Model Predictive Control (MPC) is a well-developed and widely-used control design method, in which the control input is computed by solving an optimization problem at every sampling period. Traditionally, MPC has been associated with control of slow processes, with sampling times in the seconds/minutes/hours range, because an optimization problem must be solved online. However, dramatic increases in computing power and recent developments in code generation for convex optimization, which tailor to specific optimization problem structure, are allowing the use of MPC in fast processes, with sampling times in the millisecond range. In this paper, a MPC control design for a miniature remote-controlled coaxial helicopter is developed and experimentally validated. The nonlinear dynamic behavior of the helicopter was identified, simplified and approximated by a Linear Time Varying (LTV) model. A custom convex optimization solver was generated for the specific MPC problem structure and integrated into a controller, which was tested in simulation and implemented on a hardware testbed. A performance analysis shows that the MPC approach performs better than a tuned Proportional Integral Differential (PID) controller.