This paper addresses the composite control problem of aero-engine systems under actuator faults and input saturation constraints. A novel n-step extended state observer (ESO) is proposed to precisely estimate actuator fault signals. Based on this estimation, a model predictive control (MPC) framework is developed to optimize system performance while explicitly addressing input saturation. Unlike conventional observer-based MPC strategies that depend on feedback compensation, the proposed approach directly integrates the estimated fault signal into the predictive model, enabling simultaneous fault estimation and compensation. This integration significantly enhances fault tolerance and control accuracy. Simulation results demonstrate that the proposed method effectively estimates actuator faults and ensures safe, reliable, and efficient aero-engine operation within predefined safety constraints. The approach is shown to be robust and capable of maintaining system stability under adverse conditions.