Modeling and simulation of the inverted pendulum control system

The inverted pendulum is a common, interesting control problem that involves many basic elements of control theory. This paper deals with modeling and simulation of the inverted pendulum. This system is unstable and highly nonlinear with one input - voltage of a DC motor which can change position of the cart and two outputs - cart position and angle of the pendulum rod. First, a mathematical model of the inverted pendulum is derived, followed by stabilization of three basic control methods (Root locus, Frequency response, PID). Then, the created mathematical model is implemented into the MATLAB/Simulink environment and its properties are reflected by simulation results.