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The approach of partial stabilisation in design of discrete-time robust guidance laws against manoeuvering targets

Published online by Cambridge University Press:  28 February 2020

M.H. Shafiei Open the ORCID record for M.H. Shafiei [Opens in a new window]  and
N. Vazirpour
M.H. Shafiei*
Affiliation:
Department of Electrical and Electronics Engineering, Shiraz University of Technology, Modares Blvd. Shiraz, Iran
N. Vazirpour
Affiliation:
Department of Electrical and Electronics Engineering, Shiraz University of Technology, Modares Blvd. Shiraz, Iran
*
[email protected]
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Abstract

In this paper, a robust three-dimensional guidance law against manoeuvering targets is designed using the approach of discrete-time partial stabilisation. In the proposed method, the equations of the guidance problem are divided into two subsystems where the asymptotic stability is desired only for the first one. The control input of the second subsystem is designed such that the collision to be ensured in a short time. Despite recent advances in technology and implementation of digital controllers, the design of guidance laws with the approach of discrete-time partial stabilisation has not been done, till now. One of the advantages of this paper is to design a discrete-time guidance law even with the difficulties of the discrete-time Lyapunov theorem. Moreover, the Lyapunov function is chosen based on the physics of the guidance problem (making the rate of line of sight (LOS) rotation close to zero), and it is shown that it is not possible to asymptotically stabilise the system in the case of manoeuvering targets. Nevertheless, to guarantee the collision with the target, it is enough to limit the rotation rate of LOS to a small value. Finally, simulation results are given to show the appropriate performance of the proposed guidance law.

Keywords

partial stabilisationrobust guidance lawdiscrete-time
Type
Research Article
Information
The Aeronautical Journal , Volume 124 , Issue 1277 , July 2020 , pp. 1114 - 1127
Copyright
© The Author(s) 2020. Published by Cambridge University Press on behalf of Royal Aeronautical Society

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References

REFERENCES

Tang, C.D. and Chen, H.Y.Nonlinear H∞ robust guidance law for homing missiles, J Guid Control Dyn, 1998, 21, (6), pp 882–890.Google Scholar
Song, J., Song, S. and Xu, S.Three-dimensional cooperative guidance law for multiple missiles with finite-time convergence, Aerosp Sci Technol, 2017, 67, (0), pp 193–205.CrossRefGoogle Scholar
Gao, C., Li, J., Feng, T. and Jing, W.Adaptive terminal guidance law with impact-angle constraint. Aeronaut J, 2018, 122, (1249), pp 369–389.CrossRefGoogle Scholar
He, S. and Lin, D.Sliding mode-based continuous guidance law with terminal angle constraint. Aeronaut J, 2016, 120, (1229), pp 1175–1195.CrossRefGoogle Scholar
Xiong, J.H., Tang, S.J., Guo, J. and Wang, T.N.Improved sliding mode guidance law based on fuzzy variable coefficients strategy. Aeronaut J, 2014, 118, (1202), pp 435–451.CrossRefGoogle Scholar
Shieh, C.S.Tunable H∞ robust guidance law for homing missiles. IEE Proc-Cont Theo Appl, 2004, 151, (1), pp 103–107.CrossRefGoogle Scholar
Lechevin, N, and Rabbath, CA.Lyapunov-based nonlinear Missile guidance, J Guid Control Dyn, 2004, 27, (6), pp 1096–1102.CrossRefGoogle Scholar
Binazadeh, T. and Yazdanpanah, M.J.Partial stabilization approach to 3-dimensional guidance law design, J Dyn Syst Meas Control, 2011, 133, (6), p 064504.CrossRefGoogle Scholar
Chellaboina, V.S. and Haddad, W.M.A unification between partial stability and stability theory for time-varying systems, IEEE Cont Syst Mag 2004, 22, (6), pp 66–75.Google Scholar
Shafiei, M.H. and Binazadeh, T.Partial stabilization-based guidance, ISA Trans, 2012, 51, (1), pp 141–145.CrossRefGoogle ScholarPubMed
Binazadeh, T. and Yazdanpanah, M.J.Robust partial control design for non-linear control systems: a guidance application, Proc Inst Mech Eng Part I J Syst Cont Eng, 2012, 226, (2), pp 233–242.Google Scholar
Binazadeh, T. and Yazdanpanah, M.J.Partial stabilization of uncertain nonlinear systems, ISA Trans, 2012, 51, (2), pp 298–303.CrossRefGoogle ScholarPubMed
Shafiei, M.H. and Binazadeh, T.Application of partial sliding mode in guidance problem. ISA Trans, 2013, 52, (2), pp 192–197.CrossRefGoogle ScholarPubMed
Binazadeh, T. and Shafiei, M.H.Robust stabilization of uncertain nonlinear slowly-varying systems: application in a time-varying inertia pendulum, ISA Trans, 2014, 53, (2), pp 373–379.CrossRefGoogle Scholar
Franklin, G.F., Powell, J.D., and Workman, M.L.Digital Control of Dynamic Systems (Vol. 3), CA: Addison-wesley, Menlo Park, 1998.Google Scholar
Binazadeh, T. and Shafiei, M.H.Passivity-based optimal control of discrete-time nonlinear systems. Cont Cybern, 2013, 42, (3), pp 627–637.Google Scholar
Baleghi, N.A., and Shafiei, M.H.Stability analysis for discrete-time switched systems with uncertain time delay and affine parametric uncertainties. Trans Inst Meas Cont, 2018, 40, (4), pp 1150–1157.CrossRefGoogle Scholar
Hanselmann, H.Implementation of digital controllers—A survey. Automatica, 1987, 23, (1), pp 7–32.CrossRefGoogle Scholar
Paiz, C., and Porrmann, M. The utilization of reconfigurable hardware to implement digital controllers: a review. Proceedings of IEEE International Symposium on Industrial Electronics, Vigo, Spain, June 2007, pp 2380–2385.CrossRefGoogle Scholar
Monmasson, E. and Cirstea, M.N.FPGA design methodology for industrial control systems—A review, IEEE Trans Ind Electron, 2007, 54, (4), pp 1824–1842.CrossRefGoogle Scholar
Yan, H., Fahroo, F., and Ross, I.M. Real-time computation of neighboring optimal control laws. Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, Monterey, California, August 2002, pp 46–57.CrossRefGoogle Scholar
Malisoff, M., and Mazenc, F.Constructions of strict Lyapunov functions for discrete-time and hybrid time-varying systems. Nonlinear Anal: Hybrid Syst, 2008, 2, (2), pp 394–407.Google Scholar
He, S., Wang, W., and Wang, J.Discrete-time super-twisting guidance law with actuator faults consideration. Asian J. Control, 2017, 19, (5), pp 1854–1861.Google Scholar
Zhou, D., Sun, S., Zhou, J.Y., and Teo, K.L.A discrete sliding-mode guidance law. J Dyn Syst Meas Cont, 2015, 137, (2), pp 024501.CrossRefGoogle Scholar
Zhang, Y., Liu, J., Lian, W., and Yang, L. Discrete sliding mode guidance law considering dynamic characteristics for autopilot. Proceedings of 33rd Youth Academic Annual Conference of Chinese Association of Automation, Jiangsu, China, May 2018, pp 77–81.CrossRefGoogle Scholar