Design Of Linear Parameter Varying Controllers For Turbo-fan Engines

With the improvement of the control performance of aero-engine,the traditional gain-scheduled control which is widely used in engineering is unable to meet the design requirements of the aero-engine control system.Therefore,based on the nonlinear component-level model of a turbofan engine,a system design method based on Linear Parameter Varying(LPV)is applied in the research of turbofan engine modeling and control.Aiming at the modeling problem of LPV system,the state variable model at different operating equilibrium is built based on the component-level model.The dynamic performance of the aero-engine change continuously with the rotation speed of the high-pressured rotor which is taken as the scheduling parameter.Meanwhile,based on the linear model established by the small perturbation-least squares fitting method,the method of polynomial fitting is used to get the single scheduling parameter LPV model of aero-engine.The dynamic performance of the areo-engine differs greatly in different attitude and Mach number.Based on the single scheduling parameter LPV model,the attitude and Mach number are added as the scheduling parameters,and the multi-cell method is used to connect the single scheduling parameter LPV model in different vertexes.The simulation results show that the accuracy of multi-scheduling parameters LPV model satisfied the requirements.Based on the LPV model of turbofan engine,the theory of Sum of Squares Programming(SOSP)is applied to the design of LPV robust controller.The controller is validated on the non-linear component-level model of turbofan engine.The simulation results show that the controller has a high control quality,whether it is based on single scheduling parameters or multi-scheduling parameters.For the problem of switching LPV control,the stability of switched LPV system is analyzed by using Lyapunov function method.Based on Lyapunov function,the condition of switching stability is given by the dwell time constraint.Finally,the hysteresis switching and smooth switching are used to switching LPV control in the full envelope.In the stability analysis of the system,the stability analysis method based on the average dwell time is extended according to the multi-scheduling parameter LPV model.So that the restriction of the average dwell time to the switching LPV system is reduced to the restriction of multi-cell vertexes in different subsystems.In the switching strategy,the traditional hysteresis switching strategy is improved by combining the characteristics of multi-cell system.By finding the common quadratic Lyapunov function for the locally overlapped region and guaranteeing the continuity of Lyapunov function during the switching.The hysteresis switching strategy can also eliminate the buffeting caused by frequent switching.Based on the two points above,a new hysteresis switching LPV control method is proposed.On the smooth switching strategy,it is ensured that the controller switch smoothly by setting a smooth transition region between the two subsystems.The smooth transformation of the parameters eliminates the step of controller parameters between different subsystems.Simulation results show that both switching strategies can ensure the stability of switching system and have good control quality throughout the entire flight envelope.