International Journal of Robust and Nonlinear Control

Research Article

A Liouvillian systems approach for the trajectory planning-based control of helicopter models

Corresponding Author

Hebertt Sira-Ramírez

[email protected]

CINVESTAV-IPN, Departamento de Ingeniería Eléctrica, Apartado Postal 14-740, 07300 México, D.F., México

CINVESTAV-IPN, Departamento de Ingeniería Eléctrica, Apartado Postal 14-740, 07300 México, D.F., México===Search for more papers by this author

Rafael Castro-Linares,

Rafael Castro-Linares

CINVESTAV-IPN, Departamento de Ingeniería Eléctrica, Apartado Postal 14-740, 07300 México, D.F., México

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Eduardo Licéaga-Castro,

Eduardo Licéaga-Castro

Department of Mathematics, Glasgow Caledonian University, Glasgow G4 OBA, Scotland, U.K.

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Hebertt Sira-Ramírez,

Corresponding Author

Hebertt Sira-Ramírez

[email protected]

CINVESTAV-IPN, Departamento de Ingeniería Eléctrica, Apartado Postal 14-740, 07300 México, D.F., México

CINVESTAV-IPN, Departamento de Ingeniería Eléctrica, Apartado Postal 14-740, 07300 México, D.F., México===Search for more papers by this author

Rafael Castro-Linares,

Rafael Castro-Linares

CINVESTAV-IPN, Departamento de Ingeniería Eléctrica, Apartado Postal 14-740, 07300 México, D.F., México

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Eduardo Licéaga-Castro,

Eduardo Licéaga-Castro

Department of Mathematics, Glasgow Caledonian University, Glasgow G4 OBA, Scotland, U.K.

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First published: 09 March 2000

https://doi.org/10.1002/(SICI)1099-1239(20000415)10:4<301::AID-RNC474>3.0.CO;2-Q

Citations: 19

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Abstract

A feedback regulation scheme, based on off-line trajectory planning and an approximate state linearization, is proposed for the hover-to-hover stabilization of simplified, underactuated, models of a helicopter system. The approach, based on the ‘Liouvillian’ character of the helicopter kinematic equations, advantageously uses the total, or partial, differential flatness property of the system models. The controller performance is evaluated through digital computer simulations which include initial state setting errors of significant magnitudes. Copyright © 2000 John Wiley & Sons, Ltd.

REFERENCES

1 Liceaga-Castro E, Bradley R, Castro-Linares R. Helicopter control design using feedback linearization techniques In Proceedings of the 28th IEEE Conference on Decision and Control, Tampa, FL, U.S.A., December 1989; 533–534.
Google Scholar
2 Fliess M. Generalized controller canonical forms for linear and nonlinear dynamics. IEEE Transactions on Automatic Control 1990; AC-35: 994–1001.
10.1109/9.58527
Web of Science® Google Scholar
3 Sira-Ramírez H, Zribi M, Ahmad S. Dynamic sliding mode control approach fora vertical flight regulation in helicopters. IEE Proceedings, Control Theory and Applications 1994; 141(1): 19–24.
10.1049/ip-cta:19949624
Web of Science® Google Scholar
4 van Nieuwstadt M, Murray RM. Outer flatness: trajectory generation for a model helicopter. Proceedings of the 1997 European Control Conference, ECC'97, (CD-Rom version), Brussels, Belgium, July 1997.
Google Scholar
5 Fliess M, Lévine J, Martín Ph, Rouchon P. Sur les systèmes nonlinéaires différentiellement plats 1992; I-315: 619–624.
Google Scholar
6 Fliess M, Lévine J, Martín Ph, Rouchon P. Flatness and defect of nonlinear systems: introductory theory and examples. International Journal of Control 1995; 61: 1327–1361.
10.1080/00207179508921959
Web of Science® Google Scholar
7 Fliess M, Lévine J, Martín Ph, Rouchon P. Lie–Bäcklund approach to dynamic feedback equivalence and flatness. In Lecture Notes in Control and Information Sciences, Vol. 247, pp. 247–268, F Garofalo, L Glielmo. (eds.). Springer: London, 1996.
Google Scholar
8 Thomson DG, Bradley R. Prediction of the dynamic characteristics of helicopters in Constrained flight. Aeronautica Journal of The Aeronautical Royal Society, December 1990.
Google Scholar
9 Thomson DG, Bradley R. Recent developments in the calculation of inverse dynamic solutions of the helicopter equations of motion. Proceedings of the U.K. Simulation Council Triennial Conference, September 1987.
Google Scholar
10 Mullhaupt P, Srinivasan B, Levine J, Bonvin D. A toy more difficult to control than the real thing. In Proceedings 1997 European Control Conference, ECC'97, (CD-Rom version), Brussels, Belgium, July 1997.
Google Scholar
11 Chelouah A. Extensions of differential flat fields and Liouvillian systems. Proceedings of the 36th Conference on Decision and Control, San Diego, CA, U.S.A., December 1997; 4268–4273.
Google Scholar
12 Martín Ph, Devasia S, Paden B. A different look at output tracking of a VTOL aircraft. Automatica 1996; 32(1): 101–107.
10.1016/0005-1098(95)00099-2
Web of Science® Google Scholar
13 Liceaga-Castro E. Dynamic analysis of an elementary rotor-craft: Part I. Technical Report PR/MAT/ELC/96–52, Department of Mathematics, Glasgow Caledonian University, Scotland, 1996.
Google Scholar
14 Bradley R. The flying brick exposed: nonlinear control of a basic helicopter model. Technical Report TR/MAT/RB/6, Department of Mathematics, Glasgow Caledonian University, Scotland, 1996.
Google Scholar
15 Chelouah A, Petitot M. Finitely discretizable nonlinear systems: concepts and definitions. Proceedings of the 34th IEEE Conference on Decision and Control, New Orleans, LA, U.S.A., December 1995; 19–24.
Google Scholar
16 Fliess M, Sira-Ramírez H, and Márquez-Contreras R. On the regulation of non-minimum phase outputs: a flatness based approach. In Perspectives in Control ( D Normand-Cyrot. ed.), Communications and Control Springer: London, 1998.
10.1007/978-1-4471-1276-1_11
Google Scholar
17 Charlet B, Levine J, Marino R. Sufficient conditions for dynamic state feedback linearization SIAM Journal of Control and Optimization 1991; 29: 38–57.
10.1137/0329002
Web of Science® Google Scholar
18 Rugh W. Linear System Theory ( 2nd Edn.), Prentice-Hall: Upper Saddle River, NJ, 1996.
Google Scholar
19 Cellier FM, Desoer ChA. Linear System Theory, Spinger Texts in Electrical Engineering, Springer: Berlin, 1991.
10.1007/978-1-4612-0957-7
Google Scholar

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Volume10, Issue4

Special Issue:CONTROL OF UNDERACTUATED NONLINEAR SYSTEMS

15 April 2000

Pages 301-320

A Liouvillian systems approach for the trajectory planning-based control of helicopter models

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A Liouvillian systems approach for the trajectory planning-based control of helicopter models

Abstract

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