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This paper investigates model predictive control (MPC) techniques based on hybrid models for a multi-mass magnetic actuator. The actuator has four operating modes depending on the mutual interaction of two moving masses and is modeled as a hybrid dynamical system. The control law optimizes a performance index and enforces several types of constraints: soft-landing during collisions to reduce mechanical wear, current limits and consequent position-dependent nonlinear bounds on the available magnetic force, and restrictions on the positions of the moving masses. Two different approaches are considered: (i) a hybrid MPC design based on the full two- mass model, and (ii) a switched MPC control design, which switches between two simpler hybrid MPC controllers, one for the case in which the masses are moving in contact, and the other case where the masses are decoupled, commanded by a simple switching logic. Simulation results and performance comparisons of the two control schemes are discussed.