CN111306989B - Hypersonic velocity reentry guidance method based on steady glide trajectory analytic solution - Google Patents

Abstract

The present invention is a hypersonic reentry guidance method based on the analytical solution of the smooth gliding trajectory, which comprises the following steps: 1. Establishing a dynamic model of the aircraft; 2. Establishing a constraint model; 3. Guidance method for the initial descent stage; 4. Smoothing Guidance method for gliding segment; 5. Guidance method for height adjustment segment; the advantages are: prediction and correction of longitudinal and transverse distance based on 3D ballistic analytical solution, which greatly reduces the amount of calculation, improves the calculation speed, and is convenient for real-time application to airborne systems superior. The lateral movement is determined by two tilt reversal points, the position of the first reversal point is corrected to control the terminal traverse error, and the position of the second reversal point is corrected to satisfy the terminal speed constraint. Compared with the traditional method of using the heading error threshold to control the lateral motion, the number of inversions is reduced, the energy utilization efficiency is improved, and the demand for the control system is reduced. The height adjustment section uses the idea of proportional guidance to make the terminal tilt angle converge to 0, which enhances the target strike effect.

Description

A Hypersonic Reentry Guidance Method Based on the Analytical Solution of Smooth Glide Trajectory

technical field

The invention provides a hypersonic reentry guidance method based on an analytical solution of a smooth gliding trajectory, belonging to the fields of aerospace technology and weapon technology

Background technique

The design of the reentry guidance law is the core technology for whether the hypersonic reentry glide vehicle can complete the precision strike mission. The ultimate goal of reentry guidance is to successfully guide the hypersonic reentry vehicle to the designated target under the condition of satisfying the path constraints and terminal constraints.

The re-entry vehicle is subject to strict path constraints during the re-entry process. However, it has been difficult for traditional algorithms to deal with the path constraints, which brings difficulties and challenges to the online generation of the trajectory and the online calculation of the guidance law. At the same time, because the extremely fast gliding flight speed puts forward higher requirements for calculation time, the time constraint of online guidance law command generation is very strong. For the task of target repositioning, the algorithm requires strong adaptability and rapidity. , to meet the requirements of large maneuvering missions.

SUMMARY OF THE INVENTION

Aiming at the above problems of hypersonic vehicle reentry guidance, a high-precision hyperglide reentry guidance method based on 3D ballistic analytical solution was proposed. Firstly, an auxiliary geocentric rotation coordinate system is constructed, and based on this, a new dynamic model of longitudinal, transverse and heading angles with respect to energy is established, which is beneficial to decoupling highly nonlinear and strongly coupled dynamic models. And linearization, the three-dimensional ballistic analytical solution is obtained, and the guidance method is designed based on this analytical solution. The guidance method uses the longitudinal analytical solution to plan the longitudinal reference profile in real time, uses the lateral analytical solution to correct the first reversal point to eliminate the lateral error, and uses several ballistic simulations to correct the second inversion point to ensure the terminal speed constraint, Corrected minimum angle of attack to ensure terminal height constraints.

The present invention is a hypersonic reentry guidance method based on the analytical solution of the smooth gliding trajectory, characterized in that it comprises the following steps:

Step 1: Build the aircraft dynamics model;

A hypersonic vehicle generally refers to an aircraft with a flight Mach number greater than 5 that achieves hypersonic flight in the atmosphere and across the atmosphere. Under the background of the rotating earth, using the standard atmospheric model and the inverse square gravitational field model, the six-degree-of-freedom dynamic equation of the hypersonic vehicle is established as follows:

where d/dt is the derivation of time, t is time, h is altitude, R is range, λ is longitude, φ is latitude, V is the velocity of the aircraft relative to the earth, γ is the ballistic inclination, and ψ is the heading of the aircraft Angle, based on the local north direction, σ is the tilt angle, _Re is the radius of the earth, taking the value 6378.137km, ω _e is the angular velocity of the earth's rotation, g is the acceleration of gravity; L=ρV ² SC _L /2m is the acceleration of lift, D= ρV ² SC _D /2m is the drag acceleration, and _CL and CD are the lift coefficient and drag coefficient, respectively _.

Step 2: Establish a constraint model;

The re-entry vehicle needs to meet the process constraints such as heat flux density, dynamic pressure and overload during flight, which are expressed as follows:

The parameter ρ ₀ represents the nominal atmospheric density, e the natural constant, h the altitude above sea level, h _S the nominal altitude, n the overload, and m the mass.

表示最大允许热流密度值；n表示允许过载值；n_max表示最大允许过载值；q表示允许动压值；q_max表示最大允许动压值。where K _Q is the heat flux density coefficient;

Indicates the maximum allowable heat flux value; n indicates the allowable overload value; n _max indicates the maximum allowable overload value; q indicates the allowable dynamic pressure value; q _max indicates the maximum allowable dynamic pressure value.

In addition, due to the capability constraints of the flight control system, the rate of change of the control variables (angle of attack α and angle of roll σ) also satisfies the constraints:

In addition to the process constraints, the aircraft should also satisfy the terminal constraints, as follows: V _TAEM = 2000m/s, H _TAEM = 25km, R _tm = 100km, σ _TAEM ≈0°, γ _TAEM ≈0° and Δψ _TAEM ≈0°. The subscripts TAEM stands for terminal volume. V _TAEM , H _TAEM , σ _TAEM , γ _TAEM , and Δψ _TAEM represent terminal velocity, terminal altitude, terminal roll angle, terminal ballistic inclination angle, and terminal heading angle error, respectively. R _tm represents the projectile distance.

Step 3: Guidance method for the initial descent segment;

According to the characteristics of the re-entry trajectory, it is divided into three parts: the initial descent section, the smooth glide section and the height adjustment section. The initial descent segment is designed to allow for a smoother glide segment into which the trajectory transitions more smoothly. Most of the whole flight trajectory is in the smooth gliding segment, which not only determines the range, speed and altitude of the flight terminal, but also determines whether the aircraft can meet various process constraints. The height adjustment segment is the last stage of the trajectory, which is related to whether the trajectory can strictly meet the terminal constraints. The flight speed and flight altitude of the aircraft in this section are relatively low, which puts forward more stringent requirements for the guidance method of the design height adjustment section.

时，意味着升力可以满足平稳滑翔需求，所以此时攻角可以平缓地从最大攻角过渡到参考攻角剖面α_bsl。In the initial descent stage, the variation of the control quantity has little effect on the flight, so the angle of attack and the angle of inclination are designed with a fixed size to avoid the altitude change. In order to reduce the heat flux density and increase the range, the starting point of the trajectory should be set higher. Therefore, the maximum angle of attack α _max = 20deg and zero roll angle are selected for flight here. When the rate of change of ballistic inclination

, which means that the lift can meet the requirement of smooth gliding, so the angle of attack can smoothly transition from the maximum angle of attack to the reference angle of attack profile α _bsl .

At this stage, the commanded attack and roll angles are designed as follows:

σ _cmd = 0 (12)

in,

Δγ=γ-γ _SG (13)

为0的时候的弹道倾角与平稳滑翔弹道倾角的偏差值。Among them, γ _SG represents the inclination angle of the smooth gliding trajectory, and k _γ represents the feedback coefficient and the value here is 5. When Δγ=0, the aircraft enters the smooth gliding phase. The parameter α _cmd is the commanded angle of attack; σ _cmd is the commanded inclination angle; Δγ is the deviation between the current ballistic inclination and the stable gliding ballistic inclination; Δγ ₁ is the change rate of the current ballistic inclination

When it is 0, the deviation between the ballistic inclination and the smooth gliding ballistic inclination.

Step 4: Guidance method for smooth gliding segment;

The ballistic planning of the smooth glide phase is the basis of the proposed guidance algorithm, which needs to make the aircraft approach the target while guaranteeing the process constraints. The algorithm is based on a new three-dimensional analytical solution to determine the longitudinal and lateral range profiles. Here we first briefly introduce the new analytical solution for ballistics.

In order to cater for the characteristic that the re-entry trajectory is much longer than the horizontal, the following two coordinate systems are first established, which can intuitively represent the meaning of the vertical and horizontal.

轴指向飞行器初始位置，

轴位于过飞行器与目标点的大圆平面内，且垂直于

轴，

轴可根据右手定则确定。Define an auxiliary geocentric rotation reference system (AGR coordinate system) that rotates with the earth: the origin is at the center of the earth E,

The axis points to the initial position of the aircraft,

The axis lies in the great circle plane passing through the aircraft and the target point, and is perpendicular to the

axis,

The axis can be determined according to the right-hand rule.

轴铅垂向下指向地心，

轴指向AGR坐标系中

指向的“北”方，

轴由右手定则确定。At the same time, define the local generalized north-east lower coordinate system (GNED coordinate system): the vertical projection point of the origin o on the ground from the center of mass M of the aircraft;

The axis points vertically downward to the center of the earth,

The axis points in the AGR coordinate system

pointing to the "north" side,

The axis is determined by the right-hand rule.

定义横程为

其中

和

分别表示AGR坐标系中的广义经度和广义纬度。Define the vertical as

Define the traverse as

in

and

represent the generalized longitude and generalized latitude in the AGR coordinate system, respectively.

Define energy as

Define the vertical lift-drag ratio Lcosσ/D=L ₁ /D, and the lateral lift-drag ratio Lsinσ/D=L ₂ /D. This generalized latitude-longitude coordinate system in the AGR coordinate axis facilitates linearization and decoupling of complex dynamic models to obtain the following three-dimensional ballistic analytical solutions.

R^*＝R_e+H；in,

R ^* = _Re +H;

h_ij,i＝1,2；j＝0,1,α₁和p_ij,i＝1,2；j＝0,1,2,3,4均为常值系数。E,E₀分别表示当前能量与初始能量值；x_E表示能量积分变量；L₁表示纵向平面内的升力值；x_C0表示初始横程值；

表示GNED坐标系下的初始航向角误差；

表示GNED坐标系下的航向角误差。

h _ij ,i=1,2; j=0,1,α ₁ and p _ij ,i=1,2;j=0,1,2,3,4 are constant coefficients. E, E ₀ represent the current energy and initial energy value respectively; x _E represents the energy integral variable; L ₁ represents the lift value in the longitudinal plane; x _C0 represents the initial transverse value;

Represents the initial heading angle error in the GNED coordinate system;

Indicates the heading angle error in the GNED coordinate system.

Due to the high accuracy of the analytical solution, it can be applied to the derivation of the guidance method to reduce the computational complexity and improve the universality.

1. Baseline angle of attack design

Because the analytical solution is designed with energy as the independent variable, in order to use the analytical solution more conveniently, all reference profiles in this guidance method also use energy as the independent variable. The reference angle of attack profile α _bsl is designed as:

Among them, E _α =-5.55×10 ⁷ J/kg is located near the junction of the smooth glide segment and the final height adjustment segment. In order to exert the maximum capability of the aircraft, the design angle of attack is the angle of attack corresponding to the maximum lift-drag ratio, that is, α ₁ =10deg. The angle of attack is designed to be a quadratic function of energy so that the angle of attack can transition smoothly from α ₁ to α ₂ . In this guidance method, α ₂ =6deg is preset for the first time, and then ballistic simulation is applied to correct it to strictly satisfy the terminal height constraint. When the design of the angle of attack profile is completed, the corresponding reference lift-to-drag ratio profile (L/D) _bsl is also determined.

2. Benchmark lift-drag ratio profile design

In order to meet the range requirements, the designed longitudinal lift-drag ratio profile is as follows

Wherein, let the terminal longitudinal range analytical solution x _Df be equal to the remaining range, then L ₁ /D ₁ can be obtained. Design L ₁ /D ₂ =L/D(E _TAEM ), where E _TAEM is the terminal energy, such that when x _E =E _TAEM , (L ₁ /D) _bsl | _{E = E_TAEM} =(Lcosσ _TAEM /D) _bsl =L/D(E _TAEM ), the inclination angle σ _TAEM of the terminal can be made zero. Through the form of design formula (20), the roll angle can be controlled to be approximately constant during the flight.

与从地球中心指向飞行器的矢量

之间的夹角。则剩余射程可表示为：Therefore, in order to solve L ₁ /D ₁ , the remaining range x _Df needs to be calculated first. In the GER coordinate system, η is defined as the vector pointing from the center of the earth to the aircraft

Vector with aircraft pointing from the center of the earth

the angle between. Then the remaining range can be expressed as:

x _Df = R _e η-S _TAEM (21)

Among them, S _TAEM represents the distance to the target at the end of the re-entry segment.

The process of solving L ₁ /D ₁ can be described as follows:

When E≥E _α , there is

x _D (E _α ,E)+x _D (E _TAEM ,E _α )=x _Df (22)

in,

in,

and there is,

in,

c ₂ =(a ₁ -c ₁ d ₀ )/d ₁ (28)

c ₃ =a ₀ -c ₂ d ₀ (29)

Solving equation (22), we can get

in,

When E<E _α , the aircraft is mainly in the altitude adjustment stage, and the value of L ₁ /D ₁ is no longer updated.

3. Design of reference lateral lift-drag ratio and reference roll angle

为满足终端横程约束，设计横向升阻比剖面如下：The modulus value of the lateral lift-drag ratio can be determined by the previously planned (L/D) _bsl and the longitudinal lift-drag ratio (L ₁ /D) _bsl , which is

In order to meet the terminal transverse constraints, the designed lateral lift-drag ratio profile is as follows:

Among them, E _BR1 and E _BR2 represent the first and second tilt reversal points, respectively. sgn is a symbolic variable representing the direction of the initial roll reversal. After the lateral lift-drag ratio profile is obtained, the reference dip angle profile σ _bsl is also determined, which is expressed as follows:

Among them, (L/D) _real represents the actual lift-drag ratio profile.

4. Tilt reversal point correction algorithm

In this algorithm, the roll reversal point is designed based on the analytical solution of the lateral run to eliminate the terminal run error. There are two tilt reversal points arranged here. First design and correct the first reversal point E _BR1 . Shilling the second reversal point E _BR2 =E _α , the terminal stroke x _C (E _TAEM ,E) is only a function of E _BR1 . It can be seen from equation (17) that the terminal traverse x _Cf can be expressed as a piecewise function of E _BR1 as follows:

Among them, F and G are self-defined functions, and the expressions are as follows

Among them, the parameters x _E2 , x _E1 express the upper and lower bounds of the energy; k is a constant from 1 to 5; P ₁ represents the polynomial fitting coefficient.

Taking the derivative of _EBR1 with respect to equation (38), we can get

i＝0,1,2,3,4。为了使终端横程误差为0，即需要满足x_Cf(E_BR1)＝0。因此这个算法的本质在于求解非线性方程x_Cf(E_BR1)＝0的根，用牛顿法求解方法如下：Among them, the right limit at E=E _BR1 is represented by a superscript ⁺ , and the left limit at E=E _BR1 is represented by a superscript ^- . Since L ₂ /D _bsl is discontinuous at E=E _BR1 , we have

i=0,1,2,3,4. In order to make the terminal traverse error 0, it is necessary to satisfy x _Cf (E _BR1 )=0. Therefore, the essence of this algorithm is to solve the root of the nonlinear equation x _Cf (E _BR1 )=0. The Newton method is used to solve it as follows:

和

并不一样，

表示E_BR1的k次幂，

表示第k次迭代的E_BR1值。求解停止设置为

因此x_Cf(E_BR1)随着E_BR1单调变化，此非线性方程的解通过简单的几次迭代即可得到。parameter

and

not the same,

represents E _BR1 to the power of k,

Represents the value of E _BR1 for the k-th iteration. Solve Stop is set to

Therefore x _Cf (E _BR1 ) varies monotonically with E _BR1 , and the solution to this nonlinear equation can be obtained in a few simple iterations.

5. Design of command angle of attack and tilt angle

In order to ensure the tracking accuracy of the reference profile, the ballistic damping control technology is used to suppress the long-period and weakly damped oscillation of the re-entry trajectory. The design command angle of attack α _cmd and command tilt angle σ _cmd are as follows:

α _cmd =α _bsl +cosσ _bsl K _γ (γ _SG -γ) (43)

Among them, K _γ is the feedback coefficient, the value is 5; γ _SG is the approximate solution of the inclination angle of the smooth gliding trajectory, which can be expressed as follows

Among them, S is the reference area of the aircraft; C _L is the lift coefficient; ρ is the air density.

The smooth gliding segment needs to satisfy the process constraints, so the process constraints of equations (8)-(10) are transformed into the inclination angle constraints, which are expressed as follows

Among them, L _max is the maximum lift, and the expression is as follows:

Among them, H _min corresponds to the lowest boundary of the gliding height, which can be obtained through process constraints; the constant coefficient k _σ =-50. Therefore, in order to satisfy the process constraints, the tilt angle needs to satisfy the following conditions:

|σ _cmd |≤σ _max (50)

Step 5: Guidance method for height adjustment segment;

1. Command angle of attack and second reversal point correction.

( ₁ ) Correction algorithm for command angle of attack α2

In order to satisfy the terminal height constraint, a ballistic simulation is used here to correct the command angle of attack α ₂ . According to the deviation between the terminal height H _f obtained by the ballistic simulation and the terminal constraint height H _TAEM , the final command angle of attack α ₂ is obtained by further correction. In the following variables, the subscript f represents the terminal value calculated by the ballistic simulation, and the subscript TAEM represents the terminal constraint value.

可以近似为0，因此可分别假设cosγ_f＝1,cosσ_f＝1和

所以根据式(6)可以得到：Since γ _f ,σ _f and

can be approximated to 0, so it can be assumed that cosγ _f =1, cosσ _f =1 and

So according to formula (6), we can get:

Among them, C _L(est) (α _bsl (E _f )) represents the lift coefficient corresponding to the terminal angle of attack in the ballistic simulation, and q _f represents the terminal dynamic pressure.

According to the terminal constraints, there are

表示修正后的指令攻角，φ_f、ψ_f、V_f、H_f分别表示弹道仿真计算得到的终端纬度、航向角、速度、高度；q_TAEM、φ_TAEM、ψ_TAEM、V_TAEM、H_TAEM分别表示终端约束的动压值、纬度值、航向角值、速度值、高度值。in,

Represents the corrected commanded angle of attack, φ _f , ψ _f , V _f , and H _f respectively represent the terminal latitude, heading angle, speed, and altitude calculated by ballistic simulation; q _TAEM , φ _TAEM , ψ _TAEM , V _TAEM , H _TAEM Respectively represent the dynamic pressure value, latitude value, heading angle value, speed value, and altitude value of the terminal constraint.

通过令式(51)等于式(52)可以得到：Under the assumptions of φ _f = φ _TAEM and ψ _f = ψ _TAEM , the linearization

By making equation (51) equal to equation (52), we can get:

表示升力系数对攻角的导数；因此，式(53)中求解出的α₂可带入式(19)中作为基准攻角进行制导控制。Among them, E _f represents the terminal energy value calculated by ballistic simulation;

represents the derivative of the lift coefficient with respect to the angle of attack; therefore, α ₂ solved in Equation (53) can be brought into Equation (19) as the reference angle of attack for guidance control.

(2) Correction algorithm for the second inclination reversal point E _BR2

The height adjustment stage is designed with proportional guidance law for guidance. Through the analysis of the guidance algorithm, it can be seen that if the E _BR2 is reduced, the guidance law command will generate a larger pitch angle to eliminate the larger heading error generated during the last roll reversal, thereby reducing the longitudinal lift-to-drag ratio. , reducing the terminal velocity V _f . Therefore, V _f can be regarded as a monotonic function with respect to E _BR2 . To ensure terminal constraints, this problem can be viewed as a problem of solving the solution of the nonlinear equation V _f (E _BR2 )=V _TAEM . Here, the secant method is used to solve the problem, and V _f is predicted through multiple ballistic simulations, and the value of E _BR2 is adjusted according to the deviation of the predicted value from the terminal constraint.

E _BR2 The condition for ending iterative correction is that the obtained deviation satisfies

2. Baseline tilt angle

可以表示为After the second roll reversal, the aircraft enters the altitude adjustment phase. At this stage, the reference angle of attack is still determined by equation (19), and the reference tilt angle is controlled by the proportional guidance guidance law. line-of-sight rate

It can be expressed as

Then, the lateral maneuvering acceleration command a _L2 obtained by proportional guidance is as follows

表示第二次倾侧反转时的纵程。假设飞行器近似平稳滑翔，则纵向平面内的合力加速度为0。因此，纵向机动加速度指令a_L1为Among them, k _PN is the lateral acceleration maneuvering coefficient, and its value is

Indicates the longitudinal distance at the second roll reversal. Assuming that the aircraft glides approximately smoothly, the resultant acceleration in the longitudinal plane is zero. Therefore, the longitudinal maneuvering acceleration command a _L1 is

Therefore, the reference tilt angle can be obtained as

3. Command angle of attack and tilt angle

指令攻角与倾侧角可以表示如下：In order to ensure the terminal speed constraint, the remaining glide distance reference profile with energy as the independent variable is tracked by adjusting the angle of attack.

The commanded attack angle and pitch angle can be expressed as follows:

表示剩余射程，值可以通过之前的最后一次弹道仿真获得。Among them, the value of k _α can be adjusted in time according to the task, and generally can be selected as 2π/(1.8×10 ⁷ );

Indicates the remaining range, the value can be obtained from the last ballistic simulation before.

To satisfy the process constraints, as before, the roll angle still needs to satisfy the following requirements:

|σ _cmd |≤σ _max (61)

Through the above five steps, a hypersonic reentry guidance method based on the analytical solution of the smooth gliding trajectory can be obtained.

The present invention is a hypersonic reentry guidance method based on the analytical solution of the smooth gliding trajectory, and has the advantages of:

(1) The prediction and correction of the longitudinal and transverse distances based on the three-dimensional ballistic analytical solution greatly reduces the amount of calculation, improves the calculation speed, and is convenient for real-time application to airborne systems.

(2) The lateral movement is determined by two tilt reversal points, the position of the first reversal point is corrected to control the terminal traverse error, and the position of the second reversal point is corrected to satisfy the terminal speed constraint. Compared with the traditional method of using the heading error threshold to control the lateral motion, the method reduces the number of roll reversals, improves the energy utilization efficiency, and reduces the demand for the control system.

(3) The height adjustment section uses the idea of proportional guidance to make the terminal tilt angle converge to 0, which enhances the target strike effect.

Description of drawings

Figure 1 is a schematic diagram of the geocentric equatorial rotating coordinate system (GER) and the local northeast lower coordinate system (NED).

FIG. 2 is a schematic diagram of an auxiliary geocentric rotation frame of reference (AGR) and an auxiliary local northeast lower coordinate system (GNED).

Figure 3 is the latitude and longitude curves of five target states.

Figure 4 is a height-energy curve for five target states.

Figure 5 is a velocity-energy curve for five target states.

Figure 6 is an angle of attack-energy curve for five target states.

FIG. 7 is a tilt angle-energy curve for five target states.

Fig. 8 is the ballistic inclination-energy curve of five target states.

Figure 9 is a heading error-energy curve for five target states.

In the above figure, the symbols and codes involved are explained as follows:

表示地心赤道旋转坐标系(GER)，o_xyz表示当地北东下坐标系(NED)，North表示北向，East表示东向。h是海拔高度，R是射程，λ是经度，φ是纬度，V是飞行器相对于地球的速率，γ是弹道倾角，ψ是飞行器航向角，以当地北向为基准，σ是倾侧角。图2中，

表示辅助地心旋转参照系(AGR)，

表示当地北东下坐标系(NED)，Axis表示地球极轴。M是飞行器当前位置点，o是飞行器当前位置点在地球表面的投影点。T是目标点，o_T是目标点在地球表面的投影点。ω_ex表示地球自转角速度在

轴的分量，ω_ey表示地球自转角速度在

轴的分量，ω_zx表示地球自转角速度在

轴的分量。图3中，Longitude表示经度，Latitude表示纬度，T1-T5代表五个不同目标的算例。图4中，Altitude表示高度，Energy表示能量，H表示弹道仿真得到的高度曲线，H_min表示满足过程约束的最小高度边界。图5中，Velocity表示高度，Energy表示能量。图6中，Angle of Attack表示攻角，Energy表示能量。图7中，Bank Angle表示倾侧角，Energy表示能量。图8中，Flight-pathAngle表示倾侧角，Energy表示能量。图9中，Heading Angle表示航向角，Energy表示能量。In Figure 1,

Represents the geocentric equatorial rotation coordinate system (GER), o _xyz represents the local north-east lower coordinate system (NED), North represents the north direction, and East represents the east direction. h is the altitude, R is the range, λ is the longitude, φ is the latitude, V is the velocity of the aircraft relative to the earth, γ is the ballistic inclination, ψ is the heading angle of the aircraft, based on the local north direction, and σ is the roll angle. In Figure 2,

represents the auxiliary geocentric rotation frame of reference (AGR),

Represents the local Northeast Lower Coordinate System (NED), and Axis represents the Earth's polar axis. M is the current position of the aircraft, and o is the projection of the current position of the aircraft on the surface of the earth. T is the target point, o _T is the projected point of the target point on the earth's surface. ω _ex represents the angular velocity of the earth's rotation in

The component of the axis, ω _ey represents the angular velocity of the earth's rotation in

The component of the axis, ω _zx represents the angular velocity of the earth's rotation in

Axis components. In Figure 3, Longitude represents longitude, Latitude represents latitude, and T1-T5 represent the calculation examples of five different targets. In Figure 4, Altitude represents altitude, Energy represents energy, H represents the altitude curve obtained by ballistic simulation, and H _min represents the minimum altitude boundary that satisfies the process constraints. In Figure 5, Velocity represents height, and Energy represents energy. In Figure 6, Angle of Attack represents the angle of attack, and Energy represents energy. In Fig. 7, Bank Angle represents the bank angle, and Energy represents the energy. In Fig. 8, Flight-pathAngle represents the tilt angle, and Energy represents energy. In Figure 9, Heading Angle represents the heading angle, and Energy represents the energy.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and implementation cases.

Aiming at the above problems of hypersonic vehicle reentry guidance, a high-precision hyperglide reentry guidance method based on 3D ballistic analytical solution was proposed. Firstly, an auxiliary geocentric rotation coordinate system is constructed, and based on this, a new dynamic model of longitudinal, transverse and heading angles with respect to energy is established, which is beneficial to decoupling highly nonlinear and strongly coupled dynamic models. And linearization, the three-dimensional ballistic analytical solution is obtained, and the guidance method is designed based on this analytical solution. The guidance method uses the longitudinal analytical solution to plan the longitudinal reference profile in real time, uses the lateral analytical solution to correct the first reversal point to eliminate the lateral error, and uses several ballistic simulations to correct the second inversion point to ensure the terminal speed constraint, Corrected minimum angle of attack to ensure terminal height constraints.

The present invention is a hypersonic reentry guidance method based on the analytical solution of the smooth gliding trajectory, characterized in that it comprises the following steps:

Step 1: Build the aircraft dynamics model;

As shown in Figure 1, establish the geocentric equatorial rotating coordinate system (GER coordinate system): the origin is at the earth's center E, the z _e axis is perpendicular to the earth's equatorial surface and points to the north pole; the x _e axis and the y _e axis are in the equatorial plane, and perpendicular to each other. The coordinate system rotates with the earth, and its rotational angular velocity around the z _e axis is the earth's rotation angular velocity ω _e .

Local North-East Lower Coordinate System (NED Coordinate System): Define the vertical projection point of the origin o at the center of mass M of the aircraft to the ground; the x-axis points to the local north, the y-axis points to the local east, and the z-axis points vertically downward to the center of the earth.

Under the background of the rotating earth, using the standard atmospheric model and the inverse square gravitational field model, the six-degree-of-freedom dynamic equation of the hypersonic vehicle is established as follows:

where d/dt is the derivation of time, t is time, h is altitude, R is range, λ is longitude, φ is latitude, V is the velocity of the aircraft relative to the earth, γ is the ballistic inclination, and ψ is the heading of the aircraft Angle, based on the local north direction, σ is the tilt angle, _Re is the radius of the earth, taking the value 6378.137km, ω _e is the angular velocity of the earth's rotation, L=ρV ² SC _L /2m is the lift acceleration, D=ρV ² SC _D / 2m is the drag acceleration; S is the reference area of the aircraft; C _L is the lift coefficient; ρ is the air density.

Step 2: Establish a constraint model;

The re-entry vehicle needs to meet the process constraints such as heat flux density, dynamic pressure and overload during flight, which are expressed as follows:

表示最大允许热流密度值；n_max表示最大允许过载值；q_max表示最大允许动压值.此外，由于飞行控制系统的能力制约，控制量(攻角α和倾侧角σ)的变化率也满足约束：

where K _Q is the heat flux density coefficient;

Represents the maximum allowable heat flux density value; n _max represents the maximum allowable overload value; q _max represents the maximum allowable dynamic pressure value. In addition, due to the ability of the flight control system, the rate of change of the control variables (angle of attack α and angle of tilt σ) also satisfies constraint:

In addition to the process constraints, the aircraft should also satisfy the terminal constraints, which are: V _TAEM = 2000m/s, H _TAEM = 25km, R _tm = 100km, σ _TAEM ≈0°, γ _TAEM ≈0° and Δψ _TAEM ≈0°.

Step 3: Guidance method for the initial descent segment;

According to the characteristics of the re-entry trajectory, it is divided into three parts: the initial descent section, the smooth glide section and the height adjustment section. The initial descent segment is designed to allow for a smoother glide segment into which the trajectory transitions more smoothly. Most of the whole flight trajectory is in the smooth gliding segment, which not only determines the range, speed and altitude of the flight terminal, but also determines whether the aircraft can meet various process constraints. The height adjustment segment is the last stage of the trajectory, which is related to whether the trajectory can strictly meet the terminal constraints. The flight speed and flight altitude of the aircraft in this section are relatively low, which puts forward more stringent requirements for the guidance method of the design height adjustment section.

时，意味着升力可以满足平稳滑翔需求，所以此时攻角可以平缓地从最大攻角过渡到参考攻角α_bsl。In the initial descent stage, the variation of the control quantity has little effect on the flight, so the angle of attack and the angle of inclination are designed with a fixed size to avoid the altitude change. In order to reduce the heat flux density and increase the range, the starting point of the trajectory should be set higher. Therefore, the maximum angle of attack α _max = 20deg and zero roll angle are selected for flight here. When the rate of change of ballistic inclination

, which means that the lift can meet the needs of smooth gliding, so the angle of attack can smoothly transition from the maximum angle of attack to the reference angle of attack α _bsl .

At this stage, the commanded attack and roll angles are designed as follows:

σ _cmd = 0 (12)

in,

Δγ=γ-γ _SG (13)

Among them, γ _SG represents the inclination angle of the smooth gliding trajectory, and k _γ represents the feedback coefficient and the value here is 5. When Δγ=0, the aircraft enters the smooth gliding phase.

Step 4: Guidance method for smooth gliding segment;

The ballistic planning of the smooth glide phase is the basis of the proposed guidance algorithm, which needs to make the aircraft approach the target while guaranteeing the process constraints. The algorithm is based on a new three-dimensional analytical solution to determine the longitudinal and lateral range profiles. Here we first briefly introduce the new analytical solution for ballistics.

As shown in Figure 2, in order to cater for the characteristic that the re-entry trajectory is much longer than the horizontal, the following two coordinate systems are first established, which can intuitively represent the meaning of the vertical and horizontal.

轴指向飞行器初始位置，

轴位于过飞行器与目标点的大圆平面内，且垂直于

轴，

轴可根据右手定则确定。Define an auxiliary geocentric rotation reference system (AGR coordinate system) that rotates with the earth: the origin is at the center of the earth E,

The axis points to the initial position of the aircraft,

The axis lies in the great circle plane passing through the aircraft and the target point, and is perpendicular to the

axis,

The axis can be determined according to the right-hand rule.

轴铅垂向下指向地心，

轴指向AGR坐标系中

指向的“北”方，

轴由右手定则确定。At the same time, define the local generalized north-east lower coordinate system (GNED coordinate system): the vertical projection point of the origin o on the ground from the center of mass M of the aircraft;

The axis points vertically downward to the center of the earth,

The axis points in the AGR coordinate system

pointing to the "north" side,

The axis is determined by the right-hand rule.

定义横程为

其中

和

分别表示AGR坐标系中的广义经度和广义纬度。Define the vertical as

Define the traverse as

in

and

represent the generalized longitude and generalized latitude in the AGR coordinate system, respectively.

Define energy as

This generalized latitude-longitude coordinate system in the AGR coordinate axis facilitates linearization and decoupling of complex dynamic models to obtain the following three-dimensional ballistic analytical solutions.

R^*＝R_e+H；in,

R ^* = _Re +H;

h_ij,i＝1,2；j＝0,1,α₁和p_ij,i＝1,2；j＝0,1,2,3,4均为常值系数。由于该解析解具有很高的精度，可将其应用于制导方法推导中，以减少计算量提高普适性。

h _ij ,i=1,2; j=0,1,α ₁ and p _ij ,i=1,2;j=0,1,2,3,4 are constant coefficients. Due to the high accuracy of the analytical solution, it can be applied to the derivation of the guidance method to reduce the computational complexity and improve the universality.

6. Baseline angle of attack design

Because the analytical solution is designed with energy as the independent variable, in order to use the analytical solution more conveniently, all reference profiles in this guidance method also use energy as the independent variable. The reference angle of attack profile is designed as:

Among them, E _α =-5.55×10 ⁷ J/kg is located near the junction of the smooth glide segment and the final height adjustment segment. In order to exert the maximum capability of the aircraft, the design angle of attack is the angle of attack corresponding to the maximum lift-drag ratio, that is, α ₁ =10deg. The angle of attack is designed to be a quadratic function of energy so that the angle of attack can transition smoothly from α ₁ to α ₂ . In this guidance method, α ₂ =6deg is preset for the first time, and then ballistic simulation is applied to correct it to strictly satisfy the terminal height constraint. When the design of the angle of attack profile is completed, the corresponding lift-drag ratio profile L/D _bsl is also determined.

7. Benchmark lift-drag ratio profile design

In order to meet the range requirements, the designed longitudinal lift-drag ratio profile is as follows

Wherein, let the longitudinal analytical solution equal to the remaining range, then L ₁ /D ₁ can be obtained. L ₁ /D ₂ =L/D(E _TAEM ) is designed so that the tilt angle of the terminal is zero. Through the form of design formula (20), the roll angle can be controlled to be approximately constant during the flight.

与从地球中心指向飞行器的矢量

之间的夹角。则剩余射程可表示为：Therefore, in order to solve L ₁ /D ₁ , the remaining range x _Df needs to be calculated first. In the GER coordinate system, η is defined as the vector pointing from the center of the earth to the aircraft

Vector with aircraft pointing from the center of the earth

the angle between. Then the remaining range can be expressed as:

x _Df = R _e η-S _TAEM (21)

Among them, S _TAEM represents the distance to the target at the end of the re-entry segment.

The process of solving L ₁ /D ₁ can be described as follows:

When E≥E _α , there is

x _D (E _α ,E)+x _D (E _TAEM ,E _α )=x _Df (22)

in,

in,

and there is,

in,

c ₂ =(a ₁ -c ₁ d ₀ )/d ₁ (28)

c ₃ =a ₀ -c ₂ d ₀ (29)

Solving equation (22), we can get

in,

When E<E _α , the aircraft is mainly in the altitude adjustment stage, and the value of L ₁ /D ₁ is no longer updated.

8. Design of reference lateral lift-drag ratio and reference roll angle

为满足终端横程约束，设计横向升阻比剖面如下：The modulus value of the lateral lift-drag ratio can be determined by the previously planned L/D _bsl and the longitudinal lift-drag ratio L ₁ /D _bs , which is

In order to meet the terminal transverse constraints, the designed lateral lift-drag ratio profile is as follows:

Among them, E _BR1 and E _BR2 represent the first and second tilt reversal points, respectively. sgn is a symbolic variable representing the direction of the initial roll reversal. After the lateral lift-drag ratio profile is obtained, the inclination angle profile is also determined, which is expressed as follows:

Among them, L/D _real represents the actual lift-drag ratio profile.

9. Tilt reversal point correction algorithm

In this algorithm, the roll reversal point is designed based on the analytical solution of the lateral run to eliminate the terminal run error. There are two tilt reversal points arranged here. First design and correct the first reversal point E _BR1 . Shilling the second reversal point E _BR2 =E _α , the terminal stroke x _C (E _TAEM ,E) is only a function of E _BR1 . It can be seen from equation (17) that the terminal traverse can be expressed as a piecewise function of E _BR1 as follows:

in,

Taking the derivative of _EBR1 with respect to equation (38), we can get

i＝0,1,2,3,4。为了使终端横程误差为0，即需要满足x_Cf(E_BR1)＝0。因此这个算法的本质在于求解非线性方程x_Cf(E_BR1)＝0的根，用牛顿法求解方法如下：Among them, the right limit at E=E _BR1 is represented by a superscript ⁺ , and the left limit at E=E _BR1 is represented by a superscript ^- . Since L ₂ /D _bsl is discontinuous at E=E _BR1 , we have

i=0,1,2,3,4. In order to make the terminal traverse error 0, it is necessary to satisfy x _Cf (E _BR1 )=0. Therefore, the essence of this algorithm is to solve the root of the nonlinear equation x _Cf (E _BR1 )=0. The Newton method is used to solve it as follows:

因此x_Cf(E_BR1)随着E_BR1单调变化，此非线性方程的解通过简单的几次迭代即可得到。Solve Stop is set to

Therefore x _Cf (E _BR1 ) varies monotonically with E _BR1 , and the solution to this nonlinear equation can be obtained in a few simple iterations.

10. Design of command angle of attack and tilt angle

In order to ensure the tracking accuracy of the reference profile, the ballistic damping control technology is used to suppress the long-period and weakly damped oscillation of the re-entry trajectory. The design command attack and roll angles are as follows:

α _cmd =α _bsl +cosσ _bsl K _γ (γ _SG -γ) (43)

Among them, K _γ is the feedback coefficient, the value is 5; γ _SG is the approximate solution of the inclination angle of the smooth gliding trajectory, which can be expressed as follows

The smooth gliding segment needs to satisfy the process constraints, so the process constraints of equations (8)-(10) are transformed into the inclination angle constraints, which are expressed as follows

in,

Among them, H _min corresponds to the lowest boundary of the gliding height, which can be obtained through process constraints; the constant coefficient k _σ =-50. Therefore, in order to satisfy the process constraints, the tilt angle needs to satisfy the following conditions:

|σ _cmd |≤σ _max (50)

Step 5: Guidance method for height adjustment segment;

4. Command angle of attack and second reversal point correction.

( ₃ ) Correction algorithm of command angle of attack α2

In order to satisfy the terminal height constraint, a ballistic simulation is used here to correct the command angle of attack α ₂ . According to the deviation between the terminal height H _f obtained by the ballistic simulation and the terminal constraint height H _TAEM , the final command angle of attack α ₂ is obtained by further correction. In the following variables, the subscript f represents the terminal value calculated by the ballistic simulation, and the subscript TAEM represents the terminal constraint value.

可以近似为0，因此可分别假设cosγ_f＝1,cosσ_f＝1和

所以根据式(6)可以得到：Since γ _f ,σ _f and

can be approximated to 0, so it can be assumed that cosγ _f =1, cosσ _f =1 and

So according to formula (6), we can get:

Among them, C _L(est) (α _bsl (E _f )) represents the lift coefficient corresponding to the terminal angle of attack in the ballistic simulation, and q _f represents the terminal dynamic pressure.

According to the terminal constraints, there are

表示修正后的指令攻角。in,

Indicates the modified command angle of attack.

通过令式(51)等于式(52)可以得到：Under the assumptions of φ _f = φ _TAEM and ψ _f = ψ _TAEM , the linearization

By making equation (51) equal to equation (52), we can get:

Therefore, α ₂ solved in Equation (53) can be brought into Equation (19) as a reference angle of attack for guidance control.

(4) Second inclination reversal point E _BR2 correction algorithm

The height adjustment stage is designed with proportional guidance law for guidance. Through the analysis of the guidance algorithm, it can be seen that if the E _BR2 is reduced, the guidance law command will generate a larger pitch angle to eliminate the larger heading error generated during the last roll reversal, thereby reducing the longitudinal lift-to-drag ratio. , reducing the terminal velocity V _f . Therefore, V _f can be regarded as a monotonic function with respect to E _BR2 . To ensure terminal constraints, this problem can be viewed as a problem of solving the solution of the nonlinear equation V _f (E _BR2 )=V _TAEM . Here, the secant method is used to solve the problem, and V _f is predicted through multiple ballistic simulations, and the value of E _BR2 is adjusted according to the deviation of the predicted value from the terminal constraint.

E _BR2 The condition for ending iterative correction is that the obtained deviation satisfies

5. Reference tilt angle

After the second roll reversal, the aircraft enters the altitude adjustment phase. At this stage, the reference angle of attack is still determined by equation (19), and the reference tilt angle is controlled by the proportional guidance guidance law. The line-of-sight angular rate can be expressed as

Then, the lateral maneuvering acceleration command obtained by proportional guidance is as follows

表示第二次倾侧反转时的纵程。假设飞行器近似平稳滑翔，则纵向平面内的合力加速度为0。因此，有in,

Indicates the longitudinal distance at the second roll reversal. Assuming that the aircraft glides approximately smoothly, the resultant acceleration in the longitudinal plane is zero. Therefore, there is

Therefore, the reference tilt angle can be obtained as

6. Command angle of attack and roll angle

指令攻角与倾侧角可以表示如下：In order to ensure the terminal speed constraint, the remaining glide distance reference profile with energy as the independent variable is tracked by adjusting the angle of attack.

The commanded attack angle and pitch angle can be expressed as follows:

的值可以通过之前的最后一次弹道仿真获得。Among them, the value of k _α can be adjusted in time according to the task, and generally can be selected as 2π/(1.8×10 ⁷ );

The value of can be obtained from the last ballistic simulation before.

To satisfy the process constraints, as before, the roll angle still needs to satisfy the following requirements:

|σ _cmd |≤σ _max (61)

Through the above five steps, a hypersonic reentry guidance method based on the analytical solution of the smooth gliding trajectory can be obtained.

In order to prove the universality of the guidance method, five examples with different target positions are considered here. Denote five different target points with T1 to T5, which are set as (-77°, 0°) (T1), (-34°, -32.5°) (T2), (5°, -50°) (T3), (65°, -33°) (T4) and (118°, 0°) (T5). The initial conditions were all h ₀ =80 km, V ₀ =7200 m/s, λ ₀ =0°, θ ₀ =45° and γ ₀ =0°. ψ ₀ points to the target and is determined by the target position. The terminal constraints are all V _TAEM =2000m/s, H _TAEM =25km and R _tm =100km. The simulation results are shown in Figure 3 to Figure 9.

In Figure 3, the red circle represents the range of 100km from the target. It is easy to see from the figure that all the ballistic trajectories fall on the circle, which proves that the guidance method can satisfy the terminal distance constraint. Table 1 shows other state quantities such as terminal range, speed, altitude, bank angle, ballistic inclination angle, and heading error.

Table 1 Simulation results

It can be seen from Figure 4 that all the examples satisfy the terminal process constraints except for the two examples of flying westward. This is because when the aircraft flies westward, the Coriolis force is directed downward, which reduces the gliding height and increases the heat flux density. Furthermore, according to Fig. 4-Fig. 9 and Table 1, we can easily see that all the examples satisfy V _f ≈ V _TAEM = 2000m/s, H _f ≈ H _TAEM = 25 km, R _tm = 100 km, σ _f ≈ Terminal constraints for 0°, γ _f ≈ 0° and Δψ _f ≈ 0°.

To sum up, through the above steps, the method of the present invention is deduced, that is, a hypersonic reentry guidance method based on the analytical solution of the smooth gliding trajectory. The simulation results of the case show that the method of the present invention can meet various requirements for reentry guidance. Constraints, and because the method is based on the ballistic analytical solution design, it has the characteristics of high precision and small amount of calculation, and can be applied to the airborne system of the aircraft in real time.

Claims (2)

1. A hypersonic velocity reentry guidance method based on steady glide trajectory analytic solution is characterized in that: the method comprises the following steps:

the method comprises the following steps: establishing an aircraft dynamics model;

under the background of the rotating earth, a standard atmosphere model and an inverse square gravitational field model are adopted to establish a six-degree-of-freedom kinetic equation of the hypersonic aerocraft as follows:

where d/dt represents the derivative over time, t is time, h is altitude, R is range, λ is longitude, φ is latitude, V is the velocity of the aircraft relative to the earth, γ is the ballistic inclination, ψ is the aircraft heading angle, based on local north, σ is the roll angle, R is the altitude, and R is the altitude, where_eIs the radius of the earth, and takes the value of 6378.137km, omega_eIs the angular velocity of rotation of the earth, g represents the acceleration of gravity; l ═ ρ V²SC_LThe lift acceleration is given by/2 m, and D is equal to rho V²SC_D(2 m) is the acceleration of resistance, C_L、C_DRespectively a lift coefficient and a drag coefficient;

step two: establishing a constraint model;

the reentry vehicle needs to meet the process constraints of heat flux density, dynamic pressure and overload during flight, as follows:

parameter p₀Denotes nominal atmospheric density, e denotes natural constant, h denotes altitude, h_SRepresenting nominal height, n representing overload, m representing mass;

wherein, K_QIs the heat flux density coefficient;

representing a maximum allowable heat flow density value; n is_maxRepresents a maximum allowable overload value; q represents an allowable dynamic pressure value; q. q.s_maxRepresents the maximum allowable dynamic pressure value;

furthermore, due to the capability constraints of the flight control system, the rate of change of the control quantity also satisfies the constraint:

in addition to process constraints, the aircraft should also satisfy terminal constraints, with: v_TAEM＝2000m/s,H_TAEM＝25km,R_tm＝100km,σ_TAEM≈0°,γ_TAEM≈0°andΔψ_TAEM0 °, where subscript TAEM denotes the terminal amount; v_TAEM、H_TAEM、σ_TAEM、γ_TAEM、Δψ_TAEMRespectively representing the terminal speed, the terminal height, the terminal roll angle, the terminal trajectory inclination angle and the terminal course angle error; r_tmRepresenting the shot-eye distance;

step three: an initial descent stage guidance method;

in the initial descent phase, the maximum angle of attack α is selected_maxFlying at 20deg and zero roll angle; rate of change of ballistic inclination

By time, it is meant that lift meets the smooth gliding requirement, so that the angle of attack transitions smoothly from the maximum angle of attack to the reference angle of attack α_bsl；

At this stage, the command angle of attack and the command roll angle are designed as follows:

σ_cmd＝0 (12)

wherein,

Δγ＝γ-γ_SG (13)

wherein, γ_SGRepresenting the angle of inclination, k, of the smooth gliding trajectory_γRepresents the feedback coefficient and takes the value of 5; when the delta gamma is 0, the aircraft enters a stable gliding stage; parameter alpha_cmdIs an instruction angle of attack; sigma_cmdIs a commanded roll angle; delta gamma is the deviation of the current trajectory inclination angle and the steady glide trajectory inclination angle; delta gamma₁As the rate of change of ballistic inclination

A deviation value of the trajectory inclination angle when it is 0 from the steady glide trajectory inclination angle;

step four: a steady glide phase guidance method;

ballistic planning in the steady glide phase is the basis of the proposed guidance algorithm, and the aircraft needs to approach the target while process constraints are ensured;

firstly, establishing the following two coordinate systems, and intuitively obtaining the meanings of representing the longitudinal course and the transverse course;

defining an auxiliary earth center rotation reference system (AGR coordinate system) rotating along with the earth: the origin is at the geocentric E,

the shaft points to the initial position of the aircraft,

the axis is located in a large circular plane passing through the aircraft and the target point and is vertical to the aircraftIn a direction perpendicular to

The shaft is provided with a plurality of axial holes,

the axis is determined according to the right-hand rule;

meanwhile, local generalized north, east and down coordinate systems, i.e. GNED coordinate systems, are defined: the vertical projection point of the origin o from the mass center M of the aircraft to the ground;

the axis is vertically downwards directed to the center of the earth,

axis-oriented AGR coordinate system

The direction of the "north" direction is,

the axis is determined by the right hand rule;

define the longitudinal extent as

Define the course as

Wherein

And

respectively representing a generalized longitude and a generalized latitude in an AGR coordinate system;

defining the energy as

Defining the longitudinal lift-to-drag ratio Lcos sigma/D ═ L₁D, transverse lift-drag ratio Lsin sigma/D ═ L₂D; the generalized longitude and latitude coordinate system in the AGR coordinate axis is beneficial to linearizing and decoupling a complex dynamic model, and the following three-dimensional ballistic analysis solution is obtained;

wherein,

and p_ijI is 1, 2; j is 0,1,2,3 and 4 are constant coefficients; e, E₀Respectively representing the current energy and the initial energy value; x is the number of_ERepresenting an energy integral variable; l is₁Representing lift values in a longitudinal plane; x is the number of_C0Representing an initial traverse value;

representing an initial course angle error under a GNED coordinate system;

representing the course angle error under the GNED coordinate system;

4.1 datum Angle of attack design

All reference profiles in the guidance method also adopt energy as independent variables; reference angle of attack alpha_bslThe design is as follows:

wherein E is_α＝-5.55×10⁷J/kg is positioned near the junction point of the stable gliding section and the last height adjusting section; alpha is alpha₁And alpha₂Two reference angle of attack parameters; to maximize the capacity of the aircraft, design alpha₁For maximum lift-to-drag ratio corresponding to angle of attack, i.e. alpha₁10 deg; the quadratic function of the energy of the angle of attack is designed so that the angle of attack is from alpha₁Smoothly transits to alpha₂(ii) a In this guidance method, α is preset for the first time₂If the terminal height is 6deg, trajectory simulation is applied to correct the terminal height to strictly meet the terminal height constraint; when the design of the attack angle section is finished, the corresponding reference lift-drag ratio section (L/D)_bslIs also determined accordingly;

4.2 benchmark lift-drag ratio profile design

In order to meet the requirement of the range, a standard lift-drag ratio profile is designed as follows:

wherein, let the terminal longitudinal analysis solve x_DfEqual to the remaining range, i.e. obtaining L₁/D₁(ii) a Design L₁/D₂＝L/D(E_TAEM) In which E_TAEMIs terminal energy, so when x_E＝E_TAEMWhen the temperature of the water is higher than the set temperature,

(L₁/D)_bsl|_{E＝E_TAEM}＝(Lcosσ_TAEM/D)_bsl＝L/D(E_TAEM) So that the terminal is inclined at an angle σ_TAEMIs 0; by means of the form of the design formula (20), the terminal roll angle is controlled to be approximately constant in the flying process;

therefore, to solve for L₁/D₁First, the remaining range x needs to be calculated_Df(ii) a In the GER coordinate system, η is defined as a vector pointing from the center of the earth to the aircraft

Vector directed to aircraft from earth center

The included angle between them; the remaining range is then expressed as:

x_Df＝R_eη-S_TAEM (21)

wherein S is_TAEMIndicating the distance to the target at the end of the reentry segment;

solving for L₁/D₁The process of (a) is described as follows:

when E is more than or equal to E_αWhen there is

x_D(E_α,E)+x_D(E_TAEM,E_α)＝x_Df (22)

Wherein,

wherein,

and is provided with a plurality of groups of the following components,

wherein,

c₂＝(a₁-c₁d₀)/d₁ (28)

c₃＝a₀-c₂d₀ (29)

the formula (22) is solved to obtain

Wherein,

when E < E_αWhen the aircraft is in the altitude adjustment stage, L is not updated any more₁/D₁A value of (d);

4.3 reference transverse lift-drag ratio and reference roll angle design

The module value of the reference transverse lift-drag ratio is well planned from the previous (L/D)_bslAnd longitudinal lift-to-drag ratio (L)₁/D)_bslIs determined as

In order to meet the terminal traverse constraint, the design reference transverse lift-drag ratio is as follows:

wherein E is_BR1And E_BR2Respectively representing a first and a second roll reversal point; sgn is a sign variable representing the initial roll reversal direction; after obtaining the reference transverse lift-drag ratio, the reference roll angle sigma_bslIt was also determined that this is expressed as follows:

wherein, (L/D)_realRepresenting the actual lift-to-drag ratio profile;

4.4 roll reversal Point correction Algorithm

Designing a roll reversal point based on a traverse analytic solution to eliminate a terminal traverse error; arranging two tilting reversal points; the first reversal point E is first designed and corrected_BR1(ii) a First order second reversal point E_BR2＝E_αThen the terminal traverse x_C(E_TAEME) is only E_BR1A function of (a); as seen from the formula (17), the terminal traverse x_CfIs represented by E_BR1The piecewise function of (c) is as follows:

f, G is a custom function, and the expression is as follows

Wherein, the parameter x_E2,x_E1Expressing upper and lower energy bounds; k is a constant of 1 to 5; p₁Representing a polynomial fitting coefficient;

obtaining E from equation (38)_BR1Derivative of (2) can be obtained

Wherein E ═ E_BR1Upper mark for right limit of⁺Is represented by E ═ E_BR1Upper mark for left limit of department^-Represents; because L is₂/D_bslWhen E is equal to E_BR1Is not continuous in place, so there is

In order to make the terminal traverse error 0, x needs to be satisfied_Cf(E_BR1) 0; the essence of this algorithm is therefore to solve the non-linear equation x_Cf(E_BR1) Root 0, the newton method is as follows:

parameter(s)

And

and not the same as the above-mentioned case,

represents E_BR1To the power of k in the first order,

e representing the kth iteration_BR1A value; solution stop set to

Thus x_Cf(E_BR1) With E_BR1Monotonously changing, and the solution of the nonlinear equation is obtained by simple iterations;

4.5 Command attack Angle and Command roll Angle design

In order to ensure the tracking precision of the reference profile, a trajectory damping control technology is adopted to inhibit the oscillation of long-period and weak damping existing in a reentry trajectory; design command angle of attack alpha_cmdAnd the command roll angle sigma_cmdThe following were used:

α_cmd＝α_bsl+cosσ_bslK_γ(γ_SG-γ) (43)

wherein, K_γIs a feedback coefficient, and takes the value of 5; gamma ray_SGIs an approximate solution to the angle of inclination of the smooth glide trajectory, as shown below

Wherein S is the aircraft reference area; c_LIs the coefficient of lift; ρ is the air density;

the smooth glide phase needs to satisfy the process constraint, so the process constraint of equation (8) -10 is converted into the command roll angle constraint, which is expressed as follows

Wherein L is_maxFor maximum lift, the expression is as follows:

wherein H_minThe lowest boundary corresponding to the glide height is obtained through process constraint; constant coefficient k_σ-50; thus, to satisfy the process constraints, the following conditions need to be satisfied for the commanded roll angle:

|σ_cmd|≤σ_max (50)

step five: a height adjustment section guidance method;

5.1 correcting the command attack angle and the second reversal point;

(1) reference angle of attack parameter alpha₂Correction algorithm

In order to meet the height constraint of the terminal, a primary trajectory simulation is adopted to correct a reference attack angle parameter alpha₂(ii) a Terminal height H obtained from trajectory simulation_fAnd terminal constraint height H_TAEMThe deviation between the two parameters is further corrected to obtain the final reference attack angle parameter alpha₂(ii) a In the following variables, subscript f represents a terminal value obtained by ballistic simulation calculation, and subscript TAEM represents a terminal constraint value;

due to gamma_f,σ_fAnd

is approximately 0, so cos γ is assumed separately_f＝1,cosσ_f1 and

therefore, it is obtained from equation (6):

wherein, C_L(est)(α_bsl(E_f) Q) represents the lift coefficient, q, corresponding to the terminal angle of attack in a ballistic simulation_fRepresenting terminal dynamic pressure; according to terminal constraints, have

Wherein,

indicating the corrected command angle of attack, phi_f、ψ_f、V_f、H_fRespectively representing terminal latitude, course angle, speed and height obtained by trajectory simulation calculation; q. q.s_TAEM、φ_TAEM、ψ_TAEM、V_TAEM、H_TAEMRespectively representing a dynamic pressure value, a latitude value, a course angle value, a speed value and a height value of terminal constraint; at phi_f＝φ_TAEMAnd psi_f＝ψ_TAEMUnder the assumption of (1), linearizing

By making equation (51) equal to equation (52), we obtain:

wherein E is_fRepresenting a terminal energy value obtained by ballistic simulation calculation;

representing the derivative of the lift coefficient with respect to the angle of attack; therefore, α solved in the formula (53)₂Taking the belt-in type (19) as a reference attack angle to conduct guidance control;

(2) second roll reversal point E_BR2Correction algorithm

In the height adjustment stage, guidance is designed by adopting a proportional guidance law; through the analysis of the guidance algorithm, if E is reduced_BR2The guidance law command will generate a larger roll angle to eliminate a larger course error generated during the last roll reversal, so that the longitudinal lift-drag ratio is reduced, and the terminal speed V is reduced_f(ii) a Thus, V_fIs regarded as relating to E_BR2A monotonic function of (a); to guarantee the terminal constraints, this problem is treated as solving the nonlinear equation V_f(E_BR2)＝V_TAEMThe problem of the solution of (a); solving by adopting a secant method, and simulating V by a plurality of trajectories_fMaking a prediction and adjusting E according to the deviation of the predicted value from the terminal constraint_BR2A value of (d);

E_BR2the condition for ending the iterative correction is that the calculated deviation satisfies

5.2 reference roll angle

After the second roll reversal, the aircraft enters a height adjustment phase; at this stage, the reference angle of attack is still determined by equation (19), and the reference roll angle is controlled by the proportional guidance law; angular rate of view

Is shown as

Then, the lateral maneuvering acceleration command a obtained by the proportional guidance_L2As follows

Wherein k is_PNIs a transverse acceleration maneuvering coefficient and takes the value as

Represents the longitudinal stroke at the time of the second tilt reversal; assuming that the aircraft glides approximately smoothly, the resultant acceleration in the longitudinal plane is 0; thus, the longitudinal maneuvering acceleration command a_L1Is composed of

So that the reference roll angle is

5.3 Command Angle of attack and Command roll

To ensure terminal velocity constraints, the energy-independent residual glide distance reference profile is tracked by adjusting the angle of attack

The commanded angle of attack and commanded roll angle are expressed as follows:

wherein k is_αThe value of (2) is selected as 2 pi/(1.8 × 10) according to task timely adjustment⁷)；

Representing the remaining range, obtained by the last trajectory simulation before;

to meet the process constraints, as before, the commanded roll angle still needs to meet the following requirements:

|σ_cmd|≤σ_max (61)

through the five steps, the hypersonic reentry guidance method based on the steady glide trajectory analytic solution is obtained.

2. The hypersonic re-entry guidance method based on the smooth gliding trajectory analytic solution as claimed in claim 1, characterized in that: the hypersonic flight vehicle is an aircraft with a flight Mach number larger than 5 and capable of realizing hypersonic flight in an atmosphere layer and a trans-atmosphere layer.

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