Fuzzy sliding mode control for inverted pendulum swing-up with restricted travel

Swinging up an inverted pendulum is a common benchmark task for the investigation of automatic control techniques. In this paper we introduce a new Fuzzy Sliding Mode (FSM) technique for swinging-up an inverted pendulum and controlling the connected cart, while minimizing the swing-up time, the cart travel and the required control action. The FSM technique adopted is based on a piecewise linear sliding manifold that is bent towards the far off zones of the pole phase plane, thus enabling the reduction of the control action. Further, in order to limit the cart overshoot two variable gains were inserted in the cart controller. We tested our technique both on a nonlinear model, including friction, and on a lab equipment: we report both on the upwards stabilization and swing-up. The pendulum upwards equilibrium point was made globally stable.