Comparative analysis of the saturated sliding mode and LQR controllers applied to an inverted pendulum

The balancing of an inverted pendulum with an horizontal motion of the cart is a classical problem treated in the area of control. In this paper we present briefly the inverted pendulum and its modeling. After that we describe two controllers to swing a pendulum attached to a cart from an initial downwards position to an upright position and maintain that state. The first is the sliding mode control (SMC) where we present the design methodology for a class of linear saturated systems. The second is the classic Linear Quadratic Regulator (LQR) control. The constraint of saturation is reported on the control vector. To highlight results we present a comparative analysis with a SMC and LQR controllers with saturation.