Research On Multivariable Control Of Turbofan Engine Based On Equilibrium Manifold Model

With the continuous improvement of the performance requirements for modern advanced fighters which work in the complex and wide-scale operating conditions,the important problem faced by control system designers is to use less control energy to satisfy the requirements of high mobility operations,and ensure that engine safety margin indicators do not exceed the limit.Modeling plays an important role in the design of control systems.The unique structure of aero-engines leads to differences for control system design.The equilibrium manifold model is used to alleviate the huge workload of traditional linear parameter varying(LPV)models,and preserve some of the nonlinear characteristics for the system by considering changes in the internal variables of the system when designing the controller.In order to solve the multivariable control problem of aeroengines working in broad operating conditions,the expansion of the equilibrium manifold model to the MIMO system and the multivariable control method based on this model are carried out as follows:First,the identification of the equilibrium manifold model is carried out.By summarizing the previous researches on the equilibrium manifold model,the overall structure of the equilibrium manifold model is given,which is different from the general linearization method.The main properties of the equilibrium manifold model are introduced,and the feasibility of constructing the linear model by this method is guaranteed.The MIMO equilibrium manifold model can describe the characteristics of the turbofan engine with complex nonlinearity.The application of the so-called “two-step” modeling method in equilibrium manifold model is studied.Adjustable scheduling variables play a significant role in the accuracy of the model,and the equilibrium manifold model with higher steady state and dynamic state precision is obtained.The research work of the equilibrium manifold model provides a model basis for the subsequent control system design.Secondly,based on the diversification of aeroengine control variables brought by high performance requirements,a multivariable H∞ control design based on equilibrium manifold model is proposed.The equilibrium manifold modeling method can get the state space model which can design the controller through it.By analyzing the main properties of the equilibrium manifold model and completing the missing parameters of the state space model,the linear results can be used for multivariable controller design.The open-loop characteristic simulation is carried out.Simultaneously,the stability analysis and relative gain array analysis are used to obtain the final scheduling variable of the equilibrium manifold model for control system design.The simulation results show that the multivariable controller has good control performance at the design point.However,it cannot guarantee satisfactory control effect when the engine is running under a wide range of operating conditions.The linearization application of the equilibrium manifold model is given,and the effectiveness of the robust multivariable control based on this model is verified in a certain range,but it also exposes some limitations which lead to the next research work.Thirdly,the equilibrium manifold model is used as a tool to design the multivariable control of turbofan engines considering the LPV control method.The LPV model can be obtained through the equilibrium manifold model including the timevarying characteristics of the internal parameters.Based on the equilibrium manifold model,the LPV for robust gain scheduling controller design is constructed.The augmented model of turbofan engine based on the equilibrium manifold method is obtained by the state expansion method,so that the model satisfies the assumptions required for robust LPV control.Comparing the difficulty of applying the robust gain scheduling control principle in the polynomial LPV model,it is easier to get the controller by using the polytope technique in the design process.The simulation results show that the robust gain scheduling controller based on the equilibrium manifold model can effectively improve the output of the control system when the internal parameters change.However,the engine nonlinearity caused by the change of flight conditions should also be considered.Finally,using the switched LPV control method to incorporate the variation characteristics of flight conditions in the control system,and the multivariable control problem of turbofan engine based on equilibrium manifold model is studied.The sufficient conditions for guaranteeing the asymptotic stability of the system based on Lyapunov function are given.The method of common Lyapunov function is considered to design a switched LPV controller that guarantees the stability of the switching process.In order to reduce the difficulty of designing the controller,a special control strategy is proposed to use the flight condition as the command signals for switching,without increasing the complexity of the equilibrium manifold model.A smooth transition switching strategy is used to avoid chattering and significant kicking during the switching process.The control results show that the switched LPV controller can switch in any direction and has good control effect in the large-scale running envelope.