Control of an Inverted Pendulum

The balancing of an inverted pendulum by moving a cart along a horizontal track is a classic problem in the area of control. This paper will describe two methods to swing a pendulum attached to a cart from an initial downwards position to an upright position and maintain that state. A nonlinear heuristic controller and an energy controller have been implemented in order to swing the pendulum to an upright position. After the pendulum is swung up, a linear quadratic regulator state feedback optimal controller has been implemented to maintain the balanced state. The heuristic controller outputs a repetitive signal at the appropriate moment and is finely tuned for the specific experimental setup. The energy controller adds an appropriate amount of energy into the pendulum system in order to achieve a desired energy state. The optimal state feedback controller is a stabilizing controller based on a model linearized around the upright position and is effective when the cart-pendulum system is near the balanced state. The pendulum has been swung from the downwards position to the upright position using both methods and the experimental results are reported.