Implementation and Control of an Inverted Pendulum on a Cart

Abstract

An Inverted Pendulum on a Cart is a common system often used as a benchmark problem for control systems. The system consists of a cart that can move in one direction on the horizontal plane and a pendulum attached to the cart through a hinge point. The pendulum can rotate 360° on the plane made up of the vertical direction and the direction the cart can move. The system is controlled by applying a force to the cart, to make it move. This thesis consists of two goals. The first goal is to build a lab model of the Inverted Pendulum on a Cart system. The second goal is to create a controller that can swing the pendulum from a pendulum down position to a pendulum up position, and balance it in this position. The lab model is built using a track that the cart can move along, a stepper motor for applying force to the cart and a microcontroller for controlling the system. The pendulum angle and the cart position are measured using incremental encoders. A Mathematical model of the system have been derived. This forms the basis for the design of the controller and is also used for simulating and testing the system and controller in MATLAB/Simulink before it is implemented on the real system. The controller consists of three parts. An extended Kalman filter is implemented to estimate the non-measurable state. An energy-based controller is used to swing the pendulum from the down position to the up position. This controller regulates the energy in the pendulum to be close to the energy the pendulum should have when it is balanced in the upright position. When the pendulum is close to the upright position the controller will switch to a linear quadratic regulator to balance the pendulum. This controller is based on a linearized version of the mathematical system model. The lab model and the controllers have been successfully built and implemented.