CN104267733B

CN104267733B - Attitude control method of direct lateral force and aerodynamic composite missile based on hybrid predictive control

Info

Publication number: CN104267733B
Application number: CN201410578127.1A
Authority: CN
Inventors: 赵昱宇; 杨宝庆; 姚郁; 贺风华; 陈松林; 马杰
Original assignee: Harbin Institute of Technology Shenzhen
Current assignee: Harbin Institute of Technology Shenzhen
Priority date: 2014-10-25
Filing date: 2014-10-25
Publication date: 2016-09-14
Anticipated expiration: 2034-10-25
Also published as: CN104267733A

Abstract

Based on mixing the appearance control formula direct lateral force gentle Power compound missile attitude control method of PREDICTIVE CONTROL, belong to flying vehicles control field.The present invention solves existing Methods of Attitude Control Design cannot solve model nonlinear and the problem controlling input hybrid characters simultaneously.Technical key point is: sets up the direct lateral force gentle Power compound complete Attitude control model of guided missile and direct lateral force model, and by the analysis to aerodynamic characteristic, non-linear dynamic model is converted into piecewise affine model；Utilize the equivalence of piecewise affine model and mixed logical dynamics, and consider to control the hybrid characters of input, establish complex controll guided missile mixed logical dynamics；Based on mixed logical dynamics, design explicit model Predictive control law, determine that pneumatic rudder control law and attitude control engine open rule.The inventive method is applicable to aircraft guidance control field.

Description

Attitude control method of direct lateral force and aerodynamic composite missile based on hybrid predictive control

技术领域technical field

本发明涉及姿控式直接侧向力和气动力复合导弹姿态控制方法，尤其涉及基于混杂预测控制的复合导弹姿态控制方法，属于飞行器控制领域。The invention relates to an attitude control method of direct lateral force and aerodynamic compound missile attitude control, in particular to a compound missile attitude control method based on hybrid predictive control, which belongs to the field of aircraft control.

背景技术Background technique

随着目标机动能力的增强，为了实现对目标的有效拦截，要求导弹具有较快的过载响应速度。传统的纯气动力控制导弹由于受到过载响应速度的限制，已经无法满足对高机动目标精确拦截的要求。采用直接侧向力和气动力复合控制技术是提高导弹过载响应速度的有效途径，但直接侧向力的引入使得导弹制导控制系统的设计难度增加，主要体现在如下两个方面：一是直接侧向力和气动力产生复杂的耦合，使得导弹动力学模型的非线性和不确定性增加；二是直接侧向力的离散特性，使得控制设计模型具有明显的混杂特性。这两点给导弹姿态控制设计带来了新的挑战，传统姿态控制设计方法没有同时解决上述两个问题。目前关于直接侧向力和气动力复合导弹姿态控制设计的方法大多采用两步法，首先，利用非线性控制方法设计非线性姿态控制律，得到控制力矩指令；然后，选取一定的性能指标，通过优化求解，得到气动力矩指令和直接侧向力力矩指令，实现气动力和直接侧向力的指令分配。该方法由于很难考虑直接侧向力和气动力动态特性的差异，控制效果欠佳，应用范围受到限制。With the enhancement of the target's maneuverability, in order to achieve effective interception of the target, the missile is required to have a faster overload response speed. Due to the limitation of overload response speed, the traditional pure aerodynamic control missile can no longer meet the requirements of precise interception of high maneuvering targets. The use of direct lateral force and aerodynamic compound control technology is an effective way to improve the response speed of the missile overload, but the introduction of direct lateral force makes the design of the missile guidance control system more difficult, which is mainly reflected in the following two aspects: one is the direct lateral force The complex coupling of force and aerodynamic force increases the nonlinearity and uncertainty of the missile dynamics model; the second is the discrete nature of the direct lateral force, which makes the control design model have obvious mixed characteristics. These two points bring new challenges to missile attitude control design, and traditional attitude control design methods do not solve the above two problems at the same time. At present, most of the attitude control design methods of direct lateral force and aerodynamic compound missiles adopt a two-step method. First, use the nonlinear control method to design the nonlinear attitude control law to obtain the control torque command; then, select a certain performance index and optimize By solving the problem, the aerodynamic torque command and the direct lateral force torque command are obtained, and the command distribution of aerodynamic force and direct lateral force is realized. Because it is difficult to consider the difference between direct lateral force and aerodynamic characteristics, the control effect of this method is not good, and the application range is limited.

发明内容Contents of the invention

本发明的目的是提供姿控式直接侧向力和气动力复合导弹姿态控制方法，以解决现有的姿态控制设计方法无法同时解决模型非线性和控制输入混杂特性的问题。本发明为解决上述技术问题采取的技术方案是：The purpose of the present invention is to provide an attitude control method for direct lateral force and aerodynamic composite missile attitude control to solve the problem that the existing attitude control design method cannot simultaneously solve the problem of model nonlinearity and control input hybrid characteristics. The technical scheme that the present invention takes for solving the problems of the technologies described above is:

本发明所述的基于混杂预测控制的姿控式直接侧向力和气动力复合导弹姿态控制方法，是按照以下步骤实现的：The attitude control method of the attitude control type direct lateral force and aerodynamic compound missile attitude control based on hybrid predictive control in the present invention is realized according to the following steps:

步骤一、建立直接侧向力和气动力复合导弹完整姿态控制模型和直接侧向力模型，并推导俯仰方向直接侧向力的表达式，将导弹非线性动力学模型转化为分段仿射模型；Step 1. Establish a complete attitude control model and a direct lateral force model of the direct lateral force and aerodynamic compound missile, and derive the expression of the direct lateral force in the pitch direction, and convert the nonlinear dynamics model of the missile into a segmented affine model;

其中，所建立的直接侧向力和气动力复合导弹完整姿态控制模型过程如下：Among them, the complete attitude control model process of the established direct lateral force and aerodynamic compound missile is as follows:

将导弹所受重力和气动力分别在弹道坐标系上表示，得到导弹质心运动的动力学方程如下The gravity and aerodynamic force of the missile are respectively expressed in the ballistic coordinate system, and the dynamic equation of the missile center of mass motion is obtained as follows

$\{\begin{matrix} m m \overset{\cdot &Center Dot;}{V V} = = P P cos cos α α cos cos β β - - {X x}_{a a} - - mg mg sin sin θ θ + + {F f}_{{x x}_{22}}^{a a} \\ mV mV \overset{\cdot &Center Dot;}{θ θ} = = P P ((sin sin α α cos cos {γ γ}_{v v} + + cos cos α α sin sin β β sin sin {γ γ}_{v v})) + + {Y Y}_{a a} cos cos {γ γ}_{v v} - - mg mg cos cos θ θ + + {F f}_{{y the y}_{z z}}^{a a} \\ mV mV cos cos θ θ {\overset{\cdot \cdot}{ψ ψ}}_{V V} = = - - P P ((sin sin α α sin sin {γ γ}_{v v} - - cos cos α α sin sin β β cos cos {γ γ}_{v v})) - - {Y Y}_{a a} sin sin {γ γ}_{v v} - - {Z Z}_{a a} cos cos {γ γ}_{v v} - - {F f}_{{z z}_{22}}^{a a} \end{matrix} - - - - - - ((11))$

其中m为导弹质量，P为导弹尾部主发动机推力，g为重力加速度，X_a、Y_a和Z_a为导弹所受气动力在速度坐标系上的三个分量，分别是阻力、升力和侧向力，其正方向分别与速度坐标系三个轴的正方向一致；V表示导弹质心运动速度，α，β分别为攻角和侧滑角，θ，ψ_v分别为弹道倾角和弹道偏角，γ_v为速度倾斜角；为导弹所受直接侧向力在弹道坐标系上的三个分量；Among them, m is the mass of the missile, P is the thrust of the main engine at the tail of the missile, g is the acceleration of gravity, X _a , Y _a and Z _a are the three components of the aerodynamic force on the missile in the velocity coordinate system, which are drag force, lift force and lateral force respectively Force, whose positive direction is consistent with the positive direction of the three axes of the velocity coordinate system; V represents the velocity of the center of mass of the missile, α, β are the angle of attack and sideslip angle, θ, ψ _v are the ballistic inclination angle and ballistic deflection angle, respectively, γ _v is the velocity inclination angle; are the three components of the direct lateral force on the missile in the ballistic coordinate system;

假定弹体坐标系与弹体惯性主轴重合，即J_xy＝J_yz＝J_zx＝0，得到弹体坐标系中的导弹绕质心转动的动力学方程如下Assuming that the coordinate system of the projectile body coincides with the principal axis of inertia of the projectile body, that is, J _xy =J _yz =J _zx =0, the dynamic equation of the missile rotating around the center of mass in the projectile coordinate system is as follows

$\{\begin{matrix} {J J}_{x x} {\overset{\cdot \cdot}{ω ω}}_{x x} = = (({J J}_{y the y} - - {J J}_{z z})) {ω ω}_{z z} {ω ω}_{y the y} + + {M m}_{x x} \\ {J J}_{y the y} {\overset{\cdot &Center Dot;}{ω ω}}_{y the y} = = (({J J}_{z z} - - {J J}_{x x})) {ω ω}_{x x} {ω ω}_{z z} + + {M m}_{y the y} \\ {J J}_{z z} {\overset{\cdot &Center Dot;}{ω ω}}_{z z} = = (({J J}_{x x} - - {J J}_{y the y})) {ω ω}_{x x} {ω ω}_{y the y} + + {M m}_{z z} \end{matrix} - - - - - - ((22))$

其中J_x、J_y和J_z分别为导弹对弹体坐标系三个轴的转动惯量，ω_x，ω_y，ω_z分别为弹体坐标系相对地面坐标系的转动角速度ω在弹体坐标系三个轴上的分量，M_x、M_y和M_z分别为作用于导弹上所有外力对质心的力矩在弹体坐标系各轴上的分量；M_x、M_y和M_z表示为where J _x , J _y and J _z are the moments of inertia of the missile about the three axes of the projectile coordinate system respectively, ω _x , ω _y , and ω _z are the rotational angular velocity ω of the projectile coordinate system relative to the ground coordinate system in the projectile coordinate system The components on the three axes of the system, M _x , M _y and M _z are the components of the moments of all external forces acting on the missile to the center of mass on each axis of the missile coordinate system; M _x , M _y and M _z are expressed as

$\{\begin{matrix} {M m}_{x x} = = {M m}_{ex ex} + + {M m}_{{x x}_{11}}^{a a} \\ {M m}_{y the y} = = {M m}_{ey ey} + + {M m}_{{y the y}_{11}}^{a a} \\ {M m}_{z z} = = {M m}_{ez ez} + + {M m}_{{z z}_{11}}^{a a} \end{matrix} - - - - - - ((33))$

式中M_ex、M_ey和M_ez分别为作用于导弹的气动力矩在弹体坐标系各轴上的分量，分别为作用于导弹的直接侧向力矩在弹体坐标系各轴上的分量；where M _ex , M _ey and M _ez are the components of the aerodynamic moment acting on the missile on each axis of the missile body coordinate system, respectively, are the components of the direct lateral moment acting on the missile on each axis of the missile body coordinate system;

考虑侧向喷流干扰效应，同时点燃若干姿控脉冲发动机产生的直接侧向力合力和合力矩在弹体坐标系上的表示为Considering the interference effect of the lateral jet flow, the direct lateral force resultant force and resultant moment produced by simultaneously igniting several attitude control pulse engines are expressed in the projectile coordinate system as

$[\begin{matrix} {F f}_{{x x}_{11}}^{a a} \\ {F f}_{{y the y}_{11}}^{a a} \\ {F f}_{{z z}_{11}}^{a a} \end{matrix}] = = [\begin{matrix} 00 \\ {F f}_{{y the y}_{11}} + + {K K}_{{F f}_{y the y}} {F f}_{{y the y}_{11}} \\ {F f}_{{z z}_{11}} + + {K K}_{{F f}_{z z}} {F f}_{{z z}_{11}} \end{matrix}],, [\begin{matrix} {M m}_{{x x}_{11}}^{a a} \\ {M m}_{{y the y}_{11}}^{a a} \\ {M m}_{{z z}_{11}}^{a a} \end{matrix}] = = [\begin{matrix} 00 \\ {M m}_{{y the y}_{11}} + + {K K}_{{M m}_{y the y}} {M m}_{{y the y}_{11}} \\ {M m}_{{z z}_{11}} + + {K K}_{{M m}_{z z}} {M m}_{{z z}_{11}} \end{matrix}] - - - - - - ((44))$

其中，为喷流干扰推力放大因子，为喷流干扰力矩放大因子，F_y1，F_z1，M_y1，M_z1为标称直接侧向力合力和合力矩在弹体坐标系上的表示；in, is the jet disturbance thrust amplification factor, is the magnification factor of the jet disturbance moment, F _y1 , F _z1 , M _y1 , and M _z1 are the expressions of the nominal direct lateral force resultant force and resultant moment on the projectile coordinate system;

根据公式(1)至(4)推导出攻角、侧滑角和弹体角速度动态方程；According to formulas (1) to (4), the dynamic equations of angle of attack, angle of sideslip and angular velocity of projectile are deduced;

攻角和侧滑角动态方程Angle of Attack and Angle of Sideslip Dynamic Equations

$\{\begin{matrix} \overset{\cdot &Center Dot;}{α α} = = {ω ω}_{z z} + + {ω ω}_{y the y} sin sin α α tan the tan β β - - \frac{QS QS (({C C}_{y the y}^{α α} α α + + {C C}_{y the y}^{{δ δ}_{z z}} {δ δ}_{z z})) cos cos α α}{mV mV cos cos β β} - - \frac{(({F f}_{{y the y}_{11}} + + {K K}_{{F f}_{y the y}} {F f}_{{y the y}_{11}})) cos cos α α}{mV mV cos cos β β} - - \frac{{G G}_{y the y} cos cos α α}{mV mV cos cos β β} \\ \overset{\cdot &Center Dot;}{β β} = = {ω ω}_{y the y} cos cos α α + + \frac{QS QS (({C C}_{z z}^{β β} β β + + {C C}_{z z}^{{δ δ}_{y the y}} {δ δ}_{y the y})) cos cos β β}{mV mV} + + \frac{QS QS (({C C}_{y the y}^{α α} α α + + {C C}_{y the y}^{{δ δ}_{z z}} {δ δ}_{z z})) sin sin α α sin sin β β}{mV mV} \\ + + \frac{(({F f}_{{y the y}_{11}} + + {K K}_{{F f}_{y the y}} {F f}_{{y the y}_{11}})) sin sin α α sin sin β β}{mV mV} + + \frac{(({F f}_{{z z}_{11}} + + {K K}_{{F f}_{z z}} {F f}_{{z z}_{11}})) cos cos β β}{mV mV} + + \frac{{G G}_{z z} cos cos β β}{mV mV} + + \frac{{G G}_{y the y} sin sin α α sin sin β β}{mV mV} \end{matrix} - - - - - - ((55))$

弹体角速度动态方程Dynamic Equation of Projectile Angular Velocity

$\{\begin{matrix} {\overset{\cdot \cdot}{ω ω}}_{y the y} = = \frac{{M m}_{{y the y}_{11}}}{{J J}_{y the y}} + + \frac{{K K}_{{M m}_{y the y}} {M m}_{{y the y}_{11}}}{{J J}_{y the y}} + + \frac{{QSLm QSL}_{y the y}^{β β} β β}{{J J}_{y the y}} + + \frac{{QSLm QSL}_{y the y}^{{δ δ}_{y the y}} {δ δ}_{y the y}}{{J J}_{y the y}} + + \frac{{QSLm QSL}_{y the y}^{{ω ω}_{y the y}} {ω ω}_{y the y}}{{J J}_{y the y}} \\ {\overset{\cdot \cdot}{ω ω}}_{z z} = = \frac{{M m}_{{z z}_{11}}}{{J J}_{z z}} + + \frac{{K K}_{{M m}_{z z}} {M m}_{{z z}_{11}}}{{J J}_{z z}} + + \frac{{QSLm QSL}_{z z}^{α α} α α}{{J J}_{z z}} + + \frac{{QSLm QSL}_{z z}^{{δ δ}_{z z}} {δ δ}_{z z}}{{J J}_{z z}} + + \frac{{QSLm QSL}_{z z}^{{ω ω}_{z z}} {ω ω}_{z z}}{{J J}_{z z}} \end{matrix} - - - - - - ((66))$

其中，Q为动压，S为特征面积，L为特征长度，为气动参数，为单位攻角对应的法向过载系数，为单位升降舵偏角对应的法向过载系数，为单位侧滑角对应的侧向过载系数，为单位方向舵偏角对应的侧向过载系数，为偏航静稳定导数，为方向舵操纵效率，为偏航阻尼力矩系数，为俯仰静稳定导数，为升降舵操纵效率，为俯仰阻尼力矩系数，δ_y，δ_z分别为方向舵和升降舵的偏转角；式(5)-(6)即为复合控制导弹的姿态控制模型；Among them, Q is the dynamic pressure, S is the characteristic area, L is the characteristic length, is the aerodynamic parameter, is the normal overload coefficient corresponding to the unit angle of attack, is the normal overload coefficient corresponding to the unit elevator deflection angle, is the lateral overload coefficient corresponding to the unit sideslip angle, is the lateral overload coefficient corresponding to the unit rudder deflection angle, is the yaw static stability derivative, is the rudder control efficiency, is the yaw damping moment coefficient, is the pitch static stability derivative, is the elevator control efficiency, is the pitch damping moment coefficient, δ _y , δ _z are the deflection angles of the rudder and elevator respectively; formulas (5)-(6) are the attitude control models of the compound control missile;

步骤二、引入逻辑变量，构造复合控制导弹完整混合逻辑动态模型；Step 2. Introducing logic variables to construct a complete mixed logic dynamic model of compound control missiles;

步骤三、设计复合导弹姿态控制律，确定气动控制律和姿控发动机开启规律。Step 3: Design the composite missile attitude control law, determine the aerodynamic control law and the attitude control engine opening law.

本发明的有益效果是：The beneficial effects of the present invention are:

本发明与现有的复合导弹姿态控制方法相比优点在于：Compared with the existing composite missile attitude control method, the present invention has the following advantages:

(1)本发明中气动控制律的设计和姿控发动机开启规律的确定是同时完成的，并且，通过引入逻辑变量来描述分段仿射模型和直接侧向力，把复合导弹姿态控制律设计问题转化为混合逻辑动态系统的设计问题，同时解决了复合控制导弹姿态控制设计中的模型非线性和控制输入混杂特性问题。(1) The design of the aerodynamic control law and the determination of the opening law of the attitude control engine are completed simultaneously in the present invention, and describe the segmented affine model and direct lateral force by introducing logical variables, and design the composite missile attitude control law The problem is transformed into a design problem of a hybrid logic dynamic system, and at the same time, the problem of model nonlinearity and control input hybrid characteristics in the design of composite control missile attitude control is solved.

(2)本发明提出的方法适用范围更广，当考虑姿控发动机消耗情况时，只需要每一时刻重新计算可用发动机数量，改变直接侧向力与逻辑变量之间的描述关系即可。另外，本方法不但可用于姿控式复合控制导弹姿态控制设计，对于其他类型非线性导弹制导系统的控制设计同样适用，具有广阔的应用前景。(2) The method proposed by the present invention has a wider application range. When considering the attitude control engine consumption, it only needs to recalculate the number of available engines at each moment, and change the description relationship between the direct lateral force and the logical variable. In addition, this method can not only be used in the attitude control design of attitude-controlled compound control missiles, but also in the control design of other types of nonlinear missile guidance systems, and has broad application prospects.

附图说明Description of drawings

图1是本发明的流程图；Fig. 1 is a flow chart of the present invention;

图2是本发明中用到的主要坐标系的定义，以导弹的质心为原点O，其中地面坐标系Oxyz，弹体坐标系Ox₁y₁z₁，弹道坐标系Ox₂y₂z₂，以及速度坐标系Ox₃y₃z₃，α，β分别为攻角和侧滑角，θ，ψ_v分别为弹道倾角和弹道偏角；Fig. 2 is the definition of the main coordinate system used in the present invention, with the center of mass of the missile as the origin O, wherein the ground coordinate system Oxyz, the missile body coordinate system Ox ₁ y ₁ z ₁ , the ballistic coordinate system Ox ₂ y ₂ z ₂ , And the velocity coordinate system Ox ₃ y ₃ z ₃ , α, β are attack angle and side slip angle respectively, θ, ψ _v are ballistic inclination angle and ballistic deflection angle respectively;

图3是姿控发动机布局图，其中图a为奇数圈姿控脉冲发动机布局，图b为偶数圈姿控脉冲发动机布局，1、2……18表示姿控脉冲发动机在每圈内的编号；Fig. 3 is a layout diagram of the attitude control engine, wherein Figure a is the layout of the attitude control pulse engine in odd circles, and Figure b is the layout of the attitude control pulse engine in even circles, and 1, 2...18 represent the numbers of the attitude control pulse engines in each circle;

图4是姿控发动机环向展开图，其中i表示圈的编号，编号8、9、10、11、12表示姿控脉冲发动机在每圈内的编号，第i圈姿控脉冲发动机喷口圆心的连线形成的截面与弹体质心的距离为l_i，相邻两圈间距为Δl，l₁表示第1圈姿控脉冲发动机喷口圆心的连线形成的截面与弹体质心的距离；Fig. 4 is the circumferential expansion diagram of the attitude control engine, wherein i represents the numbering of the circle, and the numbers 8, 9, 10, 11, and 12 represent the numbering of the attitude control pulse engine in each circle, and the center of the nozzle circle of the i-th circle attitude control pulse engine The distance between the section formed by the connecting line and the center of mass of the projectile is l _i , the distance between two adjacent circles is Δl, and l ₁ represents the distance between the section formed by the line connecting the center of the nozzle circle of the attitude control pulse engine in the first circle and the center of mass of the projectile;

图5是发动机分区示意图，其中图a为奇数圈姿控脉冲发动机分区示意图，图b为偶数圈姿控脉冲发动机分区示意图；Figure 5 is a schematic diagram of engine partitions, where Figure a is a schematic diagram of an odd-numbered circle attitude control pulse engine division, and Figure b is a schematic diagram of an even-numbered circle attitude control pulse engine division;

图6是气动参数与攻角关系图，其中图a为与α的关系曲线，图b为与α的关系曲线，图c为与α的关系曲线，图d为与α的关系曲线，图e为与α的关系曲线，图f为与α的关系曲线；Figure 6 is a diagram of the relationship between aerodynamic parameters and angle of attack, where Figure a is The relationship curve with α, Figure b is The relationship curve with α, Figure c is The relationship curve with α, Figure d is The relationship curve with α, Figure e is The relationship curve with α, Figure f is The relationship curve with α;

图7是攻角响应曲线，其中实线代表攻角的实际值，虚线代表攻角指令值；Fig. 7 is the angle of attack response curve, wherein the solid line represents the actual value of the angle of attack, and the dotted line represents the command value of the angle of attack;

图8是舵偏角曲线；Figure 8 is the rudder angle curve;

图9是姿控发动机产生的直接侧向力曲线；Fig. 9 is the direct lateral force curve that attitude control engine produces;

图10是状态空间姿态控制律的不同分区情况。Figure 10 shows the different partitions of the state space attitude control law.

具体实施方式detailed description

具体实施方式一：结合图1、图2理解本实施方式，本实施方式所述的基于混杂预测控制的姿控式直接侧向力和气动力复合导弹姿态控制方法，是按照以下步骤实现的：Specific embodiment one: understand this embodiment in conjunction with Fig. 1, Fig. 2, the posture control type direct lateral force and aerodynamic force composite missile attitude control method based on hybrid predictive control described in this embodiment, is to realize according to the following steps:

步骤一、建立直接侧向力和气动力复合导弹完整姿态控制模型和直接侧向力模型，并推导俯仰方向直接侧向力的表达式，通过对弹体气动特性分析，将导弹非线性动力学模型转化为分段仿射模型；Step 1. Establish the complete attitude control model and direct lateral force model of the direct lateral force and aerodynamic compound missile, and derive the expression of the direct lateral force in the pitch direction. Through the analysis of the aerodynamic characteristics of the missile body, the nonlinear dynamic model of the missile Convert to a piecewise affine model;

$\{\begin{matrix} m m \overset{\cdot &Center Dot;}{V V} = = P P cos cos α α cos cos β β - - {X x}_{a a} - - mg mg sin sin θ θ + + {F f}_{{x x}_{22}}^{a a} \\ mV mV \overset{\cdot &Center Dot;}{θ θ} = = P P ((sin sin α α cos cos {γ γ}_{v v} + + cos cos α α sin sin β β sin sin {γ γ}_{v v})) + + {Y Y}_{a a} cos cos {γ γ}_{v v} - - mg mg cos cos θ θ + + {F f}_{{y the y}_{22}}^{a a} \\ mV mV cos cos θ θ \overset{\cdot \cdot}{{\overset{\cdot &Center Dot;}{ψ ψ}}_{V V} = = - - P P ((sin sin α α sin sin {γ γ}_{v v} - - cos cos α α sin sin β β cos cos {γ γ}_{v v})) - - {Y Y}_{a a} sin sin {γ γ}_{v v} - - {Z Z}_{a a} cos cos {γ γ}_{v v} - - {F f}_{{z z}_{22}}^{a a}} \end{matrix} - - - - - - ((11))$

$\{\begin{matrix} {J J}_{x x} {\overset{\cdot &Center Dot;}{ω ω}}_{x x} = = (({J J}_{y the y} - - {J J}_{z z})) {ω ω}_{z z} {ω ω}_{y the y} + + {M m}_{x x} \\ {J J}_{y the y} {\overset{\cdot &Center Dot;}{ω ω}}_{y the y} = = (({J J}_{z z} - - {J J}_{x x})) {ω ω}_{x x} {ω ω}_{z z} + + {M m}_{y the y} \\ {J J}_{z z} {\overset{\cdot \cdot}{ω ω}}_{z z} = = (({J J}_{x x} - - {J J}_{y the y})) {ω ω}_{x x} {ω ω}_{y the y} + + {M m}_{z z} \end{matrix} - - - - - - ((22))$

此外，由于姿控发动机侧向喷射燃气流时，高速喷流与空气来流之间相互干扰，形成侧向喷流干扰效应。采用喷流干扰推力放大因子和喷流干扰力矩放大因子来分别表示喷流干扰力和力矩与无侧向喷流时产生的净推力和力矩的比值；因此，考虑侧向喷流干扰效应，同时点燃若干姿控脉冲发动机产生的直接侧向力合力和合力矩在弹体坐标系上的表示为In addition, when the attitude control engine injects gas flow sideways, the high-speed jet flow and the incoming air flow interfere with each other, forming a side jet flow interference effect. Thrust Amplification Factor with Jet Disturbance and jet disturbance torque amplification factor to represent the ratios of the jet disturbance force and moment to the net thrust and moment produced without side jets; therefore, considering the side jet disturbance effect, the resultant force and resultant direct lateral force produced by several attitude control pulse engines are simultaneously ignited The moment is expressed in the projectile coordinate system as

其中，为喷流干扰推力放大因子，为喷流干扰力矩放大因子，为标称直接侧向力合力和合力矩在弹体坐标系上的表示；in, is the jet disturbance thrust amplification factor, is the amplification factor of the jet disturbance torque, is the representation of the nominal direct lateral force resultant force and resultant moment on the projectile coordinate system;

假设末制导段导弹质量不变，出于简化模型的需要，将气动数据对气动力和力矩进行线性化描述；因为大气层内拦截导弹姿态控制的目的是建立攻角和侧滑角，形成气动升力和侧向力，所以为了描述攻角、侧滑角以及弹体角速度的变化规律，根据公式(1)至(4)推导出攻角、侧滑角和弹体角速度动态方程；Assuming that the mass of the missile in the final guidance stage remains unchanged, the aerodynamic data is linearized to describe the aerodynamic force and moment for the sake of simplifying the model; because the purpose of attitude control of intercepting missiles in the atmosphere is to establish the angle of attack and sideslip angle to form aerodynamic lift and lateral force, so in order to describe the change law of angle of attack, sideslip angle and angular velocity of projectile, the dynamic equations of angle of attack, sideslip angle and angular velocity of projectile are deduced according to formulas (1) to (4);

弹体角速度动态方程Dynamic Equation of Projectile Angular Velocity

$\{\begin{matrix} {\overset{. .}{ω ω}}_{y the y} = = \frac{{M m}_{{y the y}_{11}}}{{J J}_{y the y}} + + \frac{{K K}_{{M m}_{y the y}} {M m}_{{y the y}_{11}}}{{J J}_{y the y}} + + \frac{{QSLm QSL}_{y the y}^{β β} β β}{{J J}_{y the y}} + + \frac{{QSLm QSL}_{y the y}^{{δ δ}_{y the y}} {δ δ}_{y the y}}{{J J}_{y the y}} + + \frac{{QSLm QSL}_{y the y}^{{ω ω}_{y the y}} {ω ω}_{y the y}}{{J J}_{y the y}} \\ {\overset{. .}{ω ω}}_{z z} = = \frac{{M m}_{{z z}_{11}}}{{J J}_{z z}} + + \frac{{K K}_{{M m}_{z z}} {M m}_{{z z}_{11}}}{{J J}_{z z}} + + \frac{{QSLm QSL}_{z z}^{α α} α α}{{J J}_{z z}} + + \frac{{QSLm QSL}_{z z}^{{δ δ}_{z z}} {δ δ}_{z z}}{{J J}_{z z}} + + \frac{{QSLm QSL}_{z z}^{{ω ω}_{z z}} {ω ω}_{z z}}{{J J}_{z z}} \end{matrix} - - - - - - ((66))$

步骤二、引入逻辑变量，基于分段仿射模型和混合逻辑动态模型的等价性，构造复合控制导弹完整混合逻辑动态模型；Step 2, introducing logic variables, based on the equivalence between the segmented affine model and the hybrid logic dynamic model, constructing the complete hybrid logic dynamic model of the composite control missile;

步骤三、基于混杂模型预测控制理论，设计复合导弹姿态控制律，确定气动控制律和姿控发动机开启规律。Step 3: Based on the hybrid model predictive control theory, design the composite missile attitude control law, determine the aerodynamic control law and the attitude control engine opening law.

具体实施方式二：本实施方式与具体实施方式一不同的是：建立步骤一所述的直接侧向力模型的具体过程为：Specific embodiment two: the difference between this embodiment and specific embodiment one is: the specific process of establishing the direct lateral force model described in step one is:

直接侧向力由固定安装于弹体质心前方的姿控脉冲发动机组产生，共有180个姿控脉冲发动机错位排布，沿弹体纵轴分成10圈，每圈18个姿控脉冲发动机环绕弹体排列；同一圈内相邻的姿控脉冲发动机间隔圆心角为20°，令i表示圈的编号，i＝1，2，…，10，j表示姿控脉冲发动机在每圈内的编号，j＝1，2，…，18；第i圈姿控脉冲发动机喷口圆心的连线形成的截面与弹体质心的距离为l_i，相邻两圈间距为Δl；姿控脉冲发动机组在弹体上的布局如图3和图4所示。The direct lateral force is generated by the attitude control pulse engine group fixedly installed in front of the center of mass of the missile body. There are 180 attitude control pulse engines arranged in dislocation, divided into 10 circles along the longitudinal axis of the missile body, and each circle is surrounded by 18 attitude control pulse engines. Body arrangement; The adjacent attitude control pulse motors in the same circle are spaced at a central angle of 20 °, so that i represents the numbering of the circle, i=1, 2,..., 10, j represents the numbering of the attitude control pulse motors in each circle, j=1, 2, ..., 18; the distance between the section formed by the line connecting the nozzle center of the i-th circle of the attitude control pulse engine and the center of mass of the projectile is l _i , and the distance between two adjacent circles is Δl; The layout of the body is shown in Figure 3 and Figure 4.

假设姿控脉冲发动机在无自由流时产生的稳态推力为F_m，对于编号为(i，j)的姿控脉冲发动机产生的标称直接侧向力在弹体坐标系中的表示为Assuming that the steady-state thrust produced by the attitude control pulse engine is F _m when there is no free stream, the nominal direct lateral force generated by the attitude control pulse engine with the number (i, j) is expressed in the projectile coordinate system as

$[\begin{matrix} {F f}_{{x x}_{11}}^{i i,, j j} \\ {F f}_{{y the y}_{11}}^{i i,, j j} \\ {F f}_{{z z}_{11}}^{i i,, j j} \end{matrix}] = = [\begin{matrix} 00 \\ {F f}_{m m} cos cos ((\frac{22 j j - - {i i}^{* *}}{1818} π π)) \\ - - {F f}_{m m} sin sin ((\frac{22 j j - - {i i}^{* *}}{1818})) \end{matrix}] - - - - - - ((77))$

相应地，直接侧向力矩在弹体坐标系上的表示为Correspondingly, the expression of the direct lateral moment on the projectile coordinate system is

$[\begin{matrix} {M m}_{{x x}_{11}}^{i i,, j j} \\ {M m}_{{y the y}_{11}}^{i i,, j j} \\ {M m}_{{z z}_{11}}^{i i,, j j} \end{matrix}] = = [\begin{matrix} 00 \\ {F f}_{m m} {l l}_{i i} sin sin ((\frac{22 j j - - {i i}^{* *}}{1818} π π)) \\ {F f}_{m m} {l l}_{i i} cos cos ((\frac{22 j j - - {i i}^{* *}}{1818} π π)) \end{matrix}] - - - - - - ((88))$

其中，当i为奇数时，i^*＝2；当i为偶数时，i^*＝1；Wherein, when i is an odd number, i ^* =2; when i is an even number, i ^* =1;

同时点燃若干姿控脉冲发动机产生的标称直接侧向力合力和合力矩在弹体坐标系上的表示为The nominal direct lateral force resultant force and resultant moment produced by simultaneously igniting several attitude control pulse engines are expressed in the projectile coordinate system as

$[\begin{matrix} {F f}_{{x x}_{11}} \\ {F f}_{{y the y}_{11}} \\ {F f}_{{z z}_{11}} \end{matrix}] = = [\begin{matrix} 00 \\ {Σ Σ}_{j j = = {j j}_{1,1 1,1}}^{j j = = {j j}_{11,, n no 11}} {F f}_{{y the y}_{11}}^{11,, j j} + + {Σ Σ}_{j j = = {j j}_{2,1 2,1}}^{j j = = {j j}_{22,, n no 22}} {F f}_{{y the y}_{11}}^{22,, j j} + + . . . . . . + + {Σ Σ}_{j j = = {j j}_{10,1 10,1}}^{j j = = {j j}_{1010,, n no 1010}} {F f}_{{y the y}_{11}}^{1010,, j j} \\ {Σ Σ}_{j j = = {j j}_{1,1 1,1}}^{j j = = {j j}_{11,, n no 11}} {F f}_{{z z}_{11}}^{11,, j j} + + {Σ Σ}_{j j = = {j j}_{2,1 2,1}}^{j j = = {j j}_{22,, n no 22}} {F f}_{{z z}_{11}}^{22,, j j} + + . . . . . . + + {Σ Σ}_{j j = = {j j}_{10,1 10,1}}^{j j = = {j j}_{1010,, n no 1010}} {F f}_{{z z}_{11}}^{1010,, j j} \end{matrix}] - - - - - - ((99))$

$[\begin{matrix} {M m}_{{x x}_{11}} \\ {M m}_{{y the y}_{11}} \\ {M m}_{{z z}_{11}} \end{matrix}] = = [\begin{matrix} 00 \\ {Σ Σ}_{j j = = {j j}_{1,1 1,1}}^{j j = = {j j}_{11,, n no 11}} {F f}_{{z z}_{11}}^{11,, j j} {l l}_{11} + + {Σ Σ}_{j j = = {j j}_{2,1 2,1}}^{j j = = {j j}_{22,, n no 22}} {F f}_{{z z}_{11}}^{22,, j j} {l l}_{22} + + . . . . . . + + {Σ Σ}_{j j = = {j j}_{10,1 10,1}}^{j j = = {j j}_{1010,, n no 1010}} {F f}_{{z z}_{11}}^{1010,, j j} {l l}_{1010} \\ {Σ Σ}_{j j = = {j j}_{1,1 1,1}}^{j j = = {j j}_{11,, n no 11}} {F f}_{{y the y}_{11}}^{11,, j j} {l l}_{11} + + {Σ Σ}_{j j = = {j j}_{2,1 2,1}}^{j j = = {j j}_{22,, n no 22}} {F f}_{{y the y}_{11}}^{22,, j j} {l l}_{22} + + . . . . . . + + {Σ Σ}_{j j = = {j j}_{10,1 10,1}}^{j j = = {j j}_{1010,, n no 1010}} {F f}_{{y the y}_{11}}^{1010,, j j} {l l}_{1010} \end{matrix}] - - - - - - ((1010))$

其中，j_1，1，j_1，2，…，j_1，n1表示第1圈点燃的姿控脉冲发动机的圈内编号，n1表示第1圈点燃的姿控脉冲发动机数量，依此类推；式(9)-(10)即为复合控制导弹的直接侧向力模型。Among them, j _1,1 , j _1,2 ,..., j _{1, n1} represent the circle number of the attitude control pulse engine ignited in the first circle, n1 represents the number of attitude control pulse engines ignited in the first circle, and so on; Equations (9)-(10) are the direct lateral force models of the composite control missile.

具体实施方式三：本实施方式与具体实施方式一或二不同的是：步骤一中所述的推导俯仰方向直接侧向力的表达式的具体过程为：Specific embodiment three: the difference between this embodiment and specific embodiment one or two is: the specific process of deriving the expression of the direct lateral force in the pitch direction described in step one is:

每圈18个姿控脉冲发动机分为四个点火控制区：正、负俯仰控制区和正、负偏航控制区，如图5所示。The 18 attitude control pulse engines per circle are divided into four ignition control areas: positive and negative pitch control areas and positive and negative yaw control areas, as shown in Figure 5.

由于每个姿控发动机在导弹上的安装位置固定、工作周期固定、数量有限、不可重复使用，因此在选择发动机开启数目、位置和点火顺序时需要遵循一套特定的原则。本发明做如下假设，对于每个控制区来说，每圈最多允许2个同时点火，最多允许两圈同时点火，并且只允许奇数圈内的姿控脉冲发动机同时点火或者偶数圈的姿控脉冲发动机同时点火；每个点火控制区内，姿控脉冲发动机点火时需要确保对称点火。Since the installation position of each attitude control engine on the missile is fixed, the working cycle is fixed, the number is limited, and it cannot be reused, so a set of specific principles need to be followed when selecting the number, position and firing sequence of the engines. The present invention makes the following assumptions, for each control zone, a maximum of 2 simultaneous ignitions are allowed in each circle, a maximum of two simultaneous ignitions are allowed, and only attitude control pulse engines in odd circles are allowed to ignite simultaneously or attitude control pulses in even circles The engines are ignited at the same time; in each ignition control zone, it is necessary to ensure symmetrical ignition when the attitude control pulse engine is ignited.

下面以正俯仰控制区为例给出姿控脉冲发动机产生的直接侧向力的合力和合力矩集合；Taking the positive pitch control area as an example, the resultant force and moment set of the direct lateral force generated by the attitude control pulse engine are given below;

奇数圈内编号为(i，1)，(i，2)，(i，3)，(i，17)，(i，18)的姿控脉冲发动机产生的直接侧向力在oy₁轴上的分量表示成向量The direct lateral force generated by the attitude control pulse motors numbered (i, 1), (i, 2), (i, 3), (i, 17), (i, 18) in odd circles is on the oy ₁ axis The components of are represented as vectors

${F f}_{o o} = = {[\begin{matrix} {F f}_{m m} & {F f}_{m m} cos cos \frac{π π}{99} & {F f}_{m m} cos cos \frac{22 π π}{99} & {F f}_{m m} cos cos \frac{22 π π}{99} & {F f}_{m m} cos cos \frac{π π}{99} \end{matrix}]}^{T T} - - - - - - ((1111))$

偶数圈内编号为(i，1)，(i，2)，(i，17)，(i，18)的姿控脉冲发动机产生的直接侧向力在oy₁轴上的分量表示成向量The components of the direct lateral force generated by the attitude control pulse motors numbered (i, 1), (i, 2), (i, 17), (i, 18) in the even circles on the oy ₁ axis are expressed as vectors

${F f}_{e e} = = {[\begin{matrix} {F f}_{m m} cos cos \frac{π π}{1818} & {F f}_{m m} cos cos \frac{π π}{66} & {F f}_{m m} cos cos \frac{π π}{66} & {F f}_{m m} cos cos \frac{π π}{1818} \end{matrix}]}^{T T} - - - - - - ((1212))$

设第i圈姿控脉冲发动机产生的直接侧向力为Fⁱ，要求Assuming that the direct lateral force generated by the attitude control pulse engine in the i-th circle is F ⁱ , it is required

F¹＝F⁹，F³＝F⁷，F²＝F¹⁰，F⁴＝F⁸ (13)F ¹ =F ⁹ , F ³ =F ⁷ , F ² =F ¹⁰ , F ⁴ =F ⁸ (13)

则当奇数圈脉冲发动机点火时，有Then when the odd-numbered pulse engine is ignited, there is

${F f}_{{y the y}_{11}} &Element; &Element; {{{F f}_{m m},, 22 {F f}_{m m} cos cos \frac{π π}{99},, 22 {F f}_{m m} cos cos \frac{22 π π}{99},, 22 {F f}_{m m},, 44 {F f}_{m m} cos cos \frac{π π}{99},, 44 {F f}_{m m} cos cos \frac{22 π π}{99}}}$

$\begin{matrix} {M m}_{{z z}_{11}} &Element; &Element; {{{F f}^{11} {l l}_{11} + + {F f}^{99} {l l}_{99},, {{F f}^{33} l l}_{33} + + {F f}^{77} {l l}_{77},, {F f}^{55} {l l}_{55}}} \\ = = {{{F f}^{11} (({l l}_{55} + + 44 Δl Δl)) + + {F f}^{11} (({l l}_{55} - - 44 Δl Δl)),, {F f}^{33} (({l l}_{55} + + 22 Δl Δl)) + + {F f}^{33} (({l l}_{55} - - 22 Δl Δl)),, {F f}^{55} {l l}_{55}}} \\ = = {{{F f}^{55} {l l}_{55},, 22 {F f}^{11} {l l}_{55},, 22 {F f}^{33} {l l}_{55}}} = = {F f}_{{y the y}_{11}} {l l}_{55} \\ = = {{{F f}_{m m} {l l}_{55},, 22 {F f}_{m m} cos cos \frac{π π}{99} {l l}_{55},, 22 {F f}_{m m} cos cos \frac{22 π π}{99} {l l}_{55},, 22 {F f}_{m m} {l l}_{55},, 44 {F f}_{m m} cos cos \frac{π π}{99} {l l}_{55},, 44 {F f}_{m m} cos cos \frac{22 π π}{99} {l l}_{55}}} \end{matrix} - - - - - - ((1414))$

同样，当偶数圈脉冲发动机点火时，有Likewise, when an even-numbered pulse engine fires, there is

${F f}_{{y the y}_{11}} &Element; &Element; {{22 {F f}_{m m} cos cos \frac{π π}{1818},, 22 {F f}_{m m} cos cos \frac{π π}{66},, 44 {F f}_{m m} cos cos \frac{π π}{1818},, 44 {F f}_{m m} cos cos \frac{π π}{66}}}$

$\begin{matrix} {M m}_{{z z}_{11}} &Element; &Element; {{{F f}^{22} {l l}_{22} + + {F f}^{1010} {l l}_{1010},, {F f}^{44} {l l}_{44} + + {F f}^{88} {l l}_{88},, {F f}^{66} {l l}_{66}}} \\ = = {{{F f}^{22} (({l l}_{66} + + 44 Δl Δl)) + + {F f}^{22} (({l l}_{66} - - 44 Δl Δl)),, {F f}^{44} (({l l}_{66} + + 22 Δl Δl)) + + {F f}^{44} (({l l}_{66} - - 22 Δl Δl)),, {F f}^{66} {l l}_{66}}} \\ = = {{{F f}^{66} {l l}_{66},, 22 {F f}^{22} {l l}_{66},, 22 {F f}^{44} {l l}_{66} + + = = {F f}_{{y the y}_{11}} {l l}_{66} \\ = = {{22 {F f}_{m m} cos cos \frac{π π}{1818} {l l}_{66},, 22 {F f}_{m m} cos cos \frac{π π}{66} {l l}_{66},, 44 {F f}_{m m} cos cos \frac{π π}{1818} {l l}_{66},, 44 {F f}_{m m} cos cos \frac{π π}{66} {l l}_{66}}} \end{matrix} - - - - - - ((1515))$

由于Δl很小，因此假设l₅≈l₆＝l，另外考虑发动机的点火效率避免过度消耗，不允许效率低的发动机点火，则正俯仰控制区所有姿控发动机产生的直接侧向力的合力的不同取值构成集合Since Δl is very small, assuming that l ₅ ≈ l ₆ = l, and considering the ignition efficiency of the engine to avoid excessive consumption, and not allowing low-efficiency engine ignition, the resultant force of the direct lateral force generated by all attitude control engines in the positive pitch control area The different values of form a set

${U u}_{F f}^{y the y + +} = = {{{F f}_{m m},, 22 {F f}_{m m} cos cos \frac{π π}{99},, 22 {F f}_{m m} cos cos \frac{π π}{1818},, 22 {F f}_{m m},, 44 {F f}_{m m} cos cos \frac{π π}{99},, 44 {F f}_{m m} cos cos \frac{π π}{1818}}} - - - - - - ((1616))$

合力矩的不同取值构成集合The different values of the resultant moment form a set

${U u}_{M m}^{y the y + +} = = {{{F f}_{m m} l l,, 22 {F f}_{m m} cos cos \frac{π π}{99} l l,, 22 {F f}_{m m} cos cos \frac{π π}{1818} l l,, 22 {F f}_{m m} l l,, 44 {F f}_{m m} cos cos \frac{π π}{99} l l,, 44 {F f}_{m m} cos cos \frac{π π}{1818} l l}} - - - - - - ((1717))$

由于发动机配置的对称性，负俯仰控制区所有姿控发动机产生的直接侧向力的合力的不同取值构成集合Due to the symmetry of the engine configuration, the different values of the total force of the direct lateral force generated by all the attitude control engines in the negative pitch control area form a set

${U u}_{F f}^{y the y - -} = = {{- - {F f}_{m m},, - - 22 {F f}_{m m} cos cos \frac{π π}{99},, - - 22 {F f}_{m m} cos cos \frac{π π}{1818},, - - 22 {F f}_{m m},, - - 44 {F f}_{m m} cos cos \frac{π π}{99},, - - 44 {F f}_{m m} cos cos \frac{π π}{1818}}} - - - - - - ((1818))$

每一控制周期，姿态控制系统按照一定的控制律从中选择一个控制力作为控制输入。In each control cycle, the attitude control system follows a certain control law from Select a control force as the control input.

通过上述方法，同样可以得到，正负偏航控制区所有姿控发动机产生的直接侧向力的合力的不同取值构成的集合。Through the above method, it is also possible to obtain a set composed of different values of the resultant forces of the direct lateral forces generated by all the attitude control engines in the positive and negative yaw control areas.

具体实施方式四：本实施方式与具体实施方式一至三之一不同的是：步骤一中所述的将导弹非线性动力学模型转化为分段仿射模型的具体过程为：Embodiment 4: The difference between this embodiment and Embodiment 1 to 3 is that the specific process of converting the missile nonlinear dynamics model into a segmented affine model described in step 1 is:

首先，给出该直接侧向力和气动力复合控制导弹的总体参数表，First, the overall parameter table of the direct lateral force and aerodynamic compound control missile is given,

表1导弹总体参数Table 1 General parameters of the missile

以俯仰通道为例，在末制导段忽略重力项，同时为简化分析忽略耦合项，由式(5)-(6)，得到导弹俯仰通道的非线性姿态控制模型为Taking the pitch channel as an example, the gravity term is ignored in the terminal guidance section, and the coupling term is neglected to simplify the analysis. From equations (5)-(6), the nonlinear attitude control model of the missile pitch channel is obtained as

$\{\begin{matrix} \overset{\cdot &Center Dot;}{α α} = = {ω ω}_{z z} - - \frac{QS QS (({C C}_{y the y}^{α α} α α + + {C C}_{y the y}^{{δ δ}_{z z}} {δ δ}_{z z})) cos cos α α}{mV mV} - - \frac{((11 + + {K K}_{{F f}_{y the y}})) {F f}_{{y the y}_{11}} cos cos α α}{mV mV} \\ {\overset{\cdot \cdot}{ω ω}}_{z z} = = \frac{((11 + + {K K}_{{M m}_{z z}})) {F f}_{{y the y}_{11}} l l}{{J J}_{z z}} + + \frac{QSL QSL {m m}_{z z}^{α α} α α}{{J J}_{z z}} + + \frac{QSL QSL {m m}_{z z}^{{δ δ}_{z z}} {δ δ}_{z z}}{{J J}_{z z}} + + \frac{QSL QSL {m m}_{z z}^{{ω ω}_{z z}} {ω ω}_{z z}}{{J J}_{z z}} \end{matrix} - - - - - - ((1919))$

选取系统状态x＝[α ω_z]^T，控制量u＝[δ_z F_y1]^T；在进行姿态控制设计时，我们关心的是攻角指令的跟踪情况，因此，选取系统输出为y＝α；得到非线性模型的状态空间描述如下Select the system state x＝[α ω _z ] ^T , the control quantity u＝[δ _z F _y1 ] ^T ; when designing the attitude control, we are concerned about the tracking of the command angle of attack, so the system output is selected as y＝ α; get the state space description of the nonlinear model as follows

$\begin{matrix} \overset{\cdot &Center Dot;}{x x} ((t t)) = = f f ((x x)) + + g g ((x x)) u u ((t t)) \\ \begin{matrix} y the y ((t t)) = = [[11 & 00]] x x ((t t)) \end{matrix} \end{matrix} - - - - - - ((2020))$

其中，in,

$f f ((x x)) = = [\begin{matrix} {ω ω}_{z z} - - \frac{{QSC QSC}_{y the y}^{α α} α α cos cos α α}{mV mV} \\ \frac{QSL QSL (({m m}_{z z}^{α α} α α + + {m m}_{z z}^{{ω ω}_{z z}} {ω ω}_{z z}))}{{J J}_{z z}} \end{matrix}],, g g ((x x)) = = [\begin{matrix} - - \frac{{QSC QSC}_{y the y}^{{δ δ}_{z z}} cos cos α α}{mV mV} & - - \frac{((11 + + {K K}_{{F f}_{y the y}})) cos cos α α}{mV mV} \\ \frac{{QSLm QSL}_{z z}^{{δ δ}_{z z}}}{{J J}_{z z}} & \frac{((11 + + {K K}_{{M m}_{z z}})) l l}{{J J}_{z z}} \end{matrix}]$

上式中，气动参数喷流干扰放大因子都和攻角α有关；考虑攻角是影响这些参数的决定因素，图6给出了各参数与攻角α的关系曲线。In the above formula, the aerodynamic parameters Jet Disturbance Amplification Factor All are related to the angle of attack α; considering the angle of attack is the decisive factor affecting these parameters, Figure 6 shows the relationship curve between each parameter and the angle of attack α.

攻角是使姿态控制系统呈现非线性特性的主要因素，根据给出的气动参数以及放大因子与攻角之间的关系曲线，可以看出气动参数以及放大因子与攻角呈非线性关系，当攻角在小范围内变动时，可以近似为线性关系；分别以α＝-21.25°，-8.75°，0°，8.75°，21.25°作为分界点，分成六个分区，在每一段区域内，都可以近似为线性特性；在每一段内，利用小偏差线性化的方法将姿态控制模型分段线性化；The angle of attack is the main factor that makes the attitude control system exhibit nonlinear characteristics. According to the relationship curve between the given aerodynamic parameters and the amplification factor and the angle of attack, it can be seen that the aerodynamic parameters and the amplification factor have a nonlinear relationship with the angle of attack. When When the angle of attack changes in a small range, it can be approximated as a linear relationship; with α=-21.25°, -8.75°, 0°, 8.75°, and 21.25° as the demarcation points respectively, it is divided into six partitions. In each section, can be approximated as a linear characteristic; in each segment, the attitude control model is segmented and linearized using a small deviation linearization method;

得到的分段仿射模型如下：The resulting piecewise affine model is as follows:

$\overset{\cdot \cdot}{x x} ((t t)) = = \{\begin{matrix} {a a}_{11} x x ((t t)) + + {b b}_{11} u u ((t t)) + + {e e}_{11},, & [\begin{matrix} 11 & 00 \end{matrix}] x x ((t t)) \leq \leq - - 0.37 0.37 \\ {a a}_{22} x x ((t t)) + + {b b}_{22} u u ((t t)) + + {e e}_{22},, & - - 0.37 0.37 < < [\begin{matrix} 11 & 00 \end{matrix}] x x ((t t)) \leq \leq - - 0.153 0.153 \\ {a a}_{33} x x ((t t)) + + {b b}_{33} u u ((t t)) + + {e e}_{33},, & - - 0.153 0.153 < < [\begin{matrix} 11 & 00 \end{matrix}] x x ((t t)) \leq \leq 00 \\ {a a}_{44} x x ((t t)) + + {b b}_{44} u u ((t t)) + + {e e}_{44},, & 00 < < [\begin{matrix} 11 & 00 \end{matrix}] x x ((t t)) \leq \leq 0.153 0.153 \\ {a a}_{55} x x ((t t)) + + {b b}_{55} u u ((t t)) + + {e e}_{55},, & 0.153 0.153 < < [\begin{matrix} 11 & 00 \end{matrix}] x x ((t t)) \leq \leq 0.37 0.37 \\ {a a}_{66} x x ((t t)) + + {b b}_{66} u u ((t t)) + + {e e}_{66},, & [\begin{matrix} 11 & 00 \end{matrix}] x x ((t t)) > > 0.37 0.37 \end{matrix}$

y(t)＝cx(t) (21)y(t)=cx(t) (21)

其中，in,

${a a}_{i i} = = \frac{&PartialD; &PartialD; f f ((x x))}{&PartialD; &PartialD; x x} {| |}_{x x = = {x x}_{i i 00}} = = [\begin{matrix} {a a}_{i i}^{1111} & {a a}_{i i}^{1212} \\ {a a}_{i i}^{21 twenty one} & {a a}_{i i}^{22 twenty two} \end{matrix}],, {b b}_{i i} = = g g (({x x}_{i i 00})) = = [\begin{matrix} {b b}_{i i}^{1111} & {b b}_{i i}^{1212} \\ {b b}_{i i}^{21 twenty one} & {b b}_{i i}^{22 twenty two} \end{matrix}],, {e e}_{i i} = = [\begin{matrix} {e e}_{i i}^{11} \\ {e e}_{i i}^{22} \end{matrix}]$

${a a}_{i i}^{1111} = = \frac{&PartialD; &PartialD; {f f}_{11}}{&PartialD; &PartialD; α α} {| |}_{x x = = {x x}_{i i 00}} = = - - \frac{QS QS}{mV mV} ((\frac{&PartialD; &PartialD; {C C}_{y the y}^{α α}}{&PartialD; &PartialD; α α} {| |}_{{α α = = α α}_{i i 00}} {α α}_{i i 00} cos cos (({α α}_{i i 00})) + + {C C}_{y the y}^{α α} (({α α}_{i i 00})) cos cos (({α α}_{i i 00})) - - {C C}_{y the y}^{α α} (({α α}_{i i 00})) {α α}_{i i 00} sin sin (({α α}_{i i 00}))))$

${a a}_{i i}^{1212} = = \frac{&PartialD; &PartialD; {f f}_{11}}{&PartialD; &PartialD; {ω ω}_{z z}} {| |}_{x x = = {x x}_{i i 00}} = = 11$

${a a}_{i i}^{21 twenty one} = = \frac{&PartialD; &PartialD; {f f}_{22}}{&PartialD; &PartialD; α α} {| |}_{x x = = {x x}_{i i 00}} = = \frac{QSL QSL}{{J J}_{z z}} ((\frac{&PartialD; &PartialD; {m m}_{z z}^{α α}}{&PartialD; &PartialD; α α} {| |}_{α α = = {α α}_{i i 00}} {α α}_{i i 00} + + {m m}_{z z}^{α α} (({α α}_{i i 00})) + + \frac{&PartialD; &PartialD; {m m}_{z z}^{{ω ω}_{z z}}}{&PartialD; &PartialD; α α} {| |}_{α α = = {α α}_{i i 00}} {ω ω}_{zi the zi 00}))$

${a a}_{i i}^{22 twenty two} = = \frac{&PartialD; &PartialD; {f f}_{22}}{{&PartialD; &PartialD; ω ω}_{z z}} {| |}_{x x = = {x x}_{i i 00}} = = \frac{QSL QSL}{{J J}_{z z}} {m m}_{z z}^{{ω ω}_{z z}} (({α α}_{i i 00}))$

${b b}_{i i}^{1111} = = - - \frac{QS QS}{mV mV} {C C}_{y the y}^{{δ δ}_{z z}} (({α α}_{i i 00})) cos cos (({α α}_{i i 00}))$

${b b}_{i i}^{1212} = = - - \frac{((11 + + {K K}_{{F f}_{y the y}} (({α α}_{i i 00})))) cos cos (({α α}_{i i 00}))}{mV mV}$

${b b}_{i i}^{21 twenty one} = = \frac{QSL QSL}{{J J}_{z z}} {m m}_{z z}^{{δ δ}_{z z}} (({α α}_{i i 00}))$

${b b}_{i i}^{22 twenty two} = = \frac{((11 + + {K K}_{M m}_{z z} (({α α}_{i i 00})))) l l}{{J J}_{z z}}$

${e e}_{i i}^{11} = = {a a}_{i i}^{1111} {α α}_{i i 00} + + {a a}_{i i}^{1212} {ω ω}_{zi the zi 00}$

${e e}_{i i}^{22} = = {a a}_{i i}^{21 twenty one} {α α}_{i i 00} + + {a a}_{i i}^{22 twenty two} {ω ω}_{zi the zi 00}$

c＝[1 0]c=[1 0]

其中，i＝1，2，…，6，分别对应六个分区；Wherein, i=1, 2, ..., 6, corresponding to six partitions respectively;

取采样周期T_s＝0.025s，结合图6中的气动参数与攻角的关系，得到离散的姿态控制系统状态空间表达式为Taking the sampling period T _s = 0.025s, combined with the relationship between the aerodynamic parameters and the angle of attack in Fig. 6, the state space expression of the discrete attitude control system is obtained as

$x x ((k k + + 11)) = = \{\begin{matrix} {\overset{~ ~}{a a}}_{11} x x ((k k)) + + {\overset{~ ~}{b b}}_{11} u u ((k k)) + + {\overset{~ ~}{e e}}_{11},, & [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) \leq \leq - - 0.37 0.37 \\ {\overset{~ ~}{a a}}_{22} x x ((k k)) + + {\overset{~ ~}{b b}}_{22} u u ((k k)) + + {\overset{~ ~}{e e}}_{22},, & - - 0.37 0.37 < < [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) \leq \leq - - 0.153 0.153 \\ {\overset{~ ~}{a a}}_{33} x x ((k k)) + + {\overset{~ ~}{b b}}_{33} u u ((k k)) + + {\overset{~ ~}{e e}}_{33},, & - - 0.153 0.153 < < [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) \leq \leq 00 \\ {\overset{~ ~}{a a}}_{44} x x ((k k)) + + {\overset{~ ~}{b b}}_{44} u u ((k k)) + + {\overset{~ ~}{e e}}_{44},, & 00 < < [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) \leq \leq 0.153 0.153 \\ {\overset{~ ~}{a a}}_{55} x x ((k k)) + + {\overset{~ ~}{b b}}_{55} u u ((k k)) + + {\overset{~ ~}{e e}}_{55},, & 0.153 0.153 < < [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) \leq \leq 0.37 0.37 \\ {\overset{~ ~}{a a}}_{66} x x ((k k)) + + {\overset{~ ~}{b b}}_{66} u u ((k k)) + + {\overset{~ ~}{e e}}_{66},, & [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) > > 0.37 0.37 \end{matrix}$

$y the y ((k k)) = = \overset{~ ~}{c c} x x ((k k)) - - - - - - ((22 twenty two))$

其中，in,

${\overset{~ ~}{a a}}_{11} = = [\begin{matrix} 1.04 1.04 & 0.025 0.025 \\ 0.22 0.22 & 0.995 0.995 \end{matrix}],, {\overset{~ ~}{b b}}_{11} = = [\begin{matrix} - - 0.02845 0.02845 & 1.59 1.59 \times \times 1010^{- - 66} \\ - - 2.116 2.116 & 1.42 1.42 \times \times 1010^{- - 44} \end{matrix}],, {\overset{~ ~}{e e}}_{11} = = [\begin{matrix} - - 0.0183 0.0183 \\ - - 0.1123 0.1123 \end{matrix}]$

${\overset{~ ~}{a a}}_{22} = = [\begin{matrix} 1.051 1.051 & 0.0255 0.0255 \\ 0.218 0.218 & 0.995 0.995 \end{matrix}],, {\overset{~ ~}{b b}}_{22} = = [\begin{matrix} - - 0.030 0.030 & 22 . . 1818 \times \times 1010^{- - 66} \\ - - 2.224 2.224 & 1.87 1.87 \times \times 1010^{- - 44} \end{matrix}],, {\overset{~ ~}{e e}}_{22} = = [\begin{matrix} - - 0.0175 0.0175 \\ - - 00 . . 07920792 \end{matrix}]$

${\overset{~ ~}{a a}}_{33} = = [\begin{matrix} 1.023 1.023 & 0.0252 0.0252 \\ 0.248 0.248 & 0.9951 0.9951 \end{matrix}],, {\overset{~ ~}{b b}}_{33} = = [\begin{matrix} - - 0.030 0.030 & 2.68 2.68 \times \times 1010^{- - 66} \\ - - 2.228 2.228 & 1.23 1.23 \times \times 1010^{- - 44} \end{matrix}],, {\overset{~ ~}{e e}}_{33} = = [\begin{matrix} - - 0.0031 0.0031 \\ - - 0.0376 0.0376 \end{matrix}]$

${\overset{~ ~}{a a}}_{44} = = [\begin{matrix} 0.9945 0.9945 & 0.0248 0.0248 \\ 0.2732 0.2732 & 0.9954 0.9954 \end{matrix}],, {\overset{~ ~}{b b}}_{44} = = [\begin{matrix} - - 0.032 0.032 & 2.77 2.77 \times \times 1010^{- - 66} \\ - - 2.371 2.371 & 2.32 2.32 \times \times 1010^{- - 44} \end{matrix}],, {\overset{~ ~}{e e}}_{44} = = [\begin{matrix} 00 \\ 00 \end{matrix}]$

${\overset{~ ~}{a a}}_{55} = = [\begin{matrix} 0.9697 0.9697 & 0.0245 0.0245 \\ 0.2913 0.2913 & 0.9956 0.9956 \end{matrix}],, {\overset{~ ~}{b b}}_{55} = = [\begin{matrix} - - 0.030 0.030 & 2.27 2.27 \times \times 1010^{- - 66} \\ - - 22 . . 228228 & 1.98 1.98 \times \times 1010^{- - 44} \end{matrix}],, {\overset{~ ~}{e e}}_{55} = = [\begin{matrix} - - 0.0053 0.0053 \\ 0.0454 0.0454 \end{matrix}]$

${\overset{~ ~}{a a}}_{66} = = [\begin{matrix} 0.9594 0.9594 & 0.0244 0.0244 \\ 0.3137 0.3137 & 0.9959 0.9959 \end{matrix}],, {\overset{~ ~}{b b}}_{66} = = [\begin{matrix} - - 0.029 0.029 & 1.91 1.91 \times \times 1010^{- - 66} \\ - - 2.224 2.224 & 1.73 1.73 \times \times 1010^{- - 44} \end{matrix}],, {\overset{~ ~}{e e}}_{66} = = [\begin{matrix} - - 0.0169 0.0169 \\ - - 0.1193 0.1193 \end{matrix}]$

$\overset{~ ~}{c c} = = [\begin{matrix} 11 & 00 \end{matrix}]$

k表示第k时刻，式(22)即为复合控制导弹分段仿射模型。k represents the kth moment, and Equation (22) is the segmented affine model of the composite control missile.

通过上述方法，偏航通道的分段仿射模型可以同样得到。Through the above method, the piecewise affine model of the yaw channel can also be obtained.

具体实施方式五：本实施方式与具体实施方式一至四之一不同的是：步骤二所述的构造复合控制导弹完整混合逻辑动态模型的具体过程为：Specific implementation mode five: this implementation mode is different from one of the specific implementation modes one to four in that: the specific process of constructing the complete mixed logic dynamic model of the compound control missile described in step 2 is:

引入逻辑变量δ_i(k)∈{0，1}，i＝1，2，…，6来描述分段仿射模型中的各分界点，它们满足如下对应关系Introduce logical variables δ _i (k)∈{0, 1}, i=1, 2,..., 6 to describe each boundary point in the piecewise affine model, and they satisfy the following correspondence

${{[\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) + + 0.37 0.37 \leq \leq 00}} &DoubleLeftRightArrow; &DoubleLeftRightArrow; {{{δ δ}_{11} ((k k)) = = 11}}$

${{[\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) + + 0.153 0.153 \leq \leq 00}} &DoubleLeftRightArrow; &DoubleLeftRightArrow; {{{δ δ}_{22} ((k k)) = = 11}}$

${{[\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) \leq \leq 00}} &DoubleLeftRightArrow; &DoubleLeftRightArrow; {{{δ δ}_{33} ((k k)) = = 11}}$

${{[\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) - - 0.153 0.153 \leq \leq 00}} &DoubleLeftRightArrow; &DoubleLeftRightArrow; {{{δ δ}_{44} ((k k)) = = 11}}$

${{[\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) - - 0.37 0.37 \leq \leq 00}} &DoubleLeftRightArrow; &DoubleLeftRightArrow; {{{δ δ}_{55} ((k k)) = = 11}} - - - - - - ((23 twenty three))$

式(23)可转化成等价的混合逻辑不等式约束：Equation (23) can be transformed into an equivalent mixed logic inequality constraint:

$\{\begin{matrix} [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) + + 0.37 0.37 &GreaterEqual; &Greater Equal; ϵ ϵ + + (({m m}_{11} - - ϵ ϵ)) {δ δ}_{11} ((k k)) \\ [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) + + 0.37 0.37 \leq \leq {M m}_{11} ((11 - - {δ δ}_{11} ((k k)))) \\ [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) + + 0.153 0.153 &GreaterEqual; &Greater Equal; ϵ ϵ + + (({m m}_{22} - - ϵ ϵ)) {δ δ}_{22} ((k k)) \\ [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) + + 0.153 0.153 \leq \leq {M m}_{22} ((11 - - {δ δ}_{22} ((k k)))) \\ [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) &GreaterEqual; &Greater Equal; ϵ ϵ + + (({m m}_{33} - - ϵ ϵ)) {δ δ}_{33} ((k k)) \\ [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) \leq \leq {M m}_{33} ((11 - - {δ δ}_{33} ((k k)))) \\ [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) - - 0.153 0.153 &GreaterEqual; &Greater Equal; ϵ ϵ + + (({m m}_{44} - - ϵ ϵ)) {δ δ}_{44} ((k k)) \\ [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) - - 0.153 0.153 \leq \leq {M m}_{44} ((11 - - {δ δ}_{44} ((k k)))) \\ [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) - - 0.37 0.37 &GreaterEqual; &Greater Equal; ϵ ϵ + + (({m m}_{55} - - ϵ ϵ)) {δ δ}_{55} ((k k)) \\ [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) - - 0.37 0.37 \leq \leq {M m}_{55} ((11 - - {δ δ}_{55} ((k k)))) \end{matrix} - - - - - - ((24 twenty four))$

其中，m₁＝-0.16，M₁＝0.90，m₂＝-0.377，M₂＝0.683，m₃＝-0.53，M₃＝0.53，m₄＝-0.683，M₄＝0.377，m₅＝-0.90，M₅＝0.16，ε＝10^-6；Among them, m ₁ =-0.16, M ₁ =0.90, m ₂ =-0.377, M ₂ =0.683, m ₃ =-0.53, M ₃ =0.53, m ₄ =-0.683, M ₄ =0.377, m ₅ =- 0.90, M ₅ =0.16, ε=10 ⁻⁶ ;

同时，还需引入辅助逻辑变量δ_i(k)∈{0，1}，i＝6，…，9，并且满足At the same time, it is also necessary to introduce auxiliary logic variables δ _i (k)∈{0, 1}, i=6,...,9, and satisfy

$\{\begin{matrix} {δ δ}_{66} = = ((11 - - {δ δ}_{11})) {δ δ}_{22} \\ {δ δ}_{77} = = ((11 - - {δ δ}_{22})) {δ δ}_{33} \\ {δ δ}_{88} = = ((11 - - {δ δ}_{33})) {δ δ}_{44} \\ {δ δ}_{99} = = ((11 - - {δ δ}_{44})) {δ δ}_{55} \end{matrix} - - - - - - ((2525))$

则δ₁，δ₆，δ₇，δ₈，δ₉，1-δ₅分别对应分段仿射模型的六个分区。Then δ ₁ , δ ₆ , δ ₇ , δ ₈ , δ ₉ , and 1-δ ₅ respectively correspond to the six partitions of the piecewise affine model.

将式(25)表述成混合逻辑不等式约束：Formula (25) is expressed as a mixed logic inequality constraint:

$\{\begin{matrix} - - {δ δ}_{11} + + {δ δ}_{22} - - {δ δ}_{66} \leq \leq 00 \\ {δ δ}_{11} + + {δ δ}_{66} \leq \leq 11 \\ {- - δ δ}_{22} + + {δ δ}_{66} \leq \leq 00 \\ - - {δ δ}_{22} + + {δ δ}_{33} - - {δ δ}_{77} \leq \leq 00 \\ {δ δ}_{22} + + {δ δ}_{77} \leq \leq 11 \\ - - {δ δ}_{33} + + {δ δ}_{77} \leq \leq 00 \\ - - {δ δ}_{33} + + {δ δ}_{44} - - {δ δ}_{88} \leq \leq 00 \\ {δ δ}_{33} + + {δ δ}_{88} \leq \leq 11 \\ - - {δ δ}_{44} + + {δ δ}_{88} \leq \leq 00 \\ - - {δ δ}_{44} {+ + δ δ}_{55} - - {δ δ}_{99} \leq \leq 00 \\ {δ δ}_{44} + + {δ δ}_{99} \leq \leq 11 \\ - - {δ δ}_{55} + + {δ δ}_{99} \leq \leq 00 \end{matrix} - - - - - - ((2626))$

引入辅助连续变量z_i(k)，i＝1，2，…，6，从而将分段仿射模型的每一段分区条件与相应的状态空间表达式统一起来，这些辅助连续变量如下Introduce auxiliary continuous variables z _i (k), i=1, 2, ..., 6, so as to unify each segment partition condition of the piecewise affine model with the corresponding state space expression, these auxiliary continuous variables are as follows

$\{\begin{matrix} {z z}_{11} ((k k)) = = [[{\overset{~ ~}{a a}}_{11} ((k k)) x x ((k k)) + + {\overset{~ ~}{b b}}_{11} ((k k)) u u ((k k)) + + {\overset{~ ~}{e e}}_{11}]] {δ δ}_{11} ((k k)) \\ {z z}_{22} ((k k)) = = [[{\overset{~ ~}{a a}}_{22} ((k k)) x x ((k k)) + + {\overset{~ ~}{b b}}_{22} ((k k)) u u ((k k)) + + {\overset{~ ~}{e e}}_{22}]] {δ δ}_{66} ((k k)) \\ {z z}_{33} ((k k)) = = [[{\overset{~ ~}{a a}}_{33} ((k k)) x x ((k k)) + + {\overset{~ ~}{b b}}_{33} ((k k)) u u ((k k)) + + {\overset{~ ~}{e e}}_{33}]] {δ δ}_{77} ((k k)) \\ {z z}_{44} ((k k)) = = [[{\overset{~ ~}{a a}}_{44} ((k k)) x x ((k k)) + + {\overset{~ ~}{b b}}_{44} ((k k)) u u ((k k)) + + {\overset{~ ~}{e e}}_{44}]] {δ δ}_{88} ((k k)) \\ {z z}_{55} ((k k)) = = [[{\overset{~ ~}{a a}}_{55} ((k k)) x x ((k k)) + + {\overset{~ ~}{b b}}_{55} ((k k)) u u ((k k)) + + {\overset{~ ~}{e e}}_{55}]] {δ δ}_{99} ((k k)) \\ {z z}_{66} ((k k)) = = [[{\overset{~ ~}{a a}}_{66} ((k k)) x x ((k k)) + + {\overset{~ ~}{b b}}_{66} ((k k)) u u ((k k)) + + {\overset{~ ~}{e e}}_{66}]] ((11 - - {δ δ}_{55} ((k k)))) \end{matrix} - - - - - - ((2727))$

将式(27)表述成混合逻辑不等式约束：Formula (27) is expressed as a mixed logic inequality constraint:

其中，M_f1＝[0.73 10.84]^T，m_f1＝[-0.77 -11.06]^T，M_f2＝[0.76 11.66]^T，m_f2＝[-0.79 -12.56]^T，M_f3＝[0.77 12.73]^T，m_f3＝[-0.78 -12.80]^T，M_f4＝[0.76 14.03]^T，m_f4＝[-0.76 -14.03]^T，M_f5＝[0.725 12.91]^T，m_f5＝[-0.736 -12.05]^T，M_f6＝[0.696 11.54]^T，m_f6＝[-0.73 -11.30]^T；Among them, M _f1 =[0.73 10.84] ^T , m _f1 =[-0.77 -11.06] ^T , M _f2 =[0.76 11.66] ^T , m _f2 =[-0.79 -12.56] ^T , M _f3 =[0.77 12.73] ^T , m _f3 =[-0.78 -12.80] ^T , M _f4 =[0.76 14.03] ^T , m _f4 =[-0.76 -14.03] ^T , M _f5 =[0.725 12.91] ^T , m _f5 =[-0.736 -12.05] ^T , M _f6 =[0.696 11.54] ^T , m _f6 =[-0.73 -11.30] ^T ;

结合直接侧向力和气动力复合控制导弹的总体参数表中参数和式(16)、(17)，得到俯仰方向直接侧向力取值集合为Combining the parameters in the overall parameter table of the direct lateral force and aerodynamic compound control missile and formulas (16) and (17), the value set of the direct lateral force in the pitch direction is obtained as

${U u}_{F f}^{y the y} = = {{22002200,, 4135,4333,4400,8269,8666 4135,4333,4400,8269,8666,, - - 22002200,, - - 41354135,, - - 43334333,, - - 44004400,, - - 82698269,, - - 86668666}} N N$

由于直接侧向力是离散变量，引入如下逻辑变量来描述直接侧向力 Since the direct lateral force is a discrete variable, the following logical variables are introduced to describe the direct lateral force

$\begin{matrix} {F f}_{{y the y}_{b b}} = = 22002200 {δ δ}_{{F f}_{11}} + + 41354135 {δ δ}_{{F f}_{22}} + + 43334333 {δ δ}_{{F f}_{33}} + + 44004400 {δ δ}_{{F f}_{44}} + + 82698269 {δ δ}_{{F f}_{55}} + + 86668666 {δ δ}_{{F f}_{66}} - - 22002200 {δ δ}_{{F f}_{77}} \\ - - 41354135 {δ δ}_{{F f}_{88}} - - {43334333 δ δ}_{{F f}_{99}} - - {44004400 δ δ}_{{F f}_{1010}} - - {82698269 δ δ}_{{F f}_{1111}} - - 86668666 {δ δ}_{{F f}_{1212}} \end{matrix} - - - - - - ((2929))$

式(29)中，逻辑变量满足如下约束：In formula (29), the logical variables satisfy the following constraints:

$Σ_{i = 1}^{12} δ_{F_{i}} = 0$ 或1 (30) $Σ_{i = 1}^{12} δ_{f_{i}} = 0$ or 1 (30)

其中，0描述了直接侧向力不工作，1描述了直接侧向力只能取集合中的一种；Among them, 0 describes that the direct lateral force does not work, and 1 describes that the direct lateral force can only take a set one of

记u₁＝δ_z，则式(22)中的控制输入写为Denote u ₁ = δ _z , then the control input in formula (22) is written as

$u u = = {[\begin{matrix} {u u}_{11} & {F f}_{{y the y}_{b b}} \end{matrix}]}^{T T} - - - - - - ((3131))$

根据直接侧向力和气动力复合控制导弹的总体参数表，系统状态和控制输入存在约束According to the general parameter table of direct lateral force and aerodynamic compound control missile, there are constraints on the system state and control input

x_min≤x(k)≤x_max x _min ≤ x(k) ≤ x _max

u_1min≤u₁(k)≤u_1max (32)u _1min ≤ u ₁ (k) ≤ u _1max (32)

其中，x_min＝[-0.53 -5.22]^T，x_max＝[0.53 5.22]^T，u_1min＝-0.53，u_1max＝0.53；Wherein, x _min =[-0.53 -5.22] ^T , x _max =[0.53 5.22] ^T , u _1min =-0.53, u _1max =0.53;

式(30)描述为Equation (30) is described as

${Σ Σ}_{i i = = 11}^{1212} {δ δ}_{{F f}_{i i}} \leq \leq 11 - - - - - - ((3333))$

综上，得到复合控制导弹完整混合逻辑动态模型为To sum up, the complete hybrid logic dynamic model of compound control missile is obtained as

$\{\begin{matrix} x x ((k k + + 11)) = = {Σ Σ}_{i i = = 11}^{66} {z z}_{i i} ((k k)) \\ y the y ((k k)) = = [\begin{matrix} 11 & 00 \end{matrix}] x x ((k k)) \\ s the s . . t t . . ((24 twenty four)),, ((2626)),, ((2828)),, ((2929)),, ((3333)) \end{matrix} - - - - - - ((3434)) . .$

同样，通过引入逻辑变量，采用上述方法，可以得到偏航通道的混合逻辑动态模型。Similarly, by introducing logic variables and using the above method, a mixed logic dynamic model of the yaw channel can be obtained.

具体实施方式六：本实施方式与具体实施方式一至五之一不同的是：步骤三中的设计复合导弹姿态控制律具体实施过程如下：Specific embodiment six: this embodiment is different from one of specific embodiments one to five: the specific implementation process of the design composite missile attitude control law in step 3 is as follows:

对于复合控制导弹而言，姿态控制的目标是在尽量节省燃料消耗的情况下快速跟踪姿态控制系统指令，然后维持姿态稳定。根据姿态控制目标，当前时刻姿态控制系统设计的目标可以描述为在节省燃料消耗的前提下，寻找合适的舵偏角和直接侧向力取值，也就是控制量u，使得在预测时域内的攻角跟踪误差最小，基于该目的我们构造混杂预测控制优化问题如下For compound control missiles, the goal of attitude control is to quickly follow the attitude control system instructions while saving fuel consumption as much as possible, and then maintain attitude stability. According to the attitude control goal, the goal of the attitude control system design at the current moment can be described as finding the appropriate value of the rudder deflection angle and the direct lateral force, that is, the control value u, under the premise of saving fuel consumption, so that in the prediction time domain The angle of attack tracking error is the smallest. Based on this purpose, we construct the hybrid predictive control optimization problem as follows

${J J}^{* *} = = \underset{u u ((k k)),, u u ((k k + + 11)),, δ δ ((k k)),, δ δ ((k k + + 11 | | k k)),, z z ((k k)),, z z ((k k + + 11 | | k k))}{min min} {Σ Σ}_{i i = = 11}^{N N} (({| | | | y the y ((k k + + i i | | k k)) - - {y the y}_{c c} ((k k + + i i)) | | | |}_{{Q Q}_{y the y}}^{22} + + {| | | | u u ((k k + + i i)) | | | |}_{R R}^{22}))$

$s the s . . t t . . \{\begin{matrix} \begin{matrix} MLD MLD & mode mode l l & ((3434)) \end{matrix} \\ {u u}_{11 min min} \leq \leq {u u}_{11} ((k k)),, {u u}_{11} ((k k + + 11)) \leq \leq {u u}_{11 max max} \\ {x x}_{min min} \leq \leq x x ((k k)),, x x ((k k + + 11)) \leq \leq {x x}_{max max} \end{matrix} - - - - - - ((3535))$

其中，y_c为攻角指令，y(k+i/k)为攻角预测值，N为预测时域，Q_y是输出跟踪项的加权矩阵，R是控制输入项的加权矩阵；Among them, y _c is the command of the angle of attack, y(k+i/k) is the predicted value of the angle of attack, N is the prediction time domain, Q _y is the weighted matrix of the output tracking item, and R is the weighted matrix of the control input item;

对于偏航通道来说，可以构造类似的混杂预测控制优化问题，其姿态控制律的设计过程与俯仰通道完全一致。For the yaw channel, a similar hybrid predictive control optimization problem can be constructed, and the design process of the attitude control law is exactly the same as that of the pitch channel.

利用混合整数二次规划方法及Matlab软件求解上述优化问题，即得到到气动控制律和姿控发动机开启规律，直接侧向力和气动力的分配通过调整加权矩阵Q_y和R实现。Using the mixed integer quadratic programming method and Matlab software to solve the above optimization problem, the aerodynamic control law and the opening law of the attitude control engine are obtained, and the distribution of direct lateral force and aerodynamic force is realized by adjusting the weighting matrix Q _y and R.

图7、8和9分别给出了利用本发明方法设计姿态控制律的仿真结果，图10是显式控制律分区结果。Figures 7, 8 and 9 show the simulation results of attitude control laws designed using the method of the present invention, and Figure 10 shows the partition results of explicit control laws.

Claims

1. An attitude control type direct lateral force and aerodynamic force composite missile attitude control method based on hybrid predictive control is characterized by being realized according to the following steps:

establishing a direct lateral force and aerodynamic force composite missile complete attitude control model and a direct lateral force model, deducing an expression of a direct lateral force in a pitching direction, and converting a missile nonlinear dynamics model into a piecewise affine model;

the process of the established direct lateral force and aerodynamic force composite missile complete attitude control model is as follows:

the gravity and aerodynamic force borne by the missile are respectively expressed on a trajectory coordinate system, and the dynamic equation of the missile mass center motion is obtained as follows

\{\begin{matrix} m \overset{\cdot}{V} = P c o s α c o s β - X_{a} - m g s i n θ + F_{x_{2}}^{a} \\ m V \overset{\cdot}{θ} = P ({sinαcosγ}_{v} + {cosαsinβsinγ}_{v}) + Y_{a} {cosγ}_{v} - m g c o s θ + F_{y_{2}}^{a} \\ m V \cos θ {\overset{\cdot}{ψ}}_{V} = - P ({sinαsinγ}_{v} - {cosαsinβcosγ}_{v}) - Y_{a} {sinγ}_{v} - Z_{a} {cosγ}_{v} - F_{z_{2}}^{a} \end{matrix} - - - (1)

Wherein m is missile mass, P is missile tail main engine thrust, g is gravitational acceleration, and X_a、Y_aAnd Z_aThe missile is characterized in that the missile is subjected to three components of aerodynamic force on a speed coordinate system, namely resistance, lift force and lateral force, the positive directions of the three components are respectively consistent with the positive directions of three axes of the speed coordinate system, V represents the movement speed of the missile mass center, α represents an attack angle and a sideslip angle respectively, and theta, psi_vBallistic dip and ballistic declination, gamma, respectively_vIs a velocity ramp angle;the three components of the direct lateral force borne by the missile on a trajectory coordinate system;

assuming that the projectile coordinate system coincides with the main axis of inertia of the projectile, i.e. J_xy＝J_yz＝J_zxThe kinetic equation of the missile rotating around the center of mass in the missile coordinate system is obtained as follows

\{\begin{matrix} J_{x} {\overset{\cdot}{ω}}_{x} = (J_{y} - J_{z}) ω_{z} ω_{y} + M_{x} \\ J_{y} {\overset{\cdot}{ω}}_{y} = (J_{z} - J_{x}) ω_{x} ω_{z} + M_{y} \\ J_{z} {\overset{\cdot}{ω}}_{z} = (J_{x} - J_{y}) ω_{x} ω_{y} + M_{z} \end{matrix} - - - (2)

Wherein J_x、J_yAnd J_zAre respectively the rotational inertia omega of the missile to the three axes of the missile coordinate system_x,ω_y,ω_zThe components of the rotating angular velocity omega of the projectile coordinate system relative to the ground coordinate system on three axes of the projectile coordinate system, M_x、M_yAnd M_zThe components of the moments of all external forces acting on the missile to the mass center on each axis of the missile coordinate system are respectively; m_x、M_yAnd M_zIs shown as

\{\begin{matrix} M_{x} = M_{e x} + M_{x_{1}}^{a} \\ M_{y} = M_{e y} + M_{y_{1}}^{a} \\ M_{z} = M_{e z} + M_{z_{1}}^{a} \end{matrix} - - - (3)

In the formula M_ex、M_eyAnd M_ezAre respectively the components of the aerodynamic moment acting on the missile on each axis of a missile coordinate system,the components of the direct lateral moment acting on the missile on each axis of the missile coordinate system are respectively;

the direct lateral force resultant force and resultant moment generated by simultaneously igniting a plurality of attitude control pulse engines are expressed on a bomb coordinate system by considering the interference effect of lateral jet flow

[\begin{matrix} F_{x_{1}}^{a} \\ F_{y_{1}}^{a} \\ F_{z_{1}}^{a} \end{matrix}] = [\begin{matrix} 0 \\ F_{y_{1}} + K_{F_{y}} F_{y_{1}} \\ F_{z_{1}} + K_{F_{z}} F_{z_{1}} \end{matrix}], [\begin{matrix} M_{x_{1}}^{a} \\ M_{y_{1}}^{a} \\ M_{z_{1}}^{a} \end{matrix}] = [\begin{matrix} 0 \\ M_{y_{1}} + K_{M_{y}} M_{y_{1}} \\ M_{z_{1}} + K_{M_{z}} M_{z_{1}} \end{matrix}] - - - (4)

Wherein,in order to jet the thrust amplification factor,for disturbance of the jet by a torque amplification factor, F_y1,F_z1,M_y1,M_z1The representation of the nominal direct lateral force resultant force and resultant moment on a projectile coordinate system is adopted;

deducing an attack angle, a sideslip angle and a projectile angular velocity dynamic equation according to the formulas (1) to (4);

dynamic equation of angle of attack and sideslip angle

\{\begin{matrix} \overset{\cdot}{α} = ω_{z} + ω_{y} s i n α t a n β - \frac{Q S (C_{y}^{α} α + C_{y}^{δ_{z}} δ_{z}) c o s α}{m V \cos β} - \frac{(F_{y_{1}} + K_{F_{y}} F_{y_{1}}) c o s α}{m V \cos β} - \frac{G_{y} c o s α}{m V c o s β} \\ \overset{\cdot}{β} = ω_{y} c o s α + \frac{Q S (C_{z}^{β} β + C_{z}^{δ_{y}} δ_{y}) c o s β}{m V} + \frac{Q S (C_{y}^{α} α + C_{y}^{δ_{z}} δ_{z}) s i n α s i n β}{m V} \\ + \frac{(F_{y_{1}} + K_{F_{y}} F_{y_{1}}) \sin α \sin β}{m V} + \frac{(F_{z_{1}} + K_{F_{z}} F_{z_{1}}) c o s β}{m V} + \frac{G_{z} c o s β}{m V} + \frac{G_{y} s i n α s i n β}{m V} \end{matrix} - - - (5)

Dynamic equation of angular velocity of projectile

\{\begin{matrix} {\overset{\cdot}{ω}}_{y} = \frac{M_{y_{1}}}{J_{y}} + \frac{K_{M_{y}} M_{y_{1}}}{J_{y}} + \frac{{QSLm}_{y}^{β} β}{J_{y}} + \frac{{QSLm}_{y}^{δ_{y}} δ_{y}}{J_{y}} + \frac{{QSLm}_{y}^{ω_{y}} ω_{y}}{J_{y}} \\ {\overset{\cdot}{ω}}_{z} = \frac{M_{z_{1}}}{J_{z}} + \frac{K_{M_{z}} M_{z_{1}}}{J_{z}} + \frac{{QSLm}_{z}^{α} α}{J_{z}} + \frac{{QSLm}_{z}^{δ_{z}} δ_{z}}{J_{z}} + \frac{{QSLm}_{z}^{ω_{z}} ω_{z}}{J_{z}} \end{matrix} - - - (6)

Wherein Q is dynamic pressure, S is characteristic area, L is characteristic length,as a result of the pneumatic parameters,is the normal overload coefficient corresponding to the unit attack angle,is the normal overload coefficient corresponding to the unit elevator deflection angle,is the lateral overload factor corresponding to the unit sideslip angle,is the lateral overload coefficient corresponding to the unit rudder deflection angle,for the statically stable derivative of the yaw,in order to achieve steering efficiency of the rudder,as a function of the yaw damping moment coefficient,in order to be the derivative of the pitch static stability,in order to achieve the efficiency of the elevator steering,as a function of the pitch damping moment coefficient,_y, _zdeflection angles of a rudder and an elevator respectively; the formulas (5) to (6) are the attitude control models of the composite control missiles;

introducing logic variables, and constructing a complete mixed logic dynamic model of the composite control missile;

designing a composite missile attitude control law, and determining a pneumatic control law and an attitude control engine starting law;

the specific process for establishing the direct lateral force model in the step one is as follows:

the direct lateral force is generated by an attitude control pulse engine unit fixedly arranged in front of the mass center of the projectile body, 180 attitude control pulse engines are arranged in a staggered mode and divided into 10 circles along the longitudinal axis of the projectile body, and 18 attitude control pulse engines in each circle are arranged around the projectile body; adjacent attitude control pulse engines in the same circle are spaced by a central angle of 20 degrees, wherein i represents the number of the circle, i is 1,2, …,10, j represents the number of the attitude control pulse engines in each circle, and j is 1,2, …, 18; the distance between the cross section formed by the connecting line of the circle centers of the ith circle of attitude control pulse engine nozzle and the center of mass of the projectile body is l_iThe distance between two adjacent circles is △ l, and the steady-state thrust generated by the attitude control pulse engine in the absence of free flow is assumed to be F_mThe nominal direct lateral force generated for the attitude control pulse engine with number (i, j) is expressed in the projectile coordinate system as

[\begin{matrix} F_{x_{1}}^{i, j} \\ F_{y_{1}}^{i, j} \\ F_{z_{1}}^{i, j} \end{matrix}] = [\begin{matrix} 0 \\ F_{m} \cos (\frac{2 j - i^{*}}{18} π) \\ - F_{m} \sin (\frac{2 j - i^{*}}{18} π) \end{matrix}] - - - (7)

Accordingly, the direct lateral moment is expressed in the elastic coordinate system as

[\begin{matrix} M_{x_{1}}^{i, j} \\ M_{y_{1}}^{i, j} \\ M_{z_{1}}^{i, j} \end{matrix}] = [\begin{matrix} 0 \\ F_{m} l_{i} s i n (\frac{2 j - i^{*}}{18} π) \\ F_{m} l_{i} \cos (\frac{2 j - i^{*}}{18} π) \end{matrix}] - - - (8)

Wherein, when i is odd, i^*2; when i is an even number, i^*＝1；

The nominal direct lateral force resultant force and resultant moment generated by simultaneously igniting a plurality of attitude control pulse engines are expressed on an elastic coordinate system as

[\begin{matrix} F_{x_{1}} \\ F_{y_{1}} \\ F_{z_{1}} \end{matrix}] = [\begin{matrix} 0 \\ Σ_{j = j_{1, 1}}^{j = j_{1, n 1}} F_{y_{1}}^{1, j} + Σ_{j = j_{2, 1}}^{j = j_{2, n 2}} F_{y_{1}}^{2, j} + ... + Σ_{j = j_{10, 1}}^{j = j_{10, n 10}} F_{y_{1}}^{10, j} \\ Σ_{j = j_{1, 1}}^{j = j_{1, n 1}} F_{z_{1}}^{1, j} + Σ_{j = j_{2, 1}}^{j = j_{2, n 2}} F_{z_{1}}^{2, j} + ... + Σ_{j = j_{10, 1}}^{j = j_{10, n 10}} F_{z_{1}}^{10, j} \end{matrix}] - - - (9)

[\begin{matrix} M_{x_{1}} \\ M_{y_{1}} \\ M_{z_{1}} \end{matrix}] = [\begin{matrix} 0 \\ - (Σ_{j = j_{1, 1}}^{j = j_{1, n 1}} F_{z_{1}}^{1, j} l_{1} + Σ_{j = j_{2, 1}}^{j = j_{2, n 2}} F_{z_{1}}^{2, j} l_{2} + ... + Σ_{j = j_{10, 1}}^{j = j_{10, n 10}} F_{z_{1}}^{10, j} l_{10}) \\ Σ_{j = j_{1, 1}}^{j = j_{1, n 1}} F_{y_{1}}^{1, j} l_{1} + Σ_{j = j_{2, 1}}^{j = j_{2, n 2}} F_{y_{1}}^{2, j} l_{2} + ... + Σ_{j = j_{10, 1}}^{j = j_{10, n 10}} F_{y_{1}}^{10, j} l_{10} \end{matrix}] - - - (10)

Wherein j is_1,1,j_1,2,…,j_1,n1The number in the circle of the ignition position control pulse engine of the 1 st circle is shown, n1 shows the number of the ignition position control pulse engines of the 1 st circle, and the like; the formulas (9) to (10) are direct lateral force models of the composite control missile;

the specific process of deducing the expression of the direct lateral force in the pitching direction comprises the following steps:

the attitude control pulse motors numbered (i,1), (i,2), (i,3), (i,17), (i,18) within the odd circles generate direct lateral forces at oy₁The components on the axis are represented as vectors

F_{o} = {[\begin{matrix} F_{m} & F_{m} c o s \frac{π}{9} & F_{m} c o s \frac{2 π}{9} & F_{m} c o s \frac{2 π}{9} & F_{m} c o s \frac{π}{9} \end{matrix}]}^{T} - - - (11)

The attitude control pulse engines numbered (i,1), (i,2), (i,17), (i,18) within even circles generate direct lateral forces in oy₁The components on the axis are represented as vectors

F_{e} = {[\begin{matrix} F_{m} c o s \frac{π}{18} & F_{m} c o s \frac{π}{6} & F_{m} c o s \frac{π}{6} & F_{m} c o s \frac{π}{18} \end{matrix}]}^{T} - - - (12)

Setting the direct side force generated by the ith circle of attitude control pulse engine as FⁱRequire

F¹＝F⁹,F³＝F⁷,F²＝F¹⁰,F⁴＝F⁸(13)

When the odd-number-turn pulse engine is ignited, there are

F_{y_{1}} &Element; {F_{m}, 2 F_{m} c o s \frac{π}{9}, 2 F_{m} c o s \frac{2 π}{9}, 2 F_{m}, 4 F_{m} c o s \frac{π}{9}, 4 F_{m} c o s \frac{2 π}{9}}

\begin{matrix} M_{z_{1}} &Element; {F^{1} l_{1} + F^{9} l_{9}, F^{3} l_{3} + F^{7} l_{7}, F^{5} l_{5}} \\ = {F^{1} (l_{5} + 4 Δ l) + F^{1} (l_{5} - 4 Δ l), F^{3} (l_{5} + 2 Δ l) + F^{3} (l_{5} - 2 Δ l), F^{5} l_{5}} \\ = {F^{5} l_{5}, 2 F^{1} l_{5}, 2 F^{3} l_{5}} = F_{y_{1}} l_{5} \\ = {F_{m} l_{5}, 2 F_{m} \cos \frac{π}{9} l_{5}, 2 F_{m} \cos \frac{2 π}{9} l_{5}, 2 F_{m} l_{5}, 4 F_{m} \cos \frac{π}{9} l_{5}, 4 F_{m} \cos \frac{2 π}{9} l_{5}} \end{matrix} - - - (14)

Similarly, when an even-numbered cycle pulse engine is ignited, there are

F_{y_{1}} &Element; {2 F_{m} c o s \frac{π}{18}, 2 F_{m} c o s \frac{π}{6}, 4 F_{m} c o s \frac{π}{18}, 4 F_{m} c o s \frac{π}{6}}

\begin{matrix} M_{z_{1}} &Element; {F^{2} l_{2} + F^{10} l_{10}, F^{4} l_{4} + F^{8} l_{8}, F^{6} l_{6}} \\ = {F^{2} (l_{6} + 4 Δ l) + F^{2} (l_{6} - 4 Δ l), F^{4} (l_{6} + 2 Δ l) + F^{4} (l_{6} - 2 Δ l), F^{6} l_{6}} \\ = {F^{6} l_{6}, 2 F^{2} l_{6}, 2 F^{4} l_{6}} = F_{y_{1}} l_{6} \\ = {2 F_{m} \cos \frac{π}{18} l_{6}, 2 F_{m} \cos \frac{π}{6} l_{6}, 4 F_{m} \cos \frac{π}{18} l_{6}, 4 F_{m} \cos \frac{π}{6} l_{6}} \end{matrix} - - - (15)

Different values of the resultant force of the direct lateral force generated by all attitude control engines in the positive pitching control area form a set

U_{F}^{y +} = {F_{m}, 2 F_{m} c o s \frac{π}{9}, 2 F_{m} c o s \frac{π}{18}, 2 F_{m}, 4 F_{m} c o s \frac{π}{9}, 4 F_{m} c o s \frac{π}{18}} - - - (16)

Different values of resultant moment form set

U_{M}^{y +} = {F_{m} l, 2 F_{m} c o s \frac{π}{9} l, 2 F_{m} c o s \frac{π}{18} l, 2 F_{m} l, 4 F_{m} c o s \frac{π}{9} l, 4 F_{m} c o s \frac{π}{18} l} - - - (17)

Different values of the resultant force of the direct lateral force generated by all attitude control engines in the negative pitch control area form a set

U_{F}^{y -} = {- F_{m}, - 2 F_{m} c o s \frac{π}{9}, - 2 F_{m} c o s \frac{π}{18}, - 2 F_{m}, - 4 F_{m} c o s \frac{π}{9}, - 4 F_{m} c o s \frac{π}{18}} - - - (18)

In each control period, the attitude control system follows a certain control lawSelecting a control force as a control input;

the specific process for converting the missile nonlinear dynamics model into the piecewise affine model in the step one is as follows: the nonlinear attitude control model of the missile pitch channel obtained by combining the general parameter table of the direct lateral force and aerodynamic force composite control missile is shown in the formulas (5) to (6)

\{\begin{matrix} \overset{\cdot}{α} = ω_{z} - \frac{Q S (C_{y}^{α} α + C_{y}^{δ_{z}} δ_{z}) \cos α}{m V} - \frac{(1 + K_{F_{y}}) F_{y_{1}} \cos α}{m V} \\ {\overset{\cdot}{ω}}_{z} = \frac{(1 + K_{M_{z}}) F_{y_{1}} l}{J_{z}} + \frac{{QSLm}_{z}^{α} α}{J_{z}} + \frac{{QSLm}_{z}^{δ_{z}} δ_{z}}{J_{z}} + \frac{{QSLm}_{z}^{ω_{z}} ω_{z}}{J_{z}} \end{matrix} - - - (19)

Selecting system state x ═ α ω_z]^TThe control quantity u ═ 2_zF_y1]^TSelecting the system output as y α, and describing the state space of the obtained nonlinear model as follows

\begin{matrix} \overset{\cdot}{x} (t) = f (x) + g (x) u (t) \\ y (t) = [\begin{matrix} 1 & 0 \end{matrix}] x (t) \end{matrix} - - - (20)

Wherein,

f (x) = [\begin{matrix} ω_{z} - \frac{{QSC}_{y}^{α} α \cos α}{m V} \\ \frac{Q S L (m_{z}^{α} α + m_{z}^{ω_{z}} ω_{z})}{J_{z}} \end{matrix}], g (x) = [\begin{matrix} - \frac{{QSC}_{y}^{δ_{z}} \cos α}{m V} & - \frac{(1 + K_{F_{y}}) \cos α}{m V} \\ \frac{{QSLm}_{z}^{δ_{z}}}{J_{z}} & \frac{(1 + K_{M_{z}}) l}{J_{z}} \end{matrix}]

in the above formula, the pneumatic parametersJet disturbance amplification factorAre all related to angle of attack α;

dividing the attitude control model into six partitions by taking alpha as-21.25 degrees, -8.75 degrees, 0 degrees, 8.75 degrees and 21.25 degrees as boundary points respectively, and performing piecewise linearization on the attitude control model in each segment by using a small deviation linearization method;

the resulting piecewise affine model is as follows:

\overset{\cdot}{x} (t) = \{\begin{matrix} a_{1} x (t) + b_{1} u (t) + e_{1}, & [\begin{matrix} 1 & 0 \end{matrix}] x (t) \leq - 0.37 \\ a_{2} x (t) + b_{2} u (t) + e_{2}, & - 0.37 < [\begin{matrix} 1 & 0 \end{matrix}] x (t) \leq - 0.153 \\ a_{3} x (t) + b_{3} u (t) + e_{3}, & - 0.153 < [\begin{matrix} 1 & 0 \end{matrix}] x (t) \leq 0 \\ a_{4} x (t) + b_{4} u (t) + e_{4}, & 0 < [\begin{matrix} 1 & 0 \end{matrix}] x (t) \leq 0.153 \\ a_{5} x (t) + b_{5} u (t) + e_{5}, & 0.153 < [\begin{matrix} 1 & 0 \end{matrix}] x (t) \leq 0.37 \\ a_{6} x (t) + b_{6} u (t) + e_{6}, & [\begin{matrix} 1 & 0 \end{matrix}] x (t) > 0.37 \end{matrix} - - - (21)

y(t)＝cx(t)

wherein,

a_{i} = \frac{\partial f (x)}{\partial x} |_{x = x_{i 0}} = [\begin{matrix} a_{i}^{11} & a_{i}^{12} \\ a_{i}^{21} & a_{i}^{22} \end{matrix}], b_{i} = g (x_{i 0}) = [\begin{matrix} b_{i}^{11} & b_{i}^{12} \\ b_{i}^{21} & b_{i}^{22} \end{matrix}], e_{i} = [\begin{matrix} e_{i}^{1} \\ e_{i}^{2} \end{matrix}]

a_{i}^{11} = \frac{\partial f_{1}}{\partial α} |_{x = x_{i 0}} = - \frac{Q S}{m V} (\frac{\partial C_{y}^{α}}{\partial α} |_{α = α_{i 0}} α_{i 0} c o s (α_{i 0}) + C_{y}^{α} (α_{i 0}) c o s (α_{i 0}) - C_{y}^{α} (α_{i 0}) α_{i 0} s i n (α_{i 0}))

a_{i}^{12} = \frac{\partial f_{1}}{\partial ω_{z}} |_{x = x_{i 0}} = 1

a_{i}^{21} = \frac{\partial f_{2}}{\partial α} |_{x = x_{i 0}} = \frac{Q S L}{J_{z}} (\frac{\partial m_{z}^{α}}{\partial α} |_{α = α_{i 0}} α_{i 0} + m_{z}^{α} (α_{i 0}) + \frac{\partial m_{z}^{ω_{z}}}{\partial α} |_{α = α_{i 0}} ω_{z i 0})

a_{i}^{22} = \frac{\partial f_{2}}{\partial ω_{z}} |_{x = x_{i 0}} = \frac{Q S L}{J_{z}} m_{z}^{ω_{z}} (α_{i 0})

b_{i}^{11} = - \frac{Q S}{m V} C_{y}^{δ_{z}} (α_{i 0}) c o s (α_{i 0})

b_{i}^{12} = - \frac{(1 + K_{F_{y}} (α_{i 0})) c o s (α_{i 0})}{m V}

b_{i}^{21} = \frac{Q S L}{J_{z}} m_{z}^{δ_{z}} (α_{i 0})

b_{i}^{22} = \frac{(1 + K_{M_{z}} (α_{i 0})) l}{J_{z}}

e_{i}^{1} = a_{i}^{11} α_{i 0} + a_{i}^{12} ω_{z i 0}

e_{i}^{2} = a_{i}^{21} α_{i 0} + a_{i}^{22} ω_{z i 0}

c＝[1 0]

wherein, i is 1,2, …,6, which corresponds to six subareas respectively;

taking a sampling period T_sCombining the relationship between the pneumatic parameters and the attack angle to obtain a state space expression of the discrete attitude control system as 0.025s

x (k + 1) = \{\begin{matrix} {\tilde{a}}_{1} x (k) + {\tilde{b}}_{1} u (k) + {\tilde{e}}_{1}, & [\begin{matrix} 1 & 0 \end{matrix}] x (k) \leq - 0.37 \\ {\tilde{a}}_{2} x (k) + {\tilde{b}}_{2} u (k) + {\tilde{e}}_{2}, & - 0.37 < [\begin{matrix} 1 & 0 \end{matrix}] x (k) \leq - 0.153 \\ {\tilde{a}}_{3} x (k) + {\tilde{b}}_{3} u (k) + {\tilde{e}}_{3}, & - 0.153 < [\begin{matrix} 1 & 0 \end{matrix}] x (k) \leq 0 \\ {\tilde{a}}_{4} x (k) + {\tilde{b}}_{4} u (k) + {\tilde{e}}_{4}, & 0 < [\begin{matrix} 1 & 0 \end{matrix}] x (k) \leq 0.153 \\ {\tilde{a}}_{5} x (k) + {\tilde{b}}_{5} u (k) + {\tilde{e}}_{5}, & 0.153 < [\begin{matrix} 1 & 0 \end{matrix}] x (k) \leq 0.37 \\ {\tilde{a}}_{6} x (k) + {\tilde{b}}_{6} u (k) + {\tilde{e}}_{6}, & [\begin{matrix} 1 & 0 \end{matrix}] x (k) > 0.37 \end{matrix} - - - (22)

y (k) = \tilde{c} x (k)

Wherein,

{\tilde{a}}_{1} = [\begin{matrix} 1.04 & 0.025 \\ 0.22 & 0.995 \end{matrix}], {\tilde{b}}_{1} = [\begin{matrix} - 0.02845 & 1.59 \times 10^{- 6} \\ - 2.116 & 1.42 \times 10^{- 4} \end{matrix}], {\tilde{e}}_{1} = [\begin{matrix} - 0.0183 \\ - 0.1123 \end{matrix}]

{\tilde{a}}_{2} = [\begin{matrix} 1.051 & 0.0255 \\ 0.218 & 0.995 \end{matrix}], {\tilde{b}}_{2} = [\begin{matrix} - 0.030 & 2.18 \times 10^{- 6} \\ - 2.224 & 1.87 \times 10^{- 4} \end{matrix}], {\tilde{e}}_{2} = [\begin{matrix} - 0.0175 \\ - 0.0792 \end{matrix}]

{\tilde{a}}_{3} = [\begin{matrix} 1.023 & 0.0252 \\ 0.248 & 0.9951 \end{matrix}], {\tilde{b}}_{3} = [\begin{matrix} - 0.030 & 2.68 \times 10^{- 6} \\ - 2.228 & 2.23 \times 10^{- 4} \end{matrix}], {\tilde{e}}_{3} = [\begin{matrix} - 0.0031 \\ - 0.0376 \end{matrix}]

{\tilde{a}}_{4} = [\begin{matrix} 0.9945 & 0.0248 \\ 0.2732 & 0.9954 \end{matrix}], {\tilde{b}}_{4} = [\begin{matrix} - 0.032 & 2.77 \times 10^{- 6} \\ - 2.371 & 2.32 \times 10^{- 4} \end{matrix}], {\tilde{e}}_{4} = [\begin{matrix} 0 \\ 0 \end{matrix}]

{\tilde{a}}_{5} = [\begin{matrix} 0.9697 & 0.0245 \\ 0.2913 & 0.9956 \end{matrix}], {\tilde{b}}_{5} = [\begin{matrix} - 0.030 & 2.27 \times 10^{- 6} \\ - 2.228 & 1.98 \times 10^{- 4} \end{matrix}], {\tilde{e}}_{5} = [\begin{matrix} - 0.0053 \\ 0.0454 \end{matrix}]

{\tilde{a}}_{6} = [\begin{matrix} 0.9594 & 0.0244 \\ 0.3137 & 0.9959 \end{matrix}], {\tilde{b}}_{6} = [\begin{matrix} - 0.029 & 1.91 \times 10^{- 6} \\ - 2.224 & 1.73 \times 10^{- 4} \end{matrix}], {\tilde{e}}_{6} = [\begin{matrix} - 0.0169 \\ 0.1193 \end{matrix}]

\tilde{c} = [\begin{matrix} 1 & 0 \end{matrix}]

k represents the kth moment, and the equation (22) is the piecewise affine model of the composite control missile.

2. The hybrid predictive control-based attitude control type direct lateral force and aerodynamic force composite missile attitude control method according to claim 1, wherein the concrete process for constructing the complete hybrid logic dynamic model of the composite control missile in the step two is as follows:

introducing logic variables_i(k) ∈ {0,1}, i ═ 1,2, …,6, describe the demarcation points in the piecewise affine model, which satisfy the following correspondence

\begin{matrix} {[\begin{matrix} 1 & 0 \end{matrix}] x (k) + 0.37 \leq 0} &DoubleLeftRightArrow; {δ_{1} (k) = 1} \\ {[\begin{matrix} 1 & 0 \end{matrix}] x (k) + 0.153 \leq 0} &DoubleLeftRightArrow; {δ_{2} (k) = 1} \\ {[\begin{matrix} 1 & 0 \end{matrix}] x (k) \leq 0} &DoubleLeftRightArrow; {δ_{3} (k) = 1} \\ {[\begin{matrix} 1 & 0 \end{matrix}] x (k) - 0.153 \leq 0} &DoubleLeftRightArrow; {δ_{4} (k) = 1} \\ {[\begin{matrix} 1 & 0 \end{matrix}] x (k) - 0.37 \leq 0} &DoubleLeftRightArrow; {δ_{5} (k) = 1} \end{matrix} - - - (23)

Equation (23) may be translated into an equivalent hybrid logical inequality constraint:

\{\begin{matrix} [\begin{matrix} 1 & 0 \end{matrix}] x (k) + 0.37 &GreaterEqual; ϵ + (m_{1} - ϵ) δ_{1} (k) \\ [\begin{matrix} 1 & 0 \end{matrix}] x (k) + 0.37 \leq M_{1} (1 - δ_{1} (k)) \\ [\begin{matrix} 1 & 0 \end{matrix}] x (k) + 0.153 &GreaterEqual; ϵ + (m_{2} - ϵ) δ_{2} (k) \\ [\begin{matrix} 1 & 0 \end{matrix}] x (k) + 0.153 \leq M_{2} (1 - δ_{2} (k)) \\ [\begin{matrix} 1 & 0 \end{matrix}] x (k) &GreaterEqual; ϵ + (m_{3} - ϵ) δ_{3} (k) \\ [\begin{matrix} 1 & 0 \end{matrix}] x (k) \leq M_{3} (1 - δ_{3} (k)) \\ [\begin{matrix} 1 & 0 \end{matrix}] x (k) - 0.153 &GreaterEqual; ϵ + (m_{4} - ϵ) δ_{4} (k) \\ [\begin{matrix} 1 & 0 \end{matrix}] x (k) - 0.153 \leq M_{4} (1 - δ_{4} (k)) \\ [\begin{matrix} 1 & 0 \end{matrix}] x (k) - 0.37 &GreaterEqual; ϵ + (m_{5} - ϵ) δ_{5} (k) \\ [\begin{matrix} 1 & 0 \end{matrix}] x (k) - 0.37 \leq M_{5} (1 - δ_{5} (k)) \end{matrix} - - - (24)

wherein m is₁＝-0.16,M₁＝0.90,m₂＝-0.377,M₂＝0.683,m₃＝-0.53,M₃＝0.53,m₄＝-0.683,M₄＝0.377,m₅＝-0.90,M₅＝0.16,＝10^-6；

At the same time, auxiliary logic variables are introduced_i(k) ∈ {0,1}, i ═ 6, …,9, and satisfies

\{\begin{matrix} δ_{6} = (1 - δ_{1}) δ_{2} \\ δ_{7} = (1 - δ_{2}) δ_{3} \\ δ_{8} = (1 - δ_{3}) δ_{4} \\ δ_{9} = (1 - δ_{4}) δ_{5} \end{matrix} - - - (25)

Then₁,₆,₇,₈,₉,1-₅The six subareas respectively correspond to the piecewise affine model;

expression of equation (25) as a hybrid logical inequality constraint:

\{\begin{matrix} - δ_{1} + δ_{2} - δ_{6} \leq 0 \\ δ_{1} + δ_{6} \leq 1 \\ - δ_{2} + δ_{6} \leq 0 \\ - δ_{2} + δ_{3} - δ_{7} \leq 0 \\ δ_{2} + δ_{7} \leq 1 \\ - δ_{3} + δ_{7} \leq 0 \\ - δ_{3} + δ_{4} - δ_{8} \leq 0 \\ δ_{3} + δ_{8} \leq 1 \\ - δ_{4} + δ_{8} \leq 0 \\ - δ_{4} + δ_{5} - δ_{9} \leq 0 \\ δ_{4} + δ_{9} \leq 1 \\ - δ_{5} + δ_{9} \leq 0 \end{matrix} - - - (26)

introducing an auxiliary continuous variable z_i(k) I is 1,2, …,6, so as to unify each segment partition condition of the piecewise affine model with the corresponding state space expression, and the auxiliary continuous variables are as follows

\{\begin{matrix} z_{1} (k) = [{\tilde{a}}_{1} (k) x (k) + {\tilde{b}}_{1} (k) u (k) + {\tilde{e}}_{1}] δ_{1} (k) \\ z_{2} (k) = [{\tilde{a}}_{2} (k) x (k) + {\tilde{b}}_{2} (k) u (k) + {\tilde{e}}_{2}] δ_{6} (k) \\ z_{3} (k) = [{\tilde{a}}_{3} (k) x (k) + {\tilde{b}}_{3} (k) u (k) + {\tilde{e}}_{3}] δ_{7} (k) \\ z_{4} (k) = [{\tilde{a}}_{4} (k) x (k) + {\tilde{b}}_{4} (k) u (k) + {\tilde{e}}_{4}] δ_{8} (k) \\ z_{5} (k) = [{\tilde{a}}_{5} (k) x (k) + {\tilde{b}}_{5} (k) u (k) + {\tilde{e}}_{5}] δ_{9} (k) \\ z_{6} (k) = [{\tilde{a}}_{6} (k) x (k) + {\tilde{b}}_{6} (k) u (k) + {\tilde{e}}_{6}] (1 - δ_{5} (k)) \end{matrix} - - - (27)

Expression of equation (27) as a hybrid logical inequality constraint:

\{\begin{matrix} z_{1} (k) &GreaterEqual; [{\tilde{a}}_{1} (k) x (k) + {\tilde{b}}_{1} (k) u (k) + {\tilde{e}}_{1}] - M_{f 1} (1 - δ_{1} (k)) \\ z_{1} (k) \leq [{\tilde{a}}_{1} (k) x (k) + {\tilde{b}}_{1} (k) u (k) + {\tilde{e}}_{1}] - m_{f 1} (1 - δ_{1} (k)) \\ z_{1} (k) &GreaterEqual; m_{f 1} δ_{1} (k) \\ z_{1} (k) \leq M_{f 1} δ_{1} (k) \\ z_{2} (k) &GreaterEqual; [{\tilde{a}}_{2} (k) x (k) + {\tilde{b}}_{2} (k) u (k) + {\tilde{e}}_{2}] - M_{f 2} (1 - δ_{6} (k)) \\ z_{2} (k) \leq [{\tilde{a}}_{2} (k) x (k) + {\tilde{b}}_{2} (k) u (k) + {\tilde{e}}_{2}] - m_{f 2} (1 - δ_{6} (k)) \\ z_{2} (k) &GreaterEqual; m_{f 2} δ_{1} (k) \\ z_{2} (k) \leq M_{f 2} δ_{1} (k) \\ z_{3} (k) &GreaterEqual; [{\tilde{a}}_{3} (k) x (k) + {\tilde{b}}_{3} (k) u (k) + {\tilde{e}}_{3}] - M_{f 3} (1 - δ_{7} (k)) \\ z_{3} (k) \leq [{\tilde{a}}_{3} (k) x (k) + {\tilde{b}}_{3} (k) u (k) + {\tilde{e}}_{3}] - m_{f 3} (1 - δ_{7} (k)) \\ z_{3} (k) &GreaterEqual; m_{f 3} δ_{7} (k) \\ z_{3} (k) \leq M_{f 3} δ_{7} (k) \\ z_{4} (k) &GreaterEqual; [{\tilde{a}}_{4} (k) x (k) + {\tilde{b}}_{4} (k) u (k) + {\tilde{e}}_{4}] - M_{f 4} (1 - δ_{8} (k)) \\ z_{4} (k) \leq [{\tilde{a}}_{1} (k) x (k) + {\tilde{b}}_{4} (k) u (k) + {\tilde{e}}_{4}] - m_{f 4} (1 - δ_{8} (k)) \\ z_{4} (k) &GreaterEqual; m_{f 4} δ_{8} (k) \\ z_{4} (k) \leq M_{f 4} δ_{8} (k) \\ z_{5} (k) &GreaterEqual; [{\tilde{a}}_{5} (k) x (k) + {\tilde{b}}_{5} (k) u (k) + {\tilde{e}}_{5}] - M_{f 5} (1 - δ_{9} (k)) \\ z_{5} (k) \leq [{\tilde{a}}_{5} (k) x (k) + {\tilde{b}}_{5} (k) u (k) + {\tilde{e}}_{5}] - m_{f 5} (1 - δ_{9} (k)) \\ z_{5} (k) &GreaterEqual; m_{f 5} δ_{9} (k) \\ z_{5} (k) \leq M_{f 5} δ_{9} (k) \\ z_{6} (k) &GreaterEqual; [{\tilde{a}}_{6} (k) x (k) + {\tilde{b}}_{6} (k) u (k) + {\tilde{e}}_{6}] - M_{f 6} δ_{5} (k) \\ z_{6} (k) \leq [{\tilde{a}}_{6} (k) x (k) + {\tilde{b}}_{6} (k) u (k) + {\tilde{e}}_{6}] - m_{f 6} δ_{5} (k) \\ z_{6} (k) &GreaterEqual; m_{f 6} (1 - δ_{5} (k)) \\ z_{6} (k) \leq M_{f 6} (1 - δ_{5} (k)) \end{matrix} - - - (28)

wherein M is_f1＝[0.73 10.84]^T,m_f1＝[-0.77 -11.06]^T,M_f2＝[0.76 11.66]^T,m_f2＝[-0.79 -12.56]^T，M_f3＝[0.77 12.73]^T,m_f3＝[-0.78 -12.80]^T,M_f4＝[0.76 14.03]^T,m_f4＝[-0.76 -14.03]^T,M_f5＝[0.725 12.91]^T,m_f5＝[-0.736 -12.05]^T,M_f6＝[0.696 11.54]^T,m_f6＝[-0.73 -11.30]^T；

Combining parameters in the general parameter table of the direct lateral force and aerodynamic force composite control missile and formulas (16) and (17), obtaining a pitch direction direct lateral force value set as

U_{F}^{y} = {2200,4135,4333,4400,8269,8666, - 2200, - 4135, - 4333, - 4400, - 8269, - 8666} N

The following logic variables were introducedTo describe the direct lateral force

U_{F}^{y} = {2200, 4135, 4333, 4400, 8269, 8666, - 2200, - 4135, - 4333, - 4400, - 8269, - 8666} N

In equation (29), the logical variables satisfy the following constraints:

or 1 (30)

Where 0 describes that direct lateral forces do not work and 1 describes that direct lateral forces can only be taken togetherOne of (1);

remember u₁＝_zThen the control input in equation (22) is written as

u = {[\begin{matrix} u_{1} & F_{y_{b}} \end{matrix}]}^{T} - - - (31)

According to the general parameter table of the direct lateral force and aerodynamic force composite control missile, the system state and control input are constrained

\begin{matrix} x_{\min} \leq x (k) \leq x_{\max} \\ u_{1 \min} \leq u_{1} (k) \leq u_{1 \max} \end{matrix} - - - (32)

Wherein x is_min＝[-0.53 -5.22]^T,x_max＝[0.53 5.22]^T,u_1min＝-0.53,u_1max＝0.53；

Formula (30) is described as

Σ_{i = 1}^{12} δ_{F_{i}} \leq 1 - - - (33)

To sum up, the obtained complete mixed logic dynamic model of the composite control missile is

\{\begin{matrix} x (k + 1) = Σ_{i = 1}^{6} z_{i} (k) \\ y (k) = [\begin{matrix} 1 & 0 \end{matrix}] x (k) \\ s . t . (24), (26), (28), (29), (33) \end{matrix} - - - (34) .

3. The hybrid predictive control-based attitude control type direct lateral force and aerodynamic force composite missile attitude control method according to claim 1, characterized in that the specific implementation process of the attitude control law of the designed composite missile in the third step is as follows:

the construction of the hybrid predictive control optimization problem is as follows

J^{*} = \min_{u (k), u (k + 1), δ (k), δ (k + 1 | k), z (k), z (k + 1 | k)} Σ_{i = 1}^{N} (| | y (k + i | k) - y_{c} (k + i) | |_{Q_{y}}^{2} + | | u (k + i) | |_{R}^{2})

s . t . \{\begin{matrix} \begin{matrix} M L D & \mod e l & (34) \end{matrix} \\ u_{1 \min} \leq u_{1} (k), u_{1} (k + 1) \leq u_{1 m a x} \\ x_{m i n} \leq x (k), x (k + 1) \leq x_{m a x} \end{matrix} - - - (35)

Wherein, y_cFor the angle of attack instruction, y (k + i/k) is the predicted value of the angle of attack, N is the predicted time domain, Q_yIs the weighting matrix of the output trace entries, R is the weighting matrix of the control entries;

solving the optimization problem by using a mixed integer quadratic programming method and Matlab software, namely obtaining the starting rule of a pneumatic control law and an attitude control engine, and adjusting a weighting matrix Q to distribute direct lateral force and aerodynamic force_yAnd R implementation.