Haptic training simulators generally consist of three major components, namely a human operator, a haptic interface, and a virtual environment. Appropriate dynamic modeling of each of these components can have far-reaching implications for the whole system's performance improvement in terms of transparency, the analogy to the real environment, and stability. In this paper, we developed a virtual-based haptic training simulator for Endoscopic Sinus Surgery (ESS) by doing a dynamic characterization of the phenomenological sinus tissue fracture in the virtual environment, using an input-constrained linear parametric variable model. A parallel robot manipulator equipped with a calibrated force sensor is employed as a haptic interface. A lumped five-parameter single-degree-of-freedom mass-stiffness-damping impedance model is assigned to the operator's arm dynamic. A robust online output feedback quasi-min-max model predictive control (MPC) framework is proposed to stabilize the system during the switching between the piecewise linear dynamics of the virtual environment. The simulations and the experimental results demonstrate the effectiveness of the proposed control algorithm in terms of robustness and convergence to the desired impedance quantities.