Abstract

A combination between an adaptive sliding mode observer and a backstepping sliding mode controller is designed for a Lipschitz nonlinear system. This combination guaranties the tracking of trajectory, estimation of both the unmeasured state and the unknown parameters. A parameter variation margin is defined for that the combination is robust. The simulation results prove the combination robustness when the parameters are constants or varied in a defined margin.

References

• A. Benallegue, A. Mokhtari and L. Fridman “High-order sliding-mode observer for a quadrotor UAV” International Journal of Robust and Nonlinear Control, 2007
• M. Bahrami, B. Ebrahimi and G. R. Ansarifar “Sliding Mode Observer and Control Design with Adaptive Parameter Estimation for a Supersonic Flight Vehicle” International Journal of Aerospace Engineering, 2010
• Saadaoui,H.,De leon,J.,djemai,M. and Barbo,J.P “High order sliding mode and adaptive observers for a class of switched systems with unknown parameter : A comparative study” Proceeding of the 45th IEEE conference on decision and control, December 13-15,San diego ,CA , USA, 2006.
• Elleuch,D.and Damak,T “Adaptive sliding mode observer for Lipchitz nonlinear systems with varying parameters” 10th International conference on Sciences and Techniques of Automatic control & computer engineering, December 20-22, Hammamet, Tunisia, 2009, pp.1821–1833.
• Antonio Ficola, Michele La Cava “A sliding mode controller for a two-joint robot with an elastic link” Mathematics and Computers in Simulation , vol 41, 1996, pp: 559-569
• Ming Chang Pai “Design of adaptive sliding mode controller for robust tracking and model following” Journal of the Franklin Institute vol 347, 2010, pp:1837–1849
• K B Mohanty “A Fuzzy Sliding Mode Controller for a Field-Oriented Induction Motor Drive” Journal of the institution of engineers (India) vol 86,2005, pp:160-165
• S. Laghrouche, F. Plestan and A. Glumineau “A higher order sliding mode controller for a class of MIMO nonlinear systems: application to PM synchronous motor control” Proceeding in the American control conference Boston Massachusetts, June 30-July 2 , 2004.
• A.Ferrara, L.Giacomini “On modular backstepping design with second order sliding modes” Automatica, vol 37, 2001, pp: 129-135.
• Chia-Hua Lua, Yean-Ren Hwanga, Yu-Ta Shena “Backstepping sliding mode tracking control of a vane-type air motor X–Y table motion system” ISA Transactions, 2010
• A.J. Koshkouei, K. Burnham and A.Zinober ”Modern Sliding Mode Control Theory”, Springer-Verlag Berlin Heidelberg,pp:269-290, 2008
• Jing Zhou, ChangyunWen “Adaptive Backstepping Control of Uncertain Systems Nonsmooth Nonlinearities, Interactions or Time-Variations” Lecture Notes in Control and Information Sciences, Springer-Verlag Berlin Heidelberg, 2008
• K.C. Veluvolu, Y.C. Soh “ nonlinear sliding mode state and unknown input estimations : a new perspective” Proceeding of the international conference on advances control and optimization of dynamical systems, 2007
• A.M. Pertew H.J. Marquez and Q. Zhao “design of unknown input observers for Lipschitz nonlinear systems” American control conference, USA, June 8-10, 2005.
• J.M. Daly, D.W.L. Wang “ output feedback sliding mode control in the presence of unknown disturbances” systems and control letters vol 58, 2009, pp:188-193.
• P. Batista, C. Silvestre and P. Oliveira “ observer design for a class of kinematic systems” proceeding of the 46th IEEE conference on decision and control, New Orleans, L.A, USA, Dec. 12-14, 2007.
• H.L.Choi, J.T.Lim “Output feedback stabilization for a class of lipschitz nonlinear systems” The institute of electronics, information and communication engineers trans. fundamentals, vol. E88-A, N°2, February 2005.
• P.R.Pagilla and Y.Zhu “controller and observer design for Lipschitz nonlinear systems” Proceeding of the American control conference, Boston Massachusetts, June 30-July 2, 2004.
• H.Saadaoui, De leon, M.djemai, J.P Barbo “High order sliding mode and adaptive observers for a class of switched systems with unknown parameter: A comparative study’’. Proceeding of the 45th IEEE conference on decision and control san diego ,CA , USA. December 13-15 2006.
• Y. M. Cho and R.Rajamani “A systematic approach to adaptive synthesis for nonlinear systems” IEEE 1995 pp 478-482