Felipe Beltrán | Institute of Technology, Ciudad Obregón |
David Vázquez | Institute of Technology, Ciudad Obregón |
Daniel Quintana | Institute of Technology, Ciudad Obregón |
Miguel Bernal | Institute of Technology, Ciudad Obregón |
Victor Estrada-Manzo | Universidad Polit´ecnica de Pachuca |
https://doi.org/10.58571/CNCA.AMCA.2022.028
Resumen: Discontinuous observer-based convex control of an underactuated rotatory system, better known as the Furuta pendulum, is the subject of this report. It is shown that a slight generalization of the traditional discontinuous observer design allows applying it to the referred plant. Since the observer gains are obtained via linear matrix inequalities and convex rewriting of nonlinear terms, convex control comes at hand as a better fit to drive the system to the upright position. Simulation and real-time results are presented which prove the effectiveness of the proposal.
¿Cómo citar?
Felipe Beltrán, David Vázquez, Daniel Quintana, Miguel Bernal & Victor Estrada-Manzo. Memorias del Congreso Nacional de Control Automático, pp. 115-120, 2022. https://doi.org/10.58571/CNCA.AMCA.2022.028
Palabras clave
Control de Sistemas No Lineales; Control Robusto; Control Discontinuo (modos deslizantes)
Referencias
- Angeli, D. (2001). Almost global stabilization of the inverted pendulum via continuous state feedback. Automatica, 37(7), 1103–1108.
- Begovich, O., Sanchez, E.N., and Maldonado, M. (2002). Takagi-Sugeno fuzzy scheme for real-time trajectory tracking of an underactuated robot. IEEE Transactions on Control Systems Technology, 10(1), 14–20.
- Bernal, M., Sala, A., Lendek, Z., and Guerra, T. (2022). Analysis and Synthesis of Nonlinear Control Systems: A convex optimsation approach. Springer, Cham.
- Boyd, S., Ghaoui, L.E., Feron, E., and Belakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, volume 15. SIAM: Studies In Applied Mathematics, Philadelphia, USA.
- Edwards, C. and Spurgeon, S. (1994). On the development of discontinuous observers. International Journal of Control, 59(5), 1211–1229.
- Edwards, C. and Spurgeon, S. (1998). Sliding mode control: theory and applications. Crc Press.
- Farwig, M., Zu, H., and Unbehauen, H. (1990). Discrete computer control of a triple-inverted pendulum. Optimal Control Applications and Methods, 11(2), 157–171.
- Furuta, K., Kajiwara, H., and Kosuge, K. (1980). Digital control of a double inverted pendulum on an inclined rail. International Journal of control, 32(5), 907–924.
- Furuta, K., Yamakita, M., and Kobayashi, S. (1992). Swing-up control of inverted pendulum using pseudostate feedback. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 206(4), 263–269.
- Gahinet, P., Nemirovski, A., Laub, A.J., and Chilali, M. (1995). LMI Control Toolbox. Math Works, Natick, USA.
- Quanser, I. (2006). Mechatronics Control Kit User’s Manual (Instructor). Mathworks, inc, Natick, MA.
- Quintana, D., Estrada-Manzo, V., and Bernal, M. (2020). An exact handling of the gradient for overcoming persistent problems in nonlinear observer design via convex optimization techniques. Fuzzy Sets and Systems.
- Spong, M.W., Corke, P., and Lozano, R. (2001). Nonlinear control of the reaction wheel pendulum. Automatica, 37(11), 1845–1851.
- Sturm, J. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11-12, 625–653.
- Tanaka, K. and Wang, H. (2001). Fuzzy Control Systems Design and Analysis: A linear matrix inequality approach. John Wiley & Sons, New York.
- Taniguchi, T., Tanaka, K., and Wang, H. (2001). Model construction, rule reduction and robust compensation for generalized form of Takagi-Sugeno fuzzy systems. IEEE Transactions on Fuzzy Systems, 9(2), 525–537.
- Vázquez, D., Arceo, J., M´arquez, R., Estrada-Manzo, V., and Bernal, M. (2016). Lmi-based nonlinear control of the furuta pendulum. In Congreso Nacional de Control Automático, 122–127.
- Walcott, B. and Zak, S. (1987). State observation of nonlinear uncertain dynamical systems. IEEE Transactions on Automatic Control, 32(2), 166–170.
- Walcott, B., Corless, M.J., and ˙Zak, S. (1987). Comparative study of non-linear state-observation techniques. International Journal of Control, 45(6), 2109–2132.
- Walcott, B.L. and Zak, S.H. (1988). Combined observercontroller synthesis for uncertain dynamical systems with applications. IEEE Transactions on systems, man, and cybernetics, 18(1), 88–104.
- Wang, H., Tanaka, K., and Griffin, M. (1996). An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Transactions on Fuzzy Systems, 4(1), 14–23.