This paper describes a real-time multi-objective predictive control strategy for the wheelchair ergometer platform, which allows simulating the manual wheelchair (MWC) propulsion in virtual reality (VR). A nonlinear least-square method is used to build the predictive wheelchair ergometer model, where the trust-region-reflective algorithm is adopted. A detailed study of the wheelchair dynamics, and its performance on the rollers, and the frictions are presented. The main contribution is the implementation of a wheelchair ergometer model into a proposed controller in order to provide realistic navigation within the VR world by accurately detecting and tracking the rotation of the driving wheels. In particular, the proposed strategy has two objectives: 1) to generate force feedback (haptics) during the push phase (hand-to-rim contact); 2) assistance control to make the wheelchair movement more realistic in the immersive virtual environment during the recovery phase (hand-to-rim no contact). Various numerical examples emphasize the flexibility of the approach and experimental results confirm that the proposed controller successfully tracks the speed reference. It is also shown that the real-time tracking ability of the explicit MPC (eMPC) controller is superior to that of the PI controller.