A speed regulator for a force-driven cart-pole system

In this paper, we present a speed regulator for a force-driven cart-pole system. The proposed controller allows bringing the pole towards its upright position, while the cart moves asymptotically at desired constant speed, recovering the position regulation when we assign a desired constant position of the cart. The main motivation for addressing speed regulation is to broaden the scope of control of underactuated mechanical systems, because so far, the control of this class of mechanical systems has been focused primarily on position regulation; and therefore, there is few information and results available on broader control objectives, such as speed regulation. In particular, we design a speed regulator for the cart-pole system, as this system is one of the more representative test benches of underactuated mechanical system found in many automatic control research laboratories. Another novelty is the introduction of an alternative energy shaping approach for the velocity control design of a class of underactuated mechanical systems. A complete asymptotic stability analysis based on the Lyapunov theory and the Barbashin–Krasovskii theorem is presented. Local asymptotic stability is concluded. Simulation results upon a force-driven cart-pole model illustrate the performance of the proposed controller.

[1]  Arjan van der Schaft,et al.  Dynamics and control of a class of underactuated mechanical systems , 1999, IEEE Trans. Autom. Control..

[2]  Isaac Gandarilla,et al.  Control of a self-balancing robot with two degrees of freedom via IDA-PBC. , 2019, ISA transactions.

[3]  Kazunori Sakurama,et al.  Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations , 2001, Autom..

[4]  Romeo Ortega,et al.  Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment , 2002, IEEE Trans. Autom. Control..

[5]  D. Helms,et al.  The Control of Robot , 1975 .

[6]  Javier Moreno-Valenzuela,et al.  Motion Control of Underactuated Mechanical Systems , 2017 .

[7]  Alessandro Astolfi,et al.  Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one , 2004, Proceedings of the 2004 American Control Conference.

[8]  Reza Olfati-Saber,et al.  Normal forms for underactuated mechanical systems with symmetry , 2002, IEEE Trans. Autom. Control..

[9]  Rob Dekkers,et al.  Control of Robot Manipulators in Joint Space , 2005 .

[10]  Peter I. Corke,et al.  Nonlinear control of the Reaction Wheel Pendulum , 2001, Autom..

[11]  Naomi Ehrich Leonard,et al.  Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem , 2000, IEEE Trans. Autom. Control..

[12]  Rafael Kelly,et al.  Interconnection and damping assignment passivity‐based control of a class of underactuated mechanical systems with dynamic friction , 2011 .

[13]  Paul Kotyczka,et al.  Energy shaping for position and speed control of a wheeled inverted pendulum in reduced space , 2016, Autom..

[14]  R. Lozano,et al.  Stabilization of the inverted pendulum around its homoclinic orbit , 2000 .

[15]  M. Spong,et al.  Nonlinear Control of the Inertia Wheel Pendulum , 1999 .

[16]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[17]  Kazunori Sakurama,et al.  Trajectory Tracking Control of Nonholonomic Hamiltonian Systems via Generalized Canonical Transformations , 2004, Eur. J. Control.

[18]  Víctor Santibáñez,et al.  Interconnection and Damping Assignment Passivity–Based Control of an Underactuated 2–DOF Gyroscope , 2018, Int. J. Appl. Math. Comput. Sci..

[19]  Rogelio Lozano,et al.  Non-linear Control for Underactuated Mechanical Systems , 2001 .

[20]  Alessandro Astolfi,et al.  Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes , 2007, IEEE Transactions on Automatic Control.

[21]  V.M. Hernandez,et al.  A COMBINED SLIDING MODE‐GENERALIZED PI CONTROL SCHEME FOR SWINGING UP AND BALANCING THE INERTIA WHEEL PENDULUM , 2003 .

[22]  Yang Liu,et al.  Closed-loop tracking control of a pendulum-driven cart-pole underactuated system , 2008 .

[23]  Cheng-Chew Lim,et al.  Memory Output-Feedback Integral Sliding Mode Control for Furuta Pendulum Systems , 2020, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  R. Kelly,et al.  Control of the Inertia Wheel Pendulum by Bounded Torques , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[25]  Ricardo Campa,et al.  Joint position regulation of a class of underactuated mechanical systems affected by LuGre dynamic friction via the IDA-PBC method , 2020 .

[26]  Laxmidhar Behera,et al.  Swing-up control strategies for a reaction wheel pendulum , 2008, Int. J. Syst. Sci..

[27]  Rafael Kelly,et al.  Regulation of mechanisms with friction driven by brushed DC motors via IDA-PBC method , 2010, 49th IEEE Conference on Decision and Control (CDC).

[28]  Warren White,et al.  Control of nonlinear underactuated systems , 1999 .

[29]  Romeo Ortega,et al.  Energy Shaping of Mechanical Systems via PID Control and Extension to Constant Speed Tracking , 2016, IEEE Transactions on Automatic Control.

[30]  Mark W. Spong,et al.  Partial feedback linearization of underactuated mechanical systems , 1994, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'94).

[31]  Warren N. White,et al.  Direct Lyapunov approach for tracking control of underactuated mechanical systems , 2009, 2009 American Control Conference.