Mechatronic systems in the automotive applications are characterized by significant nonlinearities and tight performance specifications further exacerbated by state and input constraints. Model Predictive Control (MPC) in conjunction with hybrid modeling can be an attractive and systematic methodology to handle these challenging control problems. In this paper, we focus on a mass spring damper system actuated by an electromagnet, which is one of the most common elements in the automotive actuators, with fuel injectors representing a concrete example. We present two designs which are based, respectively, on a linear MPC approach in cascade with a nonlinear state-dependent saturation, and on a hybrid MPC approach. The performance and the complexity of the two MPC controllers are compared.