×

Finite-time observer-based backstepping control of a flexible launch vehicle. (English) Zbl 1400.93100

Summary: In this paper, a longitudinal model of a space launch vehicle was developed using the Lagrange mechanism and a free-free Euler-Bernoulli beam model. The aim was to propose a model including one flexible mode plus a nonlinear aerodynamic coefficient for nonlinear control design. We then studied the output feedback problem raised by using such a nonlinear model. The main achievement is to propose a new finite-time state observer when the measured outputs are corrupted by an unidentified flexible mode. This effect may destabilize a classical backstepping control law applied to the rigid model. To achieve this, a backstepping control law was redesigned to damp out the flexible mode, once measured and characterized. Hence a new adaptive finite time observer was developed. Closed-loop simulations show the effectiveness of the observer in combination with a redesigned backstepping control law when sensors and the launcher nozzle are collocated.

MSC:

93C10 Nonlinear systems in control theory
93C40 Adaptive control/observation systems
PDFBibTeX XMLCite
Full Text: DOI HAL

References:

[1] Adetola V and Guay M (2006) Excitation signal design for parameter convergence in adaptive control of linearizable systems. In: Proceedings of the 45th IEEE conference on decision and control, San Diego, CA, pp.447-452.
[2] Adetola, V, Guay, M (2008) Finite-time parameter estimation in adaptive control of nonlinear systems. IEEE Transactions on Automatic Control 53(3): 807-811. · Zbl 1367.93295
[3] Arcak, M, Kokotovic, PV (2000) Robust nonlinear control of systems with input unmodeled dynamics. Systems & Control Letters 41(2): 115-122. · Zbl 0985.93050
[4] Ahmed-Ali, T, Lamnabhi Lagarrigue, F (1999) Sliding observer-controller design for uncertain triangular nonlinear systems. IEEE Transactions on Automatic Control 4(6): 1244-1249. · Zbl 0955.93006
[5] Boiffier, JL (1998) The Dynamics of Flight: The Equations, Hoboken, NJ: Wiley.
[6] Burlion L, Duraffourg E, Ahmed-Ali T, et al. (2013) Global asymptotic stabilization for some nonlinear models of flexible aerospace vehicles. In: Proceedings of the 52nd IEEE conference on decision and control, Florence, Italy, pp.4230-4235.
[7] Clement B (2001) Multiobjective synthesis and gain scheduling: Application to an aerospace launcher guidance. PhD Dissertation, University of Paris XI, Orsay, France.
[8] Clement B, Duc G and Mauffrey S, et al. (2001) Gain scheduling for an aerospace launcher with bending modes. In: Proceedings of the 15th IFAC symposium on automatic control in aerospace, Bologna, Italy, pp.475-480.
[9] De Luca, A (2015) Flexible robots. In: Baillieul, J, Samad, T (eds) Encyclopedia of Systems and Control, London: Springer, pp. 451-458. .
[10] Duraffourg E, Burlion L, Ahmed-Ali T, et al. (2013) Non-linear control of the longitudinal rotational dynamics of a flexible aircraft. In: Proceedings of the 12th European control conference, Zürich, Switzerland, pp.335-340.
[11] Duraffourg E, Burlion L, Ahmed-Ali T, et al. (2013) Non-linear full-state control of a flexible hypersonic vehicle. In: Proceedings of the 11th IEEE international workshop on electronics control measurement signals and their application to mechatronics, Toulouse, France.
[12] Duraffourg E, Burlion L and Ahmed-Ali T (2013) Longitudinal modeling and preliminary control of a non-linear flexible launch vehicle. In: Proceedings of the 11th IFAC international workshop on adaptation and learning in control and signal processing, Caen, France.
[13] Duraffourg E, Burlion L, Ahmed-Ali T, et al. (2014) Adaptive finite-time observer for a nonlinear and flexible space launch vehicle. In: Proceedings of 19th world congress of the international federation of automatic control, Cape Town, South Africa, pp.546-551.
[14] Engel, R, Kreisselmeier, G (2002) A continuous-time observer which converges in finite time. IEEE Transactions on Automatic Control 47(7): 1202-1204. · Zbl 1364.93084
[15] Fiorentini, L, Serrani, A, Bolender, MA (2009) Nonlinear robust adaptive control of flexible air-breathing hypersonic vehicles. Journal of Guidance, Control and Dynamics 32(2): 401-416.
[16] Fliess, M, Sira-Ramirez, H (2003) An algebraic framework for linear identification. ESAIM Control, Optimisation and Calculus of Variations 9: 151-168. · Zbl 1063.93014
[17] Frosch, JA, Vallely, DP (1967) Saturn AS-501/S-IC flight control system design. Journal of Spacecraft 4(8): 1003-1009.
[18] Hervas JR and Reyhanoglu M (2012) Control of a spacecraft with time-varying propellant slosh parameters. In: Proceedings of the 12th international conference on control automation and systems, Jeju Island, Korea.
[19] Hu, Q (2009) Robust adaptive backstepping attitude and vibration control with L2-gain performance for flexible spacecraft under angular velocity constraint. Journal of Sound and Vibration 327(3-5): 285-298.
[20] Hu, X, Wu, L, Hu, C (2012) Adaptive sliding mode tracking control for a flexible air-breathing hypersonic vehicle. Journal of the Franklin Institute 349(2): 559-577. · Zbl 1254.93044
[21] Karafyllis, I, Jiang, ZP (2011) Hybrid dead-beat observers for a class of nonlinear systems. Systems and Control Letters 60: 608-617. · Zbl 1236.93030
[22] Khalil, H (1996) Nonlinear Systems, Upper Saddle River, NJ: Prentice Hall.
[23] Menold PH, Findeisen R and Allgöwer F (2003) Finite time convergent observers for nonlinear systems. In: Proceedings of the 42nd IEEE conference on decision and control, Maui, HI, pp.5673-5678.
[24] Olfati-Saber R (2000) Trajectory tracking for a flexible one-link robot using a nonlinear noncollocated output. In: Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, pp.4024-4029.
[25] Pan, H, Sun, W, Gao, H (2015a) Disturbance observer-based adaptive tracking control with actuator saturation and its application. IEEE Transactions in Automation Science and Engineering 99: 1-8.
[26] Pan, H, Sun, W, Gao, H (2015b) Finite-time stabilization for vehicle active suspension systems with hard constraints. IEEE Transactions on Intelligent Transportation Systems 16(5): 2663-2672.
[27] Perruquetti, W, Floquet, T, Moulay, E (2008) Finite-time observers: Application to secure communication. IEEE Transactions on Automatic Control 53(1): 356-360. · Zbl 1367.94361
[28] Preumont, A (2011) Vibration Control of Active Structures: An Introduction, 3rd ed. Berlin, Germany: Springer. · Zbl 1273.74002
[29] Spector, VA, Flashner, H (1990) Modelling and design implications of non-collocated control in flexible systems. ASME Journal of Dynamics Systems, Measurement and Control 11: 186-193.
[30] Spong MW (1996) Energy based control of a class of underactuated mechanical systems. In: Proceedings of the IFAC world congress, San Francisco, CA, pp.431-436.
[31] Shtessel, YB, Baev, S, Edwards, C (2010) HOSM observer for a class of nonminimum phase causal nonlinear MIMO systems. IEEE Transactions on Automatic Control 55(2): 543-548. · Zbl 1368.93058
[32] Shtessel YB, Hall CE, Baev S, et al. (2010) Flexible modes control using sliding mode observers: Application to Ares I. In: Proceedings of the AIAA guidance, navigation and control conference, Canada, Toronto.
[33] Sun, W, Pan, H, Gao, H (2016) Filter-based adaptive vibration control for active vehicle suspensions with electro-hydraulic actuators. IEEE Transactions in Vehicular Technology 65(6): 4619-4626.
[34] Yu P, Shtessel Y and Edwards C (2015) Adaptive continuous higher order sliding mode control of air breathing hypersonic missile for maximum target penetration. In: AIAA guidance, navigation, and control conference.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.