An experiment with swinging up a double pendulum using feedback control

E. S. Pyatnitskii, “Control Design for Manipulating Robots Based on Decomposition Principle,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 3 (1987).

E. S. Pyatnitskii, “Decomposition Principle for the Control of Mechanical Systems,” Dokl. Akad. Nauk SSSR 300(2) (1988).

V. I. Matyukhin and E. S. Pyatnitskii, “Motion Control of Manipulating Robots Based on Decomposition Principle with Regard to Drive Dynamics,” Avtom. Telemekh., No. 9 (1989).

F. L. Chernous’ko, “Decomposition and Suboptimal Control in Dynamical Systems,” J. Appl. Math. Mech. 54, 727–734 (1990).

F. L. Chernous’ko, “Control Synthesis in a Non-Linear Dynamical System,” J. Appl. Math. Mech. 56, 157–166 (1992).

I. M. Anan’evskii, “Two Approaches to Controlling a Mechanical System with Unknown Parameters,” J. Comput. Syst. Sci. Int. 40, 203–211 (2001).

S. A. Reshmin and F. L. Chernous’ko, “Synthesis of a Control in a Non-Linear Dynamical System Based on Decomposition,” J. Appl. Math. Mech. 62, 115–122 (1998).

N. N. Krasovskii, Rendezvous Game Problems (Nauka, Moscow, 1970; National Technical Information Service, Springfield, Virginia, 1971).

S. A. Reshmin, “The Decomposition Method for a Control Problem for an Underactuated Lagrangian System,” J. Appl. Math. Mech. 74, 108–121 (2010).

S. A. Reshmin, “Decomposition Method in the Problem of Controlling an Inverted Double Pendulum with the Use of One Control Moment,” J. Comput. Syst. Sci. Int. 44, 861–877 (2005).

A. M. Formal’skii, “On Stabilization of an Inverted Double Pendulum with One Control Torque,” J. Comput. Syst. Sci. Int. 45, 337–344 (2006).

A. M. Formal’skii, “Global Stabilization of a Double Inverted Pendulum with Control at the Hinge between the Links,” Mech. Solids 43, 687–697 (2008).

Ya. Aoustin, A. M. Formal’skii, and Yu. Martynenko, “Stabilisation of Unstable Equilibrium Postures of a Two-Link Pendulum Using a Flywheel,” J. Comput. Syst. Sci. Int. 45, 204–211 (2006).

I. F. Schaefer and R. F. Cannon, “On the Control of Unstable Mechanical Systems,” in IFAC 3rd Congress, London, 1996.

P. Absil and R. Sepulchre, “A Hybrid Control Scheme for Swing-Up Acrobatics,” in Proc. 5th European Control Conf., Porto, Portugal, 2001.

I. Fantoni, R. Lozano, and M. W. Spong, “Energy Based Control of the Pendubot,” IEEE Trans. Autom. Contr. 45 (2000).

J. Rubi, A. Rubio, and A. Avello, “Swing-Up Control Problem for a Self-Erecting Double Inverted Pendulum,” IEE Proc. Control Theory Appl. 149 (2002).

R. G. Sanfelice and A. R. Teel, “A “Throw-and-Catch” Hybrid Control Strategy for Robust Global Stabilization of Nonlinear Systems,” in Proc. 26th American Control Conf., New York, 2007.

A. M. Formalskii, “Stabilization of Unstable Mechanical Systems,” JOTA 144(2) (2010).

Ya. Aoustin, A. Formal’skii, and Yu. Martynenko, “Pendubot: Combining of Energy and Intuitive Approaches to Swing Up, Stabilization in Erected Pose,” Multibody Syst. Dyn. 25(1) (2011).

V. E. Palosh, “Investigation of the Dynamics of a Double Pendulum with Following and Conservative Forces,” J. Comput. Syst. Sci. Int., 47, 386–296 (2008).

P. D. Krut’ko and V. E. Palosh, “Stabilizing Equilibrium States of Double Pendulum Loaded by Follower and Conservative Forces,” J. Comput. Syst. Sci. Int. 48, 165–178 (2009).

J. Awrejcewicz, G. Kudra, and G. Wasilewski, “Chaotic Zones in Triple Pendulum Dynamics Observed Experimentally and Numerically,” Appl. Mech. Materials 9 (2008).

J. Awrejcewicz, G. Kudra, and G. Wasilewski, “Experimental Observations and Simulations of a Triple Physical Pendulum,” in Proc. 1st Polish Congress of Mechanics, Warsaw, 2007.

J. Awrejcewicz, S. A. Reshmin, G. Wasilewski, et al., “Swing Up a Double Pendulum by Simple Feedback Control,” in Proc. 6th EUROMECH Oscillations Conf., St. Petersburg, 2008.