CN112525221B - Advanced numerical prediction correction guidance method based on adaptive control - Google Patents

Advanced numerical prediction correction guidance method based on adaptive control Download PDF

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CN112525221B
CN112525221B CN202011364615.4A CN202011364615A CN112525221B CN 112525221 B CN112525221 B CN 112525221B CN 202011364615 A CN202011364615 A CN 202011364615A CN 112525221 B CN112525221 B CN 112525221B
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孟斌
唐青原
王晓磊
解永春
吴宏鑫
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Beijing Institute of Control Engineering
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Abstract

An advanced numerical prediction correction guidance method based on self-adaptive control comprises (1) establishing a spacecraft reentry guidance dynamics dimensionless equation considering earth rotation; (2) Converting the thermal rate limit, the load limit and the dynamic pressure limit of the aircraft into altitude reference values; (3) Performing differential stratospheric transformation on the longitudinal dynamics state of the aircraft to obtain a model taking the range and the high derivative as states; (4) designing an active disturbance rejection guidance law aiming at the voyage model; (5) designing an active disturbance rejection guidance law aiming at the high derivative model; and (6) designing a guidance law. The method provided by the invention can be used for hypersonic aircrafts, manned airships, deep space exploration entering spacecrafts and pneumatic capturing, and has better universality.

Description

一种基于自适应控制的先进数值预测校正制导方法An advanced numerical prediction and correction guidance method based on adaptive control

技术领域Technical Field

本发明涉及航空航天领域，特别是一种基于自适应控制的先进数值预测校正制导方法。The invention relates to the field of aerospace, and in particular to an advanced numerical prediction correction guidance method based on adaptive control.

背景技术Background Art

制导是航天器再入(进入)的关键技术之一，也是目前国内外航天领域的重点研究方向。由于在轨计算机性能的提高，数值预测校正制导方法在轨应用成为可能，因此也成为目前的研究热点。目前，数值预测校正制导方法是在每个制导周期，采用梯度法，由位置误差求制导变量。为了使得制导变量收敛，在每个制导周期需要对动力学积分多次，因此所需计算量大；并且当存在不确定性时，难以保证梯度法收敛；针对路径限制问题，跟踪高度参考量是当前的最新技术，但是需要离线设计反馈系数，缺乏适应性。Guidance is one of the key technologies for spacecraft reentry (entry), and it is also a key research direction in the aerospace field at home and abroad. Due to the improvement of on-orbit computer performance, the application of numerical prediction and correction guidance methods on-orbit has become possible, so it has also become a current research hotspot. At present, the numerical prediction and correction guidance method uses the gradient method in each guidance cycle to calculate the guidance variable from the position error. In order to make the guidance variable converge, the dynamics need to be integrated many times in each guidance cycle, so the required calculation amount is large; and when there is uncertainty, it is difficult to ensure the convergence of the gradient method; for the path restriction problem, tracking the altitude reference is the latest technology, but it requires offline design of the feedback coefficient and lacks adaptability.

发明内容Summary of the invention

本发明解决的技术问题是：克服现有技术的不足，提出了一种基于自适应控制的先进数值预测校正制导方法，具有快速性、收敛性和适应性，因此是一种先进的数值预测校正制导方法。本发明所提出的方法可以用于高超声速飞行器，(载人)飞船、深空探测进入航天器、气动捕获，具有较好的通用性。The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, and to propose an advanced numerical prediction correction guidance method based on adaptive control, which has rapidity, convergence and adaptability, and is therefore an advanced numerical prediction correction guidance method. The method proposed by the present invention can be used for hypersonic vehicles, (manned) spacecraft, deep space exploration entry spacecraft, and aerodynamic capture, and has good versatility.

本发明的技术方案是：一种基于自适应控制的先进数值预测校正制导方法，步骤如下：The technical solution of the present invention is: an advanced numerical prediction correction guidance method based on adaptive control, the steps are as follows:

(1)建立考虑地球自转的航天器再入制导动力学无量纲方程；(1) Establish the dimensionless equations of spacecraft reentry guidance dynamics taking into account the Earth's rotation;

(2)将飞行器的热率限制、负载限制和动压限制转化为高度参考值；(2) Convert the aircraft's thermal rate limits, load limits, and dynamic pressure limits into altitude reference values;

(3)将飞行器纵向动力学状态进行微分同胚变换，得到以航程和高度导数作为状态的模型；(3) Performing a diffeomorphic transformation on the longitudinal dynamic state of the aircraft to obtain a model with range and altitude derivatives as states;

(4)针对航程模型设计自抗扰制导律；(4) Design an anti-disturbance guidance law based on the range model;

(5)针对高度导数模型设计自抗扰制导律；(5) Design an anti-disturbance guidance law based on the altitude derivative model;

(6)设计制导律。(6) Design guidance law.

所述步骤(1)建立的方程为：The equation established in step (1) is:

Figure BDA0002805063050000021
Figure BDA0002805063050000021

其中，r表示地心距，θ和φ分别表示经度和纬度，V表示地球相对速度，γ和ψ分别表示飞行路径角和航向角，s表示预计航程；σ表示倾侧角，为制导输入；Ω表示地球自转角速度；L和D分别表示气动升力和阻力，Where r represents the distance from the center of the earth, θ and φ represent longitude and latitude respectively, V represents the relative speed of the earth, γ and ψ represent the flight path angle and heading angle respectively, s represents the expected range; σ represents the roll angle, which is the guidance input; Ω represents the angular velocity of the earth's rotation; L and D represent the aerodynamic lift and drag respectively.

Figure BDA0002805063050000022
Figure BDA0002805063050000022

Figure BDA0002805063050000023
Figure BDA0002805063050000023

R0表示地球半径，Sref和m分别表示飞行器的参考面积和质量，CL和CD分别表示升力和阻力系数，ρ表示大气密度， R0 represents the radius of the earth, Sref and m represent the reference area and mass of the aircraft, CL and CD represent the lift and drag coefficients, ρ represents the atmospheric density,

Figure BDA0002805063050000024
Figure BDA0002805063050000024

ρ0是在参考高度h0处的大气密度，βr<0，ρ 0 is the atmospheric density at the reference height h 0 , β r < 0,

h＝r-R0 (5)h＝rR 0 (5)

航天器再入中所考虑的在大气飞行中的典型的路径约束包括峰值热率

Figure BDA0002805063050000025
负载a，和动压
Figure BDA0002805063050000026
表达式分别为：Typical path constraints considered for spacecraft reentry in atmospheric flight include peak thermal rate
Figure BDA0002805063050000025
Load a, and dynamic pressure
Figure BDA0002805063050000026
The expressions are:

峰值热率：

Figure BDA0002805063050000027
Peak heat rate:
Figure BDA0002805063050000027

负载：

Figure BDA0002805063050000028
load:
Figure BDA0002805063050000028

动压：

Figure BDA0002805063050000029
Dynamic pressure:
Figure BDA0002805063050000029

其中，kQ是已知常数；

Figure BDA0002805063050000031
amax和
Figure BDA0002805063050000032
分别表示热率、负载和动压的限制。所述步骤(2)的转化结果为：Where k Q is a known constant;
Figure BDA0002805063050000031
a max and
Figure BDA0002805063050000032
Respectively represent the limits of heat rate, load and dynamic pressure. The conversion result of step (2) is:

Figure BDA0002805063050000033
Figure BDA0002805063050000033

其中：in:

sinγref＝max{sinγ,W1,W2,W3} (10)sinγ ref =max{sinγ,W 1 ,W 2 ,W 3 } (10)

Figure BDA0002805063050000034
Figure BDA0002805063050000034

Figure BDA0002805063050000035
Figure BDA0002805063050000035

Figure BDA0002805063050000036
Figure BDA0002805063050000036

其中，T表示制导周期。Wherein, T represents the guidance period.

所述步骤(3)得到的模型为：The model obtained in step (3) is:

Figure BDA0002805063050000037
Figure BDA0002805063050000037

Figure BDA0002805063050000038
Figure BDA0002805063050000038

其中，in,

y1＝s， (19)y 1 =s, (19)

Figure BDA0002805063050000039
Figure BDA0002805063050000039

所述步骤(4)的具体过程为：The specific process of step (4) is as follows:

Figure BDA00028050630500000310
Figure BDA00028050630500000310

Figure BDA00028050630500000311
Figure BDA00028050630500000311

则航程模型公式写为Then the voyage model formula is written as

Figure BDA00028050630500000312
Figure BDA00028050630500000312

针对公式(25)，设计自抗扰自适应制导律，According to formula (25), the self-disturbance rejection adaptive guidance law is designed:

Figure BDA00028050630500000313
Figure BDA00028050630500000313

其中，微分方程公式(26)的初值均选0；y1＝s通过对动力学公式(1)积分得到；sref为当前位置距离和目标位置的距离Among them, the initial values of the differential equation formula (26) are all selected as 0; y 1 =s is obtained by integrating the dynamics formula (1); s ref is the distance between the current position and the target position

sref＝arccos(sinθSsinθ+cosφScosφcos(φ-φS)) (27)s ref = arccos(sinθ S sinθ+cosφ S cosφcos(φ-φ S )) (27)

其中，θS,φS是目标点的经纬度，

Figure BDA0002805063050000041
由二阶跟踪微分器得到；l1,l2,l3,kd,kp是待调整参数。Among them, θ S , φ S are the latitude and longitude of the target point,
Figure BDA0002805063050000041
Obtained by the second-order tracking differentiator; l 1 , l 2 , l 3 , k d , k p are parameters to be adjusted.

所述步骤(5)的具体过程为：The specific process of step (5) is as follows:

记U2＝Lcosγcosσ (28)Let U 2 = Lcosγcosσ (28)

Figure BDA0002805063050000042
Figure BDA0002805063050000042

则高度导数模型公式(18)写为Then the height derivative model formula (18) is written as

Figure BDA0002805063050000043
Figure BDA0002805063050000043

针对公式(30)，设计自抗扰自适应制导律：According to formula (30), the self-disturbance rejection adaptive guidance law is designed:

Figure BDA0002805063050000044
Figure BDA0002805063050000044

其中，微分方程公式(31)的初值均选0；

Figure BDA0002805063050000045
由步骤(2)公式(9)给出，
Figure BDA0002805063050000046
由一阶跟踪微分器给出；
Figure BDA0002805063050000047
由状态量测和动力学方程公式(1)给出；p1,p2,k是待调整参数。Among them, the initial values of the differential equation formula (31) are all selected as 0;
Figure BDA0002805063050000045
Given by step (2) formula (9),
Figure BDA0002805063050000046
is given by a first-order tracking differentiator;
Figure BDA0002805063050000047
It is given by state measurement and dynamic equation formula (1); p 1 , p 2 , k are parameters to be adjusted.

所述步骤(6)设计的制导律具体为：The guidance law designed in step (6) is specifically:

Figure BDA0002805063050000048
Figure BDA0002805063050000048

本发明与现有技术相比的优点在于：The advantages of the present invention compared with the prior art are:

(1)本发明所提出的基于自适应控制的先进数值预测校正制导方法，在每个制导周期仅计算一次制导量，相比于目前已有数值预测校正制导方法，具有快速性。目前已有的数值预测校正制导方法在每个制导周期，采用梯度法，在每个制导周期需要对动力学积分多次，所需计算量大。(1) The advanced numerical prediction correction guidance method based on adaptive control proposed by the present invention only calculates the guidance amount once in each guidance cycle, which is faster than the existing numerical prediction correction guidance method. The existing numerical prediction correction guidance method uses the gradient method in each guidance cycle, and needs to integrate the dynamics multiple times in each guidance cycle, which requires a large amount of calculation.

(2)本发明所提出的基于自适应控制的先进数值预测校正制导方法，与已有数值预测校正制导方法相比，具有更强的鲁棒性、收敛性和自适应性。目前已有的数值预测校正制导方法在每个制导周期，采用梯度法，当存在不确定性时，难以保证梯度法收敛；针对路径限制问题，需要离线设计反馈系数，缺乏适应性。本发明提出的方法，采用扩张状态观测器对付不确定性问题，在线调整反馈系数，因此具有更强的鲁棒性、收敛性和自适应性。(2) The advanced numerical prediction correction guidance method based on adaptive control proposed in the present invention has stronger robustness, convergence and adaptability compared with the existing numerical prediction correction guidance method. The existing numerical prediction correction guidance method uses the gradient method in each guidance cycle. When there is uncertainty, it is difficult to ensure the convergence of the gradient method; for the path restriction problem, the feedback coefficient needs to be designed offline, which lacks adaptability. The method proposed in the present invention uses an extended state observer to deal with the uncertainty problem and adjusts the feedback coefficient online, so it has stronger robustness, convergence and adaptability.

(3)本发明所提出的方法可以用于高超声速飞行器，(载人)飞船、深空探测进入航天器、气动捕获，具有较好的通用性。(3) The method proposed in the present invention can be used for hypersonic aircraft, (manned) spacecraft, deep space exploration entry spacecraft, and aerodynamic capture, and has good versatility.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1为本发明方法流程图。FIG1 is a flow chart of the method of the present invention.

具体实施方式DETAILED DESCRIPTION

本发明针对现有技术的不足，提出一种基于自适应控制的先进数值预测校正制导方法，如图1所示，本发明通过步骤(1)-步骤(6)实现。In view of the deficiencies in the prior art, the present invention proposes an advanced numerical prediction correction guidance method based on adaptive control. As shown in FIG1 , the present invention is implemented through steps (1) to (6).

步骤(1).考虑地球自转的航天器再入制导动力学无量纲方程Step (1). Dimensionless equations of spacecraft reentry guidance dynamics considering the Earth's rotation

Figure BDA0002805063050000051
Figure BDA0002805063050000051

其中，r表示地心距，θ和φ分别表示经度和纬度，V表示地球相对速度，γ和ψ分别表示飞行路径角和航向角，s表示预计航程；σ表示倾侧角，为制导输入；Ω表示地球自转角速度；L和D分别表示气动升力和阻力，Among them, r represents the distance from the center of the earth, θ and φ represent longitude and latitude respectively, V represents the relative speed of the earth, γ and ψ represent the flight path angle and heading angle respectively, s represents the expected range; σ represents the roll angle, which is the guidance input; Ω represents the angular velocity of the earth's rotation; L and D represent the aerodynamic lift and drag respectively,

Figure BDA0002805063050000052
Figure BDA0002805063050000052

Figure BDA0002805063050000053
Figure BDA0002805063050000053

R0表示地球半径，Sref和m分别表示飞行器的参考面积和质量，CL和CD分别表示升力和阻力系数，ρ表示大气密度， R0 represents the radius of the earth, Sref and m represent the reference area and mass of the aircraft, CL and CD represent the lift and drag coefficients, ρ represents the atmospheric density,

Figure BDA0002805063050000061
Figure BDA0002805063050000061

ρ0是在参考高度h0处的大气密度，ρ0和h0已知，βr<0已知，ρ 0 is the atmospheric density at the reference height h 0 , ρ 0 and h 0 are known, β r < 0 is known,

h＝r-R0 (5)h＝rR 0 (5)

一般来说，航天器再入中所考虑的在大气飞行中的典型的路径约束包括峰值热率

Figure BDA0002805063050000062
负载a，和动压
Figure BDA0002805063050000063
其表达式分别为：In general, typical path constraints considered for spacecraft reentry in atmospheric flight include peak thermal rate
Figure BDA0002805063050000062
Load a, and dynamic pressure
Figure BDA0002805063050000063
The expressions are:

峰值热率：

Figure BDA0002805063050000064
Peak heat rate:
Figure BDA0002805063050000064

负载：

Figure BDA0002805063050000065
load:
Figure BDA0002805063050000065

动压：

Figure BDA0002805063050000066
Dynamic pressure:
Figure BDA0002805063050000066

其中，kQ是已知常数；

Figure BDA0002805063050000067
amax，和
Figure BDA0002805063050000068
分别表示热率，负载和动压的限制。Where k Q is a known constant;
Figure BDA0002805063050000067
a max , and
Figure BDA0002805063050000068
represent the limits of heat rate, load and dynamic pressure respectively.

步骤(2).将飞行器的热率限制、负载限制和动压限制转化为高度参考值，Step (2) converting the aircraft's thermal rate limit, load limit and dynamic pressure limit into altitude reference values,

Figure BDA0002805063050000069
Figure BDA0002805063050000069

其中：in:

sinγref＝max{sinγ,W1,W2,W3} (10)sinγ ref =max{sinγ,W 1 ,W 2 ,W 3 } (10)

Figure BDA00028050630500000610
Figure BDA00028050630500000610

Figure BDA00028050630500000611
Figure BDA00028050630500000611

Figure BDA00028050630500000612
Figure BDA00028050630500000612

其中，T表示制导周期。Wherein, T represents the guidance period.

公式(9)是由如下过程推导得到。通过对上述限制公式(6)-公式(8)进行微分，然后引入预测控制的方法，采用线性插值求微分，即可以得到飞行路径角的正弦sinγ和路径约束的关系。针对不同的路径约束，包括如下三种情形。Formula (9) is derived from the following process. By differentiating the above-mentioned restriction formulas (6) to (8), and then introducing the predictive control method, the relationship between the sine of the flight path angle sinγ and the path constraint can be obtained by using linear interpolation to differentiate. For different path constraints, the following three situations are included.

第一种情形：峰值热率限制公式(6)，Case 1: Peak heat rate limitation formula (6),

Figure BDA00028050630500000613
Figure BDA00028050630500000613

第二种情形：负载限制公式(7)，The second case: Load limit formula (7),

Figure BDA00028050630500000614
Figure BDA00028050630500000614

第三种情形：动压限制公式(8)，The third case: dynamic pressure limitation formula (8),

Figure BDA0002805063050000071
Figure BDA0002805063050000071

进一步，按照公式(10)定义sinγref。其意义在于，一方面，当某一限制被违背时，也即Furthermore, sinγ ref is defined according to formula (10). Its significance lies in that, on the one hand, when a certain restriction is violated, that is,

sinγ≤W1，或者sinγ≤W2，或者sinγ≤W3 sinγ≤W 1 , or sinγ≤W 2 , or sinγ≤W 3

时，hour,

sinγref＝W1，或者sinγref＝W2，或者sinγref＝W3 sinγ ref =W 1 , or sinγ ref =W 2 , or sinγ ref =W 3

另一方面，当不违背任一个限制时，On the other hand, when no restriction is violated,

sinγref＝sinγsinγ ref = sinγ

最后，由动力学公式(1)的第1个方程，和公式(10)，显然可以得到公式(9)。Finally, from the first equation of the dynamics formula (1) and formula (10), it is obvious that formula (9) can be obtained.

步骤(3).将飞行器纵向动力学状态进行微分同胚变换，得到以航程和高度导数作为状态的模型，Step (3) Perform a differential homeomorphic transformation on the longitudinal dynamic state of the aircraft to obtain a model with range and altitude derivatives as states.

Figure BDA0002805063050000072
Figure BDA0002805063050000072

Figure BDA0002805063050000073
Figure BDA0002805063050000073

其中，in,

y1＝s (19)y 1 =s (19)

Figure BDA0002805063050000074
Figure BDA0002805063050000074

公式(17)和(18)是通过如下步骤推导来的。不考虑地球自转的纵向制导方程为Formulas (17) and (18) are derived through the following steps. The longitudinal guidance equation without considering the rotation of the earth is

Figure BDA0002805063050000075
Figure BDA0002805063050000075

Figure BDA0002805063050000076
Figure BDA0002805063050000076

Figure BDA0002805063050000077
Figure BDA0002805063050000077

Figure BDA0002805063050000078
Figure BDA0002805063050000078

按照公式(19)定义y1。对y1求二阶导数，可以得到Define y 1 according to formula (19). Taking the second-order derivative of y 1 , we can get

Figure BDA0002805063050000079
Figure BDA0002805063050000079

Figure BDA0002805063050000081
Figure BDA0002805063050000081

代入公式(3)和公式(21)，即可得到公式(17)。Substituting formula (3) and formula (21) into formula (17) we can obtain formula (17).

按照公式(20)定义y2。对y2求一阶导数，可得Define y 2 according to formula (20). Taking the first-order derivative of y 2 , we get

Figure BDA0002805063050000082
Figure BDA0002805063050000082

代入公式(3)，公式(20)和公式(21)，即可得到公式(18)。Substituting into formula (3), formula (20) and formula (21), we can obtain formula (18).

选取新状态：Select a new state:

z1＝y1＝sz 1 =y 1 =s

Figure BDA0002805063050000083
Figure BDA0002805063050000083

Figure BDA0002805063050000084
Figure BDA0002805063050000084

z4＝rz 4 = r

下面论证该变换是微分同胚的。记The following proves that this transformation is a diffeomorphism.

x＝[r V γ s]T x＝[r V γ s] T

z＝[z1 z2 z3 z4]T z＝[z 1 z 2 z 3 z 4 ] T

对变换求导，可得，Taking the derivative of the transformation, we can get

Figure BDA0002805063050000085
Figure BDA0002805063050000085

公式(22)中的等号右边的矩阵的行列式是

Figure BDA0002805063050000086
表明该矩阵是非奇异的，也即变换是微分同胚的。The determinant of the matrix on the right side of the equal sign in formula (22) is
Figure BDA0002805063050000086
This shows that the matrix is nonsingular, that is, the transformation is diffeomorphic.

其内动态

Figure BDA0002805063050000087
是中立稳定的。Dynamics within
Figure BDA0002805063050000087
It is neutral and stable.

步骤(4).针对航程模型设计自抗扰制导律。Step (4). Design an anti-disturbance guidance law based on the range model.

针对公式(17)，记For formula (17),

Figure BDA0002805063050000088
Figure BDA0002805063050000088

Figure BDA0002805063050000089
Figure BDA0002805063050000089

则航程模型公式(17)可以写为Then the voyage model formula (17) can be written as

Figure BDA00028050630500000810
Figure BDA00028050630500000810

针对公式(25)，设计自抗扰自适应制导律，According to formula (25), the self-disturbance rejection adaptive guidance law is designed:

Figure BDA0002805063050000091
Figure BDA0002805063050000091

其中，微分方程公式(26)的初值均选0；y1＝s通过对动力学公式(1)积分得到，因此，该方法称为数值预测校正制导方法；sref为当前位置距离和目标位置的距离，Among them, the initial values of the differential equation formula (26) are all selected as 0; y 1 =s is obtained by integrating the dynamics formula (1), so this method is called the numerical prediction correction guidance method; s ref is the distance between the current position and the target position,

sref＝arccos(sinθSsinθ+cosφScosφcos(φ-φS)) (27)s ref = arccos(sinθ S sinθ+cosφ S cosφcos(φ-φ S )) (27)

其中，θS,φS是目标点的经纬度。

Figure BDA0002805063050000092
由二阶跟踪微分器得到；l1,l2,l3,kd,kp是待调整参数，调整方法在专著(韩京清，《自抗扰控制技术》)中有详细介绍。Among them, θ S ,φ S are the longitude and latitude of the target point.
Figure BDA0002805063050000092
Obtained by the second-order tracking differentiator; l 1 , l 2 , l 3 , k d , k p are parameters to be adjusted, and the adjustment method is introduced in detail in the monograph (Han Jingqing, "Auto-disturbance Rejection Control Technology").

步骤(5).针对高度导数模型设计自抗扰制导律。Step (5). Design an anti-disturbance guidance law based on the altitude derivative model.

针对公式(18)，记For formula (18),

U2＝Lcosγcosσ (28)U 2 = Lcosγcosσ (28)

Figure BDA0002805063050000093
Figure BDA0002805063050000093

则高度导数模型公式(18)可以写为Then the height derivative model formula (18) can be written as

Figure BDA0002805063050000094
Figure BDA0002805063050000094

针对公式(30)，设计自抗扰自适应制导律：According to formula (30), the self-disturbance rejection adaptive guidance law is designed:

Figure BDA0002805063050000095
Figure BDA0002805063050000095

其中，微分方程公式(31)的初值均选0；

Figure BDA0002805063050000096
由步骤(2)公式(9)给出，
Figure BDA0002805063050000097
由一阶跟踪微分器给出；
Figure BDA0002805063050000098
由状态量测和动力学方程公式(1)给出；p1,p2,k是待调整参数，调整方法在专著(韩京清，《自抗扰控制技术》)中有详细介绍。Among them, the initial values of the differential equation formula (31) are all selected as 0;
Figure BDA0002805063050000096
Given by step (2) formula (9),
Figure BDA0002805063050000097
is given by a first-order tracking differentiator;
Figure BDA0002805063050000098
It is given by state measurement and dynamic equation formula (1); p 1 , p 2 , k are parameters to be adjusted, and the adjustment method is introduced in detail in the monograph (Han Jingqing, "Auto-disturbance Rejection Control Technology").

步骤(6).设计制导律，Step (6). Design the guidance law,

Figure BDA0002805063050000099
Figure BDA0002805063050000099

公式(32)由下面的方法推导得出。联立公式(23)和公式(28)，通过求最小二乘解可以得到公式(32)。Formula (32) is derived by the following method: Formula (23) and Formula (28) are combined to obtain the least squares solution.

本发明未详细说明部分属本领域技术人员公知常识。Parts of the present invention that are not described in detail belong to common knowledge among those skilled in the art.

Claims (1)

1.一种基于自适应控制的先进数值预测校正制导方法，其特征在于步骤如下：1. An advanced numerical prediction and correction guidance method based on adaptive control, characterized by the following steps: (1)建立考虑地球自转的航天器再入制导动力学无量纲方程；(1) Establish the dimensionless equations of spacecraft reentry guidance dynamics taking into account the Earth's rotation; (2)将飞行器的热率限制、负载限制和动压限制转化为高度参考值；(2) Convert the aircraft's thermal rate limits, load limits, and dynamic pressure limits into altitude reference values; (3)将飞行器纵向动力学状态进行微分同胚变换，得到以航程和高度导数作为状态的模型；(3) Performing a diffeomorphic transformation on the longitudinal dynamic state of the aircraft to obtain a model with range and altitude derivatives as states; (4)针对航程模型设计自抗扰制导律；(4) Design an anti-disturbance guidance law based on the range model; (5)针对高度导数模型设计自抗扰制导律；(5) Design an anti-disturbance guidance law based on the altitude derivative model; (6)设计制导律；(6) Design guidance law; 所述步骤(1)建立的方程为：The equation established in step (1) is:
Figure FDA0004037886500000011
Figure FDA0004037886500000011
Figure FDA0004037886500000012
Figure FDA0004037886500000012
Figure FDA0004037886500000013
Figure FDA0004037886500000013
Figure FDA0004037886500000014
Figure FDA0004037886500000014
Figure FDA0004037886500000015
Figure FDA0004037886500000015
Figure FDA0004037886500000016
Figure FDA0004037886500000016
Figure FDA0004037886500000017
Figure FDA0004037886500000017
 其中，r表示地心距，θ和φ分别表示经度和纬度，V表示地球相对速度，γ和ψ分别表示飞行路径角和航向角，s表示预计航程；σ表示倾侧角，为制导输入；Ω表示地球自转角速度；L和D分别表示气动升力和阻力，Among them, r represents the distance from the center of the earth, θ and φ represent longitude and latitude respectively, V represents the relative speed of the earth, γ and ψ represent the flight path angle and heading angle respectively, s represents the expected range; σ represents the roll angle, which is the guidance input; Ω represents the angular velocity of the earth's rotation; L and D represent the aerodynamic lift and drag respectively,
Figure FDA0004037886500000018
Figure FDA0004037886500000018
Figure FDA0004037886500000019
Figure FDA0004037886500000019
 R0表示地球半径，Sref和m分别表示飞行器的参考面积和质量，CL和CD分别表示升力和阻力系数，ρ表示大气密度， R0 represents the radius of the earth, Sref and m represent the reference area and mass of the aircraft, CL and CD represent the lift and drag coefficients, ρ represents the atmospheric density,
Figure FDA0004037886500000021
Figure FDA0004037886500000021
 ρ0是在参考高度h0处的大气密度，βr＜0，ρ 0 is the atmospheric density at the reference height h 0 , β r ＜0, h＝r-R0 (5)h＝rR 0 (5) 航天器再入中所考虑的在大气飞行中的典型的路径约束包括峰值热率
Figure FDA0004037886500000022
负载a，和动压
Figure FDA0004037886500000023
表达式分别为：Typical path constraints considered for spacecraft reentry in atmospheric flight include peak thermal rate
Figure FDA0004037886500000022
Load a, and dynamic pressure
Figure FDA0004037886500000023
The expressions are: 峰值热率：
Figure FDA0004037886500000024
Peak heat rate:
Figure FDA0004037886500000024
 负载：
Figure FDA0004037886500000025
load:
Figure FDA0004037886500000025
 动压：
Figure FDA0004037886500000026
Dynamic pressure:
Figure FDA0004037886500000026
 其中，kQ是已知常数；
Figure FDA0004037886500000027
amax和
Figure FDA0004037886500000028
分别表示热率、负载和动压的限制；Where k Q is a known constant;
Figure FDA0004037886500000027
a max and
Figure FDA0004037886500000028
represent the limits of heat rate, load and dynamic pressure respectively; 所述步骤(2)的转化结果为：The conversion result of step (2) is:
Figure FDA0004037886500000029
Figure FDA0004037886500000029
 其中：in: sinγref＝max{sinγ,W1,W2,W3} (10)sinγ ref =max{sinγ,W 1 ,W 2 ,W 3 } (10)
Figure FDA00040378865000000210
Figure FDA00040378865000000210
Figure FDA00040378865000000211
Figure FDA00040378865000000211
Figure FDA00040378865000000212
Figure FDA00040378865000000212
 其中，T表示制导周期；Where, T represents the guidance period; 所述步骤(3)得到的模型为：The model obtained in step (3) is:
Figure FDA00040378865000000213
Figure FDA00040378865000000213
Figure FDA00040378865000000214
Figure FDA00040378865000000214
 其中，in, y1＝s， (19)y 1 =s, (19)
Figure FDA0004037886500000031
Figure FDA0004037886500000031
 所述步骤(4)的具体过程为：The specific process of step (4) is as follows:
Figure FDA0004037886500000032
Figure FDA0004037886500000032
Figure FDA0004037886500000033
Figure FDA0004037886500000033
 则航程模型公式写为Then the voyage model formula is written as
Figure FDA0004037886500000034
Figure FDA0004037886500000034
 针对公式(25)，设计自抗扰自适应制导律，According to formula (25), the self-disturbance rejection adaptive guidance law is designed:
Figure FDA0004037886500000035
Figure FDA0004037886500000035
Figure FDA0004037886500000036
Figure FDA0004037886500000036
Figure FDA0004037886500000037
Figure FDA0004037886500000037
Figure FDA0004037886500000038
Figure FDA0004037886500000038
 其中，微分方程公式(26)的初值均选0；y1＝s通过对动力学公式(1)积分得到；sref为当前位置距离和目标位置的距离Among them, the initial values of the differential equation formula (26) are all selected as 0; y 1 =s is obtained by integrating the dynamics formula (1); s ref is the distance between the current position and the target position sref＝arccos(sinθSsinθ+cosφScosφcos(φ-φS)) (27)s ref = arccos(sinθ S sinθ+cosφ S cosφcos(φ-φ S )) (27) 其中，θS,φS是目标点的经纬度，
Figure FDA0004037886500000039
由二阶跟踪微分器得到；l1,l2,l3,kd,kp是待调整参数；Among them, θ S , φ S are the latitude and longitude of the target point,
Figure FDA0004037886500000039
Obtained by a second-order tracking differentiator; l 1 , l 2 , l 3 , k d , k p are parameters to be adjusted; 所述步骤(5)的具体过程为：The specific process of step (5) is as follows: 记U2＝Lcosγcosσ (28)Let U 2 = Lcosγcosσ (28)
Figure FDA00040378865000000310
Figure FDA00040378865000000310
 则高度导数模型公式(18)写为Then the height derivative model formula (18) is written as
Figure FDA00040378865000000311
Figure FDA00040378865000000311
 针对公式(30)，设计自抗扰自适应制导律：According to formula (30), the self-disturbance rejection adaptive guidance law is designed:
Figure FDA00040378865000000312
Figure FDA00040378865000000312
Figure FDA00040378865000000313
Figure FDA00040378865000000313
Figure FDA00040378865000000314
Figure FDA00040378865000000314
 其中，微分方程公式(31)的初值均选0；
Figure FDA00040378865000000315
由步骤(2)公式(9)给出，
Figure FDA00040378865000000316
由一阶跟踪微分器给出；
Figure FDA0004037886500000041
由状态量测和动力学方程公式(1)给出；p1,p2,k是待调整参数；Among them, the initial values of the differential equation formula (31) are all selected as 0;
Figure FDA00040378865000000315
Given by step (2) formula (9),
Figure FDA00040378865000000316
is given by a first-order tracking differentiator;
Figure FDA0004037886500000041
It is given by the state measurement and dynamic equation formula (1); p 1 , p 2 , k are the parameters to be adjusted; 所述步骤(6)设计的制导律具体为：The guidance law designed in step (6) is specifically:
Figure FDA0004037886500000042
Figure FDA0004037886500000042
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