A neural network tracking controller construction method for a hypersonic vehicle

Abstract

The application discloses a neural network tracking controller construction method of a hypersonic vehicle, and comprises the following steps: 1, establishing a longitudinal dynamics model of the hypersonic vehicle; 2, under constant speed and constant height, a group of equilibrium points of the hypersonic vehicle are calculated according to the longitudinal dynamics model; 3, the coordinate transformation and discretization processing are performed on the group of equilibrium points, so as to construct a discrete time model of the hypersonic vehicle based on a discrete time nonlinear output regulation theory, and a closed loop system of the discrete time model of the hypersonic vehicle is constructed; 4, a feedforward function is constructed based on the closed loop system of the discrete time model of the hypersonic vehicle, and a neural network is used to approximate the feedforward function, so as to construct an output feedback controller; 5, the optimal weight value of the neural network is found, and the coordinate transformation is performed on the output feedback controller, so as to construct a neural network tracking controller. The application can realize the tracking control of the hypersonic vehicle, and has high tracking performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aircraft control, in particular to a neural network tracking controller construction method of a hypersonic aircraft. BACKGROUND

[0002] The hypersonic aircraft generally refers to a missile, an aircraft and other aircrafts with a flight speed higher than 5 Mach, which has the characteristics of fast flight speed, strong penetration ability and long range, and plays an increasingly important role in the fields of military, economy and other fields. Compared with traditional aircrafts, the hypersonic aircraft always performs tasks in a more complex and changeable environment. At the same time, the hypersonic aircraft system is a multi-input multi-output system with strong nonlinearity, strong coupling and non-minimum phase characteristics. Therefore, the tracking control problem of the hypersonic aircraft has certain challenges. The existing method usually introduces a canard as an additional control surface to realize the tracking control of the hypersonic aircraft, however, the introduction of the canard will cause the increase of the aerodynamic heat of the system, and the thermal protection requirement of the hypersonic aircraft system is high, which is difficult to realize in engineering. Therefore, the tracking control problem of the hypersonic aircraft with elevators as the only control surface still needs further research. SUMMARY

[0003] Based on the technical problems existing in the background, the present application proposes a neural network tracking controller construction method of a hypersonic aircraft, so as to realize the tracking control of the hypersonic aircraft, and improve the tracking performance and tracking accuracy.

[0004] In order to achieve the above application purposes, the present application adopts the following technical solutions:

[0005] The neural network tracking controller construction method of the hypersonic aircraft of the present application has the characteristics that it comprises the following steps:

[0006] Step 1, establishing a longitudinal dynamics model of the hypersonic aircraft;

[0007] Step 2, under the constant speed and the constant height , according to the longitudinal dynamics model, a group of equilibrium points of the hypersonic aircraft is calculated, including: the state equilibrium point and the input equilibrium point ; wherein, represents the equilibrium speed, represents the equilibrium height, represents the equilibrium track angle, represents the equilibrium attack angle, represents the equilibrium pitch angle rate, and , ; represents the equilibrium fuel-air ratio, where denotes the equilibrium elevator deflection angle, and T denotes the transpose;

[0008] Step 3, coordinate transformation and discretization are performed on a set of equilibrium points, and a discrete-time model of the hypersonic vehicle based on the discrete-time nonlinear output regulation theory is constructed, so that a closed-loop system of the discrete-time model of the hypersonic vehicle is constructed;

[0009] Step 4, based on the closed-loop system of the discrete-time model of the hypersonic vehicle, a feedforward function is constructed, and a neural network is used to approximate the feedforward function, so that an output feedback controller is constructed;

[0010] Step 5, the optimal weight value of the neural network is found, and the coordinate transformation is performed on the output feedback controller, so that a neural network tracking controller is constructed.

[0011] The neural network tracking controller construction method for the hypersonic vehicle has the characteristics that the longitudinal dynamics model of the hypersonic vehicle in step 1 is established by using formula (1):

[0012] (1)

[0013] In formula (1): are the derivatives of the speed , the height , the track angle , the attack angle and the pitch angle rate , denotes the mass of the hypersonic vehicle, denotes the gravitational acceleration, denotes the moment of inertia in the pitch direction, denotes the lift, denotes the drag, denotes the thrust, denotes the pitch moment, and has:

[0014] (2)

[0015] In formula (2): denotes the dynamic pressure, denotes the air density at the height , and , denote the nominal air density, the nominal height and the air density decay rate respectively, denotes the average aerodynamic chord, denotes the reference area, denotes the thrust moment coupling coefficient, denotes the fuel-air ratio, denotes the elevator deflection angle, denotes the lift coefficient about the pitch moment coefficient, denotes the lift coefficient about the pitch moment coefficient, denotes the drag coefficient about the pitch moment coefficient, denotes the first thrust coefficient about the pitch moment coefficient, denotes the second thrust coefficient about the pitch moment coefficient, and has:

[0016] (3)

[0017] In formula (3), , , , , , , , denote 8 thrust fitting coefficients respectively; and denote 3 lift fitting coefficients respectively, , , and denote 4 drag fitting coefficients respectively, and denote 4 thrust moment fitting coefficients respectively.

[0018] Further, the step 3 comprises:

[0019] Step 3.1, defining the hypersonic vehicle state variable , the hypersonic vehicle control input , so as to perform coordinate transformation on and by using formula (4) to obtain the state variable of the hypersonic vehicle and the control input of the hypersonic vehicle:

[0020] (4)

[0021] Step 3.2, obtaining the discretized hypersonic vehicle discrete-time model by using formula (5) :

[0022] (5)

[0023] In formula (5), denotes the state variable of the hypersonic vehicle discrete-time model at the current moment, denotes a state variable of the discrete-time model of the hypersonic vehicle at the current time instant, denotes the current a first state variable of the discrete-time model of the hypersonic vehicle at the current time instant, denotes the current a first state variable of the discrete-time model of the hypersonic vehicle at the current time instant, denotes the current a second state variable of the discrete-time model of the hypersonic vehicle at the current time instant, denotes the current a second state variable of the discrete-time model of the hypersonic vehicle at the current time instant , denotes the current a third state variable of the discrete-time model of the hypersonic vehicle at the current time instant, denotes the current a third state variable of the discrete-time model of the hypersonic vehicle at the current time instant , denotes the current a fourth state variable of the discrete-time model of the hypersonic vehicle at the current time instant, denotes the current a fourth state variable of the discrete-time model of the hypersonic vehicle at the current time instant , denotes the current a fifth state variable of the discrete-time model of the hypersonic vehicle at the current time instant, denotes the current a fifth state variable of the discrete-time model of the hypersonic vehicle at the current time instant , denotes the current a control input of the discrete-time model of the hypersonic vehicle at the current time instant, and has:

[0024] (6)

[0025] (7)

[0026] (8)

[0027] (9)

[0028] (10)

[0029] in the formulas (6) to (10), is a sampling time, denotes the current a first control input of the discrete-time model of the hypersonic vehicle at the current time instant, denotes the current the second control input of the discrete-time model of the hypersonic vehicle at time t;

[0030] Step 3.3, constructing the external system by using formula (11);

[0031] (11)

[0032] in formula (11), denotes the external system matrix, denotes the state variable of the external system, denotes the first state variable of the external system at time t, denotes the second state variable of the external system at time t; and

[0033] (12)

[0034] (13)

[0035] in formula (12) and formula (13), , denotes two frequencies, , denotes two amplitudes, denotes the first state variable of the external system at time t, denotes the second state variable of the external system at time t, denotes the third state variable of the external system at time t, denotes the fourth state variable of the external system at time t;

[0036] Step 3.4, constructing the speed reference trajectory and the height reference trajectory of the discrete-time model based on formula (11);

[0037] Step 3.5, obtaining the tracking error at time t by using formula (14), and jointly constructing a closed-loop system of the discrete-time model of the hypersonic vehicle with formula (5) and formula (11):

[0038] (14)

[0039] Further, the step 4 comprises:

[0040] Step 4.1, constructing a discrete regulator equation corresponding to the closed-loop system by using formula (15):​​

[0041] (15)

[0042] In formula (15), denotes the steady state of , denotes the steady state input of , denotes the steady state of ;

[0043] Step 4.2, defining the feedforward function wherein denotes a constant matrix, such that the neural network approximation solution of the feedforward function is found using formula (16) :

[0044] (16)

[0045] In formula (16), denotes the weight between the th neuron of the input layer and the th neuron of the hidden layer, denotes the bias between the th neuron of the input layer and the th neuron of the hidden layer, denotes the weight between the th neuron of the hidden layer and the output layer, denotes the number of neurons, denotes all weights and biases of the neural network, denotes the activation function;

[0046] Step 4.3, constructing the output feedback controller from the neural network approximation solution

[0047] , such that the output feedback controller is constructed using formula (17) :

[0048] In formula (17), denotes the state variable of the state observer at the current time instant, denotes the state variable of the state observer at the time instant, denotes the first state variable of the state observer at the current time instant, denotes the second state variable of the state observer at the current time instant, and are the two gains of the output feedback controller.

[0049] Further, the step 5 comprises:

[0050] Step 5.1, constructing a target function by using formula (18) and solving to obtain the optimal weight and bias of the neural network :

[0051] (18)

[0052] In formula (18), represents the initial time set, represents the number of samples in a period;

[0053] Step 5.2, obtaining the neural network tracking controller by using formula (19)

[0054] (19)

[0055] In formula (19), represents the control input at the current time.

[0056] Compared with the prior art, the present application has the beneficial effects that:

[0057] 1. The present application proposes a neural network tracking controller construction method for a hypersonic vehicle, which is different from the prior art method of introducing a canard deflection angle as an additional control input. The method selects the elevator deflection angle and the fuel-air ratio as the control input of the system to design the controller, avoiding the aerodynamic heating problem caused by introducing the canard deflection angle as an additional control input, and is more practical.

[0058] 2. The present application proposes a neural network tracking controller based on the discrete time output regulation theory, which solves the tracking control problem of the hypersonic vehicle, and is different from the prior art method of designing the controller based on the continuous time mathematical model, which is more conducive to digital implementation. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 is the principle block diagram of the control algorithm of the present application;

[0060] Figure 2 is the speed tracking simulation effect diagram of the hypersonic vehicle system of the present application;

[0061] Figure 3 is the height tracking simulation effect diagram of the hypersonic vehicle system of the present application;

[0062] Figure 4 is the speed tracking error diagram of the present application;

[0063] Figure 5High tracking error map for the present application. DETAILED DESCRIPTION

[0064] The application will be further described in detail below with reference to the accompanying drawings and examples.

[0065] In this embodiment, a neural network tracking controller construction method for a hypersonic vehicle is as shown in the figure, and the specific steps are as follows: Figure 1

[0066] Step 1: Establish the longitudinal dynamics model of the hypersonic vehicle in step 1 using formula (1):

[0067] (1)

[0068] In formula (1): are the derivatives of the speed , altitude , flight path angle , angle of attack and pitch rate , respectively, denotes the mass of the hypersonic vehicle, denotes the gravitational acceleration, denotes the moment of inertia in the pitch direction, denotes the lift, denotes the drag, denotes the thrust, denotes the pitch moment, and has:

[0069] (2)

[0070] In formula (2): denotes the dynamic pressure, denotes the air density at the altitude , and , denote the nominal air density, the nominal altitude and the air density decay rate, respectively, denotes the average aerodynamic chord, denotes the reference area, denotes the thrust moment coupling coefficient, denotes the fuel-air ratio, denotes the elevator deflection angle, denotes the pitch moment coefficient about , denotes the lift coefficient about , denotes the drag coefficient about , denotes the first thrust coefficient about , ​denotes the second thrust coefficient of the hypersonic vehicle, and has:

[0071] (3)

[0072] In formula (3), denote eight thrust fitting coefficients, respectively; denote three lift fitting coefficients, respectively, denote four drag fitting coefficients, respectively, denote four thrust moment fitting coefficients, respectively.

[0073] Step two, according to the longitudinal dynamics model, a set of equilibrium points of the hypersonic vehicle is calculated at constant speed and constant height , including: state equilibrium point and input equilibrium point ; wherein, denotes the equilibrium speed, denotes the equilibrium height, denotes the equilibrium track angle, denotes the equilibrium attack angle, denotes the equilibrium pitch angle rate, and , ; denotes the equilibrium fuel-air ratio, denotes the equilibrium elevator deflection angle, and T denotes transposition.

[0074] Step three, a set of equilibrium points is subjected to coordinate transformation and discretization processing, for constructing a discrete-time model of the hypersonic vehicle based on the discrete-time nonlinear output regulation theory, so as to construct a closed-loop system of the discrete-time model of the hypersonic vehicle.

[0075] Step 3.1, defining the state variable of the hypersonic vehicle and the control input of the hypersonic vehicle, so as to perform coordinate transformation on and by using formula (4), to obtain the state variable of the hypersonic vehicle and the control input of the hypersonic vehicle: ​​​​​​​​​​​​​

[0076] (4)

[0077] Step 3.2, obtaining the discretized hypersonic vehicle discrete-time model with formula (5) :

[0078] (5)

[0079] In formula (5), denotes the state variable of the hypersonic vehicle discrete-time model at the current time, denotes the state variable of the hypersonic vehicle discrete-time model at the current time, denotes the first state variable of the hypersonic vehicle discrete-time model at the current time, denotes the first state variable of the hypersonic vehicle discrete-time model at the current time, denotes the second state variable of the hypersonic vehicle discrete-time model at the current time, denotes the second state variable of the hypersonic vehicle discrete-time model at the current time , denotes the third state variable of the hypersonic vehicle discrete-time model at the current time, denotes the third state variable of the hypersonic vehicle discrete-time model at the current time , denotes the fourth state variable of the hypersonic vehicle discrete-time model at the current time, denotes the fourth state variable of the hypersonic vehicle discrete-time model at the current time , denotes the fifth state variable of the hypersonic vehicle discrete-time model at the current time, denotes the fifth state variable of the hypersonic vehicle discrete-time model at the current time , denotes the control input of the hypersonic vehicle discrete-time model at the current time, and has:

[0080] (6)

[0081] (7)

[0082] (8)

[0083] (9)

[0084] (10)

[0085] In equations (6)-(10), Sampling time, Indicates the current The first control input to the discrete-time model of the hypersonic vehicle at any given moment. Indicates the current The second control input to the discrete-time model of the hypersonic vehicle.

[0086] Step 3.3: Construct an external system using equation (11);

[0087] (11)

[0088] In equation (11), Represents the external system matrix. Represents the state variables of the external system. express The state variables of the external system at any given time, express The state variables of the external system at any given time; and we have:

[0089] (12)

[0090] (13)

[0091] In equations (12)-(13), , Indicates two frequencies. , Indicates two amplitude values. express The first state variable of the external system at time t is express The second state variable of the external system at time _____. express The third state variable of the external system at time t, express The fourth state variable of the external system at time t.

[0092] Step 3.4: Construct a discrete-time model based on equation (11) velocity reference trajectory and high reference trajectory ;

[0093] Step 3.5, using equation (14) to obtain Tracking error at time Together with equations (5) and (11), they form a closed-loop system for the discrete-time model of a hypersonic vehicle:

[0094] (14)

[0095] Step 4: Based on the closed-loop system of the hypersonic vehicle discrete-time model, construct a feedforward function and approximate the feedforward function using a neural network to construct an output feedback controller.

[0096] Step 4.1: Construct the discrete regulator equation corresponding to the closed-loop system using equation (15):

[0097] (15)

[0098] In equation (15), Indicates about steady state, Indicates about steady-state input, Indicates about The steady state;

[0099] Step 4.2: Define the feedforward function ,in, The constant matrix is ​​used to find the feedforward function using equation (16). Approximate solution of neural network :

[0100] (16)

[0101] In equation (16): Represents the first input layer The 1st neuron and the 1st hidden layer The weights between neurons, This represents the first and second layers of the input and hidden layers. Bias between neurons The hidden layer is represented by the first... The weights between each neuron and the output layer Indicates the number of neurons. This represents all values ​​and biases of the neural network. Indicates the activation function;

[0102] Step 4.3: Based on the approximate solution of the neural network Thus, the output feedback controller can be constructed using equation (17). and state observer :

[0103] (17)

[0104] In formula (17): represents the state variable of the state observer at the current time, represents the state variable of the state observer at the current time, represents the first state variable of the state observer at the current time, represents the second state variable of the state observer at the current time, and are two gains of the output feedback controller.

[0105] Step five, find the optimal weight value of the neural network, and perform coordinate transformation on the output feedback controller, so as to construct a neural network tracking controller:

[0106] Step 5.1, construct a target function by using formula (18) and solve to obtain the optimal weight value and bias of the neural network :

[0107] (18)

[0108] In formula (18): represents the initial time set, represents the number of samples in a period;

[0109] Step 5.2, obtain the neural network tracking controller by using formula (19):

[0110] (19)

[0111] In formula (19), represents the control input at the current time.

[0112] In order to verify the effectiveness of the neural network tracking controller, the control effect of the neural network tracking controller is simulated and verified. The mass of the hypersonic vehicle , the moment of inertia , and the values of various aerodynamic parameters are selected as follows:

[0113] ,

[0114] ,

[0115]

[0116] ,

[0117]

[0118]

[0119] .

[0120] Select , formula (1) can be calculated and .

[0121] Select sampling time , the controller gain matrix is set to:

[0122] ,

[0123] ;

[0124] By computer training, the training parameter is set to:

[0125] , the initial weight is .

[0126] The tracking trajectory of the embodiment is .

[0127] Figure 2 And Figure 3 respectively represent the speed tracking simulation effect diagram and the height tracking simulation effect diagram of the hypersonic vehicle, Figure 4 and Figure 5 are the speed tracking error diagram and the height tracking error diagram. From the simulation results of Figures 2-5 , it can be seen that under the action of the neural network tracking controller, the hypersonic vehicle can quickly track the speed reference signal and the height reference signal.

[0128] The above describes only the preferred specific embodiments of the present application, but the protection scope of the present application is not limited to this, any skilled person in the art, according to the technical solution and the inventive concept of the present application, makes equivalent replacement or change within the technical range disclosed by the present application, should be covered within the protection scope of the present application.

Claims

1. A method for constructing a neural network tracking controller for a hypersonic vehicle, characterized in that, Includes the following steps: Step 1: Establish the longitudinal dynamic model of the hypersonic vehicle; Step 2, at a constant speed and constant height Based on the longitudinal dynamics model, a set of equilibrium points for the hypersonic vehicle are calculated, including: state equilibrium points. and input balance point ;in, Indicates the equilibrium speed. Indicates the equilibrium height. Indicates the balance track angle, Indicates the balanced angle of attack. Represents the balanced pitch rate, and , ; Indicates the balance fuel-air ratio. Indicates the balance elevator deflection angle; T indicates transposition. Step 3: Perform coordinate transformation and discretization on a set of equilibrium points to construct a discrete-time model of a hypersonic vehicle based on the discrete-time nonlinear output regulation theory, thereby constructing a closed-loop system of the discrete-time model of the hypersonic vehicle. Step 4: Based on the closed-loop system of the discrete-time model of the hypersonic vehicle, construct a feedforward function and use a neural network to approximate the feedforward function, thereby constructing an output feedback controller; Step 5: Find the optimal weights of the neural network and perform coordinate transformation on the output feedback controller to construct the neural network tracking controller.

2. The method for constructing a neural network tracking controller for a hypersonic vehicle according to claim 1, characterized in that, The longitudinal dynamic model of the hypersonic vehicle in step 1 is established using equation (1): (1) In formula (1): They are speeds ,high track angle Angle of attack and pitch rate The derivative, Indicates the mass of a hypersonic vehicle. Represents gravitational acceleration. The moment of inertia in the pitch direction. Indicates lift. Indicates resistance. Indicates thrust. Represents the pitching moment, and has: (2) In formula (2): Indicates dynamic pressure. Indicates height The air density at that location, and , These represent the nominal air density, nominal altitude, and air density decay rate, respectively. Indicates the mean aerodynamic chord length. Indicates the reference area. This represents the thrust torque coupling coefficient. Indicates the fuel-air ratio. Indicates the elevator deflection angle. Indicates about The pitching moment coefficient, Indicates about The lift coefficient, Indicates about The drag coefficient, Indicates about The first thrust coefficient, Indicates about The second thrust coefficient is: (3) In equation (3), , , , , , , , These represent the eight thrust fitting coefficients; and These represent the three lift fitting coefficients. , , and These represent the four resistance fitting coefficients. and These represent the four thrust torque fitting coefficients.

3. The method for constructing a neural network tracking controller for a hypersonic vehicle according to claim 2, characterized in that, Step 3 includes: Step 3.1: Define the state variables of the hypersonic vehicle. Hypersonic vehicle control input Thus, using equation (4) to and Perform coordinate transformation to obtain the state variables of the hypersonic vehicle. and control inputs of hypersonic vehicles : (4) Step 3.2: Use equation (5) to obtain the discretized discrete-time model of the hypersonic vehicle. : (5) In equation (5), Indicates the current State variables of a discrete-time model of a hypersonic vehicle at any given time. express State variables of a discrete-time model of a hypersonic vehicle at any given time. Indicates the current The first state variable of the discrete-time model of the hypersonic vehicle at time t is given. express The first state variable of the discrete-time model of the hypersonic vehicle at time t is given. Indicates the current The second state variable in the discrete-time model of the hypersonic vehicle at time t is... express The second state variable of the discrete-time model of the hypersonic vehicle at time t. , express The third state variable in the discrete-time model of the hypersonic vehicle at time t is... express The third state variable of the discrete-time model of the hypersonic vehicle at time t. , Indicates the current The fourth state variable in the discrete-time model of the hypersonic vehicle at time t. express The fourth state variable of the discrete-time model of the hypersonic vehicle at time t. , Indicates the current The fifth state variable in the discrete-time model of a hypersonic vehicle at time t. express The fifth state variable of the discrete-time model of the hypersonic vehicle at time t. , Indicates the current The control inputs to the discrete-time model of the hypersonic vehicle at each moment are: (6) (7) (8) (9) (10) In equations (6)-(10), Sampling time, Indicates the current The first control input to the discrete-time model of the hypersonic vehicle at any given moment. Indicates the current The second control input to the discrete-time model of the hypersonic vehicle at any given moment; Step 3.3: Construct an external system using equation (11); (11) In equation (11), Represents the external system matrix. Represents the state variables of the external system. express The state variables of the external system at any given time, express The state variables of the external system at any given time; and we have: (12) (13) In equations (12)-(13), , Indicates two frequencies. , Indicates two amplitude values. express The first state variable of the external system at time t is express The second state variable of the external system at time t. express The third state variable of the external system at time t, express The fourth state variable of the external system at time t; Step 3.4: Construct a discrete-time model based on equation (11) Velocity reference trajectory and high reference trajectory ; Step 3.5: Using equation (14) to obtain Tracking error at any time Together with equations (5) and (11), they form a closed-loop system for the discrete-time model of a hypersonic vehicle: (14)。 4. The method for constructing a neural network tracking controller for a hypersonic vehicle according to claim 3, characterized in that, Step 4 includes: Step 4.1: Construct the discrete regulator equation corresponding to the closed-loop system using equation (15): (15) In equation (15), Indicates about steady state, Indicates about steady-state input, Indicates about The steady state; Step 4.2: Define the feedforward function ,in, The constant matrix is ​​used to find the feedforward function using equation (16). Approximate solution of neural network : (16) In equation (16): Represents the first input layer The 1st neuron and the 1st hidden layer The weights between neurons, This represents the first and second layers of the input and hidden layers. Bias between neurons The hidden layer is represented by the first... The weights between each neuron and the output layer Indicates the number of neurons. This represents all values ​​and biases of the neural network. Indicates the activation function; Step 4.3: Based on the approximate solution of the neural network Thus, an output feedback controller can be constructed using equation (17): (17) In equation (17): Indicates the current The state variables of the time-state observer, express The state variables of the time-state observer, Indicates the current The first state variable of the time-state observer, Indicates the current The second state variable of the time-state observer, and These are the two gains of the output feedback controller.

5. The method for constructing a neural network tracking controller for a hypersonic vehicle according to claim 4, characterized in that, Step 5 includes: Step 5.1: Construct the objective function using equation (18) The optimal weights and biases of the neural network are then obtained by solving the problem. : (18) In equation (18): This indicates the set initial time. This represents the number of samples in one period; Step 5.2: Obtain the neural network tracking controller using equation (19): (19) In equation (19), Indicates the current Time-based control input.

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