Choosing appropriate weighted functions in the frequency domain

and in combination with the state-space model of the real plant

the formulation of the state-space model for some generalized plant by employing the method of loop shaping and internal principle was established.The original control problem was converted to a standard H_∞ problem.The controller for the original plant was derived by means of solving optimal H_∞ dynamic output feedback controller for the generalized plant based on Linear Matrix Inequality (LMI).This design procedure was applied to a turbo-fan engine.The controller obtained by this method was verified in a wide engine operating range in the flight envelope.Simulation results of the turbofan engine nonlinear model show that the characteristics of the controller

namely

tracking characteristics

disturbance rejection and robustness

are satisfactory.