Backstepping controllers for a cart-pole system in two configurations
Fernando Henrique Gomes Zucatelli1; Magno Enrique Mendoza Meza1
1 Universidade Federal do ABC
doi:10.20906/CPS/COB-2015-1292
Resumo
The cart-pole system is an underactuated system, and it has two possible configurations: (i) Gantry, it is an stable system, but under perturbation the system shows a strong swing; (ii) Inverted pendulum, it is an inherently unstable system. The system consist on a single rod mounted on a linear cart whose axis of rotation is perpendicular to the direction of motion of the cart, it is the Linear Motion Servo Plant of the Quanser. The backstepping is a recursive design procedure, which finds a Lyapunov function and a control law, that is called ``backstepping'', such that the system is asymptotically stable. The backstepping procedure is applied to both configurations and for linear and nonlinear models. The purposes of the backstepping are for both configurations tracking a defined trajectory (here is a square wave signal) for the cart with minimum swing of the pendulum. The cart-pole with minimum swang +-5 degrees while oscilation the cart position +-60 mm in 3 seconds and also tracking a desired trajectory. The linear controller was useful to understand the various possible behaviours according to the parameters set. The backstepping design procedure proved to be suitable for the control of the Quanser equipment for both models and both configurations. The design of the nonlinear control law for the nonlinear control is the most complex, but it is the most robust. The research project is to extend and improve the control law, wherefore this paper shows the first results. A way to improve the control is considering an adaptive backstepping control with optimal parameters.
Palavras-chave: Underactuated system; Cart-pole system; backstepping control