The rotational inverted pendulum is a structure that was primarily developed by Katsuhisa Furuta. It is widely used thorough the control laboratories to demonstrate the effectiveness of nonlinear control algorithms. The rotational inverted pendulum is a nonlinear system of fourth order with a single input variable. In this article the full dynamic equations of motion of the rotational inverted pendulum are derived using Lagrangian formulation. Consequently, a comparison of obtained mathematical model with other models described and available in literature is conducted by means of computer simulations. Eventually, a complete energy build-up swing-up algorithm and fuzzy stabilization algorithm for the system are developed. The control algorithm is then implemented on a PLC device in order to control the existing laboratory stand available at the Department of Process Control . The algorithm is implemented with the use of ladder logic and structured text programming language. The robustness of elaborated balancing control is verified by subsequent real-time tests conducted on the laboratory stand.