Single inverted pendulum

Abstract

This report covers the details of developing a single inverted pendulum. An inverted pendulum uses computer control tools in order to stabilize pendulum at the upright position. A step by step description and study of the different parts of the project is presented in a simple manner supported by figures, schematics and diagrams from the very conceptual stage to the final implemented result. An inverted pendulum has been proposed as a suitable state space demonstration and experimentation device. Undergraduate textbooks cover dynamic modeling and state control of a single inverted pendulum. The controller designed consists of the state variable feedback and the observer. The state variable feedback is determined based on either pollocations or as the optimal control for the quadratic criterion function. As the observer, the minimal order state observer or a linear functional observe is employed, and it is theoretically proved that the linear functional observer for a multiple inverted pendulum can always be realized by the first order. The controller using a linear functional observer requires less computation time and controls the system in more stable way. This report begins with an outline of the research into an inverted pendulum system design and control along with mathematical modeling methods. Details of the pendulum as mechatronic system are presented and mathematical modeling of the designed system follows. Controller design and implementation is discussed next.