A swinging up controller for the Furuta pendulum based on the Total Energy Control System approach

Rodríguez-Cortés, H.

Kybernetika, Tome 55 (2019) no. 2, pp. 402-421

Abstract (VO)

This paper considers the problem of swinging up the Furuta pendulum and proposes a new smooth nonlinear swing up controller based on the concept of energy. This new controller results from the Total Energy Control System (TECS) approach in conjunction with a linearizing feedback controller. The new controller commands to the desired reference the total energy rate of the Furuta pendulum; thus, the Furuta pendulum oscillates and reaches a neighborhood of its unstable configuration while the rotation of its base remains bounded. Once the Furuta pendulum configuration is in the neighborhood of its unstable equilibrium point, a linear controller stabilizes the unstable configuration of the Furuta pendulum. Real-time experiments are included to support the theoretical developments.

Détail

DOI : 10.14736/kyb-2019-2-0402

Classification : 93C10, 93C15
Keywords: total energy control system; Furuta pendulum; swinging up control; real-time experiments

Bibliographie

[1] Aguilar-Avelar, C., Moreno-Valenzuela, J.: New feedback linearization-based control for arm trajectory tracking of the furuta pendulum. IEEE/ASME Trans. Mechatron. 21 (2016), 2, 638-648. | DOI

[2] Angeli, D.: Almost global stabilization of the inverted pendulum via continuous state feedback. Automatica 37 (2001), 7, 1103-1108. | DOI

[3] Aracil, J., Acosta, J. A., Gordillo, F.: A nonlinear hybrid controller for swinging-up and stabilizing the furuta pendulum. Control Engrg. Practice 21 (2013), 8, 989-993. | DOI

[4] Aström, K. J., Furuta, K.: Swinging up a pendulum by energy control. Automatica 36 (2002), 2, 287-295. | DOI | MR

[5] Azar, A. T., Serrano, F. E.: Adaptive Sliding Mode Control of the Furuta Pendulum. Springer International Publishing, Cham 2015, pp. 1-42. | DOI

[6] Bhat, S. P., Bernstein, D. S.: A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon. Systems Control Lett. 39 (2000), 1, 63-70. | DOI | MR

[7] Bloch, A. M., Leonard, N. E., Marsden, J. E.: Stabilization of the pendulum on a rotor arm by the method of controlled lagrangians. In: Proc. IEEE International Conference on Robotics and Automation 1999, Vol. 1, IEEE 1999, pp. 500-505. | DOI

[8] Dorf, R. C., Bishop, R. H.: Modern Control Systems. Pearson, 2011.

[9] Gluck, T., Eder, A., Kugi, A.: Swing-up control of a triple pendulum on a cart with experimental validation. Automatica 49 (2013), 3, 801-808. | DOI | MR

[10] Gordillo, F., Acosta, J. A., Aracil, J.: A new swing-up law for the furuta pendulum. Int. J. Control 76 (2003), 8, 836-844. | DOI | MR

[11] Graichen, K., Treuer, M., Zeitz, M.: Swing-up of the double pendulum on a cart by feedforward and feedback control with experimental validation. Automatica 43 (2007), 1, 63-71. | DOI | MR

[12] Hera, P. X. La, Freidovich, L. B., Shiriaev, A. S., Mettin, U.: New approach for swinging up the furuta pendulum: Theory and experiments. Mechatronics 19 (2009), 8, 1240-1250. | DOI

[13] Horibe, T., Sakamoto, N.: Optimal swing up and stabilization control for inverted pendulum via stable manifold method. IEEE Trans. Control Systems Technol. 26 (2918), 2, 708-715. | DOI

[14] Inc., Quanser Consulting: Qube servo, 2015. accessed: 2015-06-30.

[15] Koditschek, D. E.: The application of total energy as a lyapunov function for mechanical control systems. Contemporary Math. 97 (1989), 131. | DOI | MR

[16] Lambregts, A. A.: Integrated system design for flight and propulsion control using total energy principles. In: American Institute of Aeronautics and Astronautics, Aircraft Design, Systems and Technology Meeting, Fort Worth 17 (1983). | DOI

[17] Lambregts, A. A.: Vertical flight path and speed control autopilot design using total energy principles. AIAA 83-2239 (1983). | DOI

[18] Lee, J., Mukherjee, R., Khalil, H. K.: Output feedback stabilization of inverted pendulum on a cart in the presence of uncertainties. Automatica 54 (2015), 146-157. | DOI | MR

[19] Lee, T., Leok, M., McClamroch, H.: Geometric formulations of furuta pendulum control problems. Math. Engrg., Science and Aerospace (MESA) 7 (2016), 1.

[20] Lozano, R., Fantoni, I., Block, D. J.: Stabilization of the inverted pendulum around its homoclinic orbit. Systems Control Lett. 40 (2000), 3, 197-204. | DOI | MR

[21] Mazenc, F., Praly, L.: Adding integrations, saturated controls, and stabilization for feedforward systems. IEEE Trans. Automat. Control 41 (1996), 11, 1559-1578. | DOI | MR

[22] Olfati-Saber, R.: Fixed point controllers and stabilization of the cart-pole system and the rotating pendulum. In: Proc. 38th IEEE Conference on Decision and Control 1999, Vol. 2, pp. 1174-1181. | DOI

[23] Olfati-Saber, R.: Normal forms for underactuated mechanical systems with symmetry. IEEE Trans. Automat. Control 47 (2002), 2, 305-308. | DOI | MR

[24] Ortega, T., Villafuerte, R., Vázquez, C., Freidovich, L.: Performance without tweaking differentiators via a pr controller: Furuta pendulum case study. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 3777-3782. | DOI | MR

[25] Prasad, L. B., Tyagi, B., Gupta, H. O.: Optimal control of nonlinear inverted pendulum system using pid controller and lqr: Performance analysis without and with disturbance input. Int. J. Automat. Computing 11 (2014), 6, 661-670. | DOI

[26] Seman, P., Rohal-Ilkiv, B., Salaj, M., al., et: Swinging up the furuta pendulum and its stabilization via model predictive control. J. Electr. Engrg. 64 (2013), 3, 152-158. | DOI

[27] Shiriaev, A. S., Freidovich, L. B., Robertsson, A., Johansson, R., Sandberg, A.: Virtual-holonomic-constraints-based design of stable oscillations of furuta pendulum: Theory and experiments. IEEE Trans. Robotics 23 (2007), 4, 827-832. | DOI | MR

[28] Schaft, A. van der: Port-hamiltonian systems: an introductory survey. In: Proc. International Congress of Mathematicians (M. Sanz-Sole, J. Soria, J.L. Varona, and J. Verdera, eds.), Vol. III: Invited Lectures, Mathematical Society Publishing House, pp. 1339-1365, Madrid 2006. | DOI | MR

[29] Vásquez-Beltrán, M. A., Rodríguez-Cortés, H.: A total energy control system strategy for the quadrotor helicopter. In: International Conference on Unmanned Aircraft Systems 2015. | DOI