Nonlinear Control Design of 360-Degree Inverted Pendulum Systems

This paper develops a nonlinear backstepping design scheme for the control of a 360-degree inverted pendulum system. In this system, the friction between the cart and the rail is considered to approach the actual physical system. The 360-degree inverted pendulum system is divided into two zones according to angles of pendulum. The pendulum angle is defined to be zero if it is upright. Then we say that the system is inside the stabilization zone if the angle magnitude is not greater than one radian. Otherwise, the pendulum system stays in the swing-up zone. Our nonlinear design shows that the controller will successfully swing up the pendulum from downward position to upright position and centre the cart on the rail. The backstepping design scheme is employed to obtain a nonlinear controller to swing up the pendulum into the stabilization zone. As long as the pendulum reaches the stabilization zone, a linear controller designed by backstepping method will be switched to achieve the desired control objectives.

[1]  Rey-Chue Hwang,et al.  A self-tuning PID control for a class of nonlinear systems based on the Lyapunov approach , 2002 .

[2]  A. Benaskeur,et al.  Application of adaptive backstepping to the stabilization of the inverted pendulum , 1998, Conference Proceedings. IEEE Canadian Conference on Electrical and Computer Engineering (Cat. No.98TH8341).

[3]  R. Olfati-Saber.  Fixed point controllers and stabilization of the cart-pole system and the rotating pendulum , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[4]  Akira Ohsumi,et al.  Nonlinear control of swing-up and stabilization of an inverted pendulum , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[5]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[6]  Ali Saberi,et al.  Linear controller for an inverted pendulum having restricted travel: A high-and-low gain approach , 1996, Autom..

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

[8]  L. Praly,et al.  Adding integrations, saturated controls, and stabilization for feedforward systems , 1996, IEEE Trans. Autom. Control..

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

[10]  Shiuh-Jer Huang,et al.  Control of an inverted pendulum using grey prediction model , 1994, Proceedings of 1994 IEEE Industry Applications Society Annual Meeting.

[11]  A. Megretski,et al.  Controller design for a class of underactuated nonlinear systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).