In this work, the horizontal nonlinear response of a three-degree-of-freedom vertical transportation model excited by guide rail deformations is investigated. The equation of motion contains nonlinearities in the form of Duffing stiffness for the translational spring in tilting motion of the cabin. In order to improve the comfort for passengers a control strategy based on the State-dependent Ricatti Equation (SDRE) is proposed. Numerical simulations are performed to study the nonlinear behavior of the adopted mathematical model. In addition, we test the robustness of the SDRE control technique considering parametric errors and noise. The obtained results confirm that the proposed strategy can be effective in controlling the response of the system.