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

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

Technical field

The present invention relates to appearance control formula direct lateral force gentle Power compound missile attitude control method, particularly relate to based on mixing pre- The compound guided missile attitude control method of observing and controlling, belongs to flying vehicles control field.

Background technology

Along with the enhancing of target maneuver ability, in order to realize the effective interception to target, it is desirable to guided missile has and transships sound faster Answer speed.Traditional pure aerodynamic force control guided missile, owing to being limited by overload response speed, cannot meet height motor-driven The requirement of target Accurate Interception.Using the gentle Power compound of direct lateral force to control technology is to improve guided missile overload response speed Effective way, but the design difficulty that the introducing of direct lateral force makes missile guidance control system increases, and is mainly reflected in as follows Two aspects: one is that direct lateral force and aerodynamic force produce complicated coupling so that missile dynamics model non-linear and not Definitiveness increases；Two is the discrete feature of direct lateral force so that control design case model has obvious hybrid characters.These are two years old Point brings new challenge to missile attitude control design, and tradition Methods of Attitude Control Design solves above-mentioned two the most simultaneously and asks Topic.At present the method about the design of direct lateral force gentle Power compound missile attitude control uses two-step method mostly, first, Utilize nonlinear control method design nonlinear attitude control rule, obtain control moment instruction；Then, certain performance is chosen Index, by Optimization Solution, obtains aerodynamic moment instruction and direct lateral force torque command, it is achieved aerodynamic force and directly laterally The instruction distribution of power.The method, due to very difficult consideration direct lateral force and the difference of aerodynamic force dynamic characteristic, controls less effective, Range of application is restricted.

Summary of the invention

It is an object of the invention to provide appearance control formula direct lateral force gentle Power compound missile attitude control method, existing to solve Methods of Attitude Control Design cannot solve simultaneously model nonlinear and control input hybrid characters problem.The present invention solves Above-mentioned technical problem adopts the technical scheme that:

Of the present invention based on the appearance control formula direct lateral force gentle Power compound missile attitude control side mixing PREDICTIVE CONTROL Method, realizes according to following steps:

Step one, set up the direct lateral force gentle Power compound complete Attitude control model of guided missile and direct lateral force model, and The expression formula of derivation pitch orientation direct lateral force, is converted into piecewise affine model by guided missile non-linear dynamic model；

Wherein, the direct lateral force gentle Power compound guided missile complete Attitude control model process set up is as follows:

Gravity suffered by guided missile and aerodynamic force are fastened expression at ballistic coordinate respectively, obtains the kinetics equation of guided missile center of mass motion 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 guided missile quality, and P is missile tail cruising thrust, and g is acceleration of gravity, X_a、Y_aAnd Z_aFor Three components that aerodynamic force suffered by guided missile is fastened in speed coordinate, are resistance, lift and side force respectively, and its positive direction is respectively Consistent with the positive direction of three axles of velocity coordinate system；V represents guided missile centroid velocity, and α, β are respectively the angle of attack and yaw angle, θ, ψ_vIt is respectively trajectory tilt angle and trajectory deflection angle, γ_vFor speed inclination angle；Suffered by guided missile, direct lateral force is at bullet Three components in road coordinate system；

Assuming that missile coordinate system overlaps with the body principal axis of inertia, i.e. J_xy=J_yz=J_zx=0, obtain the guided missile in missile coordinate system The kinetics equation of rotation around center of mass is 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_zIt is respectively the guided missile rotary inertia to three axles of missile coordinate system, ω_x, ω_y, ω_zIt is respectively body to sit Mark system is relative to component on three axles of missile coordinate system of the rotational angular velocity ω of earth axes, M_x、M_yAnd M_zRespectively For acting on the moment to barycenter of all external force on guided missile component on each axle of missile coordinate system；M_x、M_yAnd M_zIt is expressed as

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

M in formula_ex、M_eyAnd M_ezRespectively act on the aerodynamic moment of the guided missile component on each axle of missile coordinate system,Respectively act on the directly laterally moment of the guided missile component on each axle of missile coordinate system；

Considering lateral jet interference effect, the direct lateral force simultaneously lighting the generation of some attitude control impulse motors is made a concerted effort and is made a concerted effort Square is being expressed as that missile body coordinate is fastened

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

Wherein,For Jet enterference thrust amplification factor,For the Jet enterference moment amplification factor, F_y1, F_z1, M_y1, M_z1Make a concerted effort for nominal direct lateral force and the expression fastened at missile body coordinate of resultant moment；

The angle of attack, yaw angle and body angle speed dynamical equation is derived according to formula (1) to (4)；

The angle of attack and yaw angle dynamical equation

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

Body angle speed dynamical equation

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

Wherein, Q is dynamic pressure, and S is characterized area, and L is characterized length,For Aerodynamic parameter,For the normal g-load coefficient that the unit angle of attack is corresponding,For the normal g-load system that unit elevator drift angle is corresponding Number,For the lateral overload coefficient that unit yaw angle is corresponding,For the lateral overload coefficient that unit rudder is corresponding,For driftage static-stability derivative,For rudder control efficiency,For yaw damping moment coefficient,Quiet surely for pitching Determine derivative,For elevator control efficiency,For pitching moment due to pitching velocity coefficient, δ_y, δ_zIt is respectively rudder and elevator Deflection angle；Formula (5)-(6) are the Attitude control model of complex controll guided missile；

Step 2, introducing logical variable, construct the complete mixed logical dynamics of complex controll guided missile；

Step 3, the compound guided missile attitude control law of design, determine that pneumatic control rule and attitude control engine open rule.

The invention has the beneficial effects as follows:

Present invention advantage compared with existing compound guided missile attitude control method is:

(1) in the present invention, the design of pneumatic control rule and the determination of attitude control engine unlatching rule complete simultaneously, and, Describe piecewise affine model and direct lateral force by introducing logical variable, compound guided missile attitude control law design problem is turned Turn to the design problem of mked logical dynamic system, solve the model non-thread in the design of complex controll missile attitude control simultaneously Property and control input hybrid characters problem.

(2) the method scope of application that the present invention proposes is wider, when considering attitude control engine Expenditure Levels, it is only necessary to per a period of time Recalculate available electromotor quantity quarter, change the description relation between direct lateral force and logical variable.It addition, This method may not only be applied to the design of appearance control formula complex controll missile attitude control, missile guidance system non-linear for other types The control design case of system is equally applicable, has broad application prospects.

Accompanying drawing explanation

Fig. 1 is the flow chart of the present invention；

Fig. 2 is the definition of the main coordinate system used in the present invention, with the barycenter of guided missile for initial point O, wherein earth axes Oxyz, missile coordinate system Ox₁y₁z₁, ballistic coordinate system Ox₂y₂z₂, and velocity coordinate system Ox₃y₃z₃, α, β are respectively the angle of attack And yaw angle, θ, ψ_vIt is respectively trajectory tilt angle and trajectory deflection angle；

Fig. 3 is attitude control engine layout, and wherein figure a is odd number circle attitude control impulse motor layout, and figure b is even number circle appearance Control pulsed motor layout, 1,2 ... 18 represent attitude control impulse motor numbering in often circle；

Fig. 4 is attitude control engine hoop expanded view, and wherein i represents the numbering of circle, and numbering 8,9,10,11,12 represents Attitude control impulse motor numbering in often circle, the cross section of the line formation in the i-th circle attitude control impulse motor spout center of circle and bullet The distance of the body constitution heart is l_i, space between the adjacent coils is Δ l, l₁Represent the line shape in the 1st circle attitude control impulse motor spout center of circle The cross section become and the distance of body barycenter；

Fig. 5 is electromotor subregion schematic diagram, and wherein figure a is odd number circle attitude control impulse motor subregion schematic diagram, and figure b is even A few attitude control impulse motor subregion schematic diagrams；

Fig. 6 is aerodynamic parameter and angle of attack graph of a relation, and wherein figure a isWith the relation curve of α, figure b isWith α's Relation curve, figure c isWith the relation curve of α, figure d isWith the relation curve of α, figure e isPass with α Being curve, figure f isRelation curve with α；

Fig. 7 is angle of attack response curve, and wherein solid line represents the actual value of the angle of attack, and dotted line represents angle of attack command value；

Fig. 8 is angle of rudder reflection curve；

Fig. 9 is the directly laterally force curve that attitude control engine produces；

Figure 10 is the different partitioning scenario of state space attitude control law.

Detailed description of the invention

Detailed description of the invention one: combine Fig. 1, Fig. 2 and understand present embodiment, described in present embodiment based on mixing prediction The appearance control formula direct lateral force gentle Power compound missile attitude control method controlled, realizes according to following steps:

Step one, set up the direct lateral force gentle Power compound complete Attitude control model of guided missile and direct lateral force model, and push away Lead the expression formula of pitch orientation direct lateral force, by body Aerodynamic characteristics, being turned by guided missile non-linear dynamic model Turn to piecewise affine model；

Wherein, the direct lateral force gentle Power compound guided missile complete Attitude control model process set up 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 guided missile quality, and P is missile tail cruising thrust, and g is acceleration of gravity, X_a、Y_aAnd Z_aFor guided missile Three components that suffered aerodynamic force is fastened in speed coordinate, are resistance, lift and side force respectively, its positive direction respectively with speed The positive direction of degree three axles of coordinate system is consistent；V represents guided missile centroid velocity, and α, β are respectively the angle of attack and yaw angle, θ, ψ_v It is respectively trajectory tilt angle and trajectory deflection angle, γ_vFor speed inclination angle；Suffered by guided missile, direct lateral force is sat at trajectory Three components that mark is fastened；

Assuming that missile coordinate system overlaps with the body principal axis of inertia, i.e. J_xy=J_yz=J_zx=0, obtain the guided missile in missile coordinate system around matter The kinetics equation that the heart rotates is 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_zIt is respectively the guided missile rotary inertia to three axles of missile coordinate system, ω_x, ω_y, ω_zIt is respectively missile coordinate system The component on three axles of missile coordinate system of the rotational angular velocity ω of earth axes relatively, M_x、M_yAnd M_zIt is respectively effect On guided missile, all external force are to component on each axle of missile coordinate system of the moment of barycenter；M_x、M_yAnd M_zIt is expressed as

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

M in formula_ex、M_eyAnd M_ezRespectively act on the aerodynamic moment of the guided missile component on each axle of missile coordinate system,Respectively act on the directly laterally moment of the guided missile component on each axle of missile coordinate system；

During additionally, due to attitude control engine laterally sprays combustion gas stream, high speed jet and air interfere between flowing, and form side To lateral jet.Use Jet enterference thrust amplification factorWith the Jet enterference moment amplification factorDivide Not Biao Shi Jet enterference power and moment with without the net thrust of generation during lateral jet and the ratio of moment；Accordingly, it is considered to laterally spray Stream interference effect, light simultaneously some attitude control impulse motors produce direct lateral force make a concerted effort and resultant moment in missile coordinate system On be expressed as

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

Wherein,For Jet enterference thrust amplification factor,For the Jet enterference moment amplification factor, Make a concerted effort for nominal direct lateral force and the expression fastened at missile body coordinate of resultant moment；

Assume terminal guidance section guided missile mass conservation, for the needs of simplified model, aerodynamic data is carried out line to flight force and moment Propertyization describes；Because the purpose of endoatmosphere interception guided missile gesture stability is to set up the angle of attack and yaw angle, formed aerodynamic lift and Side force, so in order to describe the angle of attack, yaw angle and the Changing Pattern of body angle speed, according to formula (1) to (4) Derive the angle of attack, yaw angle and body angle speed dynamical equation；

The angle of attack and yaw angle dynamical equation

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

Body angle speed dynamical equation

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

Wherein, Q is dynamic pressure, and S is characterized area, and L is characterized length,For gas Dynamic parameter,For the normal g-load coefficient that the unit angle of attack is corresponding,For the normal g-load coefficient that unit elevator drift angle is corresponding,For the lateral overload coefficient that unit yaw angle is corresponding,For the lateral overload coefficient that unit rudder is corresponding,For Driftage static-stability derivative,For rudder control efficiency,For yaw damping moment coefficient,For pitching static-stability derivative,For elevator control efficiency,For pitching moment due to pitching velocity coefficient, δ_y, δ_zIt is respectively rudder and the deflection angle of elevator； Formula (5)-(6) are the Attitude control model of complex controll guided missile；

Step 2, introducing logical variable, based on piecewise affine model and the equivalence of mixed logical dynamics, the compound control of structure The complete mixed logical dynamics of guided missile processed；

Step 3, based on hybrid model predictive control theory, the compound guided missile attitude control law of design, determine pneumatic control rule and appearance Rule opened by control electromotor.

Detailed description of the invention two: present embodiment is unlike detailed description of the invention one: described in establishment step one directly laterally The detailed process of power model is:

Direct lateral force is produced by the attitude control impulse motor group being fixedly installed in body barycenter front, has 180 appearance control pulses Electromotor dislocation arrangement, is divided into 10 circles along the body longitudinal axis, and often 18 attitude control impulse motors of circle arrange around body；Same In circle, adjacent attitude control impulse motor interval central angle is 20 °, makes i represent the numbering of circle, i=1,2 ..., 10, j represent appearance control Pulsed motor numbering in often circle, j=1,2 ..., 18；What the line in the i-th circle attitude control impulse motor spout center of circle was formed cuts Face is l with the distance of body barycenter_i, space between the adjacent coils is Δ l；Attitude control impulse motor group such as Fig. 3 of the layout on body Shown in Fig. 4.

Assume that the stable state thrust that attitude control impulse motor produces when without freely flowing is F_m, (i, appearance control pulse j) is sent out for numbered Nominal direct lateral force being expressed as in missile coordinate system that motivation produces

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

Correspondingly, directly laterally moment being expressed as that missile body coordinate is fastened

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

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

Light the table that nominal direct lateral force is made a concerted effort and resultant moment is fastened that some attitude control impulse motors produce at missile body coordinate simultaneously It is shown 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_1,1, j_1,2..., j_{1, n1}Represent the 1st punctuate combustion attitude control impulse motor circle in numbering, n1 represents that the 1st punctuates combustion Attitude control impulse motor quantity, the rest may be inferred；Formula (9)-(10) are the direct lateral force model of complex controll guided missile.

Detailed description of the invention three: present embodiment is unlike detailed description of the invention one or two: the derivation described in step one is bowed The detailed process of the expression formula facing upward direction direct lateral force is:

Often 18 attitude control impulse motors of circle are divided into four IGNITION CONTROL districts: positive and negative pitch control district and positive and negative driftage control zone, As shown in Figure 5.

Due to each attitude control engine fix in missile-borne installation site, the working cycle is fixed, limited amount, not reproducible make With, therefore need to follow a set of specific principle when selecting electromotor to open number, position and ignition order.The present invention does Hypothesis below, for each control zone, often circle at most permission 2 is lighted a fire simultaneously, at most allows two circles to light a fire simultaneously, And only allow the attitude control impulse motor in odd number circle to light a fire simultaneously or the attitude control impulse motor of even number circle is lighted a fire simultaneously； In each IGNITION CONTROL district, during attitude control impulse motor igniting, it is necessary to ensure that symmetrical igniting.

Be given as a example by positive pitch control district below attitude control impulse motor produce direct lateral force make a concerted effort and resultant moment set；

In odd number circle numbered (i, 1), (i, 2), (i, 3), (i, 17), the direct lateral force that the attitude control impulse motor of (i, 18) produces is at oy₁On axle Subscale be shown as vector

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

In even number circle numbered (i, 1), (i, 2), (i, 17), the direct lateral force that the attitude control impulse motor of (i, 18) produces is at oy₁Dividing on axle Scale is shown as vector

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

If the direct lateral force that the i-th circle attitude control impulse motor produces is Fⁱ, it is desirable to

F¹=F⁹, F³=F⁷, F²=F¹⁰, F⁴=F⁸ (13)

Then when odd number circle pulsed motor is lighted a fire, have

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

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

Equally, when even number circle pulsed motor is lighted a fire, have

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

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

Owing to Δ l is the least, it is therefore assumed that l₅≈l₆=l, additionally considers that the ignition effectiveness of electromotor is avoided consuming excessively, does not allow efficiency Low engine ignition, the different value structures made a concerted effort of the direct lateral force that all attitude control engines in Ze Zheng pitch control district produce Become set

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

The different values of resultant moment constitute 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 electromotor configuration, making a concerted effort not of the direct lateral force that all attitude control engines in negative pitch control district produce Set is constituted with value

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

Each control cycle, attitude control system according to certain control law fromIt is defeated for controlling that middle selection one controls masterpiece Enter.

By said method, equally obtain, the direct lateral force that all attitude control engines in positive and negative driftage control zone produce The set that the different values made a concerted effort are constituted.

Detailed description of the invention four: present embodiment is unlike one of detailed description of the invention one to three: inciting somebody to action described in step one Guided missile non-linear dynamic model is converted into the detailed process of piecewise affine model:

First, provide the gentle Power compound of this direct lateral force and control the population parameter table of guided missile,

Table 1 Missile Preliminary parameter

As a example by pitch channel, ignore gravity item at terminal guidance section, ignore coupling terms to simplify the analysis simultaneously, by formula (5)-(6), Nonlinear attitude control model to guided missile pitch channel is

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

Selecting system state x=[α ω_z]^T, controlled quentity controlled variable u=[δ_z F_y1]^T；Carry out gesture stability design time, we it is of concern that The tracking situation of angle of attack instruction, therefore, selecting system is output as y=α；The state space description obtaining nonlinear model is 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 above formula, aerodynamic parameterJet enterference amplification factorAll relevant with angle of attack；Consideration is attacked Angle is the determiner affecting these parameters, and Fig. 6 gives the relation curve of each parameter and angle of attack.

The angle of attack is the principal element making attitude control system present nonlinear characteristic, according to the aerodynamic parameter be given and amplification factor And the relation curve between the angle of attack, it can be seen that aerodynamic parameter and amplification factor are non-linear relation with the angle of attack, when the angle of attack exists In little scope during variation, can be approximated to be linear relationship；Respectively with α=-21.25 ° ,-8.75 °, 0 °, 8.75 °, 21.25 ° as separation, It is divided into six subregions, in each section of region, linear characteristic can be approximately；In each section, utilize little deviation linear The method changed is by Attitude control model piece-wise linearization；

The piecewise affine model obtained 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=1,2 ..., 6, the most corresponding six subregions；

Take sampling period T_s=0.025s, in conjunction with the relation of the aerodynamic parameter in Fig. 6 Yu the angle of attack, obtains discrete gesture stability system System state-space expression is

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

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

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 that kth moment, formula (22) are complex controll guided missile piecewise affine model.

By said method, the piecewise affine model of jaw channel can be similarly obtained.

Detailed description of the invention five: present embodiment is unlike one of detailed description of the invention one to four: the structure described in step 2 The detailed process of the complete mixed logical dynamics of complex controll guided missile is:

Introduce logical variable δ_i(k) ∈ 0,1}, i=1,2 ..., 6 describe each separation in piecewise affine model, and they meet as follows Corresponding relation

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

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

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

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

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

Formula (23) can change into equivalence mixed logic inequality constraints:

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

Wherein, 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；

Meanwhile, also need to introduce auxiliary logic variable δ_i(k) ∈ 0,1}, i=6 ..., 9, and meet

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

Then δ₁, δ₆, δ₇, δ₈, δ₉, 1-δ₅Six subregions of corresponding segments affine model respectively.

Formula (25) is stated as mixed logic inequality constraints:

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

Introduce auxiliary continuous variable z_i(k), i=1,2 ..., 6, thus by each section of subregion condition of piecewise affine model and corresponding shape State space expression formula is united, and these auxiliary continuous variables are as follows

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

Formula (27) is stated as mixed logic inequality constraints:

Wherein, 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；

Control parameter and formula (16), (17) in the population parameter table of guided missile in conjunction with the gentle Power compound of direct lateral force, obtain pitching side It is combined into direct lateral force value collection

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

Owing to direct lateral force is discrete variable, introduce following logical variableDirect lateral force is described

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

In formula (29), the satisfied following constraint of logical variable:

$\underset{i=1}{\overset{12}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_{F_i}=0$ Or 1 (30)

Wherein, 0 describes direct lateral force does not works, and 1 describes direct lateral force can only take setIn one；

Note u₁=δ_z, then the input of the control in formula (22) is written as

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

Control the population parameter table of guided missile, system mode and control input according to the gentle Power compound of direct lateral force and there is constraint

x_min≤x(k)≤x_max

u_1min≤u₁(k)≤u_1max (32)

Wherein, x_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, obtaining the complete mixed logical dynamics of complex controll guided missile is

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

Equally, by introducing logical variable, use said method, the mixed logical dynamics of jaw channel can be obtained.

Detailed description of the invention six: present embodiment is unlike one of detailed description of the invention one to five: the design in step 3 is multiple Close missile attitude control rule specific implementation process as follows:

For complex controll guided missile, the target of gesture stability is quickly to follow the tracks of attitude in the case of saving fuel consumption as far as possible Control system instructs, and then maintains attitude stabilization.According to gesture stability target, the mesh of current time Attitude Control System Design Mark can be described as, on the premise of saving fuel consumption, finding suitable angle of rudder reflection and direct lateral force value, namely controlling Amount u processed so that the angle of attack tracking error in prediction time domain is minimum, mixes PREDICTIVE CONTROL optimization based on our structure of this purpose Problem is as follows

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

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

Wherein, y_cInstructing for the angle of attack, y (k+i/k) is angle of attack predictive value, and N is prediction time domain, Q_yIt it is adding of output tracking item Weight matrix, R is the weighting matrix controlling input item；

For jaw channel, can construct and similar mix PREDICTIVE CONTROL optimization problem, the design of its attitude control law Journey is completely the same with pitch channel.

Utilize MIQP appro ach and Matlab software to solve above-mentioned optimization problem, i.e. obtain to pneumatic control rule and Attitude control engine opens rule, and the distribution of direct lateral force and aerodynamic force is by adjusting weighting matrices Q_yRealize with R.

Fig. 7,8 and 9 sets forth the simulation result utilizing the inventive method design attitude control law, and Figure 10 is explicit control System rule division result.

Claims (3)

1., based on mixing the appearance control formula direct lateral force gentle Power compound missile attitude control method of PREDICTIVE CONTROL, its feature exists Realize according to following steps in described method:

Step one, set up the direct lateral force gentle Power compound complete Attitude control model of guided missile and direct lateral force model, and The expression formula of derivation pitch orientation direct lateral force, is converted into piecewise affine model by guided missile non-linear dynamic model；

Wherein, the direct lateral force gentle Power compound guided missile complete Attitude control model process set up is as follows:

Gravity suffered by guided missile and aerodynamic force are fastened expression at ballistic coordinate respectively, obtains the kinetics equation of guided missile center of mass motion 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 guided missile quality, and P is missile tail cruising thrust, and g is acceleration of gravity, X_a、Y_aAnd Z_aFor leading Three components that aerodynamic force suffered by bullet is fastened in speed coordinate, are resistance, lift and side force respectively, its positive direction respectively with The positive direction of three axles of velocity coordinate system is consistent；V represents guided missile centroid velocity, and α, β are respectively the angle of attack and yaw angle, θ,ψ_vIt is respectively trajectory tilt angle and trajectory deflection angle, γ_vFor speed inclination angle；Suffered by guided missile, direct lateral force is at bullet Three components in road coordinate system；

Assuming that missile coordinate system overlaps with the body principal axis of inertia, i.e. J_xy=J_yz=J_zx=0, obtain guided missile in missile coordinate system around The kinetics equation that barycenter rotates is 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_zIt is respectively the guided missile rotary inertia to three axles of missile coordinate system, ω_x,ω_y,ω_zIt is respectively missile body coordinate It is the rotational angular velocity ω of the relative earth axes component on three axles of missile coordinate system, M_x、M_yAnd M_zIt is respectively Act on the moment to barycenter of all external force on guided missile component on each axle of missile coordinate system；M_x、M_yAnd M_zIt is expressed as

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

M in formula_ex、M_eyAnd M_ezRespectively act on the aerodynamic moment of the guided missile component on each axle of missile coordinate system, Respectively act on the directly laterally moment of the guided missile component on each axle of missile coordinate system；

Considering lateral jet interference effect, the direct lateral force simultaneously lighting the generation of some attitude control impulse motors is made a concerted effort and is made a concerted effort Square is being expressed as that missile body coordinate is fastened

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

Wherein,For Jet enterference thrust amplification factor,For the Jet enterference moment amplification factor, F_y1,F_z1,M_y1,M_z1Make a concerted effort for nominal direct lateral force and the expression fastened at missile body coordinate of resultant moment；

The angle of attack, yaw angle and body angle speed dynamical equation is derived according to formula (1) to (4)；

The angle of attack and yaw angle dynamical equation

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

Body angle speed dynamical equation

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

Wherein, Q is dynamic pressure, and S is characterized area, and L is characterized length,For Aerodynamic parameter,For the normal g-load coefficient that the unit angle of attack is corresponding,For the normal g-load coefficient that unit elevator drift angle is corresponding,For the lateral overload coefficient that unit yaw angle is corresponding,For the lateral overload coefficient that unit rudder is corresponding,For Driftage static-stability derivative,For rudder control efficiency,For yaw damping moment coefficient,For pitching static-stability derivative,For elevator control efficiency,For pitching moment due to pitching velocity coefficient, δ_y,δ_zIt is respectively rudder and the deflection angle of elevator； Formula (5)-(6) are the Attitude control model of complex controll guided missile；

Step 2, introducing logical variable, construct the complete mixed logical dynamics of complex controll guided missile；

Step 3, the compound guided missile attitude control law of design, determine that pneumatic control rule and attitude control engine open rule；

The detailed process of the direct lateral force model described in establishment step one is:

Direct lateral force is produced by the attitude control impulse motor group being fixedly installed in body barycenter front, has 180 appearance control arteries and veins Rushing electromotor dislocation arrangement, be divided into 10 circles along the body longitudinal axis, often 18 attitude control impulse motors of circle arrange around body；With In one circle, adjacent attitude control impulse motor interval central angle is 20 °, makes i represent the numbering of circle, i=1,2 ..., 10, j represent appearance Control pulsed motor numbering in often circle, j=1,2 ..., 18；The line in the i-th circle attitude control impulse motor spout center of circle is formed Cross section is l with the distance of body barycenter_i, space between the adjacent coils is △ l；Assume that attitude control impulse motor produces when without freely flowing Stable state thrust be F_m, (i, the nominal direct lateral force that attitude control impulse motor j) produces is in missile coordinate system for numbered In be expressed as

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

Correspondingly, directly laterally moment being expressed as that missile body coordinate is fastened

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

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

Light the nominal direct lateral force that some attitude control impulse motors produce to make a concerted effort and resultant moment is fastened at missile body coordinate simultaneously It is expressed 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_1,1,j_1,2,…,j_1,n1Represent the 1st punctuate combustion attitude control impulse motor circle in numbering, n1 represents that the 1st punctuates The attitude control impulse motor quantity of combustion, the rest may be inferred；Formula (9)-(10) are the direct lateral force model of complex controll guided missile；

The detailed process of the expression formula of described derivation pitch orientation direct lateral force is:

In odd number circle numbered (i, 1), (i, 2), (i, 3), (i, 17), the direct lateral force that the attitude control impulse motor of (i, 18) produces is at oy₁Axle On subscale be shown as vector

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

In even number circle numbered (i, 1), (i, 2), (i, 17), the direct lateral force that the attitude control impulse motor of (i, 18) produces is at oy₁On axle Subscale is shown as vector

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

If the direct lateral force that the i-th circle attitude control impulse motor produces is Fⁱ, it is desirable to

F¹=F⁹,F³=F⁷,F²=F¹⁰,F⁴=F⁸ (13)

Then when odd number circle pulsed motor is lighted a fire, have

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

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

Equally, when even number circle pulsed motor is lighted a fire, have

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

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

The different values made a concerted effort of the direct lateral force that all attitude control engines in Ze Zheng pitch control district produce constitute set

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

The different values of resultant moment constitute set

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

The different values made a concerted effort of the direct lateral force that all attitude control engines in negative pitch control district produce constitute set

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

Each control cycle, attitude control system according to certain control law fromMiddle selection one controls masterpiece for controlling Input；

The detailed process that guided missile non-linear dynamic model is converted into piecewise affine model described in step one is: combine this straight Connect the gentle Power compound of side force and control the population parameter table of guided missile, by formula (5)-(6), obtain the non-linear appearance of guided missile pitch channel State Controlling model is

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

Selecting system state x=[α ω_z]^T, controlled quentity controlled variable u=[δ_z F_y1]^T；Selecting system is output as y=α；Obtain nonlinear model The state space description of type is 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 above formula, aerodynamic parameterJet enterference amplification factorAll relevant with angle of attack；

Respectively with α=-21.25 ° ,-8.75 °, 0 °, 8.75 °, 21.25 ° as separation, are divided into six subregions, in each section, utilize little The linearizing method of deviation is by Attitude control model piece-wise linearization；

The piecewise affine model obtained 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=1,2 ..., 6, the most corresponding six subregions；

Take sampling period T_s=0.025s, in conjunction with the relation of aerodynamic parameter Yu the angle of attack, obtains discrete attitude control system state Spatial expression is

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

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

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 that kth moment, formula (22) are complex controll guided missile piecewise affine model.

The most according to claim 1 based on the appearance control formula direct lateral force gentle Power compound guided missile appearance mixing PREDICTIVE CONTROL State control method, it is characterised in that the concrete mistake of the structure complete mixed logical dynamics of complex controll guided missile described in step 2 Cheng Wei:

Introduce logical variable δ_i(k) ∈ 0,1}, i=1,2 ..., 6 describe each separation in piecewise affine model, and they meet such as Lower corresponding relation

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

Formula (23) can change into equivalence mixed logic inequality constraints:

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

Wherein, 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；

Meanwhile, also need to introduce auxiliary logic variable δ_i(k) ∈ 0,1}, i=6 ..., 9, and meet

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

Then δ₁,δ₆,δ₇,δ₈,δ₉,1-δ₅Six subregions of corresponding segments affine model respectively；

Formula (25) is stated as mixed logic inequality constraints:

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

Introduce auxiliary continuous variable z_i(k), i=1,2 ..., 6, thus by each section of subregion condition of piecewise affine model with corresponding State-space expression is united, and these auxiliary continuous variables are as follows

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

Formula (27) is stated as mixed logic inequality constraints:

$\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_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；

Control parameter and formula (16), (17) in the population parameter table of guided missile in conjunction with the gentle Power compound of direct lateral force, bowed Face upward direction direct lateral force value collection to be combined into

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

Introduce following logical variableDirect lateral force is described

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

In formula (29), the satisfied following constraint of logical variable:

Or 1 (30)

Wherein, 0 describes direct lateral force does not works, and 1 describes direct lateral force can only take setIn one；

Note u₁=δ_z, then the input of the control in formula (22) is written as

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

Control the population parameter table of guided missile, system mode and control input according to the gentle Power compound of direct lateral force and there is constraint

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

Wherein, x_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, obtaining the complete mixed logical dynamics of complex controll guided missile is

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

The most according to claim 1 based on the appearance control formula direct lateral force gentle Power compound guided missile appearance mixing PREDICTIVE CONTROL State control method, it is characterised in that it is as follows that the design in step 3 is combined guided missile attitude control law specific implementation process:

It is as follows that structure mixes PREDICTIVE CONTROL optimization problem

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

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

Wherein, y_cInstructing for the angle of attack, y (k+i/k) is angle of attack predictive value, and N is prediction time domain, Q_yIt it is adding of output tracking item Weight matrix, R is the weighting matrix controlling input item；

Utilize MIQP appro ach and Matlab software to solve above-mentioned optimization problem, i.e. obtain to pneumatic control rule and Attitude control engine opens rule, and the distribution of direct lateral force and aerodynamic force is by adjusting weighting matrices Q_yRealize with R.