Construction and Modelling of an Inverted Pendulum on a Cart

The inverted pendulum on a cart system is a classic example of a non-linear and unstable control problem. The objective of this study is to model and construct an inverted pendulum on a cart system, and then to apply control strategies to stabilize its motion. The system consists of a cart, which can move horizontally along a track, and an inverted pendulum mounted on top of the cart. The pendulum's motion is described mathematically using Lagrange's equations, which take into account the forces acting on the system. The system is then linearized using feedback linearization, and a control algorithm is designed using the linearized model. Finally, the control algorithm is implemented and tested on the physical system, demonstrating the ability to stabilize the pendulum in an upright position. The results of this study provide insight into the behavior of inverted pendulum systems and the effectiveness of various control strategies.