This paper presents a unified control scheme of the Pendubot based on nonlinear model predictive control (NMPC) and nonlinear moving horizon estimation (NMHE) with the objective of point-to-point tracking its unstable unforced and ultimately forced equilibrium positions. In order to implement it on this fast, underactuated mechatronic system, we employ the Gauss–Newton real-time iteration scheme tailored to obtain the efficient solution of the underlying nonlinear optimization problems via sequential quadratic programming. The control performance is experimentally assessed on a real-world laboratory setup featuring an execution timing analysis and hints how to further improve the computational efficiency of the proposed nonlinear estimation control scheme. Even nowadays, the number of practical NMPC applications in the millisecond range is still rather limited, and the presented NMHE-based NMPC of the Pendubot thus also represents a unique case study for control practitioners.