A Predictive Backstepping Control Method for Hypersonic Vehicles

Abstract

The present invention relates to a predictive backstepping control method for a hypersonic vehicle, comprising the following steps: S1, constructing a mathematical model of the hypersonic vehicle; S2, decoupling the mathematical model of the hypersonic vehicle 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 vehicle by solving through the speed subsystem; S4, designing a predictive backstepping controller for the altitude subsystem, taking the weighted sum of the altitude tracking error and the flight path angle as the optimization performance index, and obtaining the rudder deflection angle of the hypersonic vehicle by solving through the predictive backstepping controller; S5, controlling the hypersonic vehicle with the rudder deflection angle and the throttle opening.

Description

Technical Field

[0001] The present invention relates to the field of hypersonic vehicle control, and specifically refers to a predictive backstepping control method for hypersonic vehicles. Background Art

[0002] In order to ensure that the HV can maintain stability and strong robustness in a complex flight environment, it is necessary to continuously innovate and introduce advanced control methods and means in the design of its flight control system. Controllers designed based on traditional backstepping control, sliding mode control, and robust control methods often ignore key constraint conditions such as control surfaces and flight angles of attack. Such a design may lead to a decline in control performance or even system instability when external disturbances are strong. Therefore, problems such as constraint handling, strong nonlinearity, strong coupling, and fast time-variation are still the key problems to be solved in the design of HV control systems. As an optimal control method, predictive control can fully consider the constraint conditions of control and states when designing a controller, and is particularly suitable for dealing with multi-variable and constrained complex systems. The significant advantage of this method is that it can still achieve excellent control performance while strictly following 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 calculation time.

[0003] Designing a predictive backstepping control method for hypersonic vehicles to address the problems existing in the above-mentioned prior art is the purpose of the research of the present invention. Summary of the Invention

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

[0005] The technical solution of the present invention is as follows:

[0006] A predictive backstepping control method for hypersonic vehicles includes the following steps:

[0007] S1, constructing a mathematical model of a hypersonic vehicle;

[0008] S2, decoupling the mathematical model of the hypersonic vehicle into a speed subsystem and an altitude subsystem;

[0009] S3, using the weighted sum of speed tracking error and throttle opening as an optimization performance index, and obtaining the throttle opening of the hypersonic vehicle by solving through the speed subsystem;

[0010] S4. Design a predictive backstepping controller for the altitude subsystem, using the weighted sum of the altitude tracking error and the flight path angle as the optimization performance index, and solve for the deflection angle of the control surface of the hypersonic vehicle through the predictive backstepping controller;

[0011] S5. Control the hypersonic vehicle with the deflection angle of the control surface and the throttle opening.

[0012] Furthermore, the mathematical model of the hypersonic vehicle is represented by a series of formulas:

[0013] ;

[0014] where is the velocity, is the flight path angle, is the altitude, is the angle of attack, is the pitch angular velocity, is the elastic mode, are the gravitational acceleration, moment of inertia, vehicle mass, elastic mode frequency, and damping ratio respectively, represent the thrust, drag, lift, pitch moment, and generalized force respectively;

[0015] And, is approximately expressed as follows:

[0016] ;

[0017] where are all known constants, , , , , , , are the coefficients under nominal conditions, and the coefficients under nominal conditions are expanded as follows:

[0018] ;

[0019] where , , represent the reference area, thrust arm, and mean aerodynamic chord respectively; is the dynamic pressure, , is the air density; , , represent the fuel equivalence ratio, canard deflection angle, and elevator deflection angle of the hypersonic vehicle respectively;

[0020] , , .

[0021] Furthermore, decoupling the hypersonic vehicle mathematical model into a velocity subsystem and an altitude subsystem includes:

[0022] S2.1, assuming that the flight path angle of the hypersonic vehicle during the cruise phase is close to 0, making in the hypersonic vehicle mathematical model, defining the lift value much larger than , thus ignoring the influence of thrust on the hypersonic vehicle;

[0023] S2.2, decoupling the hypersonic vehicle mathematical model into a strict feedback form, obtaining:

[0024] ;

[0025] ;

[0026] wherein, , , , , , , , , ; is the negative gain coefficient of the canard deflection and the elevator deflection,

[0027] represents the velocity subsystem, represents the altitude subsystem.

[0028] Furthermore, S3, taking the weighted sum of the velocity tracking error and the throttle opening as the optimization performance index, obtaining the throttle opening of the hypersonic vehicle by solving through the velocity subsystem includes:

[0029] S3.1, according to the velocity subsystem , transforming the control law design of the velocity subsystem into a quadratic performance index optimization problem, and the velocity control optimization problem is expressed as:

[0030] ;

[0031] wherein, is the predicted velocity of the hypersonic vehicle, is the predicted value of the velocity reference trajectory of the hypersonic vehicle, is the fuel equivalence ratio at time is the minimum and maximum values of the fuel equivalence ratio, is the prediction step size, are the weighted matrices of the speed tracking error and the fuel equivalence ratio respectively, and J is the performance index. is the initial flight speed, and t is the moment in the prediction domain;

[0032] S3.2. Represent the speed subsystem as a linearized model related to the system state , where ;

[0033] S3.3. Discretize the linearized model to obtain the speed prediction model , where , T is the discretization step size, k represents the discrete time, is the fuel equivalence ratio at the k-th moment, are the flight speeds at the next moment and the current moment respectively.

[0034] S3.4. Transform the speed control optimization problem into a speed control quadratic programming problem through the speed prediction model;

[0035] S3.5. Solve the speed control quadratic programming problem to obtain the throttle opening of the hypersonic vehicle.

[0036] Furthermore, in S4, design a predictive backstepping controller for the altitude subsystem, using the weighted sum of the altitude tracking error and the flight path angle as the optimization performance index, and solve for the rudder deflection angle of the hypersonic vehicle through the predictive backstepping controller, including:

[0037] S4.1. Design the altitude virtual control law of the hypersonic vehicle, using the weighted sum of the altitude tracking error and the flight path angle as the optimization performance index, and transform the solution of the altitude virtual control law into an altitude control optimization problem, which is expressed as:

[0038] ;

[0039] where is the predicted state of the hypersonic vehicle, is the predicted value of the altitude reference trajectory, , represent the altitude tracking error weight and the control quantity weight matrix respectively, and both are positive definite matrices, and J is the performance index; are the minimum angle of attack and the maximum angle of attack respectively, are the minimum elevator deflection angle and the maximum elevator deflection angle respectively, is the control law at the For predicting the altitude and the initial flight altitude, is the angle of attack of the virtual control quantity, is the functional relationship between the angle of attack and which is approximately , is the pitch angle, is the function of the rudder deflection angle with respect to ;

[0040] S4.3. Transform the first formula of the altitude subsystem into the altitude discrete state - space model to obtain , where , , is the discrete step - length, and k represents the discrete time;

[0041] S4.4. Through a series of equivalent transformations, transform the altitude control optimization problem into a quadratic programming problem;

[0042] S4.5. Solve the said quadratic programming problem, and obtain the altitude virtual control law ;

[0043] S4.6. Combine the backstepping control method to design the elevator deflection angle in the said altitude virtual control law.

[0044] Furthermore, S4.6. Combining the backstepping control method, designing the elevator deflection angle in the said altitude virtual control law includes:

[0045] S4.6.1. Design the angle of attack virtual control quantity such that the ballistic inclination angle of the hypersonic vehicle tracks the altitude virtual control law designed in S4.5;

[0046] S4.6.2. Design the pitch - angle virtual control quantity such that the ballistic angle of attack of the hypersonic vehicle tracks the angle - of - attack virtual control quantity designed in S4.6.1;

[0047] S4.6.3. Design the elevator deflection angle such that the pitch angle of the hypersonic vehicle tracks the pitch - angle virtual control quantity designed in S4.6.2.

[0048] Furthermore, the designed angle - of - attack virtual control quantity is ;

[0049] The designed pitch angle Virtual control quantity is ;

[0050] Elevator deflection angle is ;

[0051] Among them, is the trajectory inclination angle 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.

[0052] Furthermore, the arctangent tracking differentiators for the angle of attack virtual control quantity , pitch angle virtual control quantity , and elevator deflection angle are designed for derivative calculation in the calculation processes of the angle of attack virtual control quantity , pitch angle virtual control quantity , and elevator deflection angle .

[0053] Furthermore, the arctangent tracking differentiator corresponding to the angle of attack virtual control quantity is: ;

[0054] The arctangent tracking differentiator corresponding to the pitch angle virtual control quantity is: ;

[0055] The arctangent tracking differentiator corresponding to the elevator deflection angle is: ;

[0056] Among them, is the state of the arctangent tracking differentiator corresponding to the angle of attack virtual control quantity , is the design parameter of the arctangent tracking differentiator corresponding to the angle of attack virtual control quantity , and their values are all greater than 0;

[0057] is the pitch angle the virtual control quantity and the state of the corresponding arctangent tracking differentiator is the pitch angle the virtual control quantity and the corresponding arctangent tracking differentiator, and their values are all greater than 0;

[0058] is the elevator deflection angle and the state of the corresponding arctangent tracking differentiator is the elevator deflection angle and the design parameters of the corresponding arctangent tracking differentiator, and their values are all greater than 0.

[0059] Therefore, the present invention provides the following effects and / or advantages:

[0060] The present invention combines backstepping control and predictive control. On the one hand, it gives play to the advantages of predictive control in dealing with constraints. On the other hand, it reduces the dimension of constraint optimization to one dimension, which can greatly reduce the online time.

[0061] In view of the constraint conditions of hypersonic vehicles, the present application adjusts the engine throttle command and the elevator deflection angle to achieve precise tracking of the reference speed and the reference altitude . Specifically, the present application decouples the mathematical model of the hypersonic vehicle into a speed subsystem and an altitude subsystem, and respectively performs different conversions on the speed subsystem and the altitude subsystem, and uses different optimized performance indicators as constraints to solve the control law of the hypersonic vehicle, so as to be able to precisely control the hypersonic vehicle.

[0062] The present application converts the speed subsystem into a linearized model and then into a discretized model, thereby transforming the speed control optimization problem into a speed control quadratic programming problem, and can solve the speed control quadratic programming problem to obtain the throttle opening of the hypersonic vehicle.

[0063] The present application designs the altitude virtual control law of the hypersonic vehicle, takes the weighted sum of the altitude tracking error and the flight path angle as the optimized performance indicator, converts the solution of the altitude virtual control law into an altitude control optimization problem, and through a series of equivalent transformations, transforms the altitude control optimization problem into a quadratic programming problem, so as to be able to solve and obtain the altitude virtual control law.

[0064] The present application uses the backstepping method to design the virtual control quantity of the angle of attack and the pitch rate The virtual control quantity and the actual control quantity - the elevator deflection angle .

[0065] In this application, the angle of attack virtual control quantity , pitch angle virtual control quantity , elevator deflection angle are respectively designed with arctangent tracking differentiators, which are used for the derivative calculation in the calculation process of the angle of attack virtual control quantity , pitch angle virtual control quantity , elevator deflection angle , avoiding the "differential explosion" problem in backstepping control.

[0066] Through the control method provided by this application, when controlling a hypersonic vehicle, the speed tracking error and altitude tracking error are smaller than those of the predictive control of the full state space model. During the control process of the designed controller, the angle of attack, elevator deflection angle, and fuel equivalence ratio are all within the constraints.

[0067] Other features and advantages of the present invention will be described in the subsequent specification, and part of them will become obvious from the specification or be understood by implementing the present invention. The objectives and other advantages of the present invention are achieved and obtained by the structures specifically pointed out in the specification and the drawings.

[0068] It should be understood that the above summary and the following detailed description of the present invention are exemplary and explanatory, and are intended to provide further explanation of the present invention as claimed. Brief Description of the Drawings

[0069] Figure 1 is a schematic flow chart provided for one embodiment of the present invention.

[0070] Figure 2 is a schematic diagram of the controller structure designed in the virtual control law design introducing backstepping control.

[0071] Figure 3 is the speed tracking and speed tracking error curve.

[0072] Figure 4 is the altitude tracking and altitude tracking error curve.

[0073] Figure 5 is the state response curve.

[0074] Figure 6 is the elastic mode response curve.

[0075] Figure 7 is the control law curve. Detailed implementation manners

[0076] For the convenience of those skilled in the art to understand, the embodiments will now be further described in detail for the present invention:

[0077] Aiming at the constraint conditions and real-time control problems faced by current hypersonic vehicles, the present invention proposes a predictive backstepping control method, aiming to achieve real-time control while dealing with the constraint conditions and improving its control performance. First, the mathematical model of the hypersonic vehicle is introduced; then, the design of the controller is discussed in detail, including the design of the predictive backstepping controller for the altitude channel and the design of the predictive controller for the velocity channel; finally, the theoretical design is verified by simulation.

[0078] Specifically, referring to Figure 1 , a predictive backstepping control method for a hypersonic vehicle includes the following steps:

[0079] S1. Construct a mathematical model of the hypersonic vehicle;

[0080] S2. Decouple the mathematical model of the hypersonic vehicle into a velocity subsystem and an altitude subsystem;

[0081] S3. Use the weighted sum of the velocity tracking error and the throttle opening as the optimization performance index, and solve for the throttle opening of the hypersonic vehicle through the velocity subsystem;

[0082] S4. Design a predictive backstepping controller for the altitude subsystem, use the weighted sum of the altitude tracking error and the flight path angle as the optimization performance index, and solve for the rudder deflection angle of the hypersonic vehicle through the predictive backstepping controller;

[0083] S5. Control the hypersonic vehicle with the rudder deflection angle and the throttle opening.

[0084] Furthermore, considering the longitudinal dynamic model of a Flexible Air-breathing Hypersonic Vehicle (FAHV), which consists of a first-order differential equation with five rigid-body states including velocity, flight path angle, altitude, angle of attack, and pitch angular velocity and six elastic modes, the mathematical model of the hypersonic vehicle is represented by a series of formulas:

[0085] ; (1)

[0086] Wherein, is the velocity, is the flight path angle, is the altitude, is the angle of attack, is the pitch angular velocity, is the elastic mode, are the gravitational acceleration, moment of inertia, vehicle mass, elastic mode frequency, and damping ratio respectively, represent the thrust, drag, lift, pitching moment, and generalized force respectively;

[0087] And, is approximately expressed as follows:

[0088] ; (2)

[0089] Among them, are all known constants, , , , , , , are the coefficients under nominal conditions. After expansion, the coefficients under nominal conditions are expressed as follows:

[0090] ; (3)

[0091] Among them, , , represent the reference area, thrust arm, and mean aerodynamic chord respectively; is the dynamic pressure, , is the air density; , , represent the fuel equivalence ratio, canard deflection, and elevator deflection of the hypersonic vehicle respectively;

[0092] , , .

[0093] Because the canard deflection and elevator deflection have a negative gain relationship, the actual control input 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 the FAHV.

[0094] The constraint conditions of the control input are:

[0095] (4)

[0096] In the formula, and are the upper and lower bounds of the fuel equivalence ratio respectively, and The elevator deflection angle are the upper and lower bounds respectively.

[0097] The constraint range of the angle of attack is:

[0098] (5)

[0099] wherein, and are the upper and lower bounds of the angle of attack respectively.

[0100] It can be seen from formulas (1), (2), (3), (4) and (5) that the longitudinal model of the hypersonic vehicle is a highly nonlinear, strongly coupled and constrained system.

[0101] Furthermore, decoupling the mathematical model of the hypersonic vehicle into a velocity subsystem and an altitude subsystem includes:

[0102] S2.1, assuming that the flight path angle of the hypersonic vehicle in the cruise stage is close to 0, making in the mathematical model of the hypersonic vehicle, defining the lift value is much greater than , thus ignoring the influence of thrust on the hypersonic vehicle;

[0103] For the convenience of controller design, it is necessary to perform a certain transformation on the nonlinear model of the hypersonic vehicle. Considering the characteristics that the speed of the hypersonic vehicle is mainly affected by the engine throttle valve and the altitude is affected by the elevator, the hypersonic vehicle is decoupled in this paper, and the system model is divided into a velocity subsystem and an altitude subsystem. The decoupling process makes the following reasonable assumptions:

[0104] Assumption 1: The flight path angle of the hypersonic vehicle in the cruise stage is a very small value, so in the formula.

[0105] Assumption 2: The angle of attack of the hypersonic vehicle in the cruise stage is small enough so that in the formula, so can be numerically ignored.

[0106] S2.2, decoupling the mathematical model of the hypersonic vehicle into a strict feedback form, we get:

[0107] (6);

[0108] (7);

[0109] Among them, the specific expressions of the functions in each formula are , , , , , , , , ;

[0110] represents the speed subsystem, represents the altitude subsystem.

[0111] Furthermore,

[0112] 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 vehicle obtained by solving through the speed subsystem includes:

[0113] S3.1. According to the speed subsystem , transform the control law design of the speed subsystem into a quadratic performance index optimization problem. The speed control optimization problem is expressed as:

[0114] (8);

[0115] Among them, is the predicted speed of the hypersonic vehicle, is the predicted value of the speed reference trajectory of the hypersonic vehicle, is the fuel equivalence ratio at time are the minimum and maximum values of the fuel equivalence ratio, is the prediction step, are the weighted matrices of the speed tracking error and the fuel equivalence ratio respectively;

[0116] S3.2. Represent the speed subsystem as a linearized model related to the system state , where ;

[0117] S3.3. Discretize the linearized model to obtain the speed prediction model , where , T is the discretization step, k represents the discrete time, is the fuel equivalence ratio at time k, are the flight speeds at the next moment and the current moment respectively.

[0118] S3.4. Transform the speed control optimization problem into a speed control quadratic programming problem through the speed prediction model;

[0119] S3.5. Solve the velocity control quadratic programming problem to obtain the throttle opening of the hypersonic vehicle.

[0120] Furthermore, in S4, design a predictive backstepping controller for the altitude subsystem, using the weighted sum of the altitude tracking error and the flight path angle as the optimization performance index. Solving through the predictive backstepping controller to obtain the rudder deflection angle of the hypersonic vehicle includes:

[0121] S4.1. Design the altitude virtual control law of the hypersonic vehicle , using the weighted sum of the altitude tracking error and the flight path angle as the optimization performance index, and transforming the solution of the altitude virtual control law into an altitude control optimization problem, which is expressed as:

[0122] (9);

[0123] where is the predicted state of the hypersonic vehicle, is the predicted value of the altitude reference trajectory, , represent the altitude tracking error weight and the control quantity weight matrix, and both are positive definite matrices. J is the performance index; are the minimum angle of attack and the maximum angle of attack respectively, are the minimum elevator deflection angle and the maximum elevator deflection angle respectively, is at time are the predicted altitude and the initial flight altitude, is the angle of attack of the virtual control quantity, is the functional relationship between the angle of attack and , approximately , is the pitch angle, is the functional relationship of the rudder deflection angle with respect to , and its expression can be deduced inversely from the subsequent backstepping control law;

[0124] S4.3. Transform the first equation of the altitude subsystem into an altitude discrete state space model to obtain , where , , is the discrete step length, and k represents the discrete time;

[0125] S4.4. Through a series of equivalent transformations, transform the altitude control optimization problem into a quadratic programming problem;

[0126] S4.5, Solve the quadratic programming problem, and obtain the altitude virtual control law through the solution. ;

[0127] S4.6, Combine the backstepping control method to design the elevator deflection angle in the altitude virtual control law.

[0128] Furthermore, S4.6, combining the backstepping control method to design the elevator deflection angle in the altitude virtual control law includes:

[0129] S4.6.1, Design the angle of attack virtual control quantity , so that the flight path angle of the hypersonic vehicle tracks the altitude virtual control law designed in S4.5;

[0130] S4.6.2, Design the pitch angle virtual control quantity , so that the angle of attack of the hypersonic vehicle tracks the angle of attack virtual control quantity designed in S4.6.1;

[0131] S4.6.3, Design the elevator deflection angle , so that the pitch angle of the hypersonic vehicle tracks the pitch angle virtual control quantity .

[0132] Furthermore, the designed angle of attack virtual control quantity is ;

[0133] The designed pitch angle virtual control quantity is ;

[0134] The elevator deflection angle is ;

[0135] wherein, is the flight path angle 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.

[0136] Steps S3 to S4 are as follows.

[0137] The control objective of this application is: in view of the constraint conditions on hypersonic vehicles, by adjusting the engine throttle command and elevator deflection angle, to achieve precise tracking of the reference speed and reference height.

[0138] When designing the backstepping controller for a hypersonic vehicle, the design steps of the altitude virtual control law for its altitude channel are as follows:

[0139] Define the altitude tracking error:

[0140] (10);

[0141] Derive the altitude error to obtain:

[0142] (11);

[0143] Then, its altitude virtual control law is designed as:

[0144] (12);

[0145] In the formula is the feedback control gain, are the altitude and altitude reference signals respectively.

[0146] Among them, the virtual control law adopts the existing control law , and specific design is carried out subsequently.

[0147] To improve the performance of the controller, the present invention introduces the optimization idea of predictive control into the design of the first-step virtual control law of backstepping control. The designed controller structure is as Figure 2 shown. For the altitude subsystem, its altitude virtual input value is obtained by online optimization solution of predictive control, and the actual input value is calculated by the backstepping method. The optimization of the speed subsystem is carried out independently. Compared with the general predictive control full-state feedback design, the dimension of optimization is reduced, thus reducing the optimization calculation time.

[0148] First, the altitude subsystem designs a strategy for controlling the hypersonic vehicle.

[0149] Step 1: Solve the virtual control input .

[0150] According to Equation (7), transform the first-step virtual input of the altitude loop into solving the following optimization problem:

[0151] (13);

[0152] In the formula, is the predicted state at from the system modelevolved from represents the weight of the altitude tracking error represents the weight of the control quantity, and both are positive definite matrices is the angle of attack of the virtual control quantity is the functional relationship between the angle of attack and and is approximately , is the pitch angle is the function of the rudder deflection angle with respect to and its expression can be inversely deduced from the subsequent backstepping control law;

[0153] The object of the optimization problem is a single-input single-output linear model, and the system is transformed into a discrete state-space model:

[0154] (14);

[0155] In the formula , , is the discrete step size k represents the discrete time. Ignoring disturbances or measurement noises, it is assumed that all output states can be measured. is the predicted state at time According to the superposition principle, k can be calculated from the state value measured at the current time and the assumed control input at future times. Therefore, the state value at future times can be iteratively calculated according to the prediction model (14):

[0156] (15);

[0157] (16);

[0158] (17);

[0159] (18);

[0160] (19);

[0161] In the formula, p represents the prediction time domain, i.e., the length of the rolling optimization time domain, which greatly affects the sum and dynamic characteristics of the control system; m is the control time domain, which represents the number of steps of the control increment change and affects the control sensitivity and the dynamic response of the system; generally take , so that the control input is only at It changes before the moment and remains unchanged afterwards, ensuring that the output error within the prediction horizon is optimized, i.e., there is:

[0162] (20);

[0163] Let , and unify the state values obtained by iterative calculation into an extended matrix. The state - space equation of the prediction model can be written as:

[0164] (21);

[0165] Let , , , , , ,

[0166] where , , , , , . Therefore, there is: . The performance index of equation (13) can be equivalently written in the following form: (22);

[0167] In the formula, and are transposes of each other and are equal. Write equation (22) in the following quadratic - programming form:

[0168] (23);

[0169] In the formula, , .

[0170] After solving the quadratic - programming problem, the control sequence is obtained. Take the first control to act on the system, i.e.:

[0171] (24);

[0172] Repeat the optimization and solution at the next moment.

[0173] Step 2: Design the virtual control input .

[0174] Define the ballistic - inclination tracking error:

[0175] (25);

[0176] For the ballistic - inclination error Derivation gives:

[0177] (26);

[0178] Set the angle of attack The virtual control quantity is:

[0179] (27);

[0180] In the formula .

[0181] Step 3: Design the virtual control input .

[0182] Define the angle of attack tracking error:

[0183] (28);

[0184] For the angle of attack error Derivation gives:

[0185] (29);

[0186] Set the pitch angle The virtual control quantity is:

[0187] (30);

[0188] In the formula .

[0189] Step 4: Design the control quantity .

[0190] Define the pitch angular velocity tracking error:

[0191] (31);

[0192] For the pitch angular velocity error Derivation gives:

[0193] (32);

[0194] For the control quantity Design the controller as:

[0195] (33);

[0196] In the formula .

[0197] Next, solve the throttle opening of the hypersonic vehicle through the velocity subsystem.

[0198] According to Equation (6), the problem of solving the speed loop is transformed into:

[0199] (34);

[0200] where, is the predicted speed at time evolved from the system model The minimum and maximum values of the fuel equivalence ratio together form the constraint range.

[0201] Ignoring the influence of the elastic mode, the optimization problem (34) is a single-input single-output system, with the controlled quantity being the speed and the control quantity being the fuel equivalence ratio .

[0202] To optimize (34), first transform the system model (6) into a linearized model related to the system state, that is:

[0203] (35);

[0204] where, . Since the state at each moment during the flight of the aircraft is known. Therefore, the model (35) is obtainable.

[0205] Then, discretize the model (35) to obtain

[0206] (36);

[0207] where, . A transformation process similar to the first step of the altitude loop can transform the optimization problem (34) into a quadratic programming problem.

[0208] Furthermore, design the arctangent tracking differentiators for the angle of attack virtual control quantity , pitch angle virtual control quantity , and elevator deflection angle respectively, for the derivative calculation during the calculation of the angle of attack virtual control quantity , pitch angle virtual control quantity , and elevator deflection angle .

[0209] Furthermore, the arctangent tracking differentiator corresponding to the angle of attack virtual control quantity is: ;

[0210] Pitch angle Virtual control variable The corresponding arctangent tracking differentiator is: ;

[0211] Elevator deflection angle The corresponding arctangent tracking differentiator is: ;

[0212] Among them, is the angle of attack Virtual control variable The state of the corresponding arctangent tracking differentiator, is the angle of attack Virtual control variable The design parameters of the corresponding arctangent tracking differentiator, and their values are all greater than 0;

[0213] is the pitch angle Virtual control variable The state of the corresponding arctangent tracking differentiator, is the pitch angle Virtual control variable The corresponding arctangent tracking differentiator, and its values are all greater than 0;

[0214] is the elevator deflection angle The state of the corresponding arctangent tracking differentiator, is the elevator deflection angle The design parameters of the corresponding arctangent tracking differentiator, and their values are all greater than 0.

[0215] Result verification

[0216] Verify the effectiveness of the controller designed by the present invention through simulation. The parameters of the altitude loop MPC controller are set as follows: The weight matrix is designed as , . The parameters of the speed loop MPC controller are set as follows: , . The parameters of the backstepping controller of the altitude loop are set as follows: . The parameters of the tracking differentiator are set as follows: , , . The simulation step size is set to 0.01 s, and the simulation time is set to 300 s. In order to highlight the advantages of the proposed method, it is compared with full state feedback predictive control and backstepping control for the speed loop in a simulation, and the results are as Figures 3 - 7As shown in the figure. In the figure, 'BSMPC-1' is the first group of BSMPC controllers using backstepping control for the speed loop, 'BSMPC-2' is the second group of BSMPC controllers using predictive control for the speed loop, and 'MPC' is the MPC controller. The initial state of the aircraft is shown in Table 1. In this section, the considered constraints are , and the control objective is set as the speed increasing from 7820 ft / s to 8820 ft / s, and the altitude increasing from 85000 ft to 86000 ft. and are generated by the following second-order filter:

[0217] (37).

[0218] In the formula, .

[0219] Table 1 Initial state of hypersonic vehicle simulation

[0220]

[0221] Figure 3 Figure a of Figure 3 is the speed tracking curve, and figure b is the speed tracking error curve, Figure 4 indicating that in the nominal environment, due to the separate setting of the optimization problem solution for the 'BSMPC-1' controller, the speed tracking error is smaller than that of the predictive control of the full state space model. Figure 4 Figure a of Figure 5 is the altitude tracking curve, and figure b is the altitude tracking error curve, Figure 7 indicating that the tracking error of the 'MPC' controller is smaller. Using the BSMPC controller can reduce the computational load while sacrificing some control performance, but the altitude tracking error can still converge to about 0.2 m. Figure 5 and Figure 7 indicating that during the control process of the designed controller, the angle of attack, elevator deflection angle, and fuel equivalence ratio are all within the constraints. Figure 6 illustrates that the elastic mode also quickly converges to 0.

[0222] To verify that the proposed BSMPC can better meet the real-time requirements of hypersonic vehicle flight compared to predictive control, a comparison is made with the predictive control algorithms of the prior art. Simulation experiments are conducted multiple times in the same computer hardware environment and simulation parameters, and the average consumption time is recorded, as shown in Table 2. From the consumption time, it can be concluded that under the 300s simulation condition, the MPC controller consumes 323s, with insufficient real-time performance. The BSMPC controller proposed in this embodiment can meet the real-time requirements of the vehicle. 'BSMPC-2' has better control performance than 'BSMPC-1', but due to solving one more optimization problem in the solution process, the computational load increases. The 'BSMPC-1' controller inherits the control performance of MPC, has a smaller computational load, and the consumption time is less than half of that of the MPC controller, greatly improving the real-time performance of the control system.

[0223] Table 2 Simulation Consumption Time

[0224]

[0225] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer-usable program code.

[0226] The present invention is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, and 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 the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0227] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means, and the instruction means implement the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0228] Although the preferred embodiments of the present invention have been described, additional changes and modifications can be made by those skilled in the art once they learn the basic creative concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0229] In the description of this specification, the description referring 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 connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms should not be understood as necessarily referring to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

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, using 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 through the speed subsystem solution; including: According to the speed subsystem, the control law design of the speed subsystem is transformed into a secondary performance index optimization problem; Represent the velocity subsystem as a linearized model related to the system state; Discretize the linearized model to obtain the speed prediction model; The speed control optimization problem is converted into a speed control quadratic programming problem through the speed prediction model; Solving the speed control quadratic programming problem to obtain the throttle opening of the hypersonic aircraft; 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 ballistic inclination angle 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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