Harbin Institute of Technology. Her main research interests include vehicle guidance and control.
Shenmin Song received his Ph.D. degree in Control Theory and Application from Harbin Institute of Technology in 1996. He carried out postdoctoral research at Tokyo University from 2000 to 2002. He is currently a professor at the School of Astronautics, Harbin Institute of Technology. His main research interests include spacecraft guidance and control, intelligent control, and nonlinear theory and application.
Huibo Zhou received her M.S. degree in College of Mathematics Normal Systems Science from Shenyang Normal University in 2006. Now she is a teacher at the School of Mathematical Science in Harbin Normal University, and at the same time she is pursuing her Ph.D. degree at the Center for Control Theory and Guidance Technology in Harbin Institute of Technology. Her main research interests include vehicle guidance and control.
Rights and permissions
About this article
Cite this article
Song, J., Song, S. & Zhou, H. Adaptive nonsingular fast terminal sliding mode guidance law with impact angle constraints. Int. J. Control Autom. Syst. 14, 99–114 (2016). https://doi.org/10.1007/s12555-014-0155-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-014-0155-8