The inverted pendulum system is a widely recognized control problem that revolves around the task of stabilizing a pendulum connected to a movable base. The primary objective is to keep the pendulum in an upright position, despite its inherent instability, by manipulating the movement of the cart. This system serves as a crucial benchmark for evaluating and testing control algorithms, finding applications in diverse domains such as robotics and industrial automation. Effectively controlling the inverted pendulum has far-reaching implications for the advancement of autonomous vehicles, bipedal robots, and other dynamic systems that rely on maintaining balance and stability. This master's thesis project aims to tackle the inverted pendulum problem from various perspectives, with three main objectives.