Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T04:22:20.303Z Has data issue: false hasContentIssue false
  • English
  • Français

Novel second-order sliding mode guidance law with an impact angle constraint that considers autopilot lag for intercepting manoeuvering targets

Published online by Cambridge University Press:  13 April 2020

W.J. Zhang Open the ORCID record for W.J. Zhang [Opens in a new window] ,
Q.L. Xia  and
W. Li
W.J. Zhang*
Affiliation:
School of Aerospace Engineering, Beijing Institute of Technology, Beijing, People’s Republic of China
Q.L. Xia
Affiliation:
School of Aerospace Engineering, Beijing Institute of Technology, Beijing, People’s Republic of China
W. Li
Affiliation:
School of Aerospace Engineering, Beijing Institute of Technology, Beijing, People’s Republic of China
*
[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A novel second-order sliding-mode-based impact angle and autopilot lag guidance law for engaging manoeuvering targets with unknown acceleration is presented in this study. A backstepping technique is applied to the design of the sliding surface. The proposed guidance law is based on a new sliding surface. It exhibits the advantage of ensuring that the sliding surface and its derivative will converge to zero in finite time while guaranteeing that the sliding surface will not cross zero until the ultimate time. The method effectively eliminates the undesired chattering of the sliding surface. To compensate for the uncertainty caused by target manoeuvering, a new observer is developed to estimate target manoeuvering. The convergence of the system is proven through a Lyapunov function and finite time convergence theory. Lastly, mathematical simulations results show that the proposed guidance law can achieve precise interception with a wide range of impact angles, thereby verifying the effectiveness of the guidance law.

Keywords

impact angle constraintsecond-order sliding modeautopilot lagmanoeuvering targetobserver
Type
Research Article
Information
The Aeronautical Journal , Volume 124 , Issue 1279 , September 2020 , pp. 1350 - 1370
Copyright
© The Author(s) 2020. Published by Cambridge University Press on behalf of Royal Aeronautical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Kim, M. and Grider, K.V.Terminal guidance for impact attitude angle constrained flight trajectories. IEEE Transactions on Aerospace and Electronic Systems, 1973, 9, (6), pp 852–859.CrossRefGoogle Scholar
Bryson, A.E. Jr. andHo, Y.C.Applied Optimal Control, Wiley, 1975, New York, NY, US.Google Scholar
Cho, H. Navigation constants in PNG law and the associated optimal control problems (in Korean), In Proceedings of Korean Automatic Control Conference, Seoul, Korea, Oct. 1992, pp 578–583.Google Scholar
Ryoo, C.K., Cho, H. and Tahk, M.J.Optimal guidance laws with terminal impact angle constraint. J Guidance, Control, and Dynamics, 2005, 28, (4), pp 724–732.CrossRefGoogle Scholar
Ratnoo, A. and Ghose, D.State-dependent Riccati-equation-based guidance law for impact angle constrained trajectories. J Guidance, Control, and Dynamics, 2009, 32, (1), pp 320–325.CrossRefGoogle Scholar
Lee, Y.I., Kim, S.H. and Tahk, M.J.Optimality of linear time-varying guidance for impact angle control. IEEE Transactions on Aerospace and Electronic Systems, 2012, 48, (3), pp 2802–2817.CrossRefGoogle Scholar
Maity, A., Oza, H.B. and Padhi, R.Generalized model predictive static programming and angle-constrained guidance of air-to-ground missiles, J Guidance, Control, and Dynamics, 2014, 37, (6), pp 1897–1913.CrossRefGoogle Scholar
Oza, H.B. and Padhi, R.Impact angle constrained suboptimal model predictive static programming guidance of air-to-ground missiles, J Guidance, Control, and Dynamics, 2012, 35, (1) pp 153–164.CrossRefGoogle Scholar
Kim, B.S., Lee, J.G. and Han, H.S.Biased PNG law for impact with angular constraint. IEEE Transactions on Aerospace and Electric Systems, 1998, 34, (1), pp 277–288.Google Scholar
Ratnoo, A. and Ghose, D.Impact angle constrained interception of stationary targets. J Guidance, Control, and Dynamics, 2008, 31, (6), pp 1816–1821.CrossRefGoogle Scholar
Ratnoo, A. and Ghose, D.Impact angle constrained guidance against nonstationary non-maneuvering targets. J Guidance, Control, and Dynamics, 2010, 32, (1), pp 269–275.CrossRefGoogle Scholar
Erer, K.S. and MerttopÇuoĞlu, O.Indirect impact-angle-control against stationary targets using biased pure proportional navigation. J Guidance, Control, and Dynamics, 2012, 35, (2), pp 700–703.CrossRefGoogle Scholar
Li, T., Zhao, R. and Chen, C.L.P, et al. Finite-time formation control of under-actuated ships using nonlinear sliding mode control. IEEE Transactions on Cybernetics, 2018, 48, (11), pp 3243–3253.CrossRefGoogle ScholarPubMed
Deyin, Y., Bin, Z. and Panshuo, L, et al. Event-triggered sliding mode control of discrete-time Markov jump systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 49, (10), pp 2016–2025.Google Scholar
Lee, C.H., Kim, T.H. and Tahk, M.J.Design of impact angle control guidance laws via high-performance sliding mode control, Proceedings of the Institution of Mech Engineers, Part G: J Aerospace Engineering, 2013, 227, (2), pp 235–253.CrossRefGoogle Scholar
Rao, S. and Ghose, D. Sliding mode control based terminal impact angle constrained guidance laws using dual sliding surfaces, Proceedings of 12th IEEE Workshop on Variable Structure Systems, IEEE Publ., Piscataway, NJ, 2012, pp 325–330.CrossRefGoogle Scholar
He, S.M. and Lin, D.F.A robust impact angle constraint guidance law with seeker’s field-of-view limit, Transaction of the Institute of Measurement and Control, 2014, 37, (3), 317–328.CrossRefGoogle Scholar
Kumar, S.R., Rao, S. and Ghose, D.Sliding-mode guidance and control for all-aspect interceptors with terminal angle constraints, J Guidance, Control, and Dynamics. 2012, 35, (4), pp 1230–1246.CrossRefGoogle Scholar
Kumar, S.R., Rao, S. and Ghose, D.Nonsingular terminal sliding mode guidance with impact angle constraints, J Guidance, Control, and Dynamics, 2014, 37, (4), pp 1114–1130.CrossRefGoogle Scholar
He, S.M., Lin, D.F. and Wang, J.Continuous second-order sliding mode based impact angle guidance law, Aerospace Science and Technology, 2015, 41, pp 199–208.CrossRefGoogle Scholar
Sun, S., Zhou, D. andHou, W.A guidance law with finite time convergence accounting for autopilot lag, Aerospace Science and Technology, 2013, 25, (1), pp 132–137.CrossRefGoogle Scholar
Zhang, T., Ge, S.S. and Hang, C.C.Adaptive neural network control for strict-feedback nonlinear systems using backstepping design, Automatica, 2000, 36, pp 1835–1846.CrossRefGoogle Scholar
Choi, J.Y. and Farrell, J.A.Adaptive observer backstepping control using neural networks, IEEE Transactions on Neural Networks, 2001, 12, (5), pp.1103–1112.CrossRefGoogle ScholarPubMed
Kuljaca, O., Swamy, N. and Lewis, F. L., et al. Design and implementation of industrial neural network controller using backstepping, Proceedings of the 40th IEEE Conference on Decision and Control, IEEE, 2001.Google Scholar
Lin, C.M. and Hsu, C.F.Recurrent-neural-network-based adaptive backstepping control for induction servomotor, IEEE Transactions on Industrial Electronics, 2005, 52, (6), pp 1677–1684.CrossRefGoogle Scholar
Hsu, C.F., Lin, C.M. and Lee, T.T.Wavelet adaptive backstepping control for a class of nonlinear systems. IEEE Transactions on neural networks, 2006, 17, (5), 1175–1183.Google ScholarPubMed
Zhao, X., Yang, H. and Karimi, H.R., et al. Adaptive neural control of MIMO nonstrict-feedback nonlinear systems with time delay. IEEE Transactions on Cybernetics, 2015, 46, (6), 1337–1349.CrossRefGoogle ScholarPubMed
Tong, S., Li, Y. and Shi, P.Observer-based adaptive fuzzy backstepping output feedback control of uncertain MIMO pure-feedback nonlinear systems, IEEE Transactions on Fuzzy Systems, 2012, 20, (4), pp 771–785.CrossRefGoogle Scholar
Wang, T., Zhang, Y. and Qiu, J., et al. Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements, IEEE Transactions on Fuzzy Systems, 2015, 23, (2), pp. 302–312.CrossRefGoogle Scholar
Du, H. and Chen, X.NN-based output feedback adaptive variable structure control for a class of non-affine nonlinear systems: a nonseparation principle design, Neuro Computing, 2009, 72, pp 2009–2016.Google Scholar
Arefi, M.M., Zarei, J. and Karimi, H.R.Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction, J Franklin Institute, 2014, 351, (8), 4302–4316.CrossRefGoogle Scholar
Dong, X., Zhao, Y. and Karimi, H.R., et al. Adaptive variable structure fuzzy neural identification and control for a class of MIMO nonlinear system, J Franklin Institute, 2013, 350, pp 1221–1247.CrossRefGoogle Scholar
Zhang, Y., Tang, S.J. and Guo, J.An adaptive fast fixed-time guidance law with an impact angle constraint for intercepting maneuvering targets. Chinese J Aeronautics, 2018, 147, (6), pp 167–184.Google Scholar
Bhat, S.P. and Bernstein, D.S. Continuous finite-time stabilization of the translational and rotational double integrators, IEEE Int Conference on Control Applications, 2002.Google Scholar
Bhat, S.P. and Bernstein, D.S.Finite-time stability of continuous autonomous systems, Soc for Industrial and Applied Mathematics, 2000, 38, (3), pp 751–766.Google Scholar
He, S.M. and Lin, D.F.Guidance laws based on model predictive control and target maneuver estimator, Transactions of the Institute of Measurement and Control, 2016, 38, (12), pp 1509–1519.CrossRefGoogle Scholar
Levant, A.Construction principles of 2-Sliding mode design, Automatica, 2007, 43, (4), pp 576–586.CrossRefGoogle Scholar
Nathan, H. and Balakrishnan, S.N.Impact Time and Angle Guidance with Sliding Mode Control, IEEE Transactions on control systems technology, 2012, 20, (6), pp 1436–1449.Google Scholar
Zhou, H.B.Study on Guidance Law and Cooperative Guidance for Multi-Missiles Based on Finite-Time and Sliding Mode Theory, Harbin Institute of Technology, 2015, Harbin, China, pp 63–66.Google Scholar