Swing-up controller synthesis of the cart-pendulum system using second order sliding modes

Orbital stabilization of an underactuated cartpendulum system is under study. The quasihomogeneous control synthesis is utilized to design a second order sliding mode controller that drives the actuated cart to a periodic reference orbit in finite time, while the non-actuated pendulum produces bounded oscillations. A modified Van der Pol oscillator is introduced into the synthesis as an asymptotic generator of the periodic motion. The resulting closed-loop system is capable of moving from one orbit to another by simply changing the parameters of the Van der Pol modification. Performance issues of the proposed synthesis are illustrated in an experimental study of the swing up/balancing control problem of moving a pendulum, located on an actuated cart, from its stable downward position to the unstable inverted position and stabilizing it about the vertical.