Abstract
The problem of simultaneous tracking of both fast and slow states for a general class of nonlinear singularly perturbed systems is addressed. A motivating example is an aircraft tracking a prescribed fast moving target, while simultaneously regulating speed and/or one or more kinematic angles. Previous results in the literature have focused on tracking outputs that are a function of the slow states alone. Moreover, global asymptotic tracking has been demonstrated only for a class of nonlinear systems that possess a unique real root for the fast states. For a more general class of nonlinear systems only local tracking results have been proven. In this paper, control laws that accomplish global tracking of both fast and slow states is developed using geometric singular perturbation methods. Global exponential stability is proven using the composite Lyapunov function approach and an upper bound necessary condition for the scalar perturbation parameter is derived. Controller performance is demonstrated through simulation of a combined longitudinal lateral/directional maneuver for a nonlinear, coupled, six degree-of-freedom model of the F/A-18A Hornet. Results presented in the paper show that the controller accomplishes global asymptotic tracking even though the desired reference trajectory requires the aircraft to switch between linear and nonlinear regimes. Asymptotic tracking while keeping all the closed-loop signals bounded and well behaved is also demonstrated. Additionally the controller is independent of the scalar perturbation parameter nor does it require knowledge of it.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arstein, Z., Gaitsgory, V.: Tracking fast trajectories along a slow dynamics: a singular perturbation approach. SIAM Journal of Control and Optimization 35(4), 1487–1507 (1997)
Calise, A.J.: Singular perturbation methods for variational problems in aircraft flight. IEEE Transactions on Automatic Control 21, 345–353 (1976)
Chen, C.C.: Global exponential stabilization for nonlinear singularly perturbed systems. In: IEEE Proceedings of Control Theory and Applications, vol. 145, pp. 377–382 (1998)
Choi, H.L., Lim, J.T.: Gain scheduling control of nonlinear singularly perturbed time-varying systems with derivative information. International Journal of Systems Science 36(6), 357–364 (2005)
Fan, Y., Lutze, F.H., MCliff, E.: Time-optimal lateral maneuvers of an aircraft. Journal of Guidance, Control and Dynamics 18, 1106–1112 (1995)
Fenichel, N.: Geometric singular perturbation theory for ordinary differential equations. Journal of Differential Equations 31, 53–98 (1979)
Georgie, J., Valasek, J.: Evaluation of longitudinal desired dynamics for dynamic-inversion controlled generic reentry vehicles. Journal of Guidance Control and Dynamics 26, 811–819 (2003)
Grujic, L.T.: On the theory and synthesis of nonlinear non-stationary tracking singularly perturbed systems. Control Theory and Advanced Technology 4(4), 395–409 (1988)
Ioannou, P., Sun, J.: Robust Adaptive Control. Prentice Hall Inc., Englewood Cliffs (2003)
Kokotovic, P., Khalil, H.K., Reilly, J.O.: Singular Perturbation Methods in Control: Analysis and Design. Academic Press, London (1986)
Li, L., Sun, F.C.: An adaptive tracking controller design for nonlinear singularly perturbed systems using fuzzy singularly perturbed model. IMA Journal of Mathematical Control and Information 26, 395–415 (2009)
Menon, P., Badgett, M.E., Walker, R.: Nonlinear flight test trajectory controllers for aircraft. Journal of Guidance 10, 67–72 (1987)
Naidu, D.S.: Singular Perturbation Methodology in Control Systems. IEEE Control Engineering Series, vol. 34 (1988)
Naidu, D.S., JCalise, A.: Singular perturbations and time scales in guidance and control of aerospace systems: A survey. Journal of Guidance, Control and Dynamics 24(6), 1057–1078 (2001)
Schaub, H., Junkins, J.L.: Analytical Mechanics of Space Systems. AIAA Education Series (2003)
Siddarth, A., Valasek, J.: Kinetic state tracking of a class of singularly perturbed systems. AIAA Journal of Guidance, Navigation and Control Accepted (to appear, 2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Siddarth, A., Valasek, J. (2011). Global Tracking Control Structures for Nonlinear Singularly Perturbed Aircraft Systems. In: Holzapfel, F., Theil, S. (eds) Advances in Aerospace Guidance, Navigation and Control. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19817-5_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-19817-5_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19816-8
Online ISBN: 978-3-642-19817-5
eBook Packages: EngineeringEngineering (R0)