Prediction backstepping control method for hypersonic flight vehicle

Abstract

The invention relates to a prediction backstepping control method for a hypersonic flight vehicle. The method comprises the following steps: S1, constructing a mathematical model of the hypersonic flight vehicle; s2, decoupling the mathematical model of the hypersonic aircraft into a speed subsystem and a height subsystem; s3, taking the weighted sum of the speed tracking error and the accelerator opening degree as an optimization performance index, and solving through the speed subsystem to obtain the accelerator opening degree of the hypersonic aircraft; s4, designing a prediction backstepping controller for the height subsystem, and solving the rudder deflection angle of the hypersonic aircraft through the prediction backstepping controller by taking the weighted sum of the height tracking error and the trajectory inclination angle as an optimization performance index; and S5, the hypersonic aircraft is controlled according to the rudder deflection angle and the accelerator opening degree.

Description

Technical Field

[0001] The present invention relates to the field of hypersonic aircraft control, and in particular to a hypersonic aircraft predictive backstepping control method. Background Art

[0002] In order to ensure that HV can maintain stability and strong robustness in complex flight environments, it is necessary to continuously innovate and introduce advanced control methods and means in the design of its flight control system. Traditional controllers designed based on backstepping control, sliding mode control and robust control methods often ignore key constraints such as control surfaces and flight angle of attack. Such a design may lead to a decrease in control performance or even system instability when external disturbances are strong. Therefore, problems such as constraint processing, strong nonlinearity, strong coupling and rapid time variation are still key problems to be solved in the design of HV control systems. Predictive control, as an optimization control method, can fully consider the control and state constraints when designing the controller, and is particularly suitable for processing multivariable and constrained complex systems. The significant advantage of this method is that it can achieve excellent control performance while strictly following the state and control constraints. However, predictive control also has certain limitations. Since it needs to solve an optimization problem in each sampling period, this leads to a significant increase in online computing time.

[0003] The purpose of the present invention is to design a predictive backstepping control method for a hypersonic aircraft in view of the above-mentioned problems in the prior art. Summary of the invention

[0004] In view of the problems existing in the above-mentioned prior art, the present invention provides a hypersonic aircraft predictive backstepping control method, which can effectively solve at least one problem existing in the above-mentioned prior art.

[0005] The technical solution of the present invention is: A hypersonic vehicle predictive backstepping control method comprises the following steps: S1, construct a mathematical model of hypersonic aircraft; S2, decoupling the hypersonic aircraft mathematical model into a speed subsystem and an altitude subsystem; S3, taking the weighted sum of the speed tracking error and the throttle opening as the optimization performance index, and obtaining the throttle opening of the hypersonic aircraft by solving the speed subsystem; S4, designing a predictive backstepping controller for the altitude subsystem, taking a weighted sum of an altitude tracking error and a trajectory inclination angle as an optimization performance index, and solving the rudder deflection angle of the hypersonic aircraft through the predictive backstepping controller; S5, controlling the hypersonic aircraft with the rudder angle and the throttle opening.

[0006] Furthermore, the hypersonic vehicle mathematical model is represented by a series of formulas: ; in, For speed, is the ballistic inclination angle, For height, is the angle of attack, is the pitch angular velocity, is the elastic mode, They are gravity acceleration, moment of inertia, vehicle mass, elastic modal frequency and damping ratio. They represent thrust, drag, lift, pitching moment and generalized force respectively; as well as, The approximate expression is as follows: ; in, are all known constants, , , , , , , is the coefficient under nominal conditions, and the coefficient under nominal conditions is expanded as follows: ; in, , , represent the reference area, thrust arm and mean aerodynamic chord respectively; is the dynamic pressure, , is the air density; , , They represent the fuel equivalence ratio, canard and elevator deflection angles of the hypersonic vehicle respectively; , , .

[0007] Further, decoupling the hypersonic aircraft mathematical model into a speed subsystem and an altitude subsystem includes: S2.1, assuming that the ballistic inclination of the hypersonic vehicle in the cruise phase is Close to 0, making the hypersonic vehicle mathematical model , define lift The value is much larger than , thus ignoring the effect of thrust on hypersonic vehicles; S2.2, decoupling the hypersonic vehicle mathematical model into a strict feedback form, we obtain: ; ; in, , , , , , , , , ; is the negative gain coefficient of canard deflection and elevator deflection, represents the speed subsystem, Represents the altitude subsystem.

[0008] Further, S3, taking the weighted sum of the speed tracking error and the throttle opening as the optimization performance index, the throttle opening of the hypersonic aircraft obtained by solving the speed subsystem includes: S3.1, according to the speed subsystem , the control law design of the speed subsystem is transformed into a secondary performance index optimization problem. The speed control optimization problem is expressed as: ; in, is the predicted speed of the hypersonic vehicle, is the predicted value of the velocity reference trajectory of the hypersonic vehicle, for The fuel equivalence ratio at the time, are the minimum and maximum values ​​of the fuel equivalence ratio, is the prediction step length, are the weighted matrices of speed tracking error and fuel equivalence ratio, J is the performance index, is the initial flight speed, t is the time in the prediction domain; S3.2, the speed subsystem Expressed as a linearized model related to the system state ,in ; S3.3, for the linearized model Discretize and get the speed prediction model ,in , T is the discretization step size, k represents the discrete moment, is the fuel equivalence ratio at time k, They are the flight speed at the next moment and the flight speed at the current moment respectively.

[0009] S3.4, converting the speed control optimization problem into a speed control quadratic programming problem through the speed prediction model; S3.5, solving the speed control quadratic programming problem to obtain the throttle opening of the hypersonic aircraft.

[0010] Further, S4, a predictive backstepping controller is designed for the altitude subsystem, and a weighted sum of altitude tracking error and trajectory inclination angle is used as an optimization performance index. The rudder deflection angle of the hypersonic aircraft obtained by solving the predictive backstepping controller includes: S4.1. Design of highly virtual control laws for hypersonic vehicles , the weighted sum of the height tracking error and the trajectory inclination is used as the optimization performance index, and the height virtual control law The solution is converted into a height control optimization problem, which is expressed as: ; in, is the predicted state of the hypersonic vehicle, is the predicted value of the altitude reference trajectory, , represents the height tracking error weight and control amount weight matrix, and both are positive definite matrices, and J is the performance index; are the minimum and maximum angle of attack, respectively. are the minimum and maximum elevator deflection angles, respectively. for The control law of the moment, To predict the altitude and initial flight altitude, Angle of attack The virtual control quantity, is the angle of attack and The functional relationship is approximately , is the pitch angle, is the rudder angle about Function of S4.3, the height subsystem The first equation of is transformed into a highly discrete state space model, and we get , where , , is the discrete step length, k represents the discrete moment; S4.4, transform the height control optimization problem into a quadratic programming problem through a series of equivalent transformations; S4.5, solve the quadratic programming problem and obtain a highly virtual control law ; S4.6. In combination with the backstepping control method, the elevator deflection angle in the altitude virtual control law is designed.

[0011] Further, in S4.6, in combination with the backstepping control method, the elevator deflection angle in the altitude virtual control law is designed to include: S4.6.1, Design Angle of Attack Virtual control volume , so that the trajectory inclination of the hypersonic vehicle tracks the highly virtual control law designed in S4.5; S4.6.2, Design Pitch Angle Virtual control volume , so that the ballistic angle of attack of the hypersonic vehicle tracks the angle of attack designed in S4.6.1 Virtual control volume ; S4.6.3, Design elevator deflection angle , so that the pitch angle of the hypersonic vehicle tracks the pitch angle designed in S4.6.2 Virtual control volume .

[0012] Furthermore, the designed angle of attack Virtual control volume for ; Designed pitch angle Virtual control volume for ; Elevator deflection angle for ; in, is the trajectory inclination tracking error, is the designed feedback gain; is the angle of attack tracking error, is the designed feedback gain; is the pitch angular velocity tracking error, is the designed feedback gain.

[0013] Furthermore, the attack angles are designed Virtual control volume , Pitch angle Virtual control volume , elevator deflection angle The inverse tangent tracking differentiator for the angle of attack Virtual control volume , Pitch angle Virtual control volume , elevator deflection angle Derivative calculation during calculation.

[0014] Furthermore, the angle of attack Virtual control volume The corresponding inverse tangent tracking differentiator is: ; Pitch Angle Virtual control volume The corresponding inverse tangent tracking differentiator is: ; Elevator deflection angle The corresponding inverse tangent tracking differentiator is: ; in, Angle of attack Virtual control volume The corresponding inverse tangent tracks the state of the differentiator, Angle of attack Virtual control volume The corresponding design parameters of the inverse tangent tracking differentiator have values ​​greater than 0; is the pitch angle Virtual control volume The corresponding inverse tangent tracks the state of the differentiator, is the pitch angle Virtual control volume The corresponding inverse tangent tracking differentiators have values ​​greater than 0; is the elevator deflection angle The corresponding inverse tangent tracks the state of the differentiator, is the elevator deflection angle The corresponding design parameters of the inverse tangent tracking differentiator are all greater than 0.

[0015] Therefore, the present invention provides the following effects and / or advantages: The present invention combines backstepping control with predictive control, which, on the one hand, takes advantage of predictive control in processing constraints, and on the other hand, reduces the dimension of constraint optimization to one dimension, thereby greatly reducing the online time.

[0016] This application aims at the constraints imposed on hypersonic aircraft by adjusting the engine throttle command. and elevator deflection angle , in order to achieve the reference speed and reference height Specifically, the present application decouples the hypersonic aircraft mathematical model into a speed subsystem and an altitude subsystem, and respectively performs different transformations on the speed subsystem and the altitude subsystem, and uses different optimization performance indicators as constraints to solve the control law of the hypersonic aircraft, thereby being able to accurately control the hypersonic aircraft.

[0017] The present application converts the speed subsystem into a linearized model and then into a discretized model, thereby converting the speed control optimization problem into a speed control quadratic programming problem, and is able to solve the speed control quadratic programming problem to obtain the throttle opening of the hypersonic aircraft.

[0018] The present application designs an altitude virtual control law for a hypersonic aircraft, takes the weighted sum of altitude tracking error and trajectory inclination as an optimization performance indicator, converts the solution of the altitude virtual control law into an altitude control optimization problem, and converts the altitude control optimization problem into a quadratic programming problem through a series of equivalent transformations, so that the altitude virtual control law can be solved.

[0019] This application uses the backstepping method to design the angle of attack Virtual control quantity , pitch rate Virtual control quantity and the actual control quantity - elevator deflection angle .

[0020] This application designs the angle of attack Virtual control volume , Pitch angle Virtual control volume , elevator deflection angle The inverse tangent tracking differentiator for the angle of attack Virtual control volume , Pitch angle Virtual control volume , elevator deflection angle The derivative calculation in the calculation process avoids the "differential explosion" problem in backstepping control.

[0021] Through the control method provided in the present application, when controlling a hypersonic aircraft, the speed tracking error and the altitude tracking error are smaller than those of the predictive control of the full state space model, and during the control process of the designed controller, the angle of attack, the rudder angle and the fuel equivalence ratio are all within the constraints.

[0022] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention are realized and obtained by the structures particularly pointed out in the description and the drawings.

[0023] It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1A flowchart diagram of one embodiment of the present invention is provided.

[0025] Figure 2 Schematic diagram of the controller structure designed to introduce the virtual control law of backstepping control.

[0026] Figure 3 It is the speed tracking and speed tracking error curve.

[0027] Figure 4 It is the height tracking and height tracking error curve.

[0028] Figure 5 is the state response curve.

[0029] Figure 6 is the elastic modal response curve.

[0030] Figure 7 is the control law curve. DETAILED DESCRIPTION

[0031] In order to facilitate understanding by those skilled in the art, the present invention is now described in further detail by way of examples: In view of the constraints and real-time control problems of current hypersonic aircraft, this paper proposes a predictive backstepping control method, which aims to achieve real-time control while dealing with the constraints and improve its control performance. First, the mathematical model of the hypersonic aircraft is introduced; then the controller design is discussed in detail, including the predictive backstepping controller design of the altitude channel and the predictive controller design of the velocity channel; finally, the theoretical design is simulated and verified.

[0032] Specifically, refer to Figure 1 , a hypersonic vehicle predictive backstepping control method, comprising the following steps: S1, construct a mathematical model of hypersonic aircraft; S2, decoupling the hypersonic aircraft mathematical model into a speed subsystem and an altitude subsystem; S3, taking the weighted sum of the speed tracking error and the throttle opening as the optimization performance index, and obtaining the throttle opening of the hypersonic aircraft by solving the speed subsystem; S4, designing a predictive backstepping controller for the altitude subsystem, taking a weighted sum of an altitude tracking error and a trajectory inclination angle as an optimization performance index, and solving the rudder deflection angle of the hypersonic aircraft through the predictive backstepping controller; S5, controlling the hypersonic aircraft with the rudder angle and the throttle opening.

[0033] Furthermore, the longitudinal dynamics model of a flexible air-breathing hypersonic vehicle (FAHV) is considered, which includes a first-order differential equation consisting of five rigid body states such as velocity, trajectory inclination, altitude, angle of attack and pitch velocity and six elastic modes. The mathematical model of the hypersonic vehicle is expressed by a series of formulas: ; (1) in, For speed, is the ballistic inclination angle, For height, is the angle of attack, is the pitch angular velocity, is the elastic mode, They are gravity acceleration, moment of inertia, vehicle mass, elastic modal frequency and damping ratio. They represent thrust, drag, lift, pitching moment and generalized force respectively; as well as, The approximate expression is as follows: ; (2) in, are all known constants, , , , , , , is the coefficient under nominal conditions, and the coefficient under nominal conditions is expanded as follows: ; (3) in, , , represent the reference area, thrust arm and mean aerodynamic chord respectively; is the dynamic pressure, , is the air density; , , They represent the fuel equivalence ratio, canard and elevator deflection angles of the hypersonic vehicle respectively; , , .

[0034] Because the canard deflection and elevator deflection have a negative gain relationship, the actual control input that needs to be designed is It can be seen from formulas (2) and (3) that the flexible state will affect the thrust, lift, drag and moment, and reduce the structural stability of FAHV.

[0035] The constraints for the control input are: (4) In the formula, and Fuel equivalence ratio The upper and lower bounds of and Elevator deflection angle The upper and lower bounds of .

[0036] The constraint range of the attack angle is: (5) In the formula, and Angle of attack The upper and lower bounds of .

[0037] It can be seen from equations (1), (2), (3), (4) and (5) that the longitudinal model of a hypersonic vehicle is a highly nonlinear, strongly coupled and constrained system.

[0038] Further, decoupling the hypersonic aircraft mathematical model into a speed subsystem and an altitude subsystem includes: S2.1, assuming that the ballistic inclination of the hypersonic vehicle in the cruise phase is Close to 0, making the hypersonic vehicle mathematical model , define lift The value is much larger than , thus ignoring the effect of thrust on hypersonic vehicles; In order to facilitate the design of the controller, the nonlinear model of the hypersonic aircraft needs to be transformed to a certain extent. Considering the characteristics that the speed of the hypersonic aircraft is mainly affected by the engine throttle and the altitude is affected by the elevator, this paper decouples the hypersonic aircraft and divides the system model into a speed subsystem and an altitude subsystem. The decoupling process makes the following reasonable assumptions: Assumption 1: The ballistic inclination of a hypersonic vehicle during the cruise phase is a very small value, so the .

[0039] Assumption 2: Angle of attack of a hypersonic vehicle during cruise phase is small enough so that ,therefore It can be neglected numerically.

[0040] S2.2, decoupling the hypersonic vehicle mathematical model into a strict feedback form, we obtain: (6); (7); Among them, the specific expressions of the functions in each formula are , , , , , , , , ; represents the speed subsystem, Represents the altitude subsystem.

[0041] Further, S3, taking the weighted sum of the speed tracking error and the throttle opening as the optimization performance index, the throttle opening of the hypersonic aircraft obtained by solving the speed subsystem includes: S3.1, according to the speed subsystem , the control law design of the speed subsystem is transformed into a secondary performance index optimization problem. The speed control optimization problem is expressed as: (8); in, is the predicted speed of the hypersonic vehicle, is the predicted value of the velocity reference trajectory of the hypersonic vehicle, for The fuel equivalence ratio at the time, are the minimum and maximum values ​​of the fuel equivalence ratio, is the prediction step length, are the weighted matrices of speed tracking error and fuel equivalence ratio respectively; S3.2, the speed subsystem Expressed as a linearized model related to the system state ,in ; S3.3, for the linearized model Discretize and get the speed prediction model ,in , T is the discretization step size, k represents the discrete moment, is the fuel equivalence ratio at time k, They are the flight speed at the next moment and the flight speed at the current moment respectively.

[0042] S3.4, converting the speed control optimization problem into a speed control quadratic programming problem through the speed prediction model; S3.5, solving the speed control quadratic programming problem to obtain the throttle opening of the hypersonic aircraft.

[0043] Further, S4, a predictive backstepping controller is designed for the altitude subsystem, and a weighted sum of altitude tracking error and trajectory inclination angle is used as an optimization performance index. The rudder deflection angle of the hypersonic aircraft obtained by solving the predictive backstepping controller includes: S4.1. Design of highly virtual control laws for hypersonic vehicles , the weighted sum of the height tracking error and the trajectory inclination is used as the optimization performance index, and the height virtual control law The solution is converted into a height control optimization problem, which is expressed as: (9); in, is the predicted state of the hypersonic vehicle, is the predicted value of the altitude reference trajectory, , represents the height tracking error weight and control amount weight matrix, and both are positive definite matrices, and J is the performance index; are the minimum and maximum angle of attack, respectively. are the minimum and maximum elevator deflection angles, respectively. for The control law of the moment, To predict the altitude and initial flight altitude, Angle of attack The virtual control quantity, is the angle of attack and The functional relationship is approximately , is the pitch angle, is the rudder angle about The function of , whose expression can be obtained by inverse deduction of the backstepping control law later; S4.3, the height subsystem The first equation of is transformed into a highly discrete state space model, and we get , where , , is the discrete step length, k represents the discrete moment; S4.4, transform the height control optimization problem into a quadratic programming problem through a series of equivalent transformations; S4.5, solve the quadratic programming problem and obtain a highly virtual control law ; S4.6. In combination with the backstepping control method, the elevator deflection angle in the altitude virtual control law is designed.

[0044] Further, in S4.6, in combination with the backstepping control method, the elevator deflection angle in the altitude virtual control law is designed to include: S4.6.1, Design Angle of Attack Virtual control volume , so that the trajectory inclination of the hypersonic vehicle tracks the highly virtual control law designed in S4.5; S4.6.2, Design Pitch Angle Virtual control volume , so that the ballistic angle of attack of the hypersonic vehicle tracks the angle of attack designed in S4.6.1 Virtual control volume ; S4.6.3, Design elevator deflection angle , so that the pitch angle of the hypersonic vehicle tracks the pitch angle designed in S4.6.2 Virtual control volume .

[0045] Furthermore, the designed angle of attack Virtual control volume for ; Designed pitch angle Virtual control volume for ; Elevator deflection angle for ; in, is the trajectory inclination tracking error, is the designed feedback gain; is the angle of attack tracking error, is the designed feedback gain; is the pitch angular velocity tracking error, is the designed feedback gain.

[0046] From step S3 to step S4, the process is as follows.

[0047] The control objective of the present application is to achieve accurate tracking of a reference speed and a reference altitude by adjusting the engine throttle valve command and the elevator deflection angle in response to the constraints imposed on the hypersonic aircraft.

[0048] When designing the backstepping controller of a hypersonic vehicle, the design steps of the altitude virtual control law of its altitude channel are as follows: Define the height tracking error: (10); Derivative of the height error yields: (11); Then, its highly virtual control law is designed as: (12); In the formula is the feedback control gain, are the altitude and altitude reference signals respectively.

[0049] The virtual control law adopts the existing control law , and carry out specific design in the follow-up.

[0050] In order to improve the performance of the controller, the present invention introduces the optimization idea of ​​predictive control into the first step of the virtual control law design of backstepping control. The designed controller structure is as follows: Figure 2 As shown. For the height subsystem, its height virtual input value is obtained by predictive control online optimization solution, and the actual input value is calculated by backstepping method. The speed subsystem is optimized independently, which reduces the optimization dimension compared to the general predictive control full state feedback design, thereby reducing the optimization calculation time.

[0051] First, the altitude subsystem designs a strategy to control the hypersonic vehicle.

[0052] Step 1: Solve for the virtual control input .

[0053] According to formula (7), the first step of the height loop is virtually input Transformed into solving the following optimization problem: (13); In the formula, for The predicted state at the moment, from the system model Evolved, represents the height tracking error weight, represents the control quantity weight, and they are all positive definite matrices, Angle of attack The virtual control quantity, is the angle of attack and The functional relationship is approximately , is the pitch angle, is the rudder angle about The function of , whose expression can be obtained by inverse deduction of the backstepping control law later; The object of the optimization problem is a linear model with a single input and a single output, which transforms the system into a discrete state space model: (14); In the formula , , To walk away from the long, k represents discrete moments. Ignoring disturbances or measurement noise, assuming that all output states can be measured, yes The predicted state at the moment. According to the superposition principle, The current k The state value measured at the moment and the control input assumed at the future time Therefore, the prediction model (14) can be used to iteratively calculate the state value at the future moment: (15); (16) ; (17); (18); (19); In the formula, p It indicates the prediction horizon, i.e. the length of the rolling optimization horizon, which greatly affects the control system and dynamic characteristics; m It is the control time domain, which indicates the number of steps of the control increment change, affecting the control sensitivity and the dynamic response of the system. , so that the control input is only It changes before the moment and remains unchanged afterwards, ensuring that the output error in the prediction time domain is optimized, that is, (20); make , unify the state values ​​obtained by iterative calculation into an extended matrix, and the state space equation of the prediction model can be written as: (twenty one); make , , , , , , in , , , , , . Therefore, we have: The performance index of formula (13) can be equivalent to the following form: (twenty two); In the formula, and They are transposed to each other and are equal, and equation (22) can be written as the following quadratic programming form: (twenty three); In the formula, , .

[0054] After solving the quadratic programming problem, the control sequence is obtained , take the first control action on the system, that is: (twenty four); Repeat the optimization solution at the next moment.

[0055] Step 2: Design Virtual Control Input .

[0056] Define the trajectory inclination tracking error: (25); Ballistic inclination error The derivative is: (26); Setting the angle of attack The virtual control quantity is: (27); In the formula .

[0057] Step 3: Design Virtual Control Input .

[0058] Define the angle of attack tracking error: (28); Angle of attack error The derivative is: (29); Setting the pitch angle The virtual control quantity is: (30); In the formula .

[0059] Step 4: Design the control volume .

[0060] Define the pitch angular velocity tracking error: (31); Pitch angular velocity error The derivative is: (32); Control quantity Design the controller as: (33); In the formula .

[0061] Next, the throttle opening of the hypersonic aircraft is obtained by solving the speed subsystem.

[0062] According to formula (6), the speed loop solution problem is transformed into: (34); In the formula, for The predicted speed of the moment, from the system model Evolved. are the minimum and maximum values ​​of the fuel equivalence ratio, which together constitute the constraint range.

[0063] Ignoring the influence of elastic modes, the optimization problem (34) is a single-input single-output system, and the controlled variable is the velocity , the control quantity is the fuel equivalence ratio .

[0064] To optimize (34), the system model (6) is first transformed into a linearized model related to the system state, that is: (35); in, Since the state of the aircraft at every moment during its flight is known, model (35) is available.

[0065] Then, the model (35) is discretized to obtain (36) ; In the formula, The transformation process similar to the first step of the height loop can transform the optimization problem (34) into a quadratic programming problem.

[0066] Furthermore, the attack angles are designed Virtual control volume , Pitch angle Virtual control volume , elevator deflection angle The inverse tangent tracking differentiator for the angle of attack Virtual control volume , Pitch angle Virtual control volume , elevator deflection angle Derivative calculation during calculation.

[0067] Furthermore, the angle of attack Virtual control volume The corresponding inverse tangent tracking differentiator is: ; Pitch Angle Virtual control volume The corresponding inverse tangent tracking differentiator is: ; Elevator deflection angle The corresponding inverse tangent tracking differentiator is: ; in, Angle of attack Virtual control volume The corresponding inverse tangent tracks the state of the differentiator, Angle of attack Virtual control volume The corresponding design parameters of the inverse tangent tracking differentiator have values ​​greater than 0; is the pitch angle Virtual control volume The corresponding inverse tangent tracks the state of the differentiator, is the pitch angle Virtual control volume The corresponding inverse tangent tracking differentiators have values ​​greater than 0; is the elevator deflection angle The corresponding inverse tangent tracks the state of the differentiator, is the elevator deflection angle The corresponding design parameters of the inverse tangent tracking differentiator are all greater than 0.

[0068] Verification The effectiveness of the controller designed by the present invention is verified by simulation. The parameters of the height loop MPC controller are set as follows: The weight matrix is ​​designed as , The speed loop MPC controller parameters are set as follows: , The backstepping controller parameters of the altitude loop are set as follows: The tracking differentiator parameters are set as follows: , , The simulation step size is set to 0.01s and the simulation time is set to 300s. In order to highlight the advantages of the proposed method, it is compared with the full state feedback predictive control and the speed loop using backstepping control. The results are shown in Figures 3 to 7As shown in the figure, 'BSMPC-1' is the first group of BSMPC controllers using backstepping control for the velocity loop, 'BSMPC-2' is the second group of BSMPC controllers using predictive control for the velocity loop, and 'MPC' is the MPC controller. The initial state of the aircraft is shown in Table 1. In this section, the constraints considered are , the control target is set to speed From 7820 ft / s to 8820 ft / s, altitude From 85,000ft to 86,000ft, and The following second-order filter is used to generate: (37).

[0069] In the formula, .

[0070] Table 1 Initial state of hypersonic vehicle simulation

[0071] Figure 3 Figure a is the speed tracking curve, and Figure b is the speed tracking error curve. Figure 3 It is shown that in the nominal environment, the speed tracking error of the 'BSMPC-1' controller is smaller than that of the predictive control of the full state space model due to the separate setting of the optimization problem solution. Figure 4 Figure a is the height tracking curve, and figure b is the height tracking error curve. Figure 4 It shows that the tracking error of the 'MPC' controller is smaller, and the use of the BSMPC controller reduces the computational load while losing some control performance, but the height tracking error can still converge to about 0.2m. Figure 5 Figure a is the track angle, Figure b is the angle of attack, and Figure c is the pitch angular velocity. Figure 7 Figure a is the fuel equivalence ratio, and Figure b is the elevator deflection angle. Figure 5 and Figure 7 It shows that during the control process of the designed controller, the angle of attack, rudder angle and fuel equivalence ratio are all within the constraint range. Figure 6 This shows that the elastic mode also converges to 0 quickly.

[0072] In order to verify that the proposed BSMPC can better meet the real-time requirements of the hypersonic aircraft flight process than predictive control, it is compared with the predictive control algorithm of the prior art, and simulation experiments are carried out multiple times in the same computer hardware environment and simulation parameters, and the average consumption time is recorded, as shown in Table 2. It can be concluded from the consumption time that under the 300s simulation condition, the MPC controller consumes 323s, and the real-time performance is insufficient. The BSMPC controller proposed in this embodiment can meet the real-time requirements of the aircraft. 'BSMPC-2' has better control performance than 'BSMPC-1', but because an additional optimization problem is solved in the solution process, the computational load increases. The 'BSMPC-1' controller inherits the MPC control performance, but has a smaller computational load and consumes less time than half of the MPC controller, which greatly improves the real-time performance of the control system.

[0073] Table 2 Simulation time

[0074] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0075] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0076] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0077] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0078] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms should not be understood as necessarily being directed to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

Claims

1. A hypersonic vehicle predictive backstepping control method, characterized in that: The following steps are involved: S1, construct a mathematical model of hypersonic aircraft; S2, decoupling the hypersonic aircraft mathematical model into a speed subsystem and an altitude subsystem; S3, taking the weighted sum of the speed tracking error and the throttle opening as the optimization performance index, and obtaining the throttle opening of the hypersonic aircraft by solving the speed subsystem; S4, designing a predictive backstepping controller for the altitude subsystem, taking a weighted sum of an altitude tracking error and a trajectory inclination angle as an optimization performance index, and solving the rudder deflection angle of the hypersonic aircraft through the predictive backstepping controller; S5, controlling the hypersonic aircraft with the rudder angle and the throttle opening.

2. A hypersonic vehicle predictive backstepping control method according to claim 1, characterized in that: The hypersonic vehicle mathematical model is expressed by a series of formulas: ； in, For speed, is the ballistic inclination angle, For height, is the angle of attack, is the pitch angular velocity, is the elastic mode, They are gravity acceleration, moment of inertia, vehicle mass, elastic modal frequency and damping ratio. They represent thrust, drag, lift, pitching moment and generalized force respectively; as well as, The approximate expression is as follows: ； in, are all known constants, , , , , , , is the coefficient under nominal conditions, and the coefficient under nominal conditions is expanded as follows: ； in, , , represent the reference area, thrust arm and mean aerodynamic chord respectively; is the dynamic pressure, , is the air density; , , They represent the fuel equivalence ratio, canard and elevator deflection angles of the hypersonic vehicle respectively; 、 、 。 3. A hypersonic vehicle predictive backstepping control method according to claim 2, characterized in that: Decoupling the hypersonic vehicle mathematical model into a speed subsystem and an altitude subsystem includes: S2.1, assuming that the ballistic inclination of the hypersonic vehicle in the cruise phase is Close to 0, making the hypersonic vehicle mathematical model , define lift The value is much larger than , thus ignoring the effect of thrust on hypersonic vehicles; S2.2, decoupling the hypersonic vehicle mathematical model into a strict feedback form, we obtain: ； ； in, , , , , , , , , ; is the negative gain coefficient of canard deflection and elevator deflection, represents the speed subsystem, Represents the altitude subsystem.

4. A hypersonic vehicle predictive backstepping control method according to claim 3, characterized in that: S3, taking the weighted sum of the speed tracking error and the throttle opening as the optimization performance index, the throttle opening of the hypersonic aircraft obtained by solving the speed subsystem includes: S3.1, according to the speed subsystem , the control law design of the speed subsystem is transformed into a secondary performance index optimization problem. The speed control optimization problem is expressed as: ； in, is the predicted speed of the hypersonic vehicle, is the predicted value of the velocity reference trajectory of the hypersonic vehicle, for The fuel equivalence ratio at the time, are the minimum and maximum values ​​of the fuel equivalence ratio, is the prediction step length, are the weighted matrices of speed tracking error and fuel equivalence ratio, J is the performance index, is the initial flight speed, t is the time in the prediction domain; S3.2, the speed subsystem Expressed as a linearized model related to the system state ,in ; S3.3, for the linearized model Discretize and get the speed prediction model ,in , T is the discretization step size, k represents the discrete moment, is the fuel equivalence ratio at time k, are respectively the flight speed at the next moment and the flight speed at the current moment; S3.4, converting the speed control optimization problem into a speed control quadratic programming problem through the speed prediction model; S3.5, solving the speed control quadratic programming problem to obtain the throttle opening of the hypersonic aircraft.

5. A hypersonic vehicle predictive backstepping control method according to claim 3, characterized in that: S4, designing a predictive backstepping controller for the altitude subsystem, taking the weighted sum of the altitude tracking error and the trajectory inclination angle as the optimization performance index, and solving the rudder deflection angle of the hypersonic aircraft by the predictive backstepping controller includes: S4.

1. Design of highly virtual control laws for hypersonic vehicles , the weighted sum of the height tracking error and the trajectory inclination is used as the optimization performance index, and the height virtual control law The solution is converted into a height control optimization problem, which is expressed as: ； in, is the predicted state of the hypersonic vehicle, is the predicted value of the altitude reference trajectory, , represents the height tracking error weight and control amount weight matrix, and both are positive definite matrices, and J is the performance index; are the minimum and maximum angle of attack, respectively. are the minimum and maximum elevator deflection angles, respectively. for The control law of the moment, To predict the altitude and initial flight altitude, Angle of attack The virtual control quantity, is the angle of attack and The functional relationship is approximately , is the pitch angle, is the rudder angle about Function of S4.3, the height subsystem The first equation of is transformed into a highly discrete state space model, and we get , where , , is the discrete step length, k represents the discrete moment; S4.4, transform the height control optimization problem into a quadratic programming problem through a series of equivalent transformations; S4.5, solve the quadratic programming problem and obtain a highly virtual control law ; S4.

6. In combination with the backstepping control method, the elevator deflection angle in the altitude virtual control law is designed.

6. A hypersonic vehicle predictive backstepping control method according to claim 5, characterized in that: S4.6, in combination with the backstepping control method, the elevator deflection angle in the altitude virtual control law is designed to include: S4.6.1, Design Angle of Attack Virtual control volume , so that the trajectory inclination of the hypersonic vehicle tracks the highly virtual control law designed in S4.5; S4.6.2, Design Pitch Angle Virtual control volume , so that the ballistic angle of attack of the hypersonic vehicle tracks the angle of attack designed in S4.6.1 Virtual control volume ; S4.6.3, Design elevator deflection angle , so that the pitch angle of the hypersonic vehicle tracks the pitch angle designed in S4.6.2 Virtual control volume .

7. A hypersonic vehicle predictive backstepping control method according to claim 6, characterized in that: Designed angle of attack Virtual control volume for ; Designed pitch angle Virtual control volume for ; Elevator deflection angle for ; in, is the trajectory inclination tracking error, is the designed feedback gain; is the angle of attack tracking error, is the designed feedback gain; is the pitch angular velocity tracking error, is the designed feedback gain.

8. A hypersonic vehicle predictive backstepping control method according to claim 7, characterized in that: Design angle of attack Virtual control volume , Pitch angle Virtual control volume , elevator deflection angle The inverse tangent tracking differentiator for the angle of attack Virtual control volume , Pitch angle Virtual control volume , elevator deflection angle Derivative calculation during calculation.

9. A hypersonic vehicle predictive backstepping control method according to claim 8, characterized in that: Angle of attack Virtual control volume The corresponding inverse tangent tracking differentiator is: ; Pitch Angle Virtual control volume The corresponding inverse tangent tracking differentiator is: ; Elevator deflection angle The corresponding inverse tangent tracking differentiator is: ; in, Angle of attack Virtual control volume The corresponding inverse tangent tracks the state of the differentiator, Angle of attack Virtual control volume The corresponding design parameters of the inverse tangent tracking differentiator have values ​​greater than 0; is the pitch angle Virtual control volume The corresponding inverse tangent tracks the state of the differentiator, is the pitch angle Virtual control volume The corresponding inverse tangent tracking differentiators have values ​​greater than 0; is the elevator deflection angle The corresponding inverse tangent tracks the state of the differentiator, is the elevator deflection angle The corresponding design parameters of the inverse tangent tracking differentiator are all greater than 0.

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