Model predictive control (MPC) is popular in applications with slow dynamics because of its advantages in handling constraints and multivariable optimization. But for aeroengines, it is difficult to obtain an exact prediction model, which will lead to offsets in tracking. Besides, deploying MPC to embedded controllers for real-time control is a well-known challenge. Therefore, this paper presents a switched linear MPC, which incorporates the augmented prediction models with error integrator for offset-free tracking, the sparse-based quadratic programming formula for solving MPC, and a reset strategy for achieving bumpless transfer at the switching instant. Further, on the hardware board we developed, six hardware-related acceleration strategies are explored and evaluated for real-time performance. Then, eight cases of five objects are tested, whose results indicate a significant speedup of around 50 times. At last, the hardware-in-the-loop tests of the turbofan engine and the real bench tests of the micro-turbojet engine are performed, which verifies the superiority, real-time performance, and potential for practical applications.