Neural network tracking controller construction method of hypersonic aircraft

Abstract

The invention discloses a method for constructing a neural network tracking controller of a hypersonic flight vehicle. The method comprises the following steps: 1, establishing a longitudinal dynamic model of the hypersonic flight vehicle; 2, calculating a group of balance points of the hypersonic aircraft according to the longitudinal dynamic model at a constant speed and a constant height; 3, performing coordinate transformation and discretization processing on the group of balance points to construct a discrete time model of the hypersonic flight vehicle based on a discrete time nonlinear output regulation theory so as to construct a closed-loop system of the discrete time model of the hypersonic flight vehicle; 4, constructing a feed-forward function based on a closed-loop system of the discrete time model of the hypersonic aircraft, and approaching the feed-forward function by adopting a neural network to construct an output feedback controller; and 5, finding the optimal weight of the neural network, and performing coordinate transformation on an output feedback controller to construct a neural network tracking controller. According to the invention, tracking control of the hypersonic flight vehicle can be realized, and tracking performance with relatively high precision is realized.

Description

Technical Field

[0001] The present invention relates to the field of aircraft control, and in particular to a method for constructing a neural network tracking controller for a hypersonic aircraft. Background Art

[0002] Hypersonic aircraft generally refer to aircraft such as missiles and aircraft with a flight speed higher than Mach 5. They have the characteristics of high flight speed, strong penetration capability, and long range, and play an increasingly important role in the military, economic and other fields. Compared with traditional aircraft, hypersonic aircraft always perform tasks in more complex and changeable environments. At the same time, the hypersonic aircraft system is a multi-input and multi-output system with strong nonlinearity, strong coupling, and non-minimum phase characteristics. Therefore, its tracking control problem is challenging. Existing methods usually introduce canards as additional control surfaces to achieve tracking control of hypersonic aircraft. However, the introduction of canards will lead to an increase in the aerodynamic heat of the system, and the thermal protection requirements of the hypersonic aircraft system are high, which is difficult to achieve in engineering. Therefore, the tracking control problem of hypersonic aircraft with elevators as the only control surfaces needs further study. Summary of the invention

[0003] Based on the technical problems existing in the background technology, the present invention proposes a method for constructing a neural network tracking controller for a hypersonic aircraft, in order to achieve tracking control of the hypersonic aircraft and improve tracking performance and tracking accuracy.

[0004] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0005] The method for constructing a neural network tracking controller for a hypersonic aircraft of the present invention is characterized in that it comprises the following steps:

[0006] Step 1, establishing a longitudinal dynamic model of a hypersonic vehicle;

[0007] Step 2, at constant speed and constant height Under the longitudinal dynamics model, a set of equilibrium points of the hypersonic vehicle are calculated, including: state equilibrium point and input balance point ;in, represents the equilibrium speed, Indicates the equilibrium height, represents the equilibrium track angle, represents the equilibrium angle of attack, represents the equilibrium pitch rate, and , ; represents the balanced fuel-air ratio, represents the trim elevator deflection angle, and T represents transposition;

[0008] Step 3, coordinate transformation and discretization processing are performed on a set of equilibrium points to construct a discrete-time model of a hypersonic aircraft based on discrete-time nonlinear output regulation theory, thereby constructing a closed-loop system of the discrete-time model of the hypersonic aircraft;

[0009] Step 4, constructing a feedforward function based on a closed-loop system of a discrete-time model of a hypersonic aircraft, and using a neural network to approximate the feedforward function, thereby constructing an output feedback controller;

[0010] Step 5, find the optimal weights of the neural network and perform coordinate transformation on the output feedback controller to construct a neural network tracking controller.

[0011] The method for constructing a neural network tracking controller for a hypersonic aircraft according to the present invention is also characterized in that the longitudinal dynamics model of the hypersonic aircraft in step 1 is established using formula (1):

[0012] (1)

[0013] In formula (1): Speed ,high , track angle , angle of attack and pitch rate The derivative of represents the mass of the hypersonic vehicle, represents the acceleration due to gravity, represents the moment of inertia in the pitch direction, represents lift, Indicates resistance, Indicates thrust, represents the pitching moment, and:

[0014] (2)

[0015] In formula (2): Indicates dynamic pressure, Indicates height The air density at , denote the nominal air density, nominal altitude and air density decay rate respectively, represents the mean aerodynamic chord length, represents the reference area, represents the thrust-torque coupling coefficient, represents the fuel-air ratio, represents 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:

[0016] (3)

[0017] In formula (3), , , , , , , , They represent 8 thrust fitting coefficients respectively; and Represent the three lift fitting coefficients respectively, , , and Represent the four resistance fitting coefficients respectively. and They represent the four thrust and torque fitting coefficients respectively.

[0018] Furthermore, the step 3 comprises:

[0019] Step 3.1: Define hypersonic vehicle state variables , hypersonic vehicle control input , so using formula (4) and Perform coordinate transformation to obtain the state variables of the hypersonic vehicle and control inputs for hypersonic vehicles :

[0020] (4)

[0021] Step 3.2: Use equation (5) to obtain the discrete-time model of the hypersonic vehicle. :

[0022] (5)

[0023] In formula (5), Indicates the current The state variables of the discrete-time model of the hypersonic vehicle at time t, express The state variables of the discrete-time model of the hypersonic vehicle at time t, Indicates the current The first state variable of the discrete-time model of the hypersonic vehicle at time , express The first state variable of the discrete-time model of the hypersonic vehicle at time , Indicates the current The second state variable of the discrete-time model of the hypersonic vehicle at time , express The second state variable of the discrete-time model of a hypersonic vehicle at time , express The third state variable of the discrete-time model of the hypersonic vehicle at time , express The third state variable of the discrete-time model of hypersonic vehicle at time , Indicates the current The fourth state variable of the discrete-time model of the hypersonic vehicle at time , express The fourth state variable of the discrete-time model of hypersonic aircraft at time , Indicates the current The fifth state variable of the discrete-time model of the hypersonic vehicle at time , express The fifth state variable of the discrete-time model of hypersonic vehicle at time , Indicates the current The control input of the discrete-time model of the hypersonic vehicle at time t is:

[0024] (6)

[0025] (7)

[0026] (8)

[0027] (9)

[0028] (10)

[0029] In formula (6) to formula (10), is the sampling time, Indicates the current The first control input of the discrete-time model of the hypersonic vehicle at time , Indicates the current A second control input to the discrete-time model of the hypersonic vehicle at time instant;

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

[0031] (11)

[0032] In formula (11), represents the external system matrix, represents the state variables of the external system, express The state variables of the external system at time express The state variables of the external system at time; and:

[0033] (12)

[0034] (13)

[0035] In formula (12)-formula (13), , Represents 2 frequencies, , Represents 2 amplitudes, express The first state variable of the external system at time , express The second state variable of the external system at time , express The third state variable of the external system at time , express The fourth state variable of the external system at time t;

[0036] Step 3.4: Construct a discrete time model based on formula (11) The velocity reference trajectory and altitude reference trajectory ;

[0037] Step 3.5: Use formula (14) to get Tracking error at time , and together with equations (5) and (11), form a closed-loop system of the discrete-time model of a hypersonic vehicle:

[0038] (14)

[0039] Further, the step 4 comprises:

[0040] Step 4.1: Use equation (15) to construct the discrete regulator equation corresponding to the closed-loop system:

[0041] (15)

[0042] In formula (15), Indicates about The steady state Indicates about The steady-state input Indicates about The steady state state;

[0043] Step 4.2: Define the feedforward function ,in, Represents the constant matrix, so we can use formula (16) to find the feedforward function Neural network approximate solution :

[0044] (16)

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

[0046] Step 4.3: Approximate solution based on neural network , and thus use formula (17) to construct the output feedback controller:

[0047] (17)

[0048] In formula (17): Indicates the current The state variables of the state observer at each moment, express The state variables of the state observer at each moment, Indicates the current The first state variable of the state observer at time instant, Indicates the current The second state variable of the state observer at time instant, and are the 2 gains of the output feedback controller.

[0049] Further, the step 5 comprises:

[0050] Step 5.1: Use formula (18) to construct the objective function And solve to get the optimal weights and bias of the neural network :

[0051] (18)

[0052] In formula (18): Indicates the initial time set. Indicates the number of samples in one cycle;

[0053] Step 5.2: Use equation (19) to obtain the neural network tracking controller:

[0054] (19)

[0055] In formula (19), Indicates the current Control input at any time.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. The present invention proposes a method for constructing a neural network tracking controller for a hypersonic aircraft. Different from the existing method of introducing canard angle as an additional control input, this method selects elevator angle and fuel-air ratio as the control input of the system to design the controller, thus avoiding the aerodynamic heat problem caused by introducing canard angle as an additional control input, and is more practical.

[0058] 2. The present invention proposes a neural network tracking controller based on discrete-time output regulation theory, which solves the tracking control problem of hypersonic aircraft. Different from the existing controller design method based on continuous-time mathematical model, this method is more conducive to digital realization. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a principle block diagram of the control algorithm of the present invention;

[0060] Figure 2 This is a speed tracking simulation effect diagram of the hypersonic aircraft system of the present invention;

[0061] Figure 3 This is a diagram showing the effect of a height tracking simulation of a hypersonic aircraft system of the present invention;

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

[0063] Figure 5This is a height tracking error diagram of the present invention. DETAILED DESCRIPTION

[0064] The invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0065] In this embodiment, a method for constructing a neural network tracking controller for a hypersonic vehicle is provided. Figure 1 As shown, the specific steps are as follows:

[0066] Step 1: Use formula (1) to establish the longitudinal dynamic model of the hypersonic vehicle in step 1:

[0067] (1)

[0068] In formula (1): Speed ,high , track angle , angle of attack and pitch rate The derivative of represents the mass of the hypersonic vehicle, represents the acceleration due to gravity, represents the moment of inertia in the pitch direction, represents lift, Indicates resistance, Indicates thrust, represents the pitching moment, and:

[0069] (2)

[0070] In formula (2): Indicates dynamic pressure, Indicates height The air density at , denote the nominal air density, nominal altitude and air density decay rate respectively, represents the mean aerodynamic chord length, represents the reference area, represents the thrust-torque coupling coefficient, represents the fuel-air ratio, represents 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:

[0071] (3)

[0072] In formula (3), , , , , , , , They represent 8 thrust fitting coefficients respectively; and Represent the three lift fitting coefficients respectively, , , and Represent the four resistance fitting coefficients respectively. and They represent the four thrust and torque fitting coefficients respectively.

[0073] Step 2: At constant speed and constant height Under the longitudinal dynamics model, a set of equilibrium points of the hypersonic vehicle are calculated, including: state equilibrium point and input balance point ;in, represents the equilibrium speed, Indicates the equilibrium height, represents the equilibrium track angle, represents the equilibrium angle of attack, represents the equilibrium pitch rate, and , ; represents the balanced fuel-air ratio, represents the trim elevator deflection angle, and T represents transposition;

[0074] Step 3: coordinate transformation and discretization processing are performed on a set of equilibrium points to construct a discrete-time model of a hypersonic aircraft based on discrete-time nonlinear output regulation theory, thereby constructing a closed-loop system of the discrete-time model of the hypersonic aircraft;

[0075] Step 3.1: Define hypersonic vehicle state variables , hypersonic vehicle control input , so using formula (4) and Perform coordinate transformation to obtain the state variables of the hypersonic vehicle and control inputs for hypersonic vehicles :

[0076] (4)

[0077] Step 3.2: Use equation (5) to obtain the discrete-time model of the hypersonic vehicle. :

[0078] (5)

[0079] In formula (5), Indicates the current The state variables of the discrete-time model of the hypersonic vehicle at time t, express The state variables of the discrete-time model of the hypersonic vehicle at time t, Indicates the current The first state variable of the discrete-time model of the hypersonic vehicle at time , express The first state variable of the discrete-time model of the hypersonic vehicle at time , Indicates the current The second state variable of the discrete-time model of the hypersonic vehicle at time , express The second state variable of the discrete-time model of a hypersonic vehicle at time , express The third state variable of the discrete-time model of the hypersonic vehicle at time , express The third state variable of the discrete-time model of hypersonic vehicle at time , Indicates the current The fourth state variable of the discrete-time model of the hypersonic vehicle at time , express The fourth state variable of the discrete-time model of hypersonic aircraft at time , Indicates the current The fifth state variable of the discrete-time model of the hypersonic vehicle at time , express The fifth state variable of the discrete-time model of hypersonic vehicle at time , Indicates the current The control input of the discrete-time model of the hypersonic vehicle at time t is:

[0080] (6)

[0081] (7)

[0082] (8)

[0083] (9)

[0084] (10)

[0085] In formula (6) to formula (10), is the sampling time, Indicates the current The first control input of the discrete-time model of the hypersonic vehicle at time , Indicates the current The second control input of the discrete-time model of the hypersonic aircraft at time instant .

[0086] Step 3.3, construct the external system using formula (11);

[0087] (11)

[0088] In formula (11), represents the external system matrix, represents the state variables of the external system, express The state variables of the external system at time express The state variables of the external system at time; and:

[0089] (12)

[0090] (13)

[0091] In formula (12)-formula (13), , Represents 2 frequencies, , Represents 2 amplitudes, express The first state variable of the external system at time , express The second state variable of the external system at time , express The third state variable of the external system at time , express The fourth state variable of the external system at time .

[0092] Step 3.4: Construct a discrete time model based on formula (11) The velocity reference trajectory and altitude reference trajectory ;

[0093] Step 3.5: Use formula (14) to get Tracking error at time , and together with equations (5) and (11), form a closed-loop system of the discrete-time model of a hypersonic vehicle:

[0094] (14)

[0095] Step 4: Based on the closed-loop system of the discrete-time model of the hypersonic aircraft, a feedforward function is constructed, and a neural network is used to approximate the feedforward function, thereby constructing an output feedback controller:

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

[0097] (15)

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

[0099] Step 4.2: Define the feedforward function ,in, Represents the constant matrix, so we can use formula (16) to find the feedforward function Neural network approximate solution :

[0100] (16)

[0101] In formula (16): The input layer neurons and the hidden layer The weights between neurons, represents the input layer and the hidden layer The bias between neurons, represents the hidden layer The weights between neurons and the output layer, represents the number of neurons, represents all weights and biases of the neural network, represents the activation function;

[0102] Step 4.3: Approximate solution based on neural network , and thus use formula (17) to construct the output feedback controller and state observer :

[0103] (17)

[0104] In formula (17): Indicates the current The state variables of the state observer at each moment, express The state variables of the state observer at each moment, Indicates the current The first state variable of the state observer at time instant, Indicates the current The second state variable of the state observer at time instant, and are the 2 gains of the output feedback controller.

[0105] Step 5: Find the optimal weights of the neural network and transform the output feedback controller to construct a neural network tracking controller:

[0106] Step 5.1: Use formula (18) to construct the objective function And solve to get the optimal weights and bias of the neural network :

[0107] (18)

[0108] In formula (18): Indicates the initial time set. Indicates the number of samples in one cycle;

[0109] Step 5.2: Use equation (19) to obtain the neural network tracking controller:

[0110] (19)

[0111] In formula (19), Indicates the current Control input at any time.

[0112] In order to verify the effectiveness of the proposed neural network tracking controller, the present invention simulates and verifies the control effect of the neural network tracking controller. , moment of inertia , the values ​​of each aerodynamic parameter are selected as follows:

[0113] ,

[0114] ,

[0115]

[0116] ,

[0117]

[0118]

[0119] .

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

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

[0122] ,

[0123] ;

[0124] Obtained through computer training, the training parameters are set as:

[0125] , the initial weight is .

[0126] The tracking trajectory of this embodiment is .

[0127] Figure 2 and Figure 3 They respectively represent the speed tracking simulation effect diagram and the altitude tracking simulation effect diagram of the hypersonic aircraft. Figure 4 and Figure 5 are the velocity tracking error diagram and the height tracking error diagram. Figure 2-Figure 5 It can be seen from the simulation results that under the action of the neural network tracking controller, the hypersonic aircraft can quickly track the speed reference signal and the altitude reference signal.

[0128] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for constructing a neural network tracking controller for a hypersonic vehicle, characterized in that: The following steps are involved: Step 1, establishing a longitudinal dynamic model of a hypersonic vehicle; Step 2, at constant speed and constant height Under the longitudinal dynamics model, a set of equilibrium points of the hypersonic vehicle are calculated, including: state equilibrium point and input balance point ;in, represents the equilibrium speed, represents the equilibrium height, represents the equilibrium track angle, represents the equilibrium angle of attack, represents the equilibrium pitch rate, and , ; represents the balanced fuel-air ratio, represents the trim elevator deflection angle, and T represents transposition; Step 3, coordinate transformation and discretization processing are performed on a set of equilibrium points to construct a discrete-time model of a hypersonic aircraft based on discrete-time nonlinear output regulation theory, thereby constructing a closed-loop system of the discrete-time model of the hypersonic aircraft; Step 4, constructing a feedforward function based on a closed-loop system of a discrete-time model of a hypersonic aircraft, and using 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 a 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 dynamics model of the hypersonic vehicle in step 1 is established using formula (1): (1) In formula (1): Speed ,high , track angle , angle of attack and pitch rate The derivative of represents the mass of the hypersonic vehicle, represents the acceleration due to gravity, represents the moment of inertia in the pitch direction, represents lift, Indicates resistance, Indicates thrust, represents the pitching moment, and: (2) In formula (2): Indicates dynamic pressure, Indicates height The air density at , denote the nominal air density, nominal altitude and air density decay rate respectively, represents the mean aerodynamic chord length, represents the reference area, represents the thrust-torque coupling coefficient, represents the fuel-air ratio, represents 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 formula (3), , , , , , , , They represent 8 thrust fitting coefficients respectively; and Represent the three lift fitting coefficients respectively, , , and Represent the four resistance fitting coefficients respectively. and They represent the four thrust and torque fitting coefficients respectively.

3. The method for constructing a neural network tracking controller for a hypersonic vehicle according to claim 2, characterized in that: The step 3 comprises: Step 3.1: Define hypersonic vehicle state variables , hypersonic vehicle control input , so using formula (4) and Perform coordinate transformation to obtain the state variables of the hypersonic vehicle and control inputs for hypersonic vehicles : (4) Step 3.2: Use equation (5) to obtain the discrete-time model of the hypersonic vehicle. : (5) In formula (5), Indicates the current The state variables of the discrete-time model of the hypersonic vehicle at time t, express The state variables of the discrete-time model of the hypersonic vehicle at time t, Indicates the current The first state variable of the discrete-time model of the hypersonic vehicle at time , express The first state variable of the discrete-time model of the hypersonic vehicle at time , Indicates the current The second state variable of the discrete-time model of the hypersonic vehicle at time , express The second state variable of the discrete-time model of a hypersonic vehicle at time , express The third state variable of the discrete-time model of the hypersonic vehicle at time , express The third state variable of the discrete-time model of hypersonic vehicle at time , Indicates the current The fourth state variable of the discrete-time model of the hypersonic vehicle at time , express The fourth state variable of the discrete-time model of hypersonic aircraft at time , Indicates the current The fifth state variable of the discrete-time model of the hypersonic vehicle at time , express The fifth state variable of the discrete-time model of hypersonic vehicle at time , Indicates the current The control input of the discrete-time model of the hypersonic vehicle at time t is: (6) (7) (8) (9) (10) In formula (6) to formula (10), is the sampling time, Indicates the current The first control input of the discrete-time model of the hypersonic vehicle at time , Indicates the current A second control input to the discrete-time model of the hypersonic vehicle at time instant; Step 3.3, construct the external system using formula (11); (11) In formula (11), represents the external system matrix, represents the state variables of the external system, express The state variables of the external system at time express The state variables of the external system at time; and: (12) (13) In formula (12)-formula (13), , Represents 2 frequencies, , Represents 2 amplitudes, express The first state variable of the external system at time , express The second state variable of the external system at time , express The third state variable of the external system at time , express The fourth state variable of the external system at time t; Step 3.4: Construct a discrete time model based on formula (11) The velocity reference trajectory and altitude reference trajectory ; Step 3.5: Use formula (14) to get Tracking error at time , and together with equations (5) and (11), form a closed-loop system of 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: The step 4 comprises: Step 4.1: Use equation (15) to construct the discrete regulator equation corresponding to the closed-loop system: (15) In formula (15), Indicates about The steady state Indicates about The steady-state input Indicates about The steady state state; Step 4.2: Define the feedforward function ,in, Represents the constant matrix, so we can use formula (16) to find the feedforward function Neural network approximate solution : (16) In formula (16): The input layer neurons and the hidden layer The weights between neurons, represents the input layer and the hidden layer The bias between neurons, represents the hidden layer The weights between neurons and the output layer, represents the number of neurons, represents all weights and biases of the neural network, represents the activation function; Step 4.3: Approximate solution based on neural network , and thus use formula (17) to construct the output feedback controller: (17) In formula (17): Indicates the current The state variables of the state observer at each moment, express The state variables of the state observer at each moment, Indicates the current The first state variable of the state observer at time instant, Indicates the current The second state variable of the state observer at time instant, and are the 2 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: The step 5 comprises: Step 5.1: Use formula (18) to construct the objective function And solve to get the optimal weights and bias of the neural network : (18) In formula (18): Indicates the initial time set. Indicates the number of samples in one cycle; Step 5.2: Use equation (19) to obtain the neural network tracking controller: (19) In formula (19), Indicates the current Control input at any time.

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