CN104267733B - Based on the appearance control formula direct lateral force gentle Power compound missile attitude control method mixing PREDICTIVE CONTROL - Google Patents

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 type direct lateral force and aerodynamic force composite missile attitude control method based on hybrid predictive control

Technical Field

The invention relates to an attitude control type direct lateral force and aerodynamic force composite missile attitude control method, in particular to a composite missile attitude control method based on hybrid predictive control, and belongs to the field of aircraft control.

Background

With the enhancement of the maneuvering capability of the target, the missile is required to have a faster overload response speed in order to realize effective interception of the target. The traditional pure aerodynamic control missile is limited by the overload response speed, so that the requirement for accurately intercepting a high maneuvering target cannot be met. The adoption of a direct lateral force and aerodynamic force composite control technology is an effective way for improving the overload response speed of the missile, but the introduction of the direct lateral force increases the design difficulty of a missile guidance control system and is mainly embodied in the following two aspects: firstly, the direct lateral force and aerodynamic force generate complex coupling, so that the nonlinearity and uncertainty of a missile dynamics model are increased; and secondly, the discrete characteristic of direct lateral force enables the control design model to have obvious hybrid characteristic. The two points bring new challenges to missile attitude control design, and the traditional attitude control design method does not solve the two problems at the same time. At present, a two-step method is mostly adopted for the attitude control design of the direct lateral force and aerodynamic force composite missile, firstly, a nonlinear attitude control law is designed by utilizing a nonlinear control method to obtain a control moment instruction; and then, selecting a certain performance index, and obtaining an aerodynamic moment instruction and a direct lateral force moment instruction through optimization solution, so as to realize instruction distribution of aerodynamic force and direct lateral force. The method has poor control effect and limited application range because the difference of direct lateral force and aerodynamic dynamic characteristics is difficult to consider.

Disclosure of Invention

The invention aims to provide an attitude control type direct lateral force and aerodynamic force composite missile attitude control method to solve the problem that the existing attitude control design method cannot simultaneously solve model nonlinearity and control input mixed characteristics. The technical scheme adopted by the invention for solving the technical problems is as follows:

the attitude control type direct lateral force and aerodynamic force composite missile attitude control method based on hybrid predictive control is 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

$\left\{\begin{array}{c}m\stackrel{\·}{V}=P\cos \mathrm{\α}\cos \mathrm{\β}-X_a-\mathrm{mg}\sin \mathrm{\θ}+F_{x_2}^a\\ \mathrm{mV}\stackrel{\·}{\mathrm{\θ}}=P(\sin \mathrm{\α}\cos {\mathrm{\γ}}_v+\cos \mathrm{\α}\sin \mathrm{\β}\sin {\mathrm{\γ}}_v)+Y_a\cos {\mathrm{\γ}}_v-\mathrm{mg}\cos \mathrm{\θ}+F_{y_z}^a\\ \mathrm{mV}\cos \mathrm{\θ}{\stackrel{\·}{\mathrm{\ψ}}}_V=-P(\sin \mathrm{\α}\sin {\mathrm{\γ}}_v-\cos \mathrm{\α}\sin \mathrm{\β}\cos {\mathrm{\γ}}_v)-Y_a\sin {\mathrm{\γ}}_v-Z_a\cos {\mathrm{\γ}}_v-F_{z_2}^a\end{array}\right.---\left(1\right)$

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

$\left\{\begin{array}{c}{J}_x{\stackrel{\·}{\mathrm{\ω}}}_x=(J_y-J_z){\mathrm{\ω}}_z{\mathrm{\ω}}_y+M_x\\ J_y{\stackrel{\·}{\mathrm{\ω}}}_y=(J_z-J_x){\mathrm{\ω}}_x{\mathrm{\ω}}_z+M_y\\ J_z{\stackrel{\·}{\mathrm{\ω}}}_z=(J_x-J_y){\mathrm{\ω}}_x{\mathrm{\ω}}_y+M_z\end{array}\right.---\left(2\right)$

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

$\left\{\begin{array}{c}{M}_x=M_{\mathrm{ex}}+M_{x_1}^a\\ M_y=M_{\mathrm{ey}}+M_{y_1}^a\\ M_z=M_{\mathrm{ez}}+M_{z_1}^a\end{array}\right.---\left(3\right)$

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

$\left[\begin{array}{c}{F}_{x_1}^a\\ F_{y_1}^a\\ F_{z_1}^a\end{array}\right]=\left[\begin{array}{c}0\\ F_{y_1}+K_{F_y}{F}_{y_1}\\ F_{z_1}+K_{F_z}{F}_{z_1}\end{array}\right],\left[\begin{array}{c}{M}_{x_1}^a\\ M_{y_1}^a\\ M_{z_1}^a\end{array}\right]=\left[\begin{array}{c}0\\ M_{y_1}+K_{M_y}{M}_{y_1}\\ M_{z_1}+K_{M_z}{M}_{z_1}\end{array}\right]---\left(4\right)$

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

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\α}}={\mathrm{\ω}}_z+{\mathrm{\ω}}_y\sin \mathrm{\α}\tan \mathrm{\β}-\frac{\mathrm{QS}(C_y^{\mathrm{\α}}\mathrm{\α}+C_y^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z)\cos \mathrm{\α}}{\mathrm{mV}\cos \mathrm{\β}}-\frac{(F_{y_1}+K_{F_y}{F}_{y_1})\cos \mathrm{\α}}{\mathrm{mV}\cos \mathrm{\β}}-\frac{G_y\cos \mathrm{\α}}{\mathrm{mV}\cos \mathrm{\β}}\\ \stackrel{\·}{\mathrm{\β}}={\mathrm{\ω}}_y\cos \mathrm{\α}+\frac{\mathrm{QS}(C_z^{\mathrm{\β}}\mathrm{\β}+C_z^{{\mathrm{\δ}}_y}{\mathrm{\δ}}_y)\cos \mathrm{\β}}{\mathrm{mV}}+\frac{\mathrm{QS}(C_y^{\mathrm{\α}}\mathrm{\α}+C_y^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z)\sin \mathrm{\α}\sin \mathrm{\β}}{\mathrm{mV}}\\ +\frac{(F_{y_1}+K_{F_y}{F}_{y_1})\sin \mathrm{\α}\sin \mathrm{\β}}{\mathrm{mV}}+\frac{(F_{z_1}+K_{F_z}{F}_{z_1})\cos \mathrm{\β}}{\mathrm{mV}}+\frac{G_z\cos \mathrm{\β}}{\mathrm{mV}}+\frac{G_y\sin \mathrm{\α}\sin \mathrm{\β}}{\mathrm{mV}}\end{array}\right.---\left(5\right)$

Dynamic equation of angular velocity of projectile

$\left\{\begin{array}{c}{\stackrel{\·}{\mathrm{\ω}}}_y=\frac{M_{y_1}}{J_y}+\frac{K_{M_y}{M}_{y_1}}{J_y}+\frac{{\mathrm{QSLm}}_y^{\mathrm{\β}}\mathrm{\β}}{J_y}+\frac{{\mathrm{QSLm}}_y^{{\mathrm{\δ}}_y}{\mathrm{\δ}}_y}{J_y}+\frac{{\mathrm{QSLm}}_y^{{\mathrm{\ω}}_y}{\mathrm{\ω}}_y}{J_y}\\ {\stackrel{\·}{\mathrm{\ω}}}_z=\frac{M_{z_1}}{J_z}+\frac{K_{M_z}{M}_{z_1}}{J_z}+\frac{{\mathrm{QSLm}}_z^{\mathrm{\α}}\mathrm{\α}}{J_z}+\frac{{\mathrm{QSLm}}_z^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z}{J_z}+\frac{{\mathrm{QSLm}}_z^{{\mathrm{\ω}}_z}{\mathrm{\ω}}_z}{J_z}\end{array}\right.---\left(6\right)$

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;

and step three, designing a composite missile attitude control law, and determining a pneumatic control law and an attitude control engine starting law.

The invention has the beneficial effects that:

compared with the existing composite missile attitude control method, the invention has the advantages that:

(1) the design of the pneumatic control law and the determination of the starting rule of the attitude control engine are completed simultaneously, and the design problem of the composite missile attitude control law is converted into the design problem of a hybrid logic dynamic system by introducing logic variables to describe a piecewise affine model and direct lateral force, and meanwhile, the problems of model nonlinearity and control input hybrid characteristic in the composite control missile attitude control design are solved.

(2) The method provided by the invention has wider application range, and when the consumption condition of the attitude control engine is considered, the number of the available engines is only required to be recalculated at each moment, and the description relation between the direct lateral force and the logic variable is changed. In addition, the method can be used for attitude control design of attitude control type composite control missiles, is also suitable for control design of other types of nonlinear missile guidance systems, and has wide application prospect.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a definition of the principal coordinate system used in the present invention, with the center of mass of the missile as the origin O, where the ground coordinate system Oxyz, the missile coordinate system Ox₁y₁z₁Ballistic coordinate system Ox₂y₂z₂And a speed coordinate system Ox₃y₃z₃α are angle of attack and sideslip angle, theta, psi_vTrajectory dip and trajectory deflection angles, respectively;

FIG. 3 is a layout diagram of an attitude control engine, wherein a is an odd-numbered circle of the attitude control pulse engine layout, b is an even-numbered circle of the attitude control pulse engine layout, and 1 and 2 … … 18 represent the number of the attitude control pulse engine in each circle;

FIG. 4 is a diagram of an attitude control engine in a ring direction, wherein i represents the number of a ring, the numbers 8, 9, 10, 11 and 12 represent the numbers of the attitude control pulse engine in each ring, and the distance between the section formed by the connecting line of the circle centers of the nozzles of the ith ring of the attitude control pulse engine and the center of mass of the projectile body is l_iThe distance between two adjacent circles is delta l, l₁The distance between a section formed by a connecting line of the center of a nozzle circle of the 1 st circle of attitude control pulse engine and the center of mass of the projectile body is represented;

FIG. 5 is a schematic view of an engine sector, wherein FIG. a is a schematic view of an odd number of rotation attitude control pulse engine sectors, and FIG. b is a schematic view of an even number of rotation attitude control pulse engine sectors;

FIG. 6 is a graph of aerodynamic parameters versus angle of attack, where graph a isGraph b is the relation curve with αGraph c is the relationship curve with αGraph d is the relationship curve with αGraph e is the relation curve with αGraph f is the relationship with αCurves with α;

FIG. 7 is an angle of attack response curve, where the solid line represents the actual value of the angle of attack and the dashed line represents the commanded value of the angle of attack;

FIG. 8 is a rudder deflection angle curve;

FIG. 9 is a direct lateral force curve generated by an attitude control engine;

FIG. 10 shows different partition cases of the state space attitude control law.

Detailed Description

The first embodiment is as follows: the embodiment is understood by combining fig. 1 and fig. 2, and the attitude control method of the hybrid predictive control-based attitude-control-based direct lateral force and aerodynamic composite missile in the embodiment is 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 through analyzing the aerodynamic characteristics of a missile body;

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

$\left\{\begin{array}{c}m\stackrel{\·}{V}=P\cos \mathrm{\α}\cos \mathrm{\β}-X_a-\mathrm{mg}\sin \mathrm{\θ}+F_{x_2}^a\\ \mathrm{mV}\stackrel{\·}{\mathrm{\θ}}=P(\sin \mathrm{\α}\cos {\mathrm{\γ}}_v+\cos \mathrm{\α}\sin \mathrm{\β}\sin {\mathrm{\γ}}_v)+Y_a\cos {\mathrm{\γ}}_v-\mathrm{mg}\cos \mathrm{\θ}+F_{y_2}^a\\ \mathrm{mV}\cos \mathrm{\θ}\stackrel{\·}{{\stackrel{\·}{\mathrm{\ψ}}}_V=-P(\sin \mathrm{\α}\sin {\mathrm{\γ}}_v-\cos \mathrm{\α}\sin \mathrm{\β}\cos {\mathrm{\γ}}_v)-Y_a\sin {\mathrm{\γ}}_v-Z_a\cos {\mathrm{\γ}}_v-F_{z_2}^a}\end{array}\right.---\left(1\right)$

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

$\left\{\begin{array}{c}{J}_x{\stackrel{\·}{\mathrm{\ω}}}_x=(J_y-J_z){\mathrm{\ω}}_z{\mathrm{\ω}}_y+M_x\\ J_y{\stackrel{\·}{\mathrm{\ω}}}_y=(J_z-J_x){\mathrm{\ω}}_x{\mathrm{\ω}}_z+M_y\\ J_z{\stackrel{\·}{\mathrm{\ω}}}_z=(J_x-J_y){\mathrm{\ω}}_x{\mathrm{\ω}}_y+M_z\end{array}\right.---\left(2\right)$

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

$\left\{\begin{array}{c}{M}_x=M_{\mathrm{ex}}+M_{x_1}^a\\ M_y=M_{\mathrm{ey}}+M_{y_1}^a\\ M_z=M_{\mathrm{ez}}+M_{z_1}^a\end{array}\right.---\left(3\right)$

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;

in addition, when the attitude control engine injects the gas flow laterally, the high-speed jet flow and the incoming air flow are mutually interfered, and a lateral jet flow interference effect is formed. Thrust amplification factor using jet disturbanceAnd jet disturbance moment amplification factorTo respectively represent the ratio of jet disturbance force and moment to the net thrust and moment generated without lateral jet; therefore, the direct lateral force resultant force and resultant moment generated by simultaneously igniting a plurality of attitude control pulse engines are expressed as follows on a bomb coordinate system by considering the interference effect of the lateral jet flow

$\left[\begin{array}{c}{F}_{x_1}^a\\ F_{y_1}^a\\ F_{z_1}^a\end{array}\right]=\left[\begin{array}{c}0\\ F_{y_1}+K_{F_y}{F}_{y_1}\\ F_{z_1}+K_{F_z}{F}_{z_1}\end{array}\right],\left[\begin{array}{c}{M}_{x_1}^a\\ M_{y_1}^a\\ M_{z_1}^a\end{array}\right]=\left[\begin{array}{c}0\\ M_{y_1}+K_{M_y}{M}_{y_1}\\ M_{z_1}+K_{M_z}{M}_{z_1}\end{array}\right]---\left(4\right)$

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

assuming that the quality of the guided missile at the final guide section is unchanged, and carrying out linear description on pneumatic force and moment by using pneumatic data according to the requirement of simplifying a model; because the attitude control of the intercepted missile in the atmosphere aims at establishing an attack angle and a sideslip angle to form aerodynamic lift and lateral force, in order to describe the change rule of the attack angle, the sideslip angle and the angular velocity of the missile, a dynamic equation of the attack angle, the sideslip angle and the angular velocity of the missile is deduced according to the formulas (1) to (4);

dynamic equation of angle of attack and sideslip angle

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\α}}={\mathrm{\ω}}_z+{\mathrm{\ω}}_y\sin \mathrm{\α}\tan \mathrm{\β}-\frac{\mathrm{QS}(C_y^{\mathrm{\α}}\mathrm{\α}+C_y^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z)\cos \mathrm{\α}}{\mathrm{mV}\cos \mathrm{\β}}-\frac{(F_{y_1}+K_{F_y}{F}_{y_1})\cos \mathrm{\α}}{\mathrm{mV}\cos \mathrm{\β}}-\frac{G_y\cos \mathrm{\α}}{\mathrm{mV}\cos \mathrm{\β}}\\ \stackrel{\·}{\mathrm{\β}}={\mathrm{\ω}}_y\cos \mathrm{\α}+\frac{\mathrm{QS}(C_z^{\mathrm{\β}}\mathrm{\β}+C_z^{{\mathrm{\δ}}_y}{\mathrm{\δ}}_y)\cos \mathrm{\β}}{\mathrm{mV}}+\frac{\mathrm{QS}(C_y^{\mathrm{\α}}\mathrm{\α}+C_y^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z)\sin \mathrm{\α}\sin \mathrm{\β}}{\mathrm{mV}}\\ +\frac{(F_{y_1}+K_{F_y}{F}_{y_1})\sin \mathrm{\α}\sin \mathrm{\β}}{\mathrm{mV}}+\frac{(F_{z_1}+K_{F_z}{F}_{z_1})\cos \mathrm{\β}}{\mathrm{mV}}+\frac{G_z\cos \mathrm{\β}}{\mathrm{mV}}+\frac{G_y\sin \mathrm{\α}\sin \mathrm{\β}}{\mathrm{mV}}\end{array}\right.---\left(5\right)$

Dynamic equation of angular velocity of projectile

$\left\{\begin{array}{c}{\stackrel{.}{\mathrm{\ω}}}_y=\frac{M_{y_1}}{J_y}+\frac{K_{M_y}{M}_{y_1}}{J_y}+\frac{{\mathrm{QSLm}}_y^{\mathrm{\β}}\mathrm{\β}}{J_y}+\frac{{\mathrm{QSLm}}_y^{{\mathrm{\δ}}_y}{\mathrm{\δ}}_y}{J_y}+\frac{{\mathrm{QSLm}}_y^{{\mathrm{\ω}}_y}{\mathrm{\ω}}_y}{J_y}\\ {\stackrel{.}{\mathrm{\ω}}}_z=\frac{M_{z_1}}{J_z}+\frac{K_{M_z}{M}_{z_1}}{J_z}+\frac{{\mathrm{QSLm}}_z^{\mathrm{\α}}\mathrm{\α}}{J_z}+\frac{{\mathrm{QSLm}}_z^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z}{J_z}+\frac{{\mathrm{QSLm}}_z^{{\mathrm{\ω}}_z}{\mathrm{\ω}}_z}{J_z}\end{array}\right.---\left(6\right)$

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 based on the equivalence of the piecewise affine model and the mixed logic dynamic model;

and thirdly, designing a composite missile attitude control law based on a hybrid model predictive control theory, and determining a pneumatic control law and an attitude control engine starting law.

The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: 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 in the same circleThe interval central angle of the attitude control pulse motor is 20 degrees, i is the number of a circle, i is 1,2, …,10, j is the number of the attitude control pulse motor 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 delta l; the layout of the attitude control pulse engine set on the projectile body is shown in fig. 3 and 4.

Assuming that the steady-state thrust generated by the attitude control pulse engine in the absence of free flow is 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

$\left[\begin{array}{c}{F}_{x_1}^{i,j}\\ F_{y_1}^{i,j}\\ F_{z_1}^{i,j}\end{array}\right]=\left[\begin{array}{c}0\\ F_m\cos \left(\frac{2j-i^{*}}{18}\mathrm{\π}\right)\\ -F_m\sin \left(\frac{2j-i^{*}}{18}\right)\end{array}\right]---\left(7\right)$

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

$\left[\begin{array}{c}{M}_{x_1}^{i,j}\\ M_{y_1}^{i,j}\\ M_{z_1}^{i,j}\end{array}\right]=\left[\begin{array}{c}0\\ F_m{l}_i\sin \left(\frac{2j-i^{*}}{18}\mathrm{\π}\right)\\ F_m{l}_i\cos \left(\frac{2j-i^{*}}{18}\mathrm{\π}\right)\end{array}\right]---\left(8\right)$

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

$\left[\begin{array}{c}{F}_{x_1}\\ F_{y_1}\\ F_{z_1}\end{array}\right]=\left[\begin{array}{c}0\\ \underset{j=j_{\mathrm{1,1}}}{\overset{j=j_{1,n1}}{\mathrm{\Σ}}}{F}_{y_1}^{1,j}+\underset{j=j_{\mathrm{2,1}}}{\overset{j=j_{2,n2}}{\mathrm{\Σ}}}{F}_{y_1}^{2,j}+...+\underset{j=j_{\mathrm{10,1}}}{\overset{j=j_{10,n10}}{\mathrm{\Σ}}}{F}_{y_1}^{10,j}\\ \underset{j=j_{\mathrm{1,1}}}{\overset{j=j_{1,n1}}{\mathrm{\Σ}}}{F}_{z_1}^{1,j}+\underset{j=j_{\mathrm{2,1}}}{\overset{j=j_{2,n2}}{\mathrm{\Σ}}}{F}_{z_1}^{2,j}+...+\underset{j=j_{\mathrm{10,1}}}{\overset{j=j_{10,n10}}{\mathrm{\Σ}}}{F}_{z_1}^{10,j}\end{array}\right]---\left(9\right)$

$\left[\begin{array}{c}{M}_{x_1}\\ M_{y_1}\\ M_{z_1}\end{array}\right]=\left[\begin{array}{c}0\\ \underset{j=j_{\mathrm{1,1}}}{\overset{j=j_{1,n1}}{\mathrm{\Σ}}}{F}_{z_1}^{1,j}{l}_1+\underset{j=j_{\mathrm{2,1}}}{\overset{j=j_{2,n2}}{\mathrm{\Σ}}}{F}_{z_1}^{2,j}{l}_2+...+\underset{j=j_{\mathrm{10,1}}}{\overset{j=j_{10,n10}}{\mathrm{\Σ}}}{F}_{z_1}^{10,j}{l}_{10}\\ \underset{j=j_{\mathrm{1,1}}}{\overset{j=j_{1,n1}}{\mathrm{\Σ}}}{F}_{y_1}^{1,j}{l}_1+\underset{j=j_{\mathrm{2,1}}}{\overset{j=j_{2,n2}}{\mathrm{\Σ}}}{F}_{y_1}^{2,j}{l}_2+...+\underset{j=j_{\mathrm{10,1}}}{\overset{j=j_{10,n10}}{\mathrm{\Σ}}}{F}_{y_1}^{10,j}{l}_{10}\end{array}\right]---\left(10\right)$

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; equations (9) - (10) are direct lateral force models of the composite control missile.

The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: the specific process for deriving the expression of the direct lateral force in the pitching direction in the step one is as follows:

each circle of 18 attitude control pulse engines is divided into four ignition control areas: positive and negative pitch control zones and positive and negative yaw control zones, as shown in fig. 5.

Because each attitude control engine is fixed in installation position on the missile, fixed in work period, limited in quantity and not reusable, a set of specific principles need to be followed when selecting the number, the positions and the ignition sequence of the engines. The invention makes the following assumptions that for each control area, at most 2 simultaneous ignitions are allowed in each circle, at most two circles are allowed to be simultaneously ignited, and only the attitude control pulse engine in an odd number of circles or the attitude control pulse engine in an even number of circles are allowed to be simultaneously ignited; in each ignition control area, symmetric ignition needs to be ensured when the attitude control pulse engine is ignited.

Taking a positive pitch control area as an example, a resultant force and resultant moment set of direct lateral force generated by the attitude control pulse engine is given;

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

$F_o={\left[\begin{array}{ccccc}{F}_m& F_m\cos \frac{\mathrm{\π}}{9}& F_m\cos \frac{2\mathrm{\π}}{9}& F_m\cos \frac{2\mathrm{\π}}{9}& F_m\cos \frac{\mathrm{\π}}{9}\end{array}\right]}^T---\left(11\right)$

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

$F_e={\left[\begin{array}{cccc}{F}_m\cos \frac{\mathrm{\π}}{18}& F_m\cos \frac{\mathrm{\π}}{6}& F_m\cos \frac{\mathrm{\π}}{6}& F_m\cos \frac{\mathrm{\π}}{18}\end{array}\right]}^T---\left(12\right)$

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

$F_{y_1}\∈\{F_m,2F_m\cos \frac{\mathrm{\π}}{9},2F_m\cos \frac{2\mathrm{\π}}{9},2F_m,4F_m\cos \frac{\mathrm{\π}}{9},4F_m\cos \frac{2\mathrm{\π}}{9}\}$

$\begin{array}{c}{M}_{z_1}\∈\{F^1{l}_1+F^9{l}_9,{F^{3}l}_3+F^7{l}_7,F^5{l}_5\}\\ =\{F^1(l_5+4\mathrm{\Δl})+F^1(l_5-4\mathrm{\Δl}),F^3(l_5+2\mathrm{\Δl})+F^3(l_5-2\mathrm{\Δl}),F^5{l}_5\}\\ =\{F^5{l}_5,2F^1{l}_5,2F^3{l}_5\}=F_{y_1}{l}_5\\ =\{F_m{l}_5,2F_m\cos \frac{\mathrm{\π}}{9}{l}_5,2F_m\cos \frac{2\mathrm{\π}}{9}{l}_5,2F_m{l}_5,4F_m\cos \frac{\mathrm{\π}}{9}{l}_5,4F_m\cos \frac{2\mathrm{\π}}{9}{l}_5\}\end{array}---\left(14\right)$

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

$F_{y_1}\∈\{2F_m\cos \frac{\mathrm{\π}}{18},2F_m\cos \frac{\mathrm{\π}}{6},4F_m\cos \frac{\mathrm{\π}}{18},4F_m\cos \frac{\mathrm{\π}}{6}\}$

$\begin{array}{c}{M}_{z_1}\∈\{F^2{l}_2+F^{10}{l}_{10},F^4{l}_4+F^8{l}_8,F^6{l}_6\}\\ =\{F^2(l_6+4\mathrm{\Δl})+F^2(l_6-4\mathrm{\Δl}),F^4(l_6+2\mathrm{\Δl})+F^4(l_6-2\mathrm{\Δl}),F^6{l}_6\}\\ =\{F^6{l}_6,2F^2{l}_6,2F^4{l}_6+=F_{y_1}{l}_6\\ =\{2F_m\cos \frac{\mathrm{\π}}{18}{l}_6,2F_m\cos \frac{\mathrm{\π}}{6}{l}_6,4F_m\cos \frac{\mathrm{\π}}{18}{l}_6,4F_m\cos \frac{\mathrm{\π}}{6}{l}_6\}\end{array}---\left(15\right)$

Since Δ l is small, assume l₅≈l₆In addition, considering the ignition efficiency of the engine to avoid excessive consumption and not allowing the ignition of the engine with low efficiency, different values of the resultant force of the direct lateral force generated by all attitude control engines in the positive pitch control area form a set

$U_F^{y+}=\{F_m,2F_m\cos \frac{\mathrm{\π}}{9},2F_m\cos \frac{\mathrm{\π}}{18},2F_m,4F_m\cos \frac{\mathrm{\π}}{9},4F_m\cos \frac{\mathrm{\π}}{18}\}---\left(16\right)$

Different values of resultant moment form set

$U_M^{y+}=\{F_{m}l,2F_m\cos \frac{\mathrm{\π}}{9}l,2F_m\cos \frac{\mathrm{\π}}{18}l,2F_{m}l,4F_m\cos \frac{\mathrm{\π}}{9}l,4F_m\cos \frac{\mathrm{\π}}{18}l\}---\left(17\right)$

Due to the symmetry of the engine configuration, 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

$U_F^{y-}=\{-F_m,-2F_m\cos \frac{\mathrm{\π}}{9},-2F_m\cos \frac{\mathrm{\π}}{18},-2F_m,-4F_m\cos \frac{\mathrm{\π}}{9},-4F_m\cos \frac{\mathrm{\π}}{18}\}---\left(18\right)$

In each control period, the attitude control system follows a certain control lawSelects one control force as the control input.

By the method, a set formed by different values of the resultant force of the direct lateral forces generated by all attitude control engines in the positive and negative yaw control areas can be obtained.

The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: the specific process for converting the missile nonlinear dynamics model into the piecewise affine model in the step one is as follows:

firstly, a general parameter table of the direct lateral force and aerodynamic force composite control missile is given,

TABLE 1 missile population parameters

Taking a pitch channel as an example, ignoring a gravity term at a final control section, and ignoring a coupling term for simplifying analysis, obtaining a nonlinear attitude control model of the missile pitch channel by equations (5) - (6)

$\left\{\begin{array}{c}\stackrel{\·}{\mathrm{\α}}={\mathrm{\ω}}_z-\frac{\mathrm{QS}(C_y^{\mathrm{\α}}\mathrm{\α}+C_y^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z)\cos \mathrm{\α}}{\mathrm{mV}}-\frac{(1+K_{F_y})F_{y_1}\cos \mathrm{\α}}{\mathrm{mV}}\\ {\stackrel{\·}{\mathrm{\ω}}}_z=\frac{(1+K_{M_z})F_{y_1}l}{J_z}+\frac{\mathrm{QSL}{m}_z^{\mathrm{\α}}\mathrm{\α}}{J_z}+\frac{\mathrm{QSL}{m}_z^{{\mathrm{\δ}}_z}{\mathrm{\δ}}_z}{J_z}+\frac{\mathrm{QSL}{m}_z^{{\mathrm{\ω}}_z}{\mathrm{\ω}}_z}{J_z}\end{array}\right.---\left(19\right)$

Selecting system state x ═ α ω_z]^TThe control quantity u ═ 2_zF_y1]^TWhen the attitude control design is carried out, the tracking condition of an attack angle command is concerned, so that the system output is selected to be y as α, and the state space of the obtained nonlinear model is described as follows

$\begin{array}{c}\stackrel{\·}{x}\left(t\right)=f\left(x\right)+g\left(x\right)u\left(t\right)\\ \begin{array}{cc}y\left(t\right)=[1& 0]x\left(t\right)\end{array}\end{array}---\left(20\right)$

Wherein,

$f\left(x\right)=\left[\begin{array}{c}{\mathrm{\ω}}_z-\frac{{\mathrm{QSC}}_y^{\mathrm{\α}}\mathrm{\α}\cos \mathrm{\α}}{\mathrm{mV}}\\ \frac{\mathrm{QSL}(m_z^{\mathrm{\α}}\mathrm{\α}+m_z^{{\mathrm{\ω}}_z}{\mathrm{\ω}}_z)}{J_z}\end{array}\right],g\left(x\right)=\left[\begin{array}{cc}-\frac{{\mathrm{QSC}}_y^{{\mathrm{\δ}}_z}\cos \mathrm{\α}}{\mathrm{mV}}& -\frac{(1+K_{F_y})\cos \mathrm{\α}}{\mathrm{mV}}\\ \frac{{\mathrm{QSLm}}_z^{{\mathrm{\δ}}_z}}{J_z}& \frac{(1+K_{M_z})l}{J_z}\end{array}\right]$

in the above formula, the pneumatic parametersJet disturbance amplification factorAll related to the angle of attack α, and considering that angle of attack is the determining factor affecting these parameters, FIG. 6 shows the relationship between each parameter and the angle of attack α.

The angle of attack is a main factor enabling the attitude control system to present nonlinear characteristics, according to the given pneumatic parameters and the relation curve between the amplification factor and the angle of attack, the pneumatic parameters and the amplification factor can be seen to present nonlinear relations with the angle of attack, and when the angle of attack changes in a small range, the linear relations can be approximated; dividing the device into six subareas by taking alpha as-21.25 degrees, -8.75 degrees, 0 degrees, 8.75 degrees and 21.25 degrees as dividing points, wherein each subarea can be approximately linear; in each segment, the attitude control model is linearized in sections by a small deviation linearization method;

the resulting piecewise affine model is as follows:

$\stackrel{\&CenterDot;}{x}\left(t\right)=\left\{\begin{array}{cc}{a}_{1}x\left(t\right)+b_{1}u\left(t\right)+e_1,& \left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\&le;-0.37\\ a_{2}x\left(t\right)+b_{2}u\left(t\right)+e_2,& -0.37<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\&le;-0.153\\ a_{3}x\left(t\right)+b_3\text{u}\left(t\right)+e_3,& -0.153<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\&le;0\\ a_{4}x\left(t\right)+b_{4}u\left(t\right)+e_4,& 0<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\&le;0.153\\ a_{5}x\left(t\right)+b_{5}u\left(t\right)+e_5,& 0.153<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\&le;0.37\\ a_{6}x\left(t\right)+b_{6}u\left(t\right)+e_6,& \left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)>0.37\end{array}\right.$

y(t)＝cx(t) (21)

wherein,

$a_i=\frac{\&PartialD;f\left(x\right)}{\&PartialD;x}{|}_{x=x_{i0}}=\left[\begin{array}{cc}{a}_i^{11}& a_i^{12}\\ a_i^{21}& a_i^{22}\end{array}\right],b_i=g\left(x_{i0}\right)=\left[\begin{array}{cc}{b}_i^{11}& b_i^{12}\\ b_i^{21}& b_i^{22}\end{array}\right],e_i=\left[\begin{array}{c}{e}_i^1\\ e_i^2\end{array}\right]$

$a_i^{11}=\frac{\&PartialD;f_1}{\&PartialD;\mathrm{\&alpha;}}{|}_{x=x_{i0}}=-\frac{\mathrm{QS}}{\mathrm{mV}}(\frac{\&PartialD;C_y^{\mathrm{\&alpha;}}}{\&PartialD;\mathrm{\&alpha;}}{|}_{{\mathrm{\&alpha;}=\mathrm{\&alpha;}}_{i0}}{\mathrm{\&alpha;}}_{i0}\cos \left({\mathrm{\&alpha;}}_{i0}\right)+C_y^{\mathrm{\&alpha;}}\left({\mathrm{\&alpha;}}_{i0}\right)\cos \left({\mathrm{\&alpha;}}_{i0}\right)-C_y^{\mathrm{\&alpha;}}\left({\mathrm{\&alpha;}}_{i0}\right){\mathrm{\&alpha;}}_{i0}\sin \left({\mathrm{\&alpha;}}_{i0}\right))$

$a_i^{12}=\frac{\&PartialD;f_1}{\&PartialD;{\mathrm{\&omega;}}_z}{|}_{x=x_{i0}}=1$

$a_i^{21}=\frac{\&PartialD;f_2}{\&PartialD;\mathrm{\&alpha;}}{|}_{x=x_{i0}}=\frac{\mathrm{QSL}}{J_z}(\frac{\&PartialD;m_z^{\mathrm{\&alpha;}}}{\&PartialD;\mathrm{\&alpha;}}{|}_{\mathrm{\&alpha;}={\mathrm{\&alpha;}}_{i0}}{\mathrm{\&alpha;}}_{i0}+m_z^{\mathrm{\&alpha;}}\left({\mathrm{\&alpha;}}_{i0}\right)+\frac{\&PartialD;m_z^{{\mathrm{\&omega;}}_z}}{\&PartialD;\mathrm{\&alpha;}}{|}_{\mathrm{\&alpha;}={\mathrm{\&alpha;}}_{i0}}{\mathrm{\&omega;}}_{\mathrm{zi}0})$

$a_i^{22}=\frac{\&PartialD;f_2}{{\&PartialD;\mathrm{\&omega;}}_z}{|}_{x=x_{i0}}=\frac{\mathrm{QSL}}{J_z}{m}_z^{{\mathrm{\&omega;}}_z}\left({\mathrm{\&alpha;}}_{i0}\right)$

$b_i^{11}=-\frac{\mathrm{QS}}{\mathrm{mV}}{C}_y^{{\mathrm{\&delta;}}_z}\left({\mathrm{\&alpha;}}_{i0}\right)\cos \left({\mathrm{\&alpha;}}_{i0}\right)$

$b_i^{12}=-\frac{(1+K_{F_y}\left({\mathrm{\&alpha;}}_{i0}\right))\cos \left({\mathrm{\&alpha;}}_{i0}\right)}{\mathrm{mV}}$

$b_i^{21}=\frac{\mathrm{QSL}}{J_z}{m}_z^{{\mathrm{\&delta;}}_z}\left({\mathrm{\&alpha;}}_{i0}\right)$

$b_i^{22}=\frac{(1+{K_M}_z\left({\mathrm{\&alpha;}}_{i0}\right))l}{J_z}$

$e_i^1=a_i^{11}{\mathrm{\&alpha;}}_{i0}+a_i^{12}{\mathrm{\&omega;}}_{\mathrm{zi}0}$

$e_i^2=a_i^{21}{\mathrm{\&alpha;}}_{i0}+a_i^{22}{\mathrm{\&omega;}}_{\mathrm{zi}0}$

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 aerodynamic parameter and the attack angle in the graph of fig. 6 to obtain a state space expression of the discrete attitude control system as 0.025s

$x(k+1)=\left\{\begin{array}{cc}{\tilde{a}}_{1}x\left(k\right)+{\tilde{b}}_{1}u\left(k\right)+{\tilde{e}}_1,& \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;-0.37\\ {\tilde{a}}_{2}x\left(k\right)+{\tilde{b}}_{2}u\left(k\right)+{\tilde{e}}_2,& -0.37<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;-0.153\\ {\tilde{a}}_{3}x\left(k\right)+{\tilde{b}}_{3}u\left(k\right)+{\tilde{e}}_3,& -0.153<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;0\\ {\tilde{a}}_{4}x\left(k\right)+{\tilde{b}}_{4}u\left(k\right)+{\tilde{e}}_4,& 0<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;0.153\\ {\tilde{a}}_{5}x\left(k\right)+{\tilde{b}}_{5}u\left(k\right)+{\tilde{e}}_5,& 0.153<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;0.37\\ {\tilde{a}}_{6}x\left(k\right)+{\tilde{b}}_{6}u\left(k\right)+{\tilde{e}}_6,& \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)>0.37\end{array}\right.$

$y\left(k\right)=\tilde{c}x\left(k\right)---\left(22\right)$

Wherein,

${\tilde{a}}_1=\left[\begin{array}{cc}1.04& 0.025\\ 0.22& 0.995\end{array}\right],{\tilde{b}}_1=\left[\begin{array}{cc}-0.02845& 1.59\&times;{10}^{-6}\\ -2.116& 1.42\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_1=\left[\begin{array}{c}-0.0183\\ -0.1123\end{array}\right]$

${\tilde{a}}_2=\left[\begin{array}{cc}1.051& 0.0255\\ 0.218& 0.995\end{array}\right],{\tilde{b}}_2=\left[\begin{array}{cc}-0.030& 2.18\&times;{10}^{-6}\\ -2.224& 1.87\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_2=\left[\begin{array}{c}-0.0175\\ -0.0792\end{array}\right]$

${\tilde{a}}_3=\left[\begin{array}{cc}1.023& 0.0252\\ 0.248& 0.9951\end{array}\right],{\tilde{b}}_3=\left[\begin{array}{cc}-0.030& 2.68\&times;{10}^{-6}\\ -2.228& 1.23\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_3=\left[\begin{array}{c}-0.0031\\ -0.0376\end{array}\right]$

${\tilde{a}}_4=\left[\begin{array}{cc}0.9945& 0.0248\\ 0.2732& 0.9954\end{array}\right],{\tilde{b}}_4=\left[\begin{array}{cc}-0.032& 2.77\&times;{10}^{-6}\\ -2.371& 2.32\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_4=\left[\begin{array}{c}0\\ 0\end{array}\right]$

${\tilde{a}}_5=\left[\begin{array}{cc}0.9697& 0.0245\\ 0.2913& 0.9956\end{array}\right],{\tilde{b}}_5=\left[\begin{array}{cc}-0.030& 2.27\&times;{10}^{-6}\\ -2.228& 1.98\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_5=\left[\begin{array}{c}-0.0053\\ 0.0454\end{array}\right]$

${\tilde{a}}_6=\left[\begin{array}{cc}0.9594& 0.0244\\ 0.3137& 0.9959\end{array}\right],{\tilde{b}}_6=\left[\begin{array}{cc}-0.029& 1.91\&times;{10}^{-6}\\ -2.224& 1.73\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_6=\left[\begin{array}{c}-0.0169\\ -0.1193\end{array}\right]$

$\tilde{c}=\left[\begin{array}{cc}1& 0\end{array}\right]$

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

By the method, a piecewise affine model of the yaw channel can be obtained as well.

The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: the concrete process for constructing the complete mixed logic dynamic model of the composite control missile 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

$\{\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.37\&le;0\}\&DoubleLeftRightArrow;\{{\mathrm{\&delta;}}_1\left(k\right)=1\}$

$\{\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.153\&le;0\}\&DoubleLeftRightArrow;\{{\mathrm{\&delta;}}_2\left(k\right)=1\}$

$\{\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;0\}\&DoubleLeftRightArrow;\{{\mathrm{\&delta;}}_3\left(k\right)=1\}$

$\{\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.153\&le;0\}\&DoubleLeftRightArrow;\{{\mathrm{\&delta;}}_4\left(k\right)=1\}$

$\{\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.37\&le;0\}\&DoubleLeftRightArrow;\{{\mathrm{\&delta;}}_5\left(k\right)=1\}---\left(23\right)$

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

$\left\{\begin{array}{c}\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.37\&GreaterEqual;\mathrm{\&epsiv;}+(m_1-\mathrm{\&epsiv;}){\mathrm{\&delta;}}_1\left(k\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.37\&le;M_1(1-{\mathrm{\&delta;}}_1\left(k\right))\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.153\&GreaterEqual;\mathrm{\&epsiv;}+(m_2-\mathrm{\&epsiv;}){\mathrm{\&delta;}}_2\left(k\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.153\&le;M_2(1-{\mathrm{\&delta;}}_2\left(k\right))\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&GreaterEqual;\mathrm{\&epsiv;}+(m_3-\mathrm{\&epsiv;}){\mathrm{\&delta;}}_3\left(k\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;M_3(1-{\mathrm{\&delta;}}_3\left(k\right))\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.153\&GreaterEqual;\mathrm{\&epsiv;}+(m_4-\mathrm{\&epsiv;}){\mathrm{\&delta;}}_4\left(k\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.153\&le;M_4(1-{\mathrm{\&delta;}}_4\left(k\right))\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.37\&GreaterEqual;\mathrm{\&epsiv;}+(m_5-\mathrm{\&epsiv;}){\mathrm{\&delta;}}_5\left(k\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.37\&le;M_5(1-{\mathrm{\&delta;}}_5\left(k\right))\end{array}\right.---\left(24\right)$

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 is 6, …,9, and satisfies

$\left\{\begin{array}{c}{\mathrm{\&delta;}}_6=(1-{\mathrm{\&delta;}}_1){\mathrm{\&delta;}}_2\\ {\mathrm{\&delta;}}_7=(1-{\mathrm{\&delta;}}_2){\mathrm{\&delta;}}_3\\ {\mathrm{\&delta;}}_8=(1-{\mathrm{\&delta;}}_3){\mathrm{\&delta;}}_4\\ {\mathrm{\&delta;}}_9=(1-{\mathrm{\&delta;}}_4){\mathrm{\&delta;}}_5\end{array}\right.---\left(25\right)$

Then₁，₆，₇，₈，₉，1-₅Corresponding to six partitions of the piecewise affine model, respectively.

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

$\left\{\begin{array}{c}-{\mathrm{\&delta;}}_1+{\mathrm{\&delta;}}_2-{\mathrm{\&delta;}}_6\&le;0\\ {\mathrm{\&delta;}}_1+{\mathrm{\&delta;}}_6\&le;1\\ {-\mathrm{\&delta;}}_2+{\mathrm{\&delta;}}_6\&le;0\\ -{\mathrm{\&delta;}}_2+{\mathrm{\&delta;}}_3-{\mathrm{\&delta;}}_7\&le;0\\ {\mathrm{\&delta;}}_2+{\mathrm{\&delta;}}_7\&le;1\\ -{\mathrm{\&delta;}}_3+{\mathrm{\&delta;}}_7\&le;0\\ -{\mathrm{\&delta;}}_3+{\mathrm{\&delta;}}_4-{\mathrm{\&delta;}}_8\&le;0\\ {\mathrm{\&delta;}}_3+{\mathrm{\&delta;}}_8\&le;1\\ -{\mathrm{\&delta;}}_4+{\mathrm{\&delta;}}_8\&le;0\\ -{\mathrm{\&delta;}}_4{+\mathrm{\&delta;}}_5-{\mathrm{\&delta;}}_9\&le;0\\ {\mathrm{\&delta;}}_4+{\mathrm{\&delta;}}_9\&le;1\\ -{\mathrm{\&delta;}}_5+{\mathrm{\&delta;}}_9\&le;0\end{array}\right.---\left(26\right)$

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

$\left\{\begin{array}{c}{z}_1\left(k\right)=[{\tilde{a}}_1\left(k\right)x\left(k\right)+{\tilde{b}}_1\left(k\right)u\left(k\right)+{\tilde{e}}_1]{\mathrm{\&delta;}}_1\left(k\right)\\ z_2\left(k\right)=[{\tilde{a}}_2\left(k\right)x\left(k\right)+{\tilde{b}}_2\left(k\right)u\left(k\right)+{\tilde{e}}_2]{\mathrm{\&delta;}}_6\left(k\right)\\ z_3\left(k\right)=[{\tilde{a}}_3\left(k\right)x\left(k\right)+{\tilde{b}}_3\left(k\right)u\left(k\right)+{\tilde{e}}_3]{\mathrm{\&delta;}}_7\left(k\right)\\ z_4\left(k\right)=[{\tilde{a}}_4\left(k\right)x\left(k\right)+{\tilde{b}}_4\left(k\right)u\left(k\right)+{\tilde{e}}_4]{\mathrm{\&delta;}}_8\left(k\right)\\ z_5\left(k\right)=[{\tilde{a}}_5\left(k\right)x\left(k\right)+{\tilde{b}}_5\left(k\right)u\left(k\right)+{\tilde{e}}_5]{\mathrm{\&delta;}}_9\left(k\right)\\ z_6\left(k\right)=[{\tilde{a}}_6\left(k\right)x\left(k\right)+{\tilde{b}}_6\left(k\right)u\left(k\right)+{\tilde{e}}_6](1-{\mathrm{\&delta;}}_5\left(k\right))\end{array}\right.---\left(27\right)$

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

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

$U_F^y=\{2200,\mathrm{4135,4333,4400,8269,8666},-2200,-4135,-4333,-4400,-8269,-8666\}N$

Since the direct lateral force is a discrete variable, the following logical variables are introducedTo describe the direct lateral force

$\begin{array}{c}{F}_{y_b}=2200{\mathrm{\&delta;}}_{F_1}+4135{\mathrm{\&delta;}}_{F_2}+4333{\mathrm{\&delta;}}_{F_3}+4400{\mathrm{\&delta;}}_{F_4}+8269{\mathrm{\&delta;}}_{F_5}+8666{\mathrm{\&delta;}}_{F_6}-2200{\mathrm{\&delta;}}_{F_7}\\ -4135{\mathrm{\&delta;}}_{F_8}-{4333\mathrm{\&delta;}}_{F_9}-{4400\mathrm{\&delta;}}_{F_{10}}-{8269\mathrm{\&delta;}}_{F_{11}}-8666{\mathrm{\&delta;}}_{F_{12}}\end{array}---\left(29\right)$

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

$\underset{i=1}{\overset{12}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_{F_i}=0$ 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

$u={\left[\begin{array}{cc}{u}_1& F_{y_b}\end{array}\right]}^T---\left(31\right)$

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

x_min≤x(k)≤x_max

u_1min≤u₁(k)≤u_1max(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

$\underset{i=1}{\overset{12}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_{F_i}\&le;1---\left(33\right)$

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

$\left\{\begin{array}{c}x(k+1)=\underset{i=1}{\overset{6}{\mathrm{\&Sigma;}}}{z}_i\left(k\right)\\ y\left(k\right)=\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\\ s.t.\left(24\right),\left(26\right),\left(28\right),\left(29\right),\left(33\right)\end{array}\right.---\left(34\right).$

Also, by introducing logic variables, a hybrid logic dynamic model of the yaw channel can be obtained by the method.

The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is: the specific implementation process of the attitude control law of the designed composite missile in the third step is as follows:

for a composite control missile, the goal of attitude control is to quickly track the attitude control system commands while saving fuel consumption as much as possible, and then maintain the attitude stable. According to the attitude control target, the design target of the attitude control system at the current moment can be described as that on the premise of saving fuel consumption, a proper rudder deflection angle and a direct lateral force value, namely a control quantity u are searched, so that the tracking error of the attack angle in a prediction time domain is minimum, and based on the aim, a hybrid prediction control optimization problem is constructed as follows

$J^{*}=\underset{u\left(k\right),u(k+1),\mathrm{\&delta;}\left(k\right),\mathrm{\&delta;}(k+1|k),z\left(k\right),z(k+1|k)}{\min }\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}({\left|\right|y(k+i|k)-y_c(k+i)\left|\right|}_{Q_y}^2+{\left|\right|u(k+i)\left|\right|}_R^2)$

$s.t.\left\{\begin{array}{c}\begin{array}{ccc}\mathrm{MLD}& \mathrm{mode}l& \left(34\right)\end{array}\\ u_{1\min }\&le;u_1\left(k\right),u_1(k+1)\&le;u_{1\max }\\ x_{\min }\&le;x\left(k\right),x(k+1)\&le;x_{\max }\end{array}\right.---\left(35\right)$

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;

for the yaw channel, a similar hybrid predictive control optimization problem can be constructed, and the design process of the attitude control law of the hybrid predictive control optimization problem is completely consistent with that of the pitch channel.

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.

FIGS. 7, 8 and 9 show the simulation results of designing attitude control laws by using the method of the present invention, and FIG. 10 shows the partitioning results of explicit control laws.

Claims (3)

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

$\left\{\begin{array}{c}m\stackrel{\&CenterDot;}{V}=Pcos\mathrm{\&alpha;}cos\mathrm{\&beta;}-X_a-mgsin\mathrm{\&theta;}+F_{x_2}^a\\ mV\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=P({\mathrm{sin\&alpha;cos\&gamma;}}_v+{\mathrm{cos\&alpha;sin\&beta;sin\&gamma;}}_v)+Y_a{\mathrm{cos\&gamma;}}_v-mgcos\mathrm{\&theta;}+F_{y_2}^a\\ mV\cos \mathrm{\&theta;}{\stackrel{\&CenterDot;}{\mathrm{\&psi;}}}_V=-P({\mathrm{sin\&alpha;sin\&gamma;}}_v-{\mathrm{cos\&alpha;sin\&beta;cos\&gamma;}}_v)-Y_a{\mathrm{sin\&gamma;}}_v-Z_a{\mathrm{cos\&gamma;}}_v-F_{z_2}^a\end{array}\right.---\left(1\right)$

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

$\left\{\begin{array}{c}{J}_x{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_x=(J_y-J_z){\mathrm{\&omega;}}_z{\mathrm{\&omega;}}_y+M_x\\ J_y{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_y=(J_z-J_x){\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z+M_y\\ J_z{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_z=(J_x-J_y){\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_y+M_z\end{array}\right.---\left(2\right)$

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

$\left\{\begin{array}{c}{M}_x=M_{ex}+M_{x_1}^a\\ M_y=M_{ey}+M_{y_1}^a\\ M_z=M_{ez}+M_{z_1}^a\end{array}\right.---\left(3\right)$

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

$\left[\begin{array}{c}{F}_{x_1}^a\\ F_{y_1}^a\\ F_{z_1}^a\end{array}\right]=\left[\begin{array}{c}0\\ F_{y_1}+K_{F_y}{F}_{y_1}\\ F_{z_1}+K_{F_z}{F}_{z_1}\end{array}\right],\left[\begin{array}{c}{M}_{x_1}^a\\ M_{y_1}^a\\ M_{z_1}^a\end{array}\right]=\left[\begin{array}{c}0\\ M_{y_1}+K_{M_y}{M}_{y_1}\\ M_{z_1}+K_{M_z}{M}_{z_1}\end{array}\right]---\left(4\right)$

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

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}={\mathrm{\&omega;}}_z+{\mathrm{\&omega;}}_{y}sin\mathrm{\&alpha;}tan\mathrm{\&beta;}-\frac{QS(C_y^{\mathrm{\&alpha;}}\mathrm{\&alpha;}+C_y^{{\mathrm{\&delta;}}_z}{\mathrm{\&delta;}}_z)cos\mathrm{\&alpha;}}{mV\cos \mathrm{\&beta;}}-\frac{(F_{y_1}+K_{F_y}{F}_{y_1})cos\mathrm{\&alpha;}}{mV\cos \mathrm{\&beta;}}-\frac{G_{y}cos\mathrm{\&alpha;}}{mVcos\mathrm{\&beta;}}\\ \stackrel{\&CenterDot;}{\mathrm{\&beta;}}={\mathrm{\&omega;}}_{y}cos\mathrm{\&alpha;}+\frac{QS(C_z^{\mathrm{\&beta;}}\mathrm{\&beta;}+C_z^{{\mathrm{\&delta;}}_y}{\mathrm{\&delta;}}_y)cos\mathrm{\&beta;}}{mV}+\frac{QS(C_y^{\mathrm{\&alpha;}}\mathrm{\&alpha;}+C_y^{{\mathrm{\&delta;}}_z}{\mathrm{\&delta;}}_z)sin\mathrm{\&alpha;}sin\mathrm{\&beta;}}{mV}\\ +\frac{(F_{y_1}+K_{F_y}{F}_{y_1})\sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}}{mV}+\frac{(F_{z_1}+K_{F_z}{F}_{z_1})cos\mathrm{\&beta;}}{mV}+\frac{G_{z}cos\mathrm{\&beta;}}{mV}+\frac{G_{y}sin\mathrm{\&alpha;}sin\mathrm{\&beta;}}{mV}\end{array}\right.---\left(5\right)$

Dynamic equation of angular velocity of projectile

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_y=\frac{M_{y_1}}{J_y}+\frac{K_{M_y}{M}_{y_1}}{J_y}+\frac{{\mathrm{QSLm}}_y^{\mathrm{\&beta;}}\mathrm{\&beta;}}{J_y}+\frac{{\mathrm{QSLm}}_y^{{\mathrm{\&delta;}}_y}{\mathrm{\&delta;}}_y}{J_y}+\frac{{\mathrm{QSLm}}_y^{{\mathrm{\&omega;}}_y}{\mathrm{\&omega;}}_y}{J_y}\\ {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_z=\frac{M_{z_1}}{J_z}+\frac{K_{M_z}{M}_{z_1}}{J_z}+\frac{{\mathrm{QSLm}}_z^{\mathrm{\&alpha;}}\mathrm{\&alpha;}}{J_z}+\frac{{\mathrm{QSLm}}_z^{{\mathrm{\&delta;}}_z}{\mathrm{\&delta;}}_z}{J_z}+\frac{{\mathrm{QSLm}}_z^{{\mathrm{\&omega;}}_z}{\mathrm{\&omega;}}_z}{J_z}\end{array}\right.---\left(6\right)$

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, z}deflection 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

$\left[\begin{array}{c}{F}_{x_1}^{i,j}\\ F_{y_1}^{i,j}\\ F_{z_1}^{i,j}\end{array}\right]=\left[\begin{array}{c}0\\ F_m\cos \left(\frac{2j-i^{*}}{18}\mathrm{\&pi;}\right)\\ -F_m\sin \left(\frac{2j-i^{*}}{18}\mathrm{\&pi;}\right)\end{array}\right]---\left(7\right)$

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

$\left[\begin{array}{c}{M}_{x_1}^{i,j}\\ M_{y_1}^{i,j}\\ M_{z_1}^{i,j}\end{array}\right]=\left[\begin{array}{c}0\\ F_m{l}_{i}sin\left(\frac{2j-i^{*}}{18}\mathrm{\&pi;}\right)\\ F_m{l}_i\cos \left(\frac{2j-i^{*}}{18}\mathrm{\&pi;}\right)\end{array}\right]---\left(8\right)$

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

$\left[\begin{array}{c}{F}_{x_1}\\ F_{y_1}\\ F_{z_1}\end{array}\right]=\left[\begin{array}{c}0\\ \underset{j=j_{1,1}}{\overset{j=j_{1,n1}}{\mathrm{\&Sigma;}}}{F}_{y_1}^{1,j}+\underset{j=j_{2,1}}{\overset{j=j_{2,n2}}{\mathrm{\&Sigma;}}}{F}_{y_1}^{2,j}+...+\underset{j=j_{10,1}}{\overset{j=j_{10,n10}}{\mathrm{\&Sigma;}}}{F}_{y_1}^{10,j}\\ \underset{j=j_{1,1}}{\overset{j=j_{1,n1}}{\mathrm{\&Sigma;}}}{F}_{z_1}^{1,j}+\underset{j=j_{2,1}}{\overset{j=j_{2,n2}}{\mathrm{\&Sigma;}}}{F}_{z_1}^{2,j}+...+\underset{j=j_{10,1}}{\overset{j=j_{10,n10}}{\mathrm{\&Sigma;}}}{F}_{z_1}^{10,j}\end{array}\right]---\left(9\right)$

$\left[\begin{array}{c}{M}_{x_1}\\ M_{y_1}\\ M_{z_1}\end{array}\right]=\left[\begin{array}{c}0\\ -\left(\underset{j=j_{1,1}}{\overset{j=j_{1,n1}}{\mathrm{\&Sigma;}}}{F}_{z_1}^{1,j}{l}_1+\underset{j=j_{2,1}}{\overset{j=j_{2,n2}}{\mathrm{\&Sigma;}}}{F}_{z_1}^{2,j}{l}_2+...+\underset{j=j_{10,1}}{\overset{j=j_{10,n10}}{\mathrm{\&Sigma;}}}{F}_{z_1}^{10,j}{l}_{10}\right)\\ \underset{j=j_{1,1}}{\overset{j=j_{1,n1}}{\mathrm{\&Sigma;}}}{F}_{y_1}^{1,j}{l}_1+\underset{j=j_{2,1}}{\overset{j=j_{2,n2}}{\mathrm{\&Sigma;}}}{F}_{y_1}^{2,j}{l}_2+...+\underset{j=j_{10,1}}{\overset{j=j_{10,n10}}{\mathrm{\&Sigma;}}}{F}_{y_1}^{10,j}{l}_{10}\end{array}\right]---\left(10\right)$

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

$F_o={\left[\begin{array}{ccccc}{F}_m& F_{m}cos\frac{\mathrm{\&pi;}}{9}& F_{m}cos\frac{2\mathrm{\&pi;}}{9}& F_{m}cos\frac{2\mathrm{\&pi;}}{9}& F_{m}cos\frac{\mathrm{\&pi;}}{9}\end{array}\right]}^T---\left(11\right)$

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

$F_e={\left[\begin{array}{cccc}{F}_{m}cos\frac{\mathrm{\&pi;}}{18}& F_{m}cos\frac{\mathrm{\&pi;}}{6}& F_{m}cos\frac{\mathrm{\&pi;}}{6}& F_{m}cos\frac{\mathrm{\&pi;}}{18}\end{array}\right]}^T---\left(12\right)$

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

$F_{y_1}\&Element;\{F_m,2F_{m}cos\frac{\mathrm{\&pi;}}{9},2F_{m}cos\frac{2\mathrm{\&pi;}}{9},2F_m,4F_{m}cos\frac{\mathrm{\&pi;}}{9},4F_{m}cos\frac{2\mathrm{\&pi;}}{9}\}$

$\begin{array}{c}{M}_{z_1}\&Element;\left\{F^1{l}_1+F^9{l}_9,F^3{l}_3+F^7{l}_7,F^5{l}_5\right\}\\ =\left\{F^1\left(l_5+4\mathrm{\&Delta;}l\right)+F^1\left(l_5-4\mathrm{\&Delta;}l\right),F^3\left(l_5+2\mathrm{\&Delta;}l\right)+F^3\left(l_5-2\mathrm{\&Delta;}l\right),F^5{l}_5\right\}\\ =\left\{F^5{l}_5,2F^1{l}_5,2F^3{l}_5\right\}=F_{y_1}{l}_5\\ =\left\{F_m{l}_5,2F_m\cos \frac{\mathrm{\&pi;}}{9}{l}_5,2F_m\cos \frac{2\mathrm{\&pi;}}{9}{l}_5,2F_m{l}_5,4F_m\cos \frac{\mathrm{\&pi;}}{9}{l}_5,4F_m\cos \frac{2\mathrm{\&pi;}}{9}{l}_5\right\}\end{array}---\left(14\right)$

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

$F_{y_1}\&Element;\{2F_{m}cos\frac{\mathrm{\&pi;}}{18},2F_{m}cos\frac{\mathrm{\&pi;}}{6},4F_{m}cos\frac{\mathrm{\&pi;}}{18},4F_{m}cos\frac{\mathrm{\&pi;}}{6}\}$

$\begin{array}{c}{M}_{z_1}\&Element;\left\{F^2{l}_2+F^{10}{l}_{10},F^4{l}_4+F^8{l}_8,F^6{l}_6\right\}\\ =\left\{F^2\left(l_6+4\mathrm{\&Delta;}l\right)+F^2\left(l_6-4\mathrm{\&Delta;}l\right),F^4\left(l_6+2\mathrm{\&Delta;}l\right)+F^4\left(l_6-2\mathrm{\&Delta;}l\right),F^6{l}_6\right\}\\ =\left\{F^6{l}_6,2F^2{l}_6,2F^4{l}_6\right\}=F_{y_1}{l}_6\\ =\left\{2F_m\cos \frac{\mathrm{\&pi;}}{18}{l}_6,2F_m\cos \frac{\mathrm{\&pi;}}{6}{l}_6,4F_m\cos \frac{\mathrm{\&pi;}}{18}{l}_6,4F_m\cos \frac{\mathrm{\&pi;}}{6}{l}_6\right\}\end{array}---\left(15\right)$

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

$U_F^{y+}=\{F_m,2F_{m}cos\frac{\mathrm{\&pi;}}{9},2F_{m}cos\frac{\mathrm{\&pi;}}{18},2F_m,4F_{m}cos\frac{\mathrm{\&pi;}}{9},4F_{m}cos\frac{\mathrm{\&pi;}}{18}\}---\left(16\right)$

Different values of resultant moment form set

$U_M^{y+}=\{F_{m}l,2F_{m}cos\frac{\mathrm{\&pi;}}{9}l,2F_{m}cos\frac{\mathrm{\&pi;}}{18}l,2F_{m}l,4F_{m}cos\frac{\mathrm{\&pi;}}{9}l,4F_{m}cos\frac{\mathrm{\&pi;}}{18}l\}---\left(17\right)$

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

$U_F^{y-}=\{-F_m,-2F_{m}cos\frac{\mathrm{\&pi;}}{9},-2F_{m}cos\frac{\mathrm{\&pi;}}{18},-2F_m,-4F_{m}cos\frac{\mathrm{\&pi;}}{9},-4F_{m}cos\frac{\mathrm{\&pi;}}{18}\}---\left(18\right)$

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)

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}={\mathrm{\&omega;}}_z-\frac{QS\left(C_y^{\mathrm{\&alpha;}}\mathrm{\&alpha;}+C_y^{{\mathrm{\&delta;}}_z}{\mathrm{\&delta;}}_z\right)\cos \mathrm{\&alpha;}}{mV}-\frac{\left(1+K_{F_y}\right)F_{y_1}\cos \mathrm{\&alpha;}}{mV}\\ {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_z=\frac{\left(1+K_{M_z}\right)F_{y_1}l}{J_z}+\frac{{\mathrm{QSLm}}_z^{\mathrm{\&alpha;}}\mathrm{\&alpha;}}{J_z}+\frac{{\mathrm{QSLm}}_z^{{\mathrm{\&delta;}}_z}{\mathrm{\&delta;}}_z}{J_z}+\frac{{\mathrm{QSLm}}_z^{{\mathrm{\&omega;}}_z}{\mathrm{\&omega;}}_z}{J_z}\end{array}\right.---\left(19\right)$

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

$\begin{array}{c}\stackrel{\&CenterDot;}{x}\left(t\right)=f\left(x\right)+g\left(x\right)u\left(t\right)\\ y\left(t\right)=\left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\end{array}---\left(20\right)$

Wherein,

$f\left(x\right)=\left[\begin{array}{c}{\mathrm{\&omega;}}_z-\frac{{\mathrm{QSC}}_y^{\mathrm{\&alpha;}}\mathrm{\&alpha;}\cos \mathrm{\&alpha;}}{mV}\\ \frac{QSL\left(m_z^{\mathrm{\&alpha;}}\mathrm{\&alpha;}+m_z^{{\mathrm{\&omega;}}_z}{\mathrm{\&omega;}}_z\right)}{J_z}\end{array}\right],g\left(x\right)=\left[\begin{array}{cc}-\frac{{\mathrm{QSC}}_y^{{\mathrm{\&delta;}}_z}\cos \mathrm{\&alpha;}}{mV}& -\frac{\left(1+K_{F_y}\right)\cos \mathrm{\&alpha;}}{mV}\\ \frac{{\mathrm{QSLm}}_z^{{\mathrm{\&delta;}}_z}}{J_z}& \frac{\left(1+K_{M_z}\right)l}{J_z}\end{array}\right]$

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:

$\stackrel{\&CenterDot;}{x}\left(t\right)=\left\{\begin{array}{cc}{a}_{1}x\left(t\right)+b_{1}u\left(t\right)+e_1,& \left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\&le;-0.37\\ a_{2}x\left(t\right)+b_{2}u\left(t\right)+e_2,& -0.37<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\&le;-0.153\\ a_{3}x\left(t\right)+b_{3}u\left(t\right)+e_3,& -0.153<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\&le;0\\ a_{4}x\left(t\right)+b_{4}u\left(t\right)+e_4,& 0<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\&le;0.153\\ a_{5}x\left(t\right)+b_{5}u\left(t\right)+e_5,& 0.153<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)\&le;0.37\\ a_{6}x\left(t\right)+b_{6}u\left(t\right)+e_6,& \left[\begin{array}{cc}1& 0\end{array}\right]x\left(t\right)>0.37\end{array}\right.---\left(21\right)$

y(t)＝cx(t)

wherein,

$a_i=\frac{\&part;f\left(x\right)}{\&part;x}{|}_{x=x_{i0}}=\left[\begin{array}{cc}{a}_i^{11}& a_i^{12}\\ a_i^{21}& a_i^{22}\end{array}\right],b_i=g\left(x_{i0}\right)=\left[\begin{array}{cc}{b}_i^{11}& b_i^{12}\\ b_i^{21}& b_i^{22}\end{array}\right],e_i=\left[\begin{array}{c}{e}_i^1\\ e_i^2\end{array}\right]$

$a_i^{11}=\frac{\&part;f_1}{\&part;\mathrm{\&alpha;}}{|}_{x=x_{i0}}=-\frac{QS}{mV}\left(\frac{\&part;C_y^{\mathrm{\&alpha;}}}{\&part;\mathrm{\&alpha;}}{|}_{\mathrm{\&alpha;}={\mathrm{\&alpha;}}_{i0}}{\mathrm{\&alpha;}}_{i0}cos\right({\mathrm{\&alpha;}}_{i0})+C_y^{\mathrm{\&alpha;}}({\mathrm{\&alpha;}}_{i0}\left)cos\right({\mathrm{\&alpha;}}_{i0})-C_y^{\mathrm{\&alpha;}}({\mathrm{\&alpha;}}_{i0}\left){\mathrm{\&alpha;}}_{i0}sin\right({\mathrm{\&alpha;}}_{i0}\left)\right)$

$a_i^{12}=\frac{\&part;f_1}{\&part;{\mathrm{\&omega;}}_z}{|}_{x=x_{i0}}=1$

$a_i^{21}=\frac{\&part;f_2}{\&part;\mathrm{\&alpha;}}{|}_{x=x_{i0}}=\frac{QSL}{J_z}(\frac{\&part;m_z^{\mathrm{\&alpha;}}}{\&part;\mathrm{\&alpha;}}{|}_{\mathrm{\&alpha;}={\mathrm{\&alpha;}}_{i0}}{\mathrm{\&alpha;}}_{i0}+m_z^{\mathrm{\&alpha;}}({\mathrm{\&alpha;}}_{i0})+\frac{\&part;m_z^{{\mathrm{\&omega;}}_z}}{\&part;\mathrm{\&alpha;}}{|}_{\mathrm{\&alpha;}={\mathrm{\&alpha;}}_{i0}}{\mathrm{\&omega;}}_{zi0})$

$a_i^{22}=\frac{\&part;f_2}{\&part;{\mathrm{\&omega;}}_z}{|}_{x=x_{i0}}=\frac{QSL}{J_z}{m}_z^{{\mathrm{\&omega;}}_z}\left({\mathrm{\&alpha;}}_{i0}\right)$

$b_i^{11}=-\frac{QS}{mV}{C}_y^{{\mathrm{\&delta;}}_z}\left({\mathrm{\&alpha;}}_{i0}\right)cos\left({\mathrm{\&alpha;}}_{i0}\right)$

$b_i^{12}=-\frac{(1+K_{F_y}({\mathrm{\&alpha;}}_{i0}\left)\right)cos\left({\mathrm{\&alpha;}}_{i0}\right)}{mV}$

$b_i^{21}=\frac{QSL}{J_z}{m}_z^{{\mathrm{\&delta;}}_z}\left({\mathrm{\&alpha;}}_{i0}\right)$

$b_i^{22}=\frac{(1+K_{M_z}({\mathrm{\&alpha;}}_{i0}\left)\right)l}{J_z}$

$e_i^1=a_i^{11}{\mathrm{\&alpha;}}_{i0}+a_i^{12}{\mathrm{\&omega;}}_{zi0}$

$e_i^2=a_i^{21}{\mathrm{\&alpha;}}_{i0}+a_i^{22}{\mathrm{\&omega;}}_{zi0}$

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

$x\left(k+1\right)=\left\{\begin{array}{cc}{\tilde{a}}_{1}x\left(k\right)+{\tilde{b}}_{1}u\left(k\right)+{\tilde{e}}_1,& \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;-0.37\\ {\tilde{a}}_{2}x\left(k\right)+{\tilde{b}}_{2}u\left(k\right)+{\tilde{e}}_2,& -0.37<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;-0.153\\ {\tilde{a}}_{3}x\left(k\right)+{\tilde{b}}_{3}u\left(k\right)+{\tilde{e}}_3,& -0.153<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;0\\ {\tilde{a}}_{4}x\left(k\right)+{\tilde{b}}_{4}u\left(k\right)+{\tilde{e}}_4,& 0<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;0.153\\ {\tilde{a}}_{5}x\left(k\right)+{\tilde{b}}_{5}u\left(k\right)+{\tilde{e}}_5,& 0.153<\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;0.37\\ {\tilde{a}}_{6}x\left(k\right)+{\tilde{b}}_{6}u\left(k\right)+{\tilde{e}}_6,& \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)>0.37\end{array}\right.---\left(22\right)$

$y\left(k\right)=\tilde{c}x\left(k\right)$

Wherein,

${\tilde{a}}_1=\left[\begin{array}{cc}1.04& 0.025\\ 0.22& 0.995\end{array}\right],{\tilde{b}}_1=\left[\begin{array}{cc}-0.02845& 1.59\&times;{10}^{-6}\\ -2.116& 1.42\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_1=\left[\begin{array}{c}-0.0183\\ -0.1123\end{array}\right]$

${\tilde{a}}_2=\left[\begin{array}{cc}1.051& 0.0255\\ 0.218& 0.995\end{array}\right],{\tilde{b}}_2=\left[\begin{array}{cc}-0.030& 2.18\&times;{10}^{-6}\\ -2.224& 1.87\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_2=\left[\begin{array}{c}-0.0175\\ -0.0792\end{array}\right]$

${\tilde{a}}_3=\left[\begin{array}{cc}1.023& 0.0252\\ 0.248& 0.9951\end{array}\right],{\tilde{b}}_3=\left[\begin{array}{cc}-0.030& 2.68\&times;{10}^{-6}\\ -2.228& 2.23\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_3=\left[\begin{array}{c}-0.0031\\ -0.0376\end{array}\right]$

${\tilde{a}}_4=\left[\begin{array}{cc}0.9945& 0.0248\\ 0.2732& 0.9954\end{array}\right],{\tilde{b}}_4=\left[\begin{array}{cc}-0.032& 2.77\&times;{10}^{-6}\\ -2.371& 2.32\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_4=\left[\begin{array}{c}0\\ 0\end{array}\right]$

${\tilde{a}}_5=\left[\begin{array}{cc}0.9697& 0.0245\\ 0.2913& 0.9956\end{array}\right],{\tilde{b}}_5=\left[\begin{array}{cc}-0.030& 2.27\&times;{10}^{-6}\\ -2.228& 1.98\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_5=\left[\begin{array}{c}-0.0053\\ 0.0454\end{array}\right]$

${\tilde{a}}_6=\left[\begin{array}{cc}0.9594& 0.0244\\ 0.3137& 0.9959\end{array}\right],{\tilde{b}}_6=\left[\begin{array}{cc}-0.029& 1.91\&times;{10}^{-6}\\ -2.224& 1.73\&times;{10}^{-4}\end{array}\right],{\tilde{e}}_6=\left[\begin{array}{c}-0.0169\\ 0.1193\end{array}\right]$

$\tilde{c}=\left[\begin{array}{cc}1& 0\end{array}\right]$

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

$\begin{array}{c}\left\{\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.37\&le;0\right\}\&DoubleLeftRightArrow;\left\{{\mathrm{\&delta;}}_1\left(k\right)=1\right\}\\ \left\{\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.153\&le;0\right\}\&DoubleLeftRightArrow;\left\{{\mathrm{\&delta;}}_2\left(k\right)=1\right\}\\ \left\{\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;0\right\}\&DoubleLeftRightArrow;\left\{{\mathrm{\&delta;}}_3\left(k\right)=1\right\}\\ \left\{\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.153\&le;0\right\}\&DoubleLeftRightArrow;\left\{{\mathrm{\&delta;}}_4\left(k\right)=1\right\}\\ \left\{\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.37\&le;0\right\}\&DoubleLeftRightArrow;\left\{{\mathrm{\&delta;}}_5\left(k\right)=1\right\}\end{array}---\left(23\right)$

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

$\left\{\begin{array}{c}\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.37\&GreaterEqual;\mathrm{\&epsiv;}+\left(m_1-\mathrm{\&epsiv;}\right){\mathrm{\&delta;}}_1\left(k\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.37\&le;M_1\left(1-{\mathrm{\&delta;}}_1\left(k\right)\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.153\&GreaterEqual;\mathrm{\&epsiv;}+\left(m_2-\mathrm{\&epsiv;}\right){\mathrm{\&delta;}}_2\left(k\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)+0.153\&le;M_2\left(1-{\mathrm{\&delta;}}_2\left(k\right)\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&GreaterEqual;\mathrm{\&epsiv;}+\left(m_3-\mathrm{\&epsiv;}\right){\mathrm{\&delta;}}_3\left(k\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\&le;M_3\left(1-{\mathrm{\&delta;}}_3\left(k\right)\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.153\&GreaterEqual;\mathrm{\&epsiv;}+\left(m_4-\mathrm{\&epsiv;}\right){\mathrm{\&delta;}}_4\left(k\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.153\&le;M_4\left(1-{\mathrm{\&delta;}}_4\left(k\right)\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.37\&GreaterEqual;\mathrm{\&epsiv;}+\left(m_5-\mathrm{\&epsiv;}\right){\mathrm{\&delta;}}_5\left(k\right)\\ \left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)-0.37\&le;M_5\left(1-{\mathrm{\&delta;}}_5\left(k\right)\right)\end{array}\right.---\left(24\right)$

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

$\left\{\begin{array}{c}{\mathrm{\&delta;}}_6=\left(1-{\mathrm{\&delta;}}_1\right){\mathrm{\&delta;}}_2\\ {\mathrm{\&delta;}}_7=\left(1-{\mathrm{\&delta;}}_2\right){\mathrm{\&delta;}}_3\\ {\mathrm{\&delta;}}_8=\left(1-{\mathrm{\&delta;}}_3\right){\mathrm{\&delta;}}_4\\ {\mathrm{\&delta;}}_9=\left(1-{\mathrm{\&delta;}}_4\right){\mathrm{\&delta;}}_5\end{array}\right.---\left(25\right)$

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:

$\left\{\begin{array}{c}-{\mathrm{\&delta;}}_1+{\mathrm{\&delta;}}_2-{\mathrm{\&delta;}}_6\&le;0\\ {\mathrm{\&delta;}}_1+{\mathrm{\&delta;}}_6\&le;1\\ -{\mathrm{\&delta;}}_2+{\mathrm{\&delta;}}_6\&le;0\\ -{\mathrm{\&delta;}}_2+{\mathrm{\&delta;}}_3-{\mathrm{\&delta;}}_7\&le;0\\ {\mathrm{\&delta;}}_2+{\mathrm{\&delta;}}_7\&le;1\\ -{\mathrm{\&delta;}}_3+{\mathrm{\&delta;}}_7\&le;0\\ -{\mathrm{\&delta;}}_3+{\mathrm{\&delta;}}_4-{\mathrm{\&delta;}}_8\&le;0\\ {\mathrm{\&delta;}}_3+{\mathrm{\&delta;}}_8\&le;1\\ -{\mathrm{\&delta;}}_4+{\mathrm{\&delta;}}_8\&le;0\\ -{\mathrm{\&delta;}}_4+{\mathrm{\&delta;}}_5-{\mathrm{\&delta;}}_9\&le;0\\ {\mathrm{\&delta;}}_4+{\mathrm{\&delta;}}_9\&le;1\\ -{\mathrm{\&delta;}}_5+{\mathrm{\&delta;}}_9\&le;0\end{array}\right.---\left(26\right)$

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

$\left\{\begin{array}{c}{z}_1\left(k\right)=\&lsqb;{\tilde{a}}_1\left(k\right)x\left(k\right)+{\tilde{b}}_1\left(k\right)u\left(k\right)+{\tilde{e}}_1\&rsqb;{\mathrm{\&delta;}}_1\left(k\right)\\ z_2\left(k\right)=\&lsqb;{\tilde{a}}_2\left(k\right)x\left(k\right)+{\tilde{b}}_2\left(k\right)u\left(k\right)+{\tilde{e}}_2\&rsqb;{\mathrm{\&delta;}}_6\left(k\right)\\ z_3\left(k\right)=\&lsqb;{\tilde{a}}_3\left(k\right)x\left(k\right)+{\tilde{b}}_3\left(k\right)u\left(k\right)+{\tilde{e}}_3\&rsqb;{\mathrm{\&delta;}}_7\left(k\right)\\ z_4\left(k\right)=\&lsqb;{\tilde{a}}_4\left(k\right)x\left(k\right)+{\tilde{b}}_4\left(k\right)u\left(k\right)+{\tilde{e}}_4\&rsqb;{\mathrm{\&delta;}}_8\left(k\right)\\ z_5\left(k\right)=\&lsqb;{\tilde{a}}_5\left(k\right)x\left(k\right)+{\tilde{b}}_5\left(k\right)u\left(k\right)+{\tilde{e}}_5\&rsqb;{\mathrm{\&delta;}}_9\left(k\right)\\ z_6\left(k\right)=\&lsqb;{\tilde{a}}_6\left(k\right)x\left(k\right)+{\tilde{b}}_6\left(k\right)u\left(k\right)+{\tilde{e}}_6\&rsqb;(1-{\mathrm{\&delta;}}_5(k\left)\right)\end{array}\right.---\left(27\right)$

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

$\left\{\begin{array}{c}{z}_1\left(k\right)\&GreaterEqual;\&lsqb;{\tilde{a}}_1\left(k\right)x\left(k\right)+{\tilde{b}}_1\left(k\right)u\left(k\right)+{\tilde{e}}_1\&rsqb;-M_{f1}\left(1-{\mathrm{\&delta;}}_1\left(k\right)\right)\\ z_1\left(k\right)\&le;\&lsqb;{\tilde{a}}_1\left(k\right)x\left(k\right)+{\tilde{b}}_1\left(k\right)u\left(k\right)+{\tilde{e}}_1\&rsqb;-m_{f1}\left(1-{\mathrm{\&delta;}}_1\left(k\right)\right)\\ z_1\left(k\right)\&GreaterEqual;m_{f1}{\mathrm{\&delta;}}_1\left(k\right)\\ z_1\left(k\right)\&le;M_{f1}{\mathrm{\&delta;}}_1\left(k\right)\\ z_2\left(k\right)\&GreaterEqual;\&lsqb;{\tilde{a}}_2\left(k\right)x\left(k\right)+{\tilde{b}}_2\left(k\right)u\left(k\right)+{\tilde{e}}_2\&rsqb;-M_{f2}\left(1-{\mathrm{\&delta;}}_6\left(k\right)\right)\\ z_2\left(k\right)\&le;\&lsqb;{\tilde{a}}_2\left(k\right)x\left(k\right)+{\tilde{b}}_2\left(k\right)u\left(k\right)+{\tilde{e}}_2\&rsqb;-m_{f2}\left(1-{\mathrm{\&delta;}}_6\left(k\right)\right)\\ z_2\left(k\right)\&GreaterEqual;m_{f2}{\mathrm{\&delta;}}_1\left(k\right)\\ z_2\left(k\right)\&le;M_{f2}{\mathrm{\&delta;}}_1\left(k\right)\\ z_3\left(k\right)\&GreaterEqual;\&lsqb;{\tilde{a}}_3\left(k\right)x\left(k\right)+{\tilde{b}}_3\left(k\right)u\left(k\right)+{\tilde{e}}_3\&rsqb;-M_{f3}\left(1-{\mathrm{\&delta;}}_7\left(k\right)\right)\\ z_3\left(k\right)\&le;\&lsqb;{\tilde{a}}_3\left(k\right)x\left(k\right)+{\tilde{b}}_3\left(k\right)u\left(k\right)+{\tilde{e}}_3\&rsqb;-m_{f3}\left(1-{\mathrm{\&delta;}}_7\left(k\right)\right)\\ z_3\left(k\right)\&GreaterEqual;m_{f3}{\mathrm{\&delta;}}_7\left(k\right)\\ z_3\left(k\right)\&le;M_{f3}{\mathrm{\&delta;}}_7\left(k\right)\\ z_4\left(k\right)\&GreaterEqual;\&lsqb;{\tilde{a}}_4\left(k\right)x\left(k\right)+{\tilde{b}}_4\left(k\right)u\left(k\right)+{\tilde{e}}_4\&rsqb;-M_{f4}\left(1-{\mathrm{\&delta;}}_8\left(k\right)\right)\\ z_4\left(k\right)\&le;\&lsqb;{\tilde{a}}_1\left(k\right)x\left(k\right)+{\tilde{b}}_4\left(k\right)u\left(k\right)+{\tilde{e}}_4\&rsqb;-m_{f4}\left(1-{\mathrm{\&delta;}}_8\left(k\right)\right)\\ z_4\left(k\right)\&GreaterEqual;m_{f4}{\mathrm{\&delta;}}_8\left(k\right)\\ z_4\left(k\right)\&le;M_{f4}{\mathrm{\&delta;}}_8\left(k\right)\\ z_5\left(k\right)\&GreaterEqual;\&lsqb;{\tilde{a}}_5\left(k\right)x\left(k\right)+{\tilde{b}}_5\left(k\right)u\left(k\right)+{\tilde{e}}_5\&rsqb;-M_{f5}\left(1-{\mathrm{\&delta;}}_9\left(k\right)\right)\\ z_5\left(k\right)\&le;\&lsqb;{\tilde{a}}_5\left(k\right)x\left(k\right)+{\tilde{b}}_5\left(k\right)u\left(k\right)+{\tilde{e}}_5\&rsqb;-m_{f5}\left(1-{\mathrm{\&delta;}}_9\left(k\right)\right)\\ z_5\left(k\right)\&GreaterEqual;m_{f5}{\mathrm{\&delta;}}_9\left(k\right)\\ z_5\left(k\right)\&le;M_{f5}{\mathrm{\&delta;}}_9\left(k\right)\\ z_6\left(k\right)\&GreaterEqual;\&lsqb;{\tilde{a}}_6\left(k\right)x\left(k\right)+{\tilde{b}}_6\left(k\right)u\left(k\right)+{\tilde{e}}_6\&rsqb;-M_{f6}{\mathrm{\&delta;}}_5\left(k\right)\\ z_6\left(k\right)\&le;\&lsqb;{\tilde{a}}_6\left(k\right)x\left(k\right)+{\tilde{b}}_6\left(k\right)u\left(k\right)+{\tilde{e}}_6\&rsqb;-m_{f6}{\mathrm{\&delta;}}_5\left(k\right)\\ z_6\left(k\right)\&GreaterEqual;m_{f6}\left(1-{\mathrm{\&delta;}}_5\left(k\right)\right)\\ z_6\left(k\right)\&le;M_{f6}\left(1-{\mathrm{\&delta;}}_5\left(k\right)\right)\end{array}\right.---\left(28\right)$

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

$U_F^y=\{\mathrm{2200,4135,4333,4400,8269,8666},-2200,-4135,-4333,-4400,-8269,-8666\}N$

The following logic variables were introducedTo describe the direct lateral force

$U_F^y=\left\{2200,4135,4333,4400,8269,8666,-2200,-4135,-4333,-4400,-8269,-8666\right\}N$

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

$u={\left[\begin{array}{cc}{u}_1& F_{y_b}\end{array}\right]}^T---\left(31\right)$

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

$\begin{array}{c}{x}_{\min }\&le;x\left(k\right)\&le;x_{\max }\\ u_{1\min }\&le;u_1\left(k\right)\&le;u_{1\max }\end{array}---\left(32\right)$

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

$\underset{i=1}{\overset{12}{\&Sigma;}}{\mathrm{\&delta;}}_{F_i}\&le;1---\left(33\right)$

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

$\left\{\begin{array}{c}x(k+1)=\underset{i=1}{\overset{6}{\mathrm{\&Sigma;}}}{z}_i\left(k\right)\\ y\left(k\right)=\left[\begin{array}{cc}1& 0\end{array}\right]x\left(k\right)\\ s.t.\left(24\right),\left(26\right),\left(28\right),\left(29\right),\left(33\right)\end{array}\right.---\left(34\right).$

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

$J^{*}=\underset{u\left(k\right),u(k+1),\mathrm{\&delta;}\left(k\right),\mathrm{\&delta;}(k+1|k),z\left(k\right),z(k+1|k)}{\min }\underset{i=1}{\overset{N}{\&Sigma;}}\left(\right|\left|y\right(k+i|k)-y_c(k+i\left)\right|{|}_{Q_y}^2+\left|\right|u\left(k+i\right)\left|{|}_R^2\right)$

$s.t.\left\{\begin{array}{c}\begin{array}{ccc}MLD& \mathrm{mod}el& \left(34\right)\end{array}\\ u_{1\min }\&le;u_1\left(k\right),u_1(k+1)\&le;u_{1max}\\ x_{min}\&le;x\left(k\right),x(k+1)\&le;x_{max}\end{array}\right.---\left(35\right)$

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.