A linear time-varying approach for robustness analyses of a re-entry flight technology demonstrator

Abstract

A novel robustness analysis technique is proposed for atmospheric re-entry applications. The problem is stated as a finite time stability (FTS) analysis of linear time-varying (LTV) systems on a compact time domain, subject to bounded variations in initial state and unknown parameters. The FTS property is formulated as the inclusion of all the possible system trajectories into a pre-specified time-varying subset of the state space. Based on assuming the involved sets are polytopes, the proposed approach allows deducing the system FTS from the property verification on a limited number of numerically computed system trajectories. An additional result is presented which allows determination of a conservative estimate of the maximum norm-bound of time-varying perturbations under which the LTV system remains finite time stable. Results of the application of the proposed technique to a re-entry technology demonstrator are presented which demonstrate its effectiveness in complementing conventional linear time invariant-based analyses. Results also show that it is computationally viable and allows linking the system robustness to a quantitative analysis of the system trajectory dispersion around the nominal one due to concurrent initial state dispersion and uncertain parameters effects, which aids in evaluating mission objectives fulfilment.

Keywords

robustness analysis linear time-varying system atmospheric re-entry finite time stability

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References

Regulation about time-varying trajectories: precision entry guidance illustrated. AIAA J. Guid. Control Dyn., 1999, 22(6), 784–790.

Tancredi

Grassi

Corraro

Filippone

Robustness analysis for terminal phases of re-entry flight. AIAA J. Guid. Control Dyn., 2009, 32(5), 1679–1683.

Cobleigh, B. R. Development of the X-33 aerodynamic uncertainty model. NASA/TP-1998-206544, 1998.

Leith

D. J.

Leithead

W. E.

Survey of gain-scheduling analysis and design. Int. J. Control, 2000, 73(11), 1001–1025.

Fujimori

Nikiforuk

P. N.

Gupta

M. M.

A flight control design of a re-entry vehicle using a double-loop control system with fuzzy gain scheduling. Proc. IMechE., Part G: J. Aerospace Engineering, 2001, 215, 1–12.

Bayle

G. P.

Space shuttle entry flight control off-nominal design considerations. AIAA J. Guid. Control Dyn., 1984, 7(1), 9–14.

Shwani, C., Nguyen, V., Tran, H., Poladian, D., and Falangas, E. Dynamics and stability and control characteristics of the X-37. In Proceedings of the AIAA Guidance and Control Conference, Montreal, Canada, 6–9 August 2001, AIAA paper 2001–4383.

Korte

Tasks and needs of the industrial clearanceprocess. Advanced techniques for clearance of flight control laws. Berlin, Springer-Verlag, 2002, 13–33.

Gayek, J.E. A survey of techniques for approximatingreachable and controllable sets. In Proceedings of the 30th Conference on Decision and control, Brighton, UK, 11–13 December 1991, 2, 1724–1730.

10.

Girard

Reachability of uncertain linear systems using zonotopes. Hybrid systems: computation and control, 2005, vol. 3414. New York, Springer, 291–305. Lecture Notes in Computer Science Series.

11.

Dorato

An overview of finite-time stability. Current trends in nonlinear systems and control, systems and control: foundations & applications, 2006, 185–194. Part II.

12.

Grujic

L. T.

Richard

J. P.

Borne

Gentina

J. C.

Stability domains, 2000, ch. 6. Boca Raton, Florida, Chapman & Hall/CRC.

13.

Amato

Ariola

Dorato

Finite time control of linear systems subject to parametric uncertainties and disturbances. Automatica, 2001, 37(9), 1459–1463.

14.

Jönsson

Robustness of trajectories with finite time extent. Automatica, 2002, 38(9), 1485–1497.

15.

Graettinger

T. J.

Krogh

B. H.

Hyperplane method for reachable state estimation for linear time-invariant systems. J. Optim. Theory Appl., 1991, 69(3), 555–588.

16.

Ziegler

G. M.

Lectures on polytopes, graduate texts inmathematics. New York, Springer-Verlag, 1995, 152–152.

17.

Fukuda, K. and Weibel, C. Computing all faces of the Minkowski sum of V-polytopes. In Proceedings of the 17th Canadian Conference on Computational geometry, 13 February 2006, pp. 253–256.

18.

Ottmann

Schuierer

Soundaralakshmi

Enumerating extreme points in higher dimensions. Nordic J. Computing, 2001, 8(2), 179–192.

19.

Corraro, F., Filippone, E., Russo, M., Verde, L., Tancredi, U., Moccia, A., and Grassi, M. Flight dynamic characterisation of the USV-flying test bed vehicle. In Proceedings of AIAA/CIRA 13th International Space Planes and Hypersonic System and Technologies Conference, Capua, Italy, 2005, AIAA-2005-3276.

20.

Etkin

Reid

L. D.

Dynamics of flight: stability and control, 3rd ed. Inc, New York, John Wiley and Sons, 1996.

21.

Rufolo, G., Roncioni, P., Marini, M., Votta, R., and Palazzo, S. Experimental and Numerical aerodynamic data integration and aerodatabase development for the PRORA-USV-FTB_1 reusable vehicle. In Proceedings of the AIAA/AHI 14th International Space Planes and Hypersonic System and Technologies Conference, Canberra, Australia, 2006, AIAA-2006-8031.

22.

Tancredi

Grassi

Corraro

Filippone

Russo

A novel approach to clearance of flight control laws over time varying trajectories. Autom. Control Aerosp., 2008, 1(1), 2008–2008.

23.

Calafiore

Dabbene

Tempo

A survey of randomized algorithms for control synthesis and performance verification. J. Complexity, 2007, 23(3), 301–316.

24.

Girard

Reachability of uncertain linear systems using zonotopes. Hybrid systems: computation and control, 2005, vol. 3414. New York, Springer, 291–305. . Lecture Notes in Computer Science Series.