Research On Nonlinear Behavior And Uncontrollable Problem For A Supersonic Airframe/Propulsion Integrated System

The object involved in this paper is a supersonic ramjet-powered waverider.Strong couplings exist in the object due to complex interactions between aerodynamics/aerothermodynamics/elastics characteristics of the airframe and the operational states of the airbreathing propulsion system.Besides the interactions between the airframe and the propulsion system mentioned above,there also exist complex interactions between the inlet and combustor in the ramjet.Therefore,this research lays special emphasis on discussing about the structural instability of the ramjet,especially for the special problems introduced by the catastrophe of property of the ramjet’s behavior.In addition,this research also aims at solving the uncontrollable problem exposed by the CIAM/NASA flight test accident in 1998.The analyses of causes of the accident reveal non-uniqueness of properties of a ramjet’s operational states,the hysteresis phenomena that appear during mode transitions and the uncontrollable problem which means the expected operational mode and state cannot be reached via control.To provide a reasonable and conclusive answer to the reason why the uncontrollable problem exists and explain the corresponding solution to it,the research is carried out as follows:Firstly,a theoretical model of a ramjet focusing on the structural instability is built.Based on the similarity of property of a ramjet’s operational states,the operational states are classified into 3 operational modes,namely,scramjet mode,ramjet mode and unstarted mode.The 4 critical conditions for mode transition between the 3 operational modes constitute the butterfly catastrophe.On the basis of functions of operational modes,the dominant dynamic equations of the following modeled ramjet consist of 3 parts,including the volumetric effects equation,the perturbation wave propagation equation and the shock dynamic equation.Therefore,a dynamic airframe/propulsion integrated model with structural instability considered is built based.The integrated model has the ability to describe the catastrophe of property of the operational states and the catastrophe of property of the behaviors and lays the foundation for researching on the uncontrollable problem later.Secondly,the concept of behavior is built based on the concepts of discrete state and discrete event as well as fundamentals of the model of finite state automaton.On account of non-uniqueness of properties of operational states,the non-uniqueness of property of behaviors is further discussed.Without considering the total temperature limit,the system has 6 criteria for behavior classification to form 12 types of system behaviors.Considering the total temperature limit,the system adds 4 criteria for behavior classification to add 22 types of system behaviors.Furthermore,the non-uniqueness of behavior categories and behavior sequences of a ramjet with variable geometry considered along climb trajecto ries is fully illustrated by simulations.The behavior category reveals that the core of the uncontrollable problem is the inexistence of the expected mode transition and the inaccessibility of the excepted operational mode.This paper displays the system’s behavior categories and behavior sequences as well as the uncontrollable problem.In order to sum up,the catastrophe problem is condensed into a conceptual framework,including the concepts of “operational state”,“operational mode”,“mode transition”,“behavior”,“behavior category”,and “behavior sequence”.The two meanings of the system’s structural instability is clearly pointed out through the framework,namely,the catastrophe of property of the operational states and the catastrophe of property of the behaviors.Finally,the relations between behavior category and maximum performance is researched based on the behavior category.The influence of the catastrophe of property of the behaviors on the minimum-time ascent trajectory and the control system design is also presented.The results reveal a negative decoupling issue between the smooth nonlinear parameter varying of performance or maximum performance and the strong nonlinear catastrophe of behavior category.Then,a selective conservative accelerate ascent trajectory is proposed.Moreover,the risk of variable-geometry control strategy which is not based on behavior control is pointed out.Therefore,to improve the ability to solve the uncontrollable problem in an airframe/propulsion integrated system,control input related to heat release is used to adjust the performance and control the operational mode,and the inputs related to geometry are utilized to improve the maximum performance and control the system’s behavior category.To sum up,a framework of control logic based on the behavior control is one promising solution to uncontrollable problems.