Stability Analysis and Optimum Controller Design for an Inverted Pendulum on Cart System

Stability analysis and control of the inverted pendulum on cart system is an important problem that has been investigated by many researchers in recent years. In this study, nonlinear modeling of the inverted pendulum on cart system is derived and free body diagram is explained. Then, the nonlinear model of the system is created in MATLAB program. In order to keep the pendulum on cart in balance, different types of controllers were designed, and stability analysis was performed by drawing root-locus curves for different controllers. The optimum controller design was obtained to keep the pendulum in balance. The impulse response of the system has been simulated and it has been proven that the designed optimum controller keeps the pendulum in balance.