In this paper we present the implementation of a model predictive controller (MPC) for real-time control of a motion simulator based on a serial robot with 8 degrees of freedom. The goal of the controller is to accurately reproduce six reference signals simultaneously (the accelerations and angular velocities in the body frame of reference) taken from a simulated or real vehicle, by moving the human participant sitting inside the cabin located at the end effector. The controller computes the optimal combined motion of all axes while keeping the axis positions, velocities and accelerations within their limits. The motion of the axes is computed every 12 ms based on a prediction horizon consisting of 60 steps, spaced 48 ms apart, thus looking ahead 2.88 s. To evaluate tracking performance, we measured the acceleration and angular velocity in the cabin using an Inertial Measurement Unit (IMU) for synthetic (doublets and triangle-doublets) and realistic (recorded car and helicopter maneuvers) reference signals. We found that fastchanging acceleration inputs excite the natural frequencies of the system, leading to severe mechanical oscillations. These oscillations can be modelled by a second-order LTI system and mitigated by including this model in the controller. The use of proper algorithms and software allows the computations to be done in real-time.