Real-time implementation and analysis of a modified energy based controller for the swing-up of an inverted pendulum on a cart

Abstract In this paper we derive a modified energy based swing-up controller using Lyapunov functions. During the derivation, all effort has been made to use a more complex dynamical model for the single inverted pendulum (SIP) system than the simplified model that is most commonly used. We consider the electrodynamics of the DC motor that drives the cart, and incorporate viscous damping friction as seen at the motor pinion. Furthermore, we use a new method to account for the limitation of having a cart-pendulum system with a finite track length. Two modifications to the controller are also discussed to make the method more appropriate for real-time implementation. One of the modifications improves robustness using a modified Lyapunov function for the derivation, while the other one incorporates viscous damping as seen at the pendulum axis. We present both simulation and real-time experimental results implemented in MATLAB Simulink.

[1]  Jun Zhao,et al.  Hybrid control for global stabilization of the cart-pendulum system , 2001, Autom..

[2]  David Angeli.  Almost global stabilization of the inverted pendulum via continuous state feedback , 2001, Autom..

[3]  Katsuhisa Furuta,et al.  Swinging up a pendulum by energy control , 1996, Autom..

[4]  Amit Patra,et al.  Swing-up and stabilization of a cart-pendulum system under restricted cart track length , 2002, Syst. Control. Lett..

[5]  Emese A. Kennedy,et al.  Real-Time Implementation of a Power Series Based Nonlinear Controller for the Balance of a Single Inverted Pendulum , 2014 .

[6]  Emese A. Kennedy,et al.  Swing-up and Stabilization of a Single Inverted Pendulum: Real-Time Implementation , 2015 .

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

[8]  Yu Peipei,et al.  Swinging-up and stabilization of the inverted pendulum by energy well and SDRE control , 2009, 2009 Chinese Control and Decision Conference.

[9]  Akira Yanou,et al.  Swing-up controller design for inverted pendulum by using energy control method based on Lyapunov function , 2010, Proceedings of the 2010 International Conference on Modelling, Identification and Control.

[10]  Chung Choo Chung,et al.  Nonlinear control of a swinging pendulum , 1995, Autom..

[11]  Olfa Boubaker,et al.  The Inverted Pendulum Benchmark in Nonlinear Control Theory: A Survey , 2013 .

[12]  Markus Schöberl,et al.  Applications of energy based control methods for the inverted pendulum on a cart , 2009, Robotics Auton. Syst..

[13]  Hien T. Tran,et al.  Real-Time Stabilization of a Single Inverted Pendulum Using a Power Series Based Controller , 2016 .