In this paper, State-Dependent Riccati Equation (SDRE) nonlinear control is used to regulate the Pendubot, a two-link underactuated robot developed at UIUC, at one of its unstable equilibrium positions. The plant is not fully feedback linearizable due to weakly nonminimum phase zero-dynamics. However, this does not present a problem for SDRE control. Presented results show that SDRE control outperforms LQR control even when the same design parameters are used. The real-time experiments are implemented using a specialized 60 MHz digital signal processor running customized code for SDRE control computation, which involves solving the Algebraic Riccati Equation online. For this highly nonlinear 4-state system, the implementation was successful at a sampling time sufficient for the particular electromechanical plant. To the authors' best knowledge, this is the first work in which SDRE control is implemented on a physical plant in realtime, where the SDRE control is repeatedly computed online.