To solve the problem of full flight envelope transient main control loop design of turbofan engine, a design method based on linear matrix inequality (LMI) is proposed. Robust stability of the closed-loop turbofan engine system in all conditions is proved by using Lyapunov inequalities. The robust performance is ensured by gain-schedule and pole-placement. Reduced order multivariable gain-schedule and minimum trace optimization algorithm are presented to guarantee the feasibility of the design method. Full flight envelope simulations based on a nonlinear turbofan engine model were done. The results show that the maximum settling time of N1cor is 4.3s and the maximum overshoot is 1.7%. The maximum settling time of N2cor is 4.5s and the maximum overshoot is 0.1%. The robust stability and consistent performance in full flight envelope are also shown in the results.

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