An attack angle control method using a neural network and a high-precision analytical solution
By using neural networks and high-precision analytical solutions, a perturbation model was established and drag coefficients were fitted, which solved the problem of the impact of missile velocity changes on attack angle control and improved the missile's strike effectiveness and accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIHANG UNIV
- Filing Date
- 2024-02-02
- Publication Date
- 2026-06-05
AI Technical Summary
Most existing missile attack angle control guidance laws assume that the missile speed remains constant, failing to effectively consider the impact of time-varying speed, resulting in low strike effectiveness.
By employing neural networks and high-precision analytical solutions, a perturbation model and drag coefficient fitting are established to construct an attack angle guidance law that considers time-varying velocity, which is then corrected using bias proportional guidance.
This improved the missile's strike effectiveness, enabled high-precision attack angle control, and enhanced the missile's strike effect.
Smart Images
Figure CN118092166B_ABST
Abstract
Description
Technical Field
[0001] This invention provides an attack angle control method that utilizes neural networks and high-precision analytical solutions, belonging to the fields of aerospace technology, weapon technology, and guidance and control. Background Technology
[0002] With advancements in protection technology, the frontal protection capabilities of tanks, ships, and other vessels have significantly improved. Therefore, to maximize lethality, missiles need to strike from specific angles. However, most current attack angle control guidance laws assume the missile's constant velocity. While these laws, derived under this assumption, still satisfy attack angle constraints, their effectiveness is low because they don't consider the impact of time-varying velocity. Therefore, it is necessary to improve attack angle control guidance laws to incorporate the effects of time-varying velocity during missile flight, thereby enhancing strike effectiveness. Summary of the Invention
[0003] Since typical attack angle control guidance laws assume that the missile's flight speed remains constant, and in actual combat missions, most missiles are unpowered and their speeds can deviate significantly, this invention proposes an attack angle guidance law that takes into account changes in missile flight speed based on neural networks and high-precision analytical solutions, thereby improving strike effectiveness.
[0004] This invention discloses an attack angle control method utilizing neural networks and high-precision analytical solutions, such as... Figure 1 As shown, the specific steps include the following:
[0005] Step 1. Establish the perturbation model
[0006] Missile terminal guidance can usually be considered as a geodetic model. Therefore, it is necessary to establish a dynamic model of the missile and analyze its small quantities to establish perturbation equations for subsequent use in solving the analytical solution of the trajectory.
[0007] The missile's dynamic model is as follows:
[0008]
[0009] Where r is the range, h is the altitude, v is the velocity, γ is the trajectory angle, g is the gravitational acceleration, m is the mass, D is the drag, and L is the lift. Assuming the standard control is zero angle of attack control, (1) can be rewritten as follows:
[0010]
[0011] in, D0 represents the initial aerodynamic drag. Among them, the gravitational acceleration at sea level g s Atmospheric density at sea level ρ sThese are constants. The right-hand side of the equation consists of small quantities. According to the theory of canonical perturbations, the state variables r, h, v, γ can be expanded as follows:
[0012]
[0013] The initial values for the zeroth and first-order components are:
[0014]
[0015]
[0016] Step 2. Solving for the zeroth order solution
[0017] After obtaining the perturbation equation, the analytical solution of the zeroth-order term in the perturbation equation is obtained by using the perturbation method with the help of approximate fitting and mathematical derivation, so as to be used for subsequent solving of the first-order solution.
[0018] Using the perturbation method, we can solve (3) to obtain the analytical solution for the zero-order term of the trajectory inclination angle:
[0019]
[0020] Where θ=-k θ t+θ0, k θ =2g s / v0,
[0021] Analytical solution of the zeroth-order velocity term:
[0022]
[0023] in,
[0024] The analytical solution for the zeroth-order term is:
[0025]
[0026] The analytical solution for the zeroth-order range term is:
[0027] r (0) =r0+k r7 t 7 +k r6 t 6 +k r5 t 5 +k r4 t 4 +k r3 t 3 +k r2 t 2 +k r1 t (9)
[0028] in,
[0029] In the above formula, r0, h0, θ0 represents the initial range, initial altitude, initial velocity, and initial trajectory inclination angle of the target ballistic trajectory during the terminal guidance phase, all of which are constants; a0, a1, a2, b0, b1, b2 are all constants related to the initial trajectory inclination angle. k is a constant related to the initial velocity and initial atmospheric drag. r1 ,k r2 ,k r3 ,k r4 ,k r5 ,k r6 For a0, a1, a2, c3, c2, c1, c0, The polynomial.
[0030] Step 3. Solving for the first-order solution
[0031] After obtaining the zeroth-order solution, the perturbation method is further used to construct a new perturbation equation to solve the analytical solution of the first-order term, and finally the guidance law is used for calculation.
[0032] The analytical solution for the first-order term of the ballistic inclination angle is:
[0033]
[0034] The analytical solution for the first-order velocity term is:
[0035]
[0036] The analytical solution for the first-order term is:
[0037]
[0038] The analytical solution to the first-order term of the range is:
[0039]
[0040] Where, k 1v1 ,k 1v2 ,k 1v3 ,k 1v4 ,k 1v5 ,k 1v6 ,k 1v7 ,k 1v8 ,k 1v9 k 1h1 ,k 1h2 ,k 1h3 ,k 1h4 ,k 1h5 ,k 1h6 ,k1h7 ,k 1h8 ,k 1h9 ,k 1h10 ,
[0041] k 1h11 ,k 1h12 ,k 1h13 k 1r1 ,k 1r2 ,k 1r3 ,k 1r4 ,k 1r5 ,k 1r6 ,k 1r7 ,k 1r8 ,k 1r9 ,k 1r10 ,k 1r11 ,k 1r12 ,k 1r13 These are all fitting coefficients in the first-order differential equation, which are only related to the missile's flight state.
[0042] Step 4. Fit the drag coefficient using a neural network.
[0043] Given a simulation state, different drag variations are obtained through Monte Carlo target shooting simulation. The values are then fitted using a quadratic function to obtain fitting coefficients. These coefficients are then fitted using a neural network, whose inputs are the initial simulation altitude, velocity, and trajectory inclination angle.
[0044]
[0045] Step 5. Attack Angle Control Guidance Law
[0046] After obtaining the analytical solution formula mentioned above, the guidance law only needs to measure the missile's current state to predict terminal flight deviations. Finally, corrections are made through offset proportional guidance to constrain the attack angle.
[0047] The off-target distance is defined as:
[0048] miss=(r des -r f sin(-γ) f (15)
[0049] Where, r des For the target position, r f For the missile position obtained from the analytical solution, γ f The terminal trajectory inclination angle is obtained from the analytical solution.
[0050] The guidance law is in the form of:
[0051]
[0052] In the above formula, Nmiss and N γ The guidance coefficient is typically taken as 3 to 5, t go This represents the remaining flight time.
[0053] The advantages of this invention are:
[0054] (1) A new perturbation equation form is proposed, and the resistance coefficient is fitted by a neural network, which further improves the accuracy of the analytical solution.
[0055] (2) By using analytical solutions, the influence of time-varying velocity on the attack angle is considered, which can improve the missile strike effectiveness.
[0056] (3) The guidance law requires a small amount of control, which is convenient for practical engineering applications. Attached Figure Description
[0057] Figure 1 This is a flowchart of the attack angle control guidance law based on neural networks and high-precision analytical solutions.
[0058] Figure 2 It is the velocity derivative graph in the perturbation term.
[0059] Figure 3 It is the derivative plot of the ballistic tilt angle in the perturbation term.
[0060] Figure 4 It is a velocity plot comparing analytical solutions.
[0061] Figure 5 It is a trajectory inclination diagram compared with the analytical solution.
[0062] Figure 6 It is a ballistic diagram compared with the analytical solution.
[0063] Figure 7 This is a graph showing the fitting results of the neural network training set.
[0064] Figure 8 This is a graph showing the fitting results of the neural network on the non-training set.
[0065] Figure 9 It is a simulation flowchart.
[0066] Figure 10 These are ballistic diagrams for three different scenarios.
[0067] Figure 11 These are trajectory inclination diagrams for three different scenarios.
[0068] Figure 12 These are ballistic diagrams comparing different methods.
[0069] Figure 13 This is a speed graph comparing different methods.
[0070] Figure 14 These are ballistic inclination diagrams comparing different methods.
[0071] Figure 15 This is a diagram comparing guidance commands using different methods.
[0072] The symbols and codes involved in the above diagram are explained as follows:
[0073] Figure 2 In, f3=-g s sinγ-Q D / m, g3=(Q D -D) / m+(g s -g)sinγ; Figure 3 In the middle, f4 = -g s cosγ / v0, g4=-gcosγ / v+g s cosγ / v0. Detailed Implementation
[0074] The following will be combined with the appendix Figure 1-12 The invention will be further described in detail with reference to the embodiments.
[0075] This invention targets air-to-ground strike scenarios. It uses a neural network to fit the drag coefficient of missile flight, then uses a perturbation method to solve for a highly accurate analytical solution, and finally implements an attack angle guidance law that takes into account the time-varying speed through offset proportional guidance.
[0076] The specific implementation of the invention is as follows:
[0077] Step 1: Establish the perturbation solution model
[0078] The air-to-ground scenario can be considered a planar geodetic model, and the missile's dynamic model is as follows:
[0079]
[0080] Where r is the range, h is the altitude, v is the velocity, γ is the trajectory angle, g is the gravitational acceleration, m is the mass, D is the drag, and L is the lift. The calculation formula is as follows:
[0081]
[0082] C L C D The lift coefficient and drag coefficient are calculated using the following formulas:
[0083]
[0084] Assuming the standard control is zero angle of attack control, (1) can be rewritten in the following form:
[0085]
[0086] in, D0 represents the initial aerodynamic drag.
[0087] Among them, the gravitational acceleration at sea level g s Atmospheric density at sea level ρ s It is a constant.
[0088] The right-hand side of the equation consists of small quantities. According to the theory of canonical perturbations, the state variables r, h, v, γ can be expanded as follows:
[0089]
[0090] The initial values for the zeroth and first-order components are:
[0091]
[0092]
[0093] Substituting (3) into (2), and ignoring the components of higher-order infinitesimals, we have:
[0094]
[0095]
[0096]
[0097]
[0098] The zeroth-order solution is as follows:
[0099]
[0100] The first-order solution is as follows:
[0101]
[0102] Among them, g (0) D represents the gravitational acceleration corresponding to the zeroth-order term of height. (0) This represents the aerodynamic drag determined by the zero-order velocity term and the zero-order altitude term.
[0103] Step 2: Solving for the zeroth order solution
[0104] For ease of solution, let's take...
[0105]
[0106] Then, we have,
[0107]
[0108] Take k θ =2g s If / v0, then integrating (15) yields the following:
[0109] θ=-k θ t+θ0 (16)
[0110] in,
[0111] Then, γ can be obtained. (0) The solution formula is as follows:
[0112]
[0113] Substitute (17) into have,
[0114]
[0115] Integrating the above equation, we can obtain...
[0116]
[0117] in, Substitute (17) and (19) into have,
[0118]
[0119] in, Integrating dh1, we have,
[0120]
[0121] Since dh2 and dh3 cannot be solved analytically for integral expressions, they are fitted as polynomial functions in time. Let them be:
[0122] dh2=a2t 2 +a1t+a0 (22)
[0123] dh3=b2t 2 +b1t+b0 (23)
[0124] Integrating it, we can obtain...
[0125]
[0126]
[0127] In summary, the analytical solution for the zeroth-order height term can be obtained as follows:
[0128]
[0129] Furthermore, from equation (17), we can obtain the expression for cosγ. (0) Perform fitting:
[0130]
[0131] Where c3, c2, c1, and c0 are fitting coefficients, and equations (19), (22), and (27) are substituted into... have,
[0132]
[0133] Integrating the above equation, we get:
[0134] r (0) =r0+k r7 t 7 +k r6 t 6 +k r5 t 5 +k r4 t 4 +k r3 t 3 +k r2 t 2 +k r1 t (29)
[0135] in,
[0136] In the above formula, r0, h0, θ0 represents the initial range, initial altitude, initial velocity, and initial trajectory inclination angle of the target ballistic trajectory during the terminal guidance phase, all of which are constants; a0, a1, a2, b0, b1, b2 are all constants related to the initial trajectory inclination angle. k is a constant related to the initial velocity and initial atmospheric drag. r1 ,k r2 ,k r3 ,k r4 ,k r5 ,k r6 For a0, a1, a2, c3, c2, c1, c0, The polynomial.
[0137] Step 3: Solving for the first-order solution
[0138] The first-order differential equation of the target control trajectory, composed of equation (13), is a linear time-varying system, which can be written as:
[0139]
[0140] In the above formula,
[0141] k 13 =cosγ (0) k 14 =-v (0) sinγ (0) k 23 =sinγ (0) k 24 =v (0) cosγ (0) k 34 =-g s cosγ (0) ,
[0142] coefficient k ij These are all zero-order component functions of the ballistic variables. The analytical expressions for the zero-order components have already been solved. In order to facilitate the solution of the first-order components, the coefficients need to be simplified.
[0143] Suppose its expression is as follows:
[0144]
[0145] The remaining expressions are:
[0146]
[0147] Where, k 44 Since it is a small quantity, it is considered to be a constant.
[0148] Define a new variable z = γ (1) Small amount ε' = k 44 Then the first-order differential equation for the trajectory inclination angle can be rewritten as:
[0149]
[0150] According to the theory of regular perturbations, let z = z (0) +ε'z (1) +o(ε), and substituting into the above equation, we get:
[0151]
[0152] Then the zeroth-order and first-order components of z can be obtained as follows:
[0153]
[0154]
[0155] Integrating the above equation yields the first-order solution for the trajectory inclination angle.
[0156]
[0157] Combining equations (30)-(31) and (36), we can solve for the first-order solutions of the remaining terms to obtain the following:
[0158]
[0159] Similarly, we can conclude that
[0160]
[0161]
[0162] After the above derivation is completed, the expression for the analytical solution is as follows:
[0163]
[0164] The simulation conditions were set with an initial range of 0m, an initial altitude of 4000m, an initial velocity of 200m / s, an initial trajectory inclination of 5deg, and a simulation time of 32.2s. The results are as follows. Figures 4-6 As shown, compared with the traditional analytical solution algorithm, the accuracy of this algorithm is further improved, especially in terms of speed.
[0165] Step 4: Fit the drag coefficient using a neural network
[0166] In step 1, we assume Q D While this is known, we actually need to calculate it using other methods. Therefore, the main factors affecting the change in the missile's drag coefficient are: ① current altitude; ② current velocity; ③ current trajectory inclination. Therefore, based on the actual combat mission, we select the following data range for neural network fitting:
[0167]
[0168] Figure 7 The data shows the fitting results for a trajectory at an altitude of 4000m, a speed of 180m / s, and a trajectory inclination of 10° (training set). Figure 8 The results show the fitting performance for a height of 933m, a speed of 203m / s, and a trajectory inclination of -41° (non-training set). The results demonstrate that neural networks have a strong advantage in fitting such highly nonlinear conditions.
[0169] Step 5: Attack Angle Control Guidance Law
[0170] The formula for defining the miss is as follows:
[0171] miss=(r des -r fsin(-γ) f (41)
[0172] Where, r cf For the target position, r f To predict the missile's terminal location, γ f To predict the terminal trajectory inclination angle.
[0173] Let the guidance law be of the form:
[0174]
[0175] Let the remaining flight time be t. go It can be easily calculated using Newton's iterative formula, usually requiring only two to three iterations. The iterative formula is as follows:
[0176]
[0177] The simulation program flow is as follows Figure 9 As shown, the simulation program flow is as follows:
[0178] 1) Obtain the current flight status of the missile.
[0179] 2) Utilize the predicted drag coefficient output by the neural network.
[0180] 3) Use analytical solutions to determine the target deviation and attack angle.
[0181] 4) Calculate control commands based on deviations.
[0182] 5) The fourth- to fifth-order Runge-Kutta algorithm is used to perform dynamic simulation of the missile's differential equations. The simulation ends when the missile encounters the target; otherwise, it jumps back to step 1).
[0183] Considering the flight control delay, the formula is as follows:
[0184] a l =(a c -a l ) / τ (44)
[0185] Wherein, the time constant τ = 0.1, and the conversion relationship between angle of attack and overload is as follows:
[0186]
[0187] The guidance coefficients are all taken as constants;
[0188] N miss =4,N γ =4 (46)
[0189] The simulation scenario is as follows:
[0190] Case Rf / m H0 / m V0 / m / s γ0 / deg γdes / deg 1 5000 4000 180 10 -60 2 6000 4000 180 10 -60 3 7000 4000 180 10 -60
[0191] The simulation results are shown below:
[0192] Case miss / m γf / deg 1 0.1883 -60.0166 2 0.7338 -59.9785 3 0.6003 -59.9688
[0193] Simulation results are as follows Figure 10 and Figure 11 As shown, both achieve precise strikes and high-precision attack angle control.
[0194] For Case 2, a comparison was made with other guidance methods, and the results are shown below:
[0195] method miss / m γf / deg Vf / m / s The method proposed in this invention 0.7338 -59.9785 262.62 Offset Proportion Guidance 0.5329 -59.7032 223.18 Sliding mode control 0.0034 -59.4281 205.62
[0196] The results are as follows Figures 12-15 As shown, the method proposed in this invention has a higher speed and stronger strike effectiveness compared to guidance laws that do not consider the influence of time-varying velocity.
Claims
1. An attack angle control method utilizing neural networks and high-precision analytical solutions, characterized in that: Includes the following steps: Step 1. Establish the perturbation model; The missile's terminal guidance is considered as a geodetic model. Therefore, a dynamic model of the missile is established and its small quantities are analyzed to establish perturbation equations for subsequent use in solving the analytical solution of the trajectory. Step 2. Solve for the zeroth order solution; After obtaining the perturbation equation, the analytical solution of the zeroth-order term in the perturbation equation is obtained by using the perturbation method, approximate fitting and mathematical derivation, so as to be used for subsequent solving of the first-order solution; Step 3. Solve for the first-order solution; After obtaining the solution for the zero-order term, the perturbation method is further used to construct a new perturbation equation to solve the analytical solution for the first-order term, which is then used to calculate the guidance law. Step 4. Fit the drag coefficient using a neural network; Given a simulation state, different resistance changes are obtained through Monte Carlo target shooting simulation. The values are then fitted using a quadratic function to obtain the fitting coefficients, and finally fitted using a neural network. Step 5. Attack angle control guidance law; After obtaining the analytical solution formula above, the guidance law needs to measure the missile's current state and predict the terminal flight deviation; finally, it is corrected through offset proportional guidance to achieve the constraint of the attack angle, specifically: Define the miss distance as: (15) in, For the target location, The missile position is obtained from the analytical solution. The terminal trajectory inclination angle obtained from the analytical solution; The guidance law is in the form of: （16） In the above formula, and The guidance coefficient is 3 to 5. This represents the remaining flight time.
2. The attack angle control method using neural networks and high-precision analytical solutions according to claim 1, characterized in that: In step 1, the missile's dynamic model is as follows: (1) in, r For range, h For height, v For speed, γ For the trajectory inclination angle, g It is the acceleration due to gravity. m For quality, D As resistance, L For lift.
3. The attack angle control method using neural networks and high-precision analytical solutions according to claim 2, characterized in that: Assuming the standard control is zero angle of attack control, equation (1) can be rewritten as follows: (2) in, , , The initial aerodynamic drag. Among them, sea level gravitational acceleration Atmospheric density at sea level It is a constant; the right half of the equation consists of small quantities.
4. The attack angle control method using neural networks and high-precision analytical solutions according to claim 3, characterized in that: According to the theory of regular perturbation, the state variables are... Expanded to: (3) The initial values for the zeroth and first-order components are: (4) (5)。 5. The attack angle control method using neural networks and high-precision analytical solutions according to claim 4, characterized in that: In step 2, the perturbation method is used to solve equation (3), and the analytical solution of the zero-order term of the trajectory inclination angle is obtained as follows: (6) in, , , ; Analytical solution of the zeroth-order velocity term: (7) in, ; The analytical solution for the zeroth-order term is: (8) The analytical solution for the zeroth-order range term is: (9) in, , , , , , , ; In the above formula, These are the initial range, initial altitude, initial velocity, and initial trajectory inclination angle of the target ballistic trajectory during the terminal guidance phase, and are all constants. All of these are constants related to the initial trajectory inclination angle; It is a constant related to the initial velocity and initial atmospheric drag; for The polynomial.
6. The attack angle control method using neural networks and high-precision analytical solutions according to claim 1, characterized in that: In step 3, the analytical solution for the first-order term of the ballistic inclination angle is: (10) The analytical solution for the first-order velocity term is: (11) The analytical solution for the first-order term is: (12) The analytical solution to the first-order term of the range is: (13) in, , ; , These are all fitting coefficients in the first-order differential equation, which are only related to the missile's flight state.
7. The attack angle control method using neural networks and high-precision analytical solutions according to claim 1, characterized in that: In step 4, the input to the neural network is the initial simulation height, velocity, and trajectory angle; (14)。