A method for dynamic modeling and attitude control of a rapid projectile

Abstract

This invention discloses a dynamic modeling and attitude control method for agile missiles. It adds a flexible and controllable parachute to the agile missile design, dividing the agile turning process into two stages. Considering the flexibility, controllability, and dynamic characteristics of the parachute, a different dynamic model is established, using the missile as the main research subject. Compared to a single rigid body model, the geometric configuration and dynamic model of this invention help the attitude controller better calculate the actual turning process, laying the foundation for improving agile turning performance. After obtaining the dynamic model, this invention designs an attitude controller for the agile missile based on a non-singular terminal sliding surface, a double power-law approaching law, and an extended state observer, ensuring that the attitude controller still has high robustness and tracking performance under internal and external disturbances.

Description

Technical Field

[0001] This invention relates to the field of new concept weapons and missile dynamics control technology, specifically to a dynamics modeling and attitude control method for a rapid-fire projectile. Background Technology

[0002] In recent years, research on agile turning in missiles has focused on the implementation of direct force aerodynamic composite control systems, control allocation, tracking error convergence speed, and dynamic compensation for uncertainties. The basic principle of agile turning in traditional agile missiles is to install a direct force jet device on the missile's nose cone, away from its center of mass, to generate a direct force control torque. This torque, combined with the control torque generated by aerodynamic rudders, rapidly changes the missile's attitude. Current research on agile missiles is based on widely used dynamic models, optimizing agile turning performance through algorithmic strategies to better control attitude. While this method offers some optimization, it is constrained by the agile missile's geometric configuration and dynamic model, and it increases the energy consumption and product cost of the direct force device. Furthermore, this method places higher demands on the upper limit of pitch angular velocity, while in practical engineering, the missile body and its components have constraints on the maximum pitch angular velocity.

[0003] Current research on the integration of missiles and parachutes only focuses on the parachute's deceleration effect on the missile, neglecting studies on maneuvering and attitude control. Research on deceleration emphasizes the parachute, ignoring the missile's degrees of freedom and forces. Furthermore, such research presupposes an uncontrolled parachute; even if the missile is presumed to be controlled, its forces are only considered under gravity, resulting in low accuracy. In modeling, existing solutions use Newton-Euler and Kirchhoff methods, yielding single-rigid-body models that cannot accurately simulate the parachute's shape changes during motion, ignoring its flexibility. Therefore, they cannot be used for precise attitude control, only providing a rough simulation of the parachute's deceleration effect on the missile.

[0004] Therefore, there is an urgent need for a modeling and attitude control method for agile turning processes, which can improve the agile turning performance of missiles, reduce energy consumption, and lower product costs. Summary of the Invention

[0005] In view of this, the present invention provides a dynamic modeling and attitude control method for a swift projectile, which can improve agile turning performance, reduce turning radius, shorten turning time, reduce energy consumption, and lower product cost.

[0006] The technical solution for realizing the present invention is as follows:

[0007] A dynamic modeling and attitude control method for a rapid-fire projectile, comprising a swift missile and a flexible, controllable parachute, is proposed. The dynamic modeling and attitude control steps are as follows:

[0008] Based on the connection between the parachute and the swift missile, the agile turn process is divided into a first stage and a second stage. The first stage is from the initial moment to the moment before entering the second stage, during which the parachute is connected to the agile missile. The second stage is from the moment after the first stage to the final moment, during which the parachute is disconnected from the agile missile and the acceleration engine is ignited.

[0009] Based on the flexible controllable force, uncontrollable force, and dynamic characteristics of the parachute generated by the contraction of the parachute lines, and the force and dynamic characteristics of the missile, a dynamic model of the swift missile in the first stage is established. The dynamic model of the swift missile in the second stage is the dynamic model of the missile itself without a parachute. Based on the dynamic model, the state equation of attitude tracking error is established, and an attitude controller is designed.

[0010] The parameters of the preset attitude controller are used to calculate the attitude control vector. The pitch angle of the swift rocket is adjusted using the attitude control vector. It is then determined whether the pitch angle reaches the desired pitch angle. If it does, the agile turn is completed; otherwise, the attitude control vector is calculated again.

[0011] Furthermore, the dynamic model of the swift projectile in the second stage is as follows:

[0012]

[0013] Among them, V b It is the missile's speed; Q b It is the missile's dynamic pressure; T is the speed-increasing engine thrust; u T It is the engine speed switch; C x These are the aerodynamic parameters of missile drag; C nα These are the aerodynamic parameters of the missile's lift generated by its angle of attack; C nδ These are the aerodynamic parameters of the missile's lift generated by the aerodynamic rudders; C mα These are the aerodynamic parameters of the missile's torque generated by the angle of attack; C mδ These are the aerodynamic parameters of the missile's torque generated by the aerodynamic rudder; g is the acceleration due to gravity; S b It is the characteristic area of ​​the missile; L b It is the characteristic length of the missile; m b It is the mass of the missile; I b It is the missile's moment of inertia; θ b It is the missile's elevation angle; α b It is the missile's angle of attack; γ b It is the missile trajectory inclination angle; q b It is the missile's pitch angular velocity; x b The x-coordinate of the missile's center of mass is y. b δ is the longitudinal coordinate of the missile's center of mass; δ is the aerodynamic rudder deflection angle and |δ|≤δ max δ max It is the maximum deflection angle that the aerodynamic rudder can achieve; FR It is the maximum thrust of the direct-force jet device; L R It is the distance from the direct force jet device to the missile's center of gravity; C Nb For missile aerodynamic parameters; L CPb This is the distance from the missile's center of mass to its center of pressure.

[0014] Furthermore, the specific method for establishing the dynamic model of the rapid projectile in the first stage is as follows:

[0015] The first-stage dynamic model is established using the Lagrange method, and its expression is as follows:

[0016]

[0017] In the formula, X = [x b y b θ b θ p ] T Let x be a generalized coordinate vector, where x b Let y be the x-coordinate of the missile's center of mass. b Let θ be the vertical coordinate of the missile's center of mass. b Let θ be the missile's elevation angle. p Let A be the umbrella pitch angle; matrix A is derived from A ij A is a 4×4 matrix composed of (i, j = 1, 2, 3, 4). ij The expression is:

[0018] A 11 =m b +m p +a 11 cos 2 θp+a 22 sin 2 θ p

[0019] A 12 =a 11 cosθ p sinθ p -a 22 sinθ p cosθ p

[0020] A 13 =m p l tb sinθ b +a 11 l tb cosθ p sin(θ b -θ p )+a 22 l tb sinθp cos(θ b -θ p )

[0021] A 14 =m p l pt sinth p +a 22 l pt sinth p

[0022] A 21 =a 11 sinth p cosθ p -a 22 cosθ p sinth p

[0023] A 22 =m b +m p +a 11 sin 2 i p +a 22 cos 2 i p

[0024] A 23 =a 11 l tb sinth p sin(θ b -θ p )-m p l tb cosθ b -a 22 l tb cosθ p cos(θ b -θ p )

[0025] A 24 =-m p l pt cosθ p -a 22 l pt cosθ p

[0026] A 31 =m p +a 11 l tb sin(θ b -θ p )cosθ p +a22 l tb cos(θ b -θ p )sinθ p

[0027] A 32 =-m p +a 11 l tb sin(θ b -θ p )sinθ p -a 22 l tb cos(θ b -θ p )cosθ p

[0028]

[0029] A 34 =m p l pt l tb cos(θ p -θ b )+a 22 l pt l tb cos(θ b -θ p )

[0030] A 41 =m p +a 22 l pt sinth p

[0031] A 42 =-m p -a 22 l pt cosθ p

[0032] A 43 =m p l pt l tb cos(θ p -θ b )+a 22 l pt l tb cos(θ b -θ p )

[0033]

[0034] matrixC for Ci A 4×1 matrix consisting of (i = 1, 2, 3, 4), C i The expression is:

[0035]

[0036]

[0037]

[0038]

[0039] The generalized force vector Q is given by Q i A 4×1 matrix consisting of (i = 1, 2, 3, 4), Q i The expression is:

[0040]

[0041]

[0042] Q3 = M b1 -F yp l tb cosθ b +F xp l tb sinθ b +F R L R u R +C mδ Q b S b L b δ

[0043]

[0044] Among them, l tb The distance from the missile's center of mass to the center of the cross-section of the missile's tail; l pt The distance from the center of mass of the parachute to the center of the cross-section of the missile's tail; m p It's the quality of the umbrella; I p It is the moment of inertia of the umbrella; It is the apparent quality along the umbrella's axis of symmetry; It is the apparent mass in the direction perpendicular to the umbrella's axis of symmetry; a 66 =k 66 I f It is the apparent moment of inertia in the direction perpendicular to the vertical plane; k 11 k 22 k 66 These are the first, second, and third apparent coefficients, respectively, where ρ is the air density. It is the volume of fluid displaced by the parachute; It is the moment of inertia of the fluid displaced by the parachute; d p It is the nominal diameter of the umbrella; It is umbrella dynamic pressure; u p ∈[-1,1] represents the ratio of the change in parachute lines to the allowable change, with contraction being positive and relaxation being negative; D is the missile drag; L1 = Q b S b C nα α b The lift is generated by the missile's angle of attack; F T It is the axial force of the parachute; F N1 =C N Q p πd p 2 / 4 is the normal force generated by the parachute angle of attack; M p1 =C mp Q p πd p 3 / 4 is the restoring torque generated by the parachute angle of attack; C N C is the aerodynamic parameter of the normal force generated by the angle of attack of the parachute; mp These are the aerodynamic parameters of the torque generated by the angle of attack of the parachute; C Nup C is the aerodynamic parameter of the normal force generated by the contraction of the parachute lines; mup It is the aerodynamic parameter of the torque generated by the contraction of the parachute lines.

[0045] M b1 It is the restoring torque generated by the missile's angle of attack, and its expression is:

[0046]

[0047] F xp F yp The uncontrollable force of a parachute has components in the horizontal and vertical directions, and its expression is:

[0048]

[0049] u 11 v 22 It is the velocity of the fluid, and its expression is:

[0050]

[0051] C du C dv It is the remainder of the fluid velocity derivative after removing the second derivative of the generalized variable, and its expression is:

[0052]

[0053] Furthermore, the state equation for the attitude tracking error is established based on the dynamic model, specifically as follows:

[0054] Based on the dynamic model of the first stage, establish the state equation of the first stage; based on the dynamic model of the second stage, establish the state equation of the second stage; based on the two state equations, establish the state equations of the attitude tracking error in the first and second stages.

[0055] Furthermore, the state equations for the attitude tracking errors in the first and second stages are expressed as follows:

[0056] With the desired missile pitch angle θ bc As the expected value of the attitude control variable, the attitude tracking error e1 and its derivative e2 are defined as follows:

[0057]

[0058] The state equation for the attitude tracking error in the first stage is:

[0059]

[0060] Among them, U pseudo =b1δ+b2u p +b3u R This is a virtual control variable.

[0061] The state equation for the attitude tracking error in the second stage is:

[0062]

[0063] Furthermore, the expression for the state equation of the first stage is:

[0064]

[0065] Where d is the sum of internal uncertainties and external disturbances of the system.

[0066] f1=GA -1 (EC), where the input matrix B = GA -1 D = [b1, b2, b3], where b1 is the first variable of the input matrix, b2 is the second variable of the input matrix, and b3 is the third variable of the input matrix; G = [0, 0, 1, 0] T It is a transformation matrix; U = [δ, u p ,u R ] T It is the attitude control vector, δ c u pc u Rc These are rudder deflection angle, flexible force, and direct force, respectively.

[0067] The expression for matrix E is:

[0068]

[0069] The expression for matrix D is:

[0070]

[0071] The expression for the state equation in the second stage is:

[0072]

[0073] Where b4 = Q b S b L b C mδ / I b b5 = F R L R / I b The expression for f2 is:

[0074]

[0075] Furthermore, the design of the attitude controller includes three parts: a non-singular terminal sliding surface, a double power-law approaching the target, and uncertainty estimation. The expression for the non-singular terminal sliding surface is:

[0076]

[0077] Where β > 0; 1 < p / q < 2; p and q are positive odd numbers; β, p, and q are adjustable parameters.

[0078] The expression for the double-power reaching law is:

[0079]

[0080] Where k1 > 0; k2 > 0; a1 > 1; 0 < a2 < 1; sgn(·) is the sign function; k1, k2, a1, and a2 are adjustable parameters.

[0081] The expression for the estimation of uncertainty is:

[0082]

[0083] Where f takes the values ​​f1 and f2 at different stages; U takes the values ​​U at different stages. pseudo and b4δ+b5u R z1 and z2 are respectively q b The estimated values ​​of d; E1 = q b-z1 is the estimation error; 0.5 < m1 < 1; m2 = 2m1 - 1; n1 = 1 / m1; n2 = n1 + m1 - 1; σ1 > 1; σ2 > 1; c1 > 0; c2 > 0.

[0084] The expression for sgmf(E1) is:

[0085]

[0086] Where μ > 0, τ > 0; m1, m2, n1, n2, c1, c2, σ1, σ2, τ and μ are adjustable parameters.

[0087] The expression for the attitude controller is:

[0088] The expression for the first stage is:

[0089]

[0090]

[0091]

[0092]

[0093] The expression for the second stage is:

[0094]

[0095]

[0096] Among them, u pmax =1 represents the maximum value of the flexible force command; δ c u pc u Rc The rudder deflection angle, flexible force, and direct force calculated by the controller are respectively passed through a first-order inertial element to obtain the δ and u that make up the attitude control vector. p u R .

[0097] Beneficial effects:

[0098] 1. This invention proposes a dynamic modeling and attitude control method for a swift missile, adding a flexible and controllable parachute to the basic agile missile design. Based on the change in geometric configuration, the agile turning process is divided into a first stage with a parachute and a second stage without a parachute. Considering the flexible and controllable force, uncontrollable force, and dynamic characteristics generated by the parachute cord contraction, as well as the force situation and dynamic characteristics of the missile, a different dynamic model from the agile missile is established, with the missile as the main research subject. The swift missile of this invention includes an agile missile and a parachute. Compared to the agile missile, it can better complete a given task and is less likely to reach the maximum pitch angular velocity, providing a basis for further reducing the turning time algorithmically after considering practical engineering factors. Compared to a single rigid body model, the geometric configuration and dynamic model of this invention can help the attitude controller better calculate the actual turning process, laying the foundation for improving agile turning performance.

[0099] 2. After obtaining the dynamic model, this invention designs an attitude controller for the swift projectile based on a non-singular terminal sliding surface, a double power-law approaching law, and an extended state observer, which enables the attitude controller to have high robustness and tracking performance.

[0100] 3. After obtaining the dynamic model, this invention designs an attitude controller for the swift projectile based on the extended state observer, which has strong anti-interference capabilities.

[0101] 4. This invention derives the dynamic model of the rapid projectile based on the Lagrange method, avoiding the solution of complex constraints and the waste of computational resources caused by the need for smaller simulation steps when numerically solving constraints. At the same time, it establishes a dynamic model with sufficiently high accuracy.

[0102] 5. The agile turn process of this invention is specifically divided into a first stage and a second stage. In the first stage, the parachute remains connected to the agile missile. Upon entering the second stage, the parachute disconnects from the agile missile and the acceleration engine ignites. Compared to the agile missile, the modeling method of this invention considers the changes brought about by different flight conditions in the agile turn process classification, resulting in more accurate modeling.

[0103] 6. This invention derives the state equation for attitude tracking error based on the state equation of the swift missile, thereby obtaining different attitude controllers that can better control the missile's pitch angle, improve agile turning performance, reduce turning radius, shorten turning time, reduce energy consumption, lower product cost, and complete the attitude control process.

[0104] 7. Compared to agile missiles, the geometric configuration and dynamic model of the swift projectile of this invention can help the attitude controller better calculate the actual turning process, reduce the turning radius, shorten the turning time, and improve the agile turning performance of the projectile.

[0105] 8. Compared to agile missiles, the geometric configuration and dynamic model of the swift projectile of this invention can help the attitude controller better calculate the actual turning process, making it less likely for the pitch angle to reach its maximum value, reducing energy consumption and lowering product costs. Attached Figure Description

[0106] Figure 1 This is a flowchart of the method of the present invention.

[0107] Figure 2 This is a geometric configuration diagram of the agile missile.

[0108] Figure 3 This is a geometric configuration diagram of a swift projectile.

[0109] Figure 4 This is a schematic diagram of the first and second stages. Detailed Implementation

[0110] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0111] To address the issues with the algorithm, this embodiment employs a parachute-missile system combining a parachute and a missile to further study the missile's agile turning process. Connecting a parachute to the agile missile delays the approach of the pitch angle to its maximum, reduces the constraints on the agile missile's geometric configuration and dynamic model, and lowers the energy consumption of the direct force device, thus saving costs. The addition of the parachute also alters the agile turning process of the swift missile. From the initial flight phase until the moment before parachute detachment, the dynamic model of the swift missile is a combined parachute-missile model. After parachute detachment, the agile missile flies independently. This embodiment defines the first and second stages of the flight process based on this, and conducts research on the dynamic model of the swift missile.

[0112] This invention provides, for example Figure 1 The method for dynamic modeling and attitude control of a rapid-fire projectile, as shown, includes the following steps:

[0113] Step 1: Based on the geometric configuration of traditional agile missiles, design the geometric configuration of the rapid missile:

[0114] like Figure 2 As shown, the geometry of a traditional agile missile is a direct force device, which can operate in the missile body coordinate system O. b X b Y b Z b O b Y b Shaft and O b Z b The shaft provides a variable, continuously adjustable direct force, and the valve opening of the direct force jet device is defined as u. R uR ∈[-1,1], along O b Y b Shaft and O b Z b The axis is positive. To achieve attitude control, this invention employs a flexible and controllable parachute, attached to the agile missile, such as... Figure 2 As shown.

[0115] like Figure 3 As shown, O b For the missile's center of mass, O p For the center of mass of the umbrella, O t O is the center of the missile tail section. b X b Y b Let O be the projectile coordinate system. p X p Y p Let be the umbrella coordinate system.

[0116] Step 2: Design the agile turning process of the swift projectile:

[0117] like Figure 4 As shown, for ease of calculation and analysis, this invention divides the agile turning process of the swift missile into two stages: In the first stage, the parachute connects to the agile missile, gradually adjusting its attitude to reach the preset pitch angle, and then enters the second stage. In the second stage, the parachute is jettisoned, and the acceleration engine is ignited; at this point, the geometry is that of a traditional agile missile. In the first stage, the control forces include the aerodynamic force of the aerodynamic rudder, the flexible force of the circular parachute, and the direct force of the direct force device; in the second stage, the control forces include the aerodynamic force of the aerodynamic rudder, the direct force of the direct force device, and the thrust of the acceleration engine.

[0118] Step 3: Design the dynamic model of the agile turning process:

[0119] This invention comprehensively considers the flexibility, controllability, and dynamic characteristics of parachutes, establishing dynamic models for different flight stages with the missile as the main research subject. This leads to different attitude controllers, enabling better control of the missile's pitch angle and completing the attitude control process. To better simulate the dynamic models of the rapid missile in the first and second stages, and to lay the foundation for analyzing attitude errors during agile turns, this invention establishes a dynamic model for the rapid missile in the first stage based on the flexible and controllable force, uncontrollable force, and dynamic characteristics generated by the parachute's line contraction, as well as the force conditions and dynamic characteristics of the missile. The dynamic model for the second stage is the dynamic model of the agile missile. Based on the above approach, this invention first obtains the dynamic model for the second stage based on the geometric configuration of the agile missile. This dynamic model is located in the missile's pitch plane, and its expression is:

[0120]

[0121] Among them, V b It is the missile's speed; Q b It is the missile's dynamic pressure; T is the speed-increasing engine thrust; u T It is the engine speed switch; C x These are the aerodynamic parameters of missile drag; C nα These are the aerodynamic parameters of the missile's lift generated by its angle of attack; C nδ These are the aerodynamic parameters of the missile's lift generated by the aerodynamic rudders; C mα These are the aerodynamic parameters of the missile's torque generated by the angle of attack; C mδ These are the aerodynamic parameters of the missile's torque generated by the aerodynamic rudder; g is the acceleration due to gravity; S b It is the characteristic area of ​​the missile; L b It is the characteristic length of the missile; m b It is the mass of the missile; I b It is the missile's moment of inertia; θ b It is the missile's elevation angle; α b It is the missile's angle of attack; γ b It is the missile trajectory inclination angle; q b It is the missile's pitch angular velocity; x b The x-coordinate of the missile's center of mass is y. b δ is the longitudinal coordinate of the missile's center of mass; δ is the aerodynamic rudder deflection angle and |δ|≤δ max δ max It is the maximum deflection angle that the aerodynamic rudder can achieve; F R It is the maximum thrust of the direct-force jet device; L R It is the distance from the direct force jet device to the missile's center of gravity; C Nb For missile aerodynamic parameters; L CPb This is the distance from the missile's center of mass to its center of pressure.

[0122] The first-stage dynamic model is obtained using the Lagrange method, and its expression is as follows:

[0123]

[0124] In the formula, X = [x b y b θ b θ p ] T Let x be a generalized coordinate vector, where x b Let y be the x-coordinate of the missile's center of mass. b Let θ be the vertical coordinate of the missile's center of mass. b Let θ be the missile's elevation angle. p Let A be the umbrella pitch angle; matrix A is derived from A ij A is a 4×4 matrix composed of (i, j = 1, 2, 3, 4). ij The expression is:

[0125] A 11 =m b +m p +a 11 cos 2 i p +a 22 sin 2 i p

[0126] A 12 =a 11 cosθ p sinth p -a 22 sinth p cosθ p

[0127] A 13 =m p l tb sinth b +a 11 l tb cosθ p sin(θ b -θ p )+a 22 l tb sinth p cos(θ b -θ p )

[0128] A 14 =m p l pt sinth p +a 22 l pt sinth p

[0129] A 21 =a 11 sinth p cosθ p -a 22 cosθ p sinth p

[0130] A 22 =m b +m p +a 11 sin 2 i p +a 22 cos 2 i p

[0131] A 23=a 11 l tb sinth p sin(θ b -θ p )-m p l tb cosθ b -a 22 l tb cosθ p cos(θ b -θ p )

[0132] A 24 =-m p l pt cosθ p -a 22 l pt cosθ p

[0133] A 31 =m p +a 11 l tb sin(θ b -θ p )cosθ p +a 22 l tb cos(θ b -θ p )sinθ p

[0134] A 32 =-m p +a 11 l tb sin(θ b -θ p sinth p -a 22 l tb cos(θ b -θ p )cosθ p

[0135]

[0136] A 34 =m p l pt l tb cos(θ p -θ b )+a 22 l pt l tb cos(θ b -θ p)

[0137] A 41 =m p +a 22 l pt sinθ p

[0138] A 42 =-m p -a 22 l pt cosθ p

[0139] A 43 =m p l pt l tb cos(θ p -θ b )+a 22 l pt l tb cos(θ b -θ p )

[0140]

[0141] Matrix C is composed of C i A 4×1 matrix consisting of (i = 1, 2, 3, 4), C i The expression is:

[0142]

[0143]

[0144]

[0145]

[0146] The generalized force vector Q is given by Q i A 4×1 matrix consisting of (i = 1, 2, 3, 4), Q i The expression is:

[0147]

[0148]

[0149] Q3 = M b1 -F yp l tb cosθ b +F xp l tb sinθ b +F R LR u R +C mδ Q b S b L b δ

[0150]

[0151] Among them, l tb The distance from the missile's center of mass to the center of the cross-section of the missile's tail; l pt The distance from the center of mass of the parachute to the center of the cross-section of the missile's tail; m p It's the quality of the umbrella; I p It is the moment of inertia of the umbrella; It is the apparent quality along the umbrella's axis of symmetry; It is the apparent mass in the direction perpendicular to the umbrella's axis of symmetry; a 66 =k 66 I f It is the apparent moment of inertia in the direction perpendicular to the vertical plane; k 11 k 22 k 66 These are the first, second, and third apparent coefficients, respectively, where ρ is the air density. It is the volume of fluid displaced by the parachute; It is the moment of inertia of the fluid displaced by the parachute; d p It is the nominal diameter of the umbrella; It is umbrella dynamic pressure; u p ∈[-1, 1] represents the ratio of the change in parachute lines to the allowable change, with contraction being positive and relaxation being negative; D is the missile drag; L1 = Q b S b C nα α b The lift is generated by the missile's angle of attack; F T It is the axial force of the parachute; F N1 =C N Q p πd p 2 / 4 is the normal force generated by the parachute angle of attack; M p1 =C mp Q p πd p 3 / 4 is the restoring torque generated by the parachute angle of attack; C N C is the aerodynamic parameter of the normal force generated by the angle of attack of the parachute; mp These are the aerodynamic parameters of the torque generated by the angle of attack of the parachute; C Nup C is the aerodynamic parameter of the normal force generated by the contraction of the parachute lines; mup These are the aerodynamic parameters of the torque generated by the contraction of the parachute lines;

[0152] M b1 It is the restoring torque generated by the missile's angle of attack, and its expression is:

[0153]

[0154] F xp F yp The uncontrollable force of a parachute has components in the horizontal and vertical directions, and its expression is:

[0155]

[0156] u 11 v 22 It is the velocity of the fluid, and its expression is:

[0157]

[0158] C du C dv It is the remainder of the fluid velocity derivative after removing the second derivative of the generalized variable, and its expression is:

[0159]

[0160] The formulas for calculating the velocities of missiles and parachutes are:

[0161]

[0162]

[0163]

[0164] Among them, u b It is the horizontal velocity of the missile; v b It is the vertical velocity of the missile; q p It is the parachute pitch angular velocity, γ p α is the parachute trajectory inclination angle; p For the angle of attack of the umbrella; V p The speed of the umbrella.

[0165] Step 5: Based on the dynamic model of the two stages, establish the state equations for the pitch plane:

[0166] The expression for the state equation in the first stage is:

[0167]

[0168] Where d is the sum of internal uncertainties and external disturbances of the system.

[0169] f1=GA -1 (EC), where the input matrix B = GA-1 D = [b1, b2, b3], where b1 is the first variable of the input matrix, b2 is the second variable of the input matrix, and b3 is the third variable of the input matrix; G = [0, 0, 1, 0] T It is a transformation matrix; U = [δ, u p ,u R ] T It is the attitude control vector, δ c u pc u Rc These are rudder deflection angle, flexible force, and direct force, respectively.

[0170] The expression for matrix E is:

[0171]

[0172] The expression for matrix D is:

[0173]

[0174] The expression for the state equation in the second stage is:

[0175]

[0176] Where b4 = Q b S b L b C mδ / I b b5 = F R L R / I b The expression for f2 is:

[0177]

[0178] Step 6: Based on the state equation obtained in Step 5, establish the state equation for the pitch angle error:

[0179] With the desired missile pitch angle θ bc As the expected value of the attitude control variable, the attitude tracking error e1 and its derivative e2 are defined as follows:

[0180]

[0181] The state equation for the attitude tracking error in the first stage is:

[0182]

[0183] Among them, U pseudo =b1δ+b2u p +b3u R This is a virtual control variable;

[0184] The state equation for the attitude tracking error in the second stage is:

[0185]

[0186] Step 7: Design the non-singular terminal sliding surface of the state equation obtained in Step 6 as follows:

[0187]

[0188] Where β > 0; 1 < p / q < 2; p and q are positive odd numbers; β, p, and q are adjustable parameters.

[0189] Step 8: Based on the non-singular terminal sliding surface obtained in Step 7, design a double power-law approaching law, the expression of which is:

[0190]

[0191] Where k1 > 0; k2 > 0; a1 > 1; 0 < a2 < 1; sgn(·) is the sign function; k1, k2, a1, and a2 are adjustable parameters.

[0192] Step 9: Estimate the uncertainties of the state equations established in Step 5 using an extended state observer. The expression for the uncertainty estimation is:

[0193]

[0194] Where f takes the values ​​f1 and f2 at different stages; U takes the values ​​U at different stages. pseudo and b4δ+b5u R z1 and z2 are respectively q b The estimated values ​​of d; E1 = q b -z1 is the estimation error; 0.5 < m1 < 1; m2 = 2m1 - 1; n1 = 1 / m1; n2 = n1 + m1 - 1; σ1 > 1; σ2 > 1; c1 > 0; c2 > 0.

[0195] The expression for sgmf(E1) is:

[0196]

[0197] Where μ > 0, τ > 0; m1, m2, n1, n2, c1, c2, σ1, σ2, τ and μ are adjustable parameters.

[0198] Step 10: Based on the non-singular terminal sliding surface, double power reaching law, and uncertainty estimation results of the state equation of the attitude tracking error, design the attitude controller:

[0199] The expression for the first stage is:

[0200]

[0201]

[0202]

[0203]

[0204] The expression for the second stage is:

[0205]

[0206]

[0207] Among them, u pmax =1 represents the maximum value of the flexible force command; δ c u pc u Rc The rudder deflection angle, flexible force, and direct force calculated by the controller are respectively passed through a first-order inertial element to obtain the δ and u that make up the attitude control vector. p u R .

[0208] like Figure 1 As shown, after designing the attitude controller, the parameters of the non-singular terminal sliding surface, the double power approach law, and the extended state observer are preset, and the attitude control vector is calculated using the attitude controller. The pitch angle of the swift projectile is adjusted using the attitude control vector, and it is determined whether the pitch angle reaches the desired pitch angle. If it does, the agile turn is completed; otherwise, the attitude control vector is calculated again.

[0209] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for dynamic modeling and attitude control of a swift projectile, characterized in that, The rapid-fire projectile comprises an agile missile and a flexible, controllable parachute. Its dynamic modeling and attitude control steps are as follows: Based on the connection between the parachute and the swift missile, the agile turn process is divided into a first stage and a second stage. The first stage is from the initial moment to the moment before entering the second stage, during which the parachute is connected to the agile missile. The second stage is from the moment after the first stage to the final moment, during which the parachute is disconnected from the agile missile and the acceleration engine is ignited. Based on the flexible controllable force, uncontrollable force, and dynamic characteristics of the parachute generated by the contraction of the parachute lines, and the force and dynamic characteristics of the missile, a dynamic model of the rapid missile in the first stage is established, and the dynamic model of the rapid missile in the second stage is the dynamic model of the agile missile itself without a parachute; based on the dynamic model, the state equation of attitude tracking error is established, and an attitude controller is designed. The parameters of the attitude controller are preset, and the attitude control vector is calculated using the designed attitude controller. The pitch angle of the swift rocket is adjusted using the attitude control vector. It is determined whether the pitch angle reaches the desired pitch angle. If it does, the agile turn is completed; otherwise, the attitude control vector is calculated again. The attitude controller design comprises three parts: a non-singular terminal sliding surface, a double power-law approaching law, and uncertainty estimation. The expression for the non-singular terminal sliding surface is as follows: in, e 1. e 2 are the attitude tracking error and its derivative, respectively; ; ; is a positive odd number; β , p , q These are adjustable parameters; The expression for the double power reaching law is: wherein ; ; ; ; is a sign function; k 1、 k 2、 a 1、 a 2 is an adjustable parameter; The expression for the uncertainty estimation is: in, Take at different stages and ; and It is an intermediate calculation expression; U Take at different stages and ; This is a virtual control variable; and It is a computational expression; These are rudder deflection angle and direct force, respectively. They are The estimated value; It is the missile's pitch rate; d It is the sum of internal uncertainties and external disturbances within the system; It is an estimation error; ; ; ; ; ; ; ; ; The expression is: in, ; m 1. m 2. n 1. n 2. c 1. c 2. σ 1. σ 2. τ and μ These are adjustable parameters; The expression for the attitude controller is: The expression for the first stage is: The expression for the second stage is: in, b 1. b 2. b 3 represents the intermediate calculation expression; It is the missile's angle of attack; It is the desired missile elevation angle The derivative; This represents the maximum value of the flexible force command. That is the maximum deflection angle that the aerodynamic rudder can achieve; The rudder deflection angle, flexible force, and direct force calculated by the controller are respectively passed through a first-order inertial element to obtain the attitude control vector. .

2. The method of claim 1, wherein, The dynamic model of the swift projectile in the second stage is as follows: in, It's the missile's speed; It is missile dynamic pressure; It is the thrust of the speed-up engine; It's the speed-up engine switch; These are the aerodynamic parameters of missile drag; These are the aerodynamic parameters of the missile's lift generated by its angle of attack; These are the aerodynamic parameters of the missile's lift generated by the aerodynamic rudders; These are the aerodynamic parameters of the torque generated by the missile's angle of attack; These are the aerodynamic parameters of the torque generated by the missile's aerodynamic rudder; It is gravitational acceleration; It is the characteristic area of ​​the missile; It is the characteristic length of the missile; It is the mass of the missile; It is the missile's moment of inertia; It is the missile's elevation angle; It is the missile's angle of attack; It is the missile's trajectory inclination angle; It is the missile's pitch rate; It is the x-coordinate of the missile's center of mass. It is the vertical coordinate of the missile's center of mass; It is the aerodynamic rudder deflection angle and , That is the maximum deflection angle that the aerodynamic rudder can achieve; It is the maximum thrust of the direct-force jet device; It is the distance from the direct force jet device to the missile's center of gravity; These are the missile's aerodynamic parameters; This is the distance from the missile's center of mass to its center of pressure.

3. The method of claim 2, wherein, The specific method for establishing the dynamic model of the rapid projectile in the first stage is as follows: The first-stage dynamic model is established using the Lagrange method, and its expression is as follows: In the formula, Let be a generalized coordinate vector, where Let x be the x-coordinate of the missile's center of mass. The vertical coordinate of the missile's center of mass, The missile's elevation angle, For the umbrella's pitch angle; matrix A For the reason The 4×4 matrix formed The expression is: matrix C is a 4 x 1 matrix, consisting of The expression for Generalized force vector Q is formed by a 4x1 matrix, The expression of is: in, This is the distance from the missile's center of mass to the center of the cross-section of the missile's tail. This is the distance from the center of mass of the parachute to the center of the cross-section of the missile's tail. It's about the quality of the umbrella; It is the moment of inertia of the umbrella; It is the apparent quality along the umbrella's axis of symmetry; It is the apparent quality in the direction of the vertical umbrella axis of symmetry; It is the apparent moment of inertia in the direction perpendicular to the vertical plane; , , These are the first, second, and third apparent coefficients, respectively. It is air density. It is the volume of fluid displaced by the parachute; It is the moment of inertia of the fluid displaced by the parachute; It is the nominal diameter of the umbrella; It is umbrella dynamic pressure; It is the ratio of the change in the parachute lines to the allowable change, with contraction being positive and relaxation being negative; It is missile drag; It is the lift generated by the missile's angle of attack; It is the axial force of the parachute; It is the normal force generated by the angle of attack of the parachute; It is the restoring torque generated by the parachute's angle of attack; These are the aerodynamic parameters of the normal force generated by the angle of attack of the parachute; These are the aerodynamic parameters of the torque generated by the angle of attack of the parachute; It is the aerodynamic parameter of the normal force generated by the contraction of the parachute lines; These are the aerodynamic parameters of the torque generated by the contraction of the parachute lines; is the restoring moment due to the missile angle of attack, which is given by , The horizontal and vertical components of the uncontrolled force of the parachute are expressed as follows: , is the velocity of the fluid, which is expressed as: , is the fluid velocity derivative of the remainder of the second derivative of the generalized variable, expressed as: 。 4. The method of claim 1, wherein, The state equation for attitude tracking error is established based on the dynamic model in the following way: Based on the dynamic model of the first stage, establish the state equation of the first stage; based on the dynamic model of the second stage, establish the state equation of the second stage; based on the two state equations, establish the state equations of the attitude tracking error in the first and second stages.

5. The method of claim 3, wherein, The expression for the state equation in the first stage is: wherein d is the sum of the internal uncertainty of the system and the external disturbance; , where the input matrix , b 1 is the first variable in the input matrix. b 2 is the second variable in the input matrix. b 3 is the third variable in the input matrix; It is a transformation matrix; It is the attitude control vector. These are respectively rudder deflection angle, flexible force, and direct force; matrix E The expression for the matrix matrix D The expression for the matrix The expression for the state equation in the second stage is: wherein ; ; The expression for is: 。 6. The method of claim 5, wherein, The state equations for the attitude tracking errors in the first and second stages are expressed as follows: at a desired missile pitch angle As a desired value of the attitude control variable, the attitude tracking error is defined e 1 and its derivative e 2 is: The state equation for the attitude tracking error in the first stage is: wherein is a virtual control variable; The state equation for the attitude tracking error in the second stage is: 。

Images