0
Research Papers

Three-Dimensional Impact Angle Guidance Laws Based on Model Predictive Control and Sliding Mode Disturbance Observer

[+] Author and Article Information
Shaoming He

School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: shaoming.he.cn@gmail.com

Wei Wang

School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: wangweiyh1@163.com

Jiang Wang

School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: wjbest2003@163.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 16, 2015; final manuscript received March 23, 2016; published online May 25, 2016. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 138(8), 081006 (May 25, 2016) (11 pages) Paper No: DS-15-1318; doi: 10.1115/1.4033272 History: Received July 16, 2015; Revised March 23, 2016

This paper presents a suboptimal three-dimensional guidance law to intercept unknown maneuvering targets with terminal angle constraint using multivariable control design. The presented guidance law is essentially a composite control method, which is constructed through a combination of standard continuous model predictive control (MPC) and adaptive multivariable sliding mode disturbance observer (SMDO). More specifically, the MPC method is utilized to obtain optimal line-of-sight (LOS) angle tracking performance for nonmaneuvering targets, while the SMDO technique is used to estimate and compensate for the unknown target maneuver online. By virtue of the adaptive nature, the proposed guidance law does not require any information on the bounds of target maneuver and its gradient except for their existence. The stability of the closed-loop guidance system is also analyzed by using Lyapunov function method. Simulation results clearly confirm the effectiveness of the proposed formulation against a maneuvering target.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Murtaugh, S. A. , and Criel, H. E. , 1996, “ Fundamentals of Proportional Navigation,” IEEE Spectrum, 3(12), pp. 75–85. [CrossRef]
Budiyono, A. , and Rachman, H. , 2011, “ Proportional Guidance and CDM Control Synthesis for a Short-Range Homing Surface-to-Air Missile,” J. Aerosp. Eng., 25(2), pp. 168–177. [CrossRef]
Nesline, F. W. , and Zarchan, P. , 1981, “ A New Look at Classical Versus Modern Homing Missile Guidance,” J. Guid. Control Dyn., 4(1), pp. 78–85. [CrossRef]
Zhou, D. , Sun, S. , and Teo, K. L. , 2009, “ Guidance Laws With Finite Time Convergence,” J. Guid. Control Dyn., 32(6), pp. 1838–1846. [CrossRef]
Zhou, D. , Qu, P. , and Sun, S. , 2013, “ A Guidance Law With Terminal Impact Angle Constraint Accounting for Missile Autopilot,” ASME J. Dyn. Syst. Meas. Control, 135(5), p. 051009. [CrossRef]
Kim, B. S. , Lee, J. G. , and Han, H. S. , 1998, “ Biased PNG Law for Impact With Angular Constraint,” IEEE Trans. Aerosp. Electron. Syst., 34(1), pp. 277–288. [CrossRef]
Manchester, I. R. , and Savkin, A. V. , 2006, “ Circular-Navigation-Guidance Law for Precision Missile/Target Engagements,” J. Guid. Control Dyn., 29(2), pp. 314–320. [CrossRef]
Erer, K. S. , and Merttopçuoglu, O. , 2012, “ Indirect Impact-Angle-Control Against Stationary Targets Using Biased Pure Proportional Navigation,” J. Guid. Control Dyn., 35(2), pp. 700–704. [CrossRef]
Lee, C. H. , Kim, T. H. , and Tahk, M. J. , 2013, “ Interception Angle Control Guidance Using Proportional Navigation With Error Feedback,” J. Guid. Control Dyn., 36(5), pp. 1556–1561. [CrossRef]
Zhang, Y. , Ma, G. , and Liu, A. , 2013, “ Guidance Law With Impact Time and Impact Angle Constraints,” Chin. J. Aeronaut., 26(4), pp. 960–966. [CrossRef]
Ryoo, C. K. , Cho, H. , and Tahk, M. J. , 2005, “ Optimal Guidance Laws With Terminal Impact Angle Constraint,” J. Guid. Control Dyn., 28(4), pp. 724–732. [CrossRef]
Ryoo, C. K. , Cho, H. , and Tahk, M. J. , 2006, “ Time-to-Go Weighted Optimal Guidance With Impact Angle Constraints,” IEEE Trans. Control Syst. Technol., 14(3), pp. 483–492. [CrossRef]
Ratnoo, A. , and Ghose, D. , 2009, “ State-Dependent Riccati-Equation-Based Guidance Law for Impact-Angle-Constrained Trajectories,” J. Guid. Control Dyn., 32(1), pp. 320–326. [CrossRef]
Lee, Y. I. , Kim, S. H. , Lee, J. I. , and Tahk, M. J. , 2012, “ Analytic Solutions of Generalized Impact-Angle-Control Guidance Law for First-Order Lag System,” J. Guid. Control Dyn., 36(1), pp. 96–112. [CrossRef]
Kumar, S. R. , Rao, S. , and Ghose, D. , 2012, “ Sliding-Mode Guidance and Control for All-Aspect Interceptors With Terminal Angle Constraints,” J. Guid. Control Dyn., 35(4), pp. 1230–1246. [CrossRef]
Cho, H. , Ryoo, C. K. , Tsourdos, A. , and White, B. , 2014, “ Optimal Impact Angle Control Guidance Law Based on Linearization About Collision Triangle,” J. Guid. Control Dyn., 37(3), pp. 958–964. [CrossRef]
Shima, T. , 2011, “ Intercept-Angle Guidance,” J. Guid. Control Dyn., 34(2), pp. 484–492. [CrossRef]
Kumar, S. R. , Rao, S. , and Ghose, D. , 2014, “ Nonsingular Terminal Sliding Mode Guidance With Impact Angle Constraints,” J. Guid. Control Dyn., 37(4), pp. 1114–1130. [CrossRef]
Xiong, S. , Wang, W. , Liu, X. , Wang, S. , and Chen, Z. , 2014, “ Guidance Law Against Maneuvering Targets With Intercept Angle Constraint,” ISA Trans., 53(4), pp. 1332–1342. [CrossRef] [PubMed]
He, S. , Lin, D. , and Wang, J. , 2015, “ Continuous Second-Order Sliding Mode Based Impact Angle Guidance Law,” Aerosp. Sci. Technol., 41, pp. 199–208. [CrossRef]
Zhang, Z. , Li, S. , and Luo, S. , 2013, “ Composite Guidance Laws Based on Sliding Mode Control With Impact Angle Constraint and Autopilot Lag,” Trans. Inst. Meas. Control, 35(6), pp. 764–776. [CrossRef]
Zhang, Z. , Li, S. , and Luo, S. , 2013, “ Terminal Guidance Laws of Missile Based on ISMC and NDOB With Impact Angle Constraint,” Aerosp. Sci. Technol., 31(1), pp. 30–41. [CrossRef]
Yang, C. D. , and Yang, C. C. , 1996, “ Analytical Solution of Three-Dimensional Realistic True Proportional Navigation,” J. Guid. Control Dyn., 19(3), pp. 569–577. [CrossRef]
Yoon, M. G. , 2010, “ Relative Circular Navigation Guidance for Three-Dimensional Impact Angle Control Problem,” J. Aerosp. Eng., 23(4), pp. 300–308. [CrossRef]
Maity, A. , Oza, H. B. , and Padhi, R. , 2014, “ Generalized Model Predictive Static Programming and Angle-Constrained Guidance of Air-to-Ground Missiles,” J. Guid. Control Dyn., 37(6), pp. 1897–1913. [CrossRef]
Chen, W. H. , Balance, D. J. , and Gawthrop, P. J. , 2003, “ Optimal Control of Nonlinear Systems: A Predictive Control Approach,” Automatica, 39(4), pp. 633–641. [CrossRef]
Yan, H. , and Ji, H. B. , 2012, “ Guidance Laws Based on Input-to-State Stability and High-Gain Observers,” IEEE Trans. Aerosp. Electron. Syst., 48(3), pp. 2518–2529. [CrossRef]
Talole, S. E. , Ghosh, A. , and Phadke, S. B. , 2006, “ Proportional Navigation Guidance Using Predictive and Time Delay Control,” Control Eng. Pract., 14(12), pp. 1445–1453. [CrossRef]
Shtessel, Y. B. , Shkolnikov, I . A. , and Levant, A. , 2007, “ Smooth Second-Order Sliding Modes: Missile Guidance Application,” Automatica, 43(8), pp. 1470–1476. [CrossRef]
Phadke, S. B. , and Talole, S. E. , 2012, “ Sliding Mode and Inertial Delay Control Based Missile Guidance,” IEEE Trans. Aerosp. Electron. Syst., 48(4), pp. 3331–3346. [CrossRef]
He, S. , Wang, J. , and Lin, D. , 2015, “ Composite Guidance Laws Using Higher Order Sliding Mode Differentiator and Disturbance Observer,” Proc. Inst. Mech. Eng., Part G, 229(13), pp. 2397–2415. [CrossRef]
Bhat, S. P. , and Bernstein, D. S. , 1998, “ Continuous Finite-Time Stabilization of the Translational and Rotational Double Integrators,” IEEE Trans. Autom. Control, 43(5), pp. 678–682. [CrossRef]
Yu, S. , Yu, X. , Shirinzadeh, B. , and Man, Z. , 2005, “ Continuous Finite-Time Control for Robotic Manipulators With Terminal Sliding Mode,” Automatica, 41(11), pp. 1957–1964. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Three-dimensional homing engagement geometry

Grahic Jump Location
Fig. 2

Simulation results for case 1: (a) LOS angular rate in elevation, (b) LOS angular rate in azimuth, (c) LOS angle in elevation, and (d) LOS angle in azimuth

Grahic Jump Location
Fig. 3

Simulation results for case 1: (a) missile acceleration in elevation, (b) missile acceleration in azimuth, (c) SMDO estimation performance, and (d) adaptive parameter

Grahic Jump Location
Fig. 4

Simulation results for case 2: (a) LOS angular rate in elevation, (b) LOS angular rate in azimuth, (c) LOS angle in elevation, (d) LOS angle in azimuth, (e) missile acceleration in elevation, and (f) missile acceleration in azimuth

Grahic Jump Location
Fig. 5

Simulation results for case 3: (a) LOS angular rate in elevation, (b) LOS angular rate in azimuth, (c) LOS angle in elevation, (d) LOS angle in azimuth, (e) missile acceleration in elevation, and (f) missile acceleration in azimuth

Grahic Jump Location
Fig. 6

Disturbance estimation performance under different k: (a) SMDO estimation performance and (b) adaptive parameter

Grahic Jump Location
Fig. 7

Disturbance estimation performance under different ci: (a) SMDO estimation performance and (b) adaptive parameter

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In