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Global stabilization for ball-and-beam systems via state and partial state feedback

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  • In this paper, we present new state and partial state feedback laws as global stabilizers of the well-known frictionless ball and beam system. Dealing with nonlinear terms in the manner different from the ones in the literature, we have achieved a new, simple state-dependent saturation control law. The key technique is to assign a suitable state-dependent saturation level function and jointly use the computation techniques of linear gains. Then, combining such a state feedback law with a homogeneous observer, we again obtain a new partial state feedback design.
    Mathematics Subject Classification: Primary: 93C10, 93D15; Secondary: 93D05.


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  • [1]

    D. Angeli and E. D. Sontag, Forward completeness, unboundedness observability, and their Lyapunov characterizations, Systems and Control Letters, 38 (1999), 209-217.doi: 10.1016/S0167-6911(99)00055-9.


    C. Barbu, R. Sepulchre, P. V. Kokotovic and W. Lin, Global asymptotic stabilization of the ball-and-beam model, in IEEE Conf. Decision Contr., San Diego, USA, (1997), 2351-2355.


    Y. H. Chang, C. W. Chang, C. W. Tao, H. W. Lin and J. S. Taur, Fuzzy sliding-mode controlfor ball and beam system with fuzzy ant colony optimization, Expert Systems with Applications, 39 (2012), 3624-3633.


    A. Chen, J. Cao and L. Huang, An estimation of upper bound of delays for global asymptotic stability of delayed Hopfield neural networks, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 49 (2002), 1028-1032.doi: 10.1109/TCSI.2002.800841.


    T. L. Chien, C. C. Chen, M. C. Tsai and Y. C. Chen, Control of AMIRA's ball and beam system via improved fuzzy feedback linearization approach, Applied Mathematical Modelling, 34 (2010), 3791-3804.doi: 10.1016/j.apm.2010.03.020.


    J. Hauser, S. Sastry and P. V. Kokotovic, Nonlinear control via approximate input-output linearization: The ball and beam example, IEEE Transactions on Automatic Control, 37 (1992), 392-398.doi: 10.1109/9.119645.


    Y. Hong, J. Huang and Y. Xu, On an output feedback finite-time stabilization problem, IEEE Transactions on Automatic Control, 46 (2001), 305-309.doi: 10.1109/9.905699.


    H. K. Khalil, Nonlinear Systems, Prentice Hall, New Jersey, 2002.


    X. Li and W. Yu, Synchronization of ball and beam systems with neural compensation, International Journal of Control, Automation, and Systems, 8 (2010), 491-496.


    W. Lin and X. Li, Synthesis of upper-triangular nonlinear systems with marginally unstable free dynamics using state-dependent saturation, Int. J. Control, 72 (1999), 1078-1086.doi: 10.1080/002071799220434.


    R. Ortega, M. W. Spong, F. Gomez-Estern and G. Blankenstein, Stabilization of a class of under-actuated mechanical system via interconnection and damping assignment, IEEE Transactions on Automatic Control, 47 (2002), 1218-1233.doi: 10.1109/TAC.2002.800770.


    C. Qian, Global output feedback stabilization of a class of upper-triangular nonlinear systems, in American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA, (2009), 3995-4000.


    S. Sastry, Nonlinear Systems: Analysis, Stability and Control, Springer, New York, 1999.doi: 10.1007/978-1-4757-3108-8.


    R. Sepulchre, Slow peaking and low-gain designs for global stabilization of nonlinear systems, IEEE Transactions on Automatic Control, 45 (2000), 453-461.doi: 10.1109/9.847724.


    R. Sepulchre, M. Jankovic and P. V. Kokotovic, Constructive Nonlinear Control, Springer, London, 1997.doi: 10.1007/978-1-4471-0967-9.


    E. D. Sontag, Remarks on stabilization and input-to-state stability, in IEEE Conf. Decision and Control, Tempa, FL, (1989), 1376-1378.


    A. R. Teel, Global stabilization and restricted tracking for multiple integrators with bounded controls, Systems and Control Letters, 18 (1992), 165-171.doi: 10.1016/0167-6911(92)90001-9.


    A. R. Teel, Semi-global stabilization of the ball and beam using output feedback, in American Control Conference, San Diego, CA, (1993), 2577-2581.


    H. Ye, H. Wang and H. B. Wang, Stabilization of a PVTOL aircraft and an inertia wheel pendulum using saturation technique, IEEE Transactions on Control Systems Technology, 15 ( 2007), 1143-1150.

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