This paper proposed a control algorithm to enhance the comfort of passengers in a vehicle equipped with Semi-Active Suspension systems, manipulating the force delivered by the Semi-Active damper. For this goal, the vertical dynamics of the car are represented through a quasi-Linear Parameter Varying (qLPV) model. Then, the algorithm resides in solving a set-constrained Model Predictive Control (MPC) problem, embedding a comfort performance index to the MPC optimization function. The sub-optimality of this algorithm resides in the fact that the MPC is synthesized considering a frozen guess for the evolution of the qLPV scheduling parameters along the prediction horizon. Assuming bounds on the variation rates of the qLPV scheduling parameters, the method enables a replacement of the original complex nonlinear LPV MPC optimization by a much simpler Quadratic Program (QP). This QP includes a Lyapunov-decreasing stage cost and embeds set-based terminal ingredients, which guarantee that the domain of attraction of the controller is enlarged and that recursive feasibility can be maintained despite the non-exact model scheduling (and suboptimality). The control structure is tested and compared to other optimal control approaches, such as a clipped Linear Quadratic Regulator. The paper ends with successful realistic nonlinear simulations of a 1/5-scaled car with Electro-Rheological suspensions, which illustrate the overall good operation and behaviour achieved with the proposed regulation algorithm. With the proposed method, the comfort of the passengers is substantially improved.