Research On Finite-time Control Methods Of Air-breathing Hypersonic Vehicle

Air-breathing hypersonic vehicle has great military value and potential economic value due to its characteristics: high velocity,long range,quick response.However,compare with conventional aircraft,high nonlinearity,strong couplings between propulsion and aerodynamics,parametric uncertainties and static instability all raise challenges in control system design of air-breathing hypersonic vehicle.Therefore,the control of climbing phase and cruise phase for hypersonic vehicle is studied in depth in this thesis.The problems this thesis focuses on i nclude: external disturbances problem,actuator faults problem,actuator saturations problem,tracking error performance and inlet constraint problem.The main research contents are given as follows:Firstly,the geometric configuration,shape parameters and flight mission profile of air-breathing hypersonic vehicle are introduced.Then the required coordinate systems and their transformation relations are defined.Next,the rigid-body dynamcis is established based on flight dynamics.T he aerodynamic models of each surface and the model of scramjet engine are constructed based on aerodynamics.Finally,by means of approximate fitting,the mathematical model and the related parameters of hypersonic vehicle are provided,which lays a foundation for the control system design in the following chapters.In order to restrain disturbances effectively and solve the control difficulties of air-breathing hypersonic vehicle,which include: high nonlinearity,static instability,strong couplings between propulsion system and aerodynamics,parametric uncertainties,an adaptive high-order super-twisting controller is designed based on high-order sliding mode theory.Firstly,feedback linearization is applied to transform the vehicle model into an affine nonlinear form and nonlinear feedback is used to solve the problem of couplings between propulsion system and aerodynamics.Then,exact robust differentiator is introduced to estimate the derivatives of tracking errors at real time,so as to solve the problem of aerodynamic uncertainties.Next,the adaptive high-order super-twisting controller is developed based on dilation scaling.The controller can dynamically adjust its own control gain s according to the values of tracking error with the changes of external disturbances,so as to enhance the robustness and response speed autonomously.Without the knowledge of upper bounds of external disturbances,the finite-time convergence of tracking errors for vehicle can be guaranteed and the chattering phenomena caused by the overestimation of control gains can be avoided.Considering hypersonic vehicle is prone to suffer from actuator faults under the effects of complex flight environment and extremely high aerodynamic heat,a robust fixed-time sliding mode controller is designed to satisfy the requirements of fault-tolerant control.Firstly,a non-singular fast fixed-time integral sliding surface is designed based on a novel fast fixed-time high-order regulator.Compared with conventional high-order regulator,the scheme can achieve faster response speed and avoid complicated adjustment process of coefficients.Then,a continuous fixed-time super-twisting-like reaching law with characteristic of second-order sliding-mode convergence is utilized to ensure that the sliding mode variables and its derivatives converge simultaneously.At last,a uniformly convergent observer is employed to estimate the lumped disturbances which include abrupt actuator faults at real time.The outputs of observer are compensated in controller to suppress the chattering phenomena and enhance the performance of fault tolerance.Through a combination of the three parts,the controller proposed can drive the tracking errors of vehicle to realize higher convergence precision and faster response speed in fixed time with the effects of actuator faults.Under the influence of actuators saturation(deflection angle of elevator and fuel-to-air ratio),an adaptive anti-saturation finite-time controller is designed.Firstly,model of vehicle is divided into two subsystems: velocity subsystem and height subsystem based on functional decomposition.Dynamic inversion controller and backstepping controller are presented for velocity subsystem and height subsystem respectively.In height subsystem,two recursive fixed settling time differentiators are introduced to estimate the d erivatives of virtual control signals exactly,which can avoid the “explosion of terms” problem and achieve finite-time convergence.Then,an adaptive fixed-time anti-saturation compensator is proposed to sovle the problem of actuator constraints.When actuator is saturated,compensator is used to drive the system to get rid of the saturated region.When actuator is not saturated no longer,auxiliary variable of compensator can converge exactly in fixed time,in order to avoid influence on convergence of original tracking error.Compared with conventional methods,the novel compensator can reduce the duration of saturation further and improve the co nvergence speed and precision of tracking errors.In order to solve the transient performance constraints of tracking errors and inlet airflow constraint of scramjet for hypersonic vehicle,a constrained prescribed performance controller is proposed.Firstly,a novel setting-time performance function is presented to limit the transient and steady-state performance of tracking errors.Compared with traditional methods,the novel fucntion can guarantee that the performance function converges to the steady state precisely at the setting time.Meanwhile,the initial convergence rate of performance function can be adjusted freely.Then,velocity and height tracking errors are unconstrained via coordinate transformation.By means of controlling the errors of transformation bounded,the prescribed-performance constraints of orginal tracking errors can be satisfied.In height subsystem,a novel fixed-time filter is designed for command filtered backstepping controller.By describing the performance of angle-of-attack tracking error and limiting the virtual control,the range of the angle of attack can be limited,so as to satisfy the inlet airflow requirements of scramjet.