Lyapunov-based controller for the inverted pendulum cart system

Nonlinear Dynamics

Volumn 40, Issue 4, 2005, Pages 367-374

  Ibañez, Carlos Aguilar ^a   Frias, O Gutiérrez ^a   Castañón, M Suárez ^a  

^a INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

Author keywords

Lyapunov based control; Nonlinear systems; Under actuated system

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; COMPUTER SIMULATION; CONTROL EQUIPMENT; CONTROL THEORY; LINEARIZATION; LYAPUNOV METHODS; MATHEMATICAL MODELS; PENDULUMS;

INVERTED PENDULUM CART SYSTEM (IPCS); LYAPUNOV-BASED CONTROL; LYAPUNOV-BASED CONTROLLER; UNDER-ACTUATED SYSTEM;

NONLINEAR SYSTEMS;

EID: 18744388846     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-005-7290-y     Document Type: Article

References (17)

1. Lozano, R., Fantoni, I., and Block, D. J., 'Stabilization on the inverted pendulum around its homoclinic orbit', System & Control Letters (40) 3, 2000, 197-204.
2. Olfati-Saber, R., 'Fixed point controllers and stabilization of the cart-pole and rotating pendulum', in Proceedings of the 38th Conference on Decision and Control, Phoenix, AZ, December 7-10, 1999, pp. 1174-1181.
3. Bloch, A. M., Leonard, N. E., and Marsden, J. E., 'Controlled lagrangians and the stabilization of mechanical systems: The first matching theorem', IEEE Transactions on Systems and Control 45, 2001, 2253-2270.
4. Furuta, K., Yamakita, M., and Kobayashi, S., 'Swing up control of inverted pendulum using pseudo-state feedback', Journal of System and Control Engineering 206, 2001, 263-269.
5. Asrom, K. J. and Furuta, K., 'Swinging up a pendulum by energy control', Automatica 36(2), 2000, 287-295.
6. Chung, C. C. and Hauser, J., 'Nonlinear control of a swinging pendulum', Automatica 31(6), 1995, 851-862.
7. Jakubczyk, B. and Respondek, W., 'On the linearization of control systems', Bulletin of the Academy of Poland Science and Mathematics 28, 1980, 517-522.
8. Shiriaev, A. S. and Fradkov, A. L., 'Stabilization of invariant sets of nonlinear systems with applications to control of oscillations', International Journal of Robust and Nonlinear Control 11, 2001, 215-240.
9. Kwakemaak, H. and Sivan R., Linear Optimal Control Systems, Wiley, New York, 1972.
10. Spong, M. W. and Praly, L., 'Control of underactuated mechanical systems using switching and saturation', in Proceedings of the Block Island Workshop on Control Using Logic Based Switching, Springer-Verlag, Berlin, 1996.
11. Spong, M. W., 'Energy-based control of aclass of underactuated mechanical systems', in IFAC World Congress, San Francisco, CA, July, 1996.
12. Olfati-Saber, R., 'Nonlinear control of underactuated mechanical systems with applications to robotic and aerospace vehicles', PhD Thesis, Department of Electrical Engineering and Computer Science of the Massachusetts Institute of Technology, Cambridge, MA, 2001.
13. Fantoni, I. and Lozano, R., Nonlinear Control for Underactuated Mechanical System, Springer-Verlag, London, 2002.
14. Sepulchre, R., Jankovíc, M., and Kokotovíc, P., Constructive Nonlinear Control, Springer-Verlag, London, 1997.
15. Khalil, H. K., Nonlinear Systems, 2nd edn., Prentice-Hall, Englewoods Cliffs, NJ, 1996.
16. Bloch, A. M., Leonard, N. E., and Marsden, J. E., 'Potential shaping and the method of controlled lagrangians', in Proceedings of the 38th Conference on Decision and Control, Phoenix, AZ, December 7-10, 1999, pp. 1652-1657.
17. Mazenc, F. and Praly, L., 'Adding integrations, saturated controls, and stabilization for feedforward systems', IEEE Transactions on Automation Control 41, 1996, 1559-1578.