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Based upon the multi-parametric programming for the linear constrained optimization program, the explicit model predictive control systems for linear time-invariable and time-variable constrained system are established respectively. The dynamic model for the mechanical vibration of elevator is developed, and schemes for vibration control of elevator and the placement of the actuator are discussed. With the established explicit model predictive control system, the active vibration control of the mechanical system of elevator is studied. Simulations are made for different working conditions of the elevator, and results show that the proposed method in this paper is effective for active vibration control of mechanical system of elevator.