CN114815888A - Affine form guidance control integrated control method - Google Patents
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Abstract
An affine guidance control integrated control method belongs to the field of missile model automatic control. The problem that an existing guidance control integration is a non-affine model, a guidance loop and a control loop cannot achieve synchronous control in one simulation step length, and control accuracy is low is solved. Establishing an affine guidance control integrated model according to a missile target relative kinematics model, a missile attitude dynamics model, system interference caused by pneumatic parameter deviation, system interference caused by steering engine installation deviation and system interference caused by missile inertial navigation equipment measurement error; control of u, d 'in the Integrated model by controlling guidance in affine form' 1 、d 2 And d 3 Obtaining x in the guidance control integrated model in the affine form 1 、x 2 And x 3 By a limit of x 1 、x 2 And x 3 The limits of (c) control the real missile. The device is used for acting on a real missile and realizing smaller miss distance.
Description
Technical Field
The invention relates to a control method of a model, and belongs to the field of missile model automatic control.
Background
In recent years, with the rapid development of hypersonic aircrafts, many studies on hypersonic aircraft control are made at home and abroad. Conventional guided munitions typically have a guidance loop designed separately from the control loop in order to reduce the complexity of the model construction and to meet the design requirements of the control algorithm. Wherein the inner loop is an autopilot control loop, and the desired flight procedure angle is generated by changing a rudder deflection command; the outer loop is a guidance loop that generates an acceleration command. However, the flight speed of a hypersonic weapon is usually over mach 5, and particularly in the last guidance stage, the hypersonic weapon has the characteristics of fast time variation, strong coupling, strong nonlinearity and strong uncertainty, and the factors cause that the traditional design method cannot meet the requirement of fast response to the miss distance and even cause the instability of a missile.
The concept of Integrated Guidance and Control (IGC) design was first proposed by Williams. The guidance loop and the control loop are considered as a whole to carry out controller design, and the coupling influence between the two loops and the interaction influence between the mass center motion and the mass center surrounding motion of the aircraft are considered, so that the response speed and the control performance of the whole are greatly improved. In the final guidance stage, the IGC method can directly solve the rudder deflection control instruction of the missile through missile-target relative information without transmitting the overload instruction output by the guidance loop to the control loop, thereby greatly reducing the response time of the system and eliminating the influence caused by the coupling uncertainty between the two loops.
Aiming at the strong coupling characteristic of a hypersonic aircraft, many scholars at home and abroad regard the aircraft as a rigid body, establish a full-state coupling model containing all states in a guidance and control loop, construct a centroid motion equation and a centroid-surrounding motion equation into a cascade system, and directly obtain a rudder deflection control instruction by using information such as a line-of-sight angle, a line-of-sight angular velocity, a flight attitude angle and the like and using methods such as sliding mode control, self-adaptive control, optimal control and the like. However, the above studies cannot completely eliminate the coupling effect between the two systems, and the methods based on optimal control all have the disadvantages of heavy computational burden, difficulty in reproducing applications, and the like. In addition, because the IGC method based on the BTT missile is not researched much, the coupling influence between the yaw loop and the roll loop of the BTT missile is rarely considered.
A Sliding Mode Control (SMC) method is used as a nonlinear method with strong robustness, and is widely applied to the problems of mechanical arm control, spacecraft rendezvous and docking and the like due to the characteristics of insensitivity to disturbance, high convergence speed and the like, however, the switching characteristic of the SMC method causes the problems of buffeting and serious damage to the output performance of an actuator.
Disclosure of Invention
The invention aims to solve the problems that the existing guidance control integration is a non-affine model, a guidance loop and a control loop cannot realize synchronous control in one simulation step length, and the control precision is low, and provides an affine guidance control integration control method.
An integrated control method for affine guidance control, comprising the following steps:
an affine form guidance control integrated model is expressed as:
in the formula (I), the compound is shown in the specification,
θ L is the inclination angle of the line of sight L To achieve the deflection angle, x 2 ＝[α β γ v ] T ，γ V Is the roll angle of the missile, alpha is the angle of attack, beta is the angle of sideslip, x 3 ＝[ω x ω y ω z ] T ，ω x ω y ω z Representing the angular velocity of the missile's missile body coordinate system relative to the ground coordinate system, u ═ δ x δ y δ z ] T U is the desired rudder deflection angle, δ z For yaw rudder angle, delta y For pitching rudder deflection angle, delta x For rolling rudder angle, d 1 、d 2 And d 3 Respectively system interference caused by pneumatic parameter deviation, system interference caused by steering engine installation deviation and system interference caused by missile inertial navigation equipment measurement error,
c 1 ＝cosθ L cosθ+sinθsinθ L cos(φ L -φ V )，c 2 ＝sinθ L sin(φ L -φ V )，c 3 ＝sinθsin(φ V -φ L )，c 4 ＝cos(φ L -φ V ) M is the missile mass, g is the gravitational acceleration, theta is the trajectory inclination angle, phi V Showing the deviation angle of the trajectory, q is dynamic pressure, S is the reference area of the missile, L is lift force, L is a coordination constant to be designed, and J y J x J z Representing the three-axis moment of inertia of the missile, m x ，m y ，m z Respectively represents the three-axis operating moment of the missile,
is coefficient of lift c y For the partial derivative of the angle of attack alpha, R is the relative distance between the missile and the target;
The invention has the beneficial effects that:
the application provides a new modeling method aiming at a BTT missile IGC model, which comprises the following steps: the differential homomorphism of the state variable is not required to be constructed, and the state variable is directly converted into an affine system model. In addition, aiming at the actuator saturation phenomenon, an auxiliary system is designed, the input saturation phenomenon is guaranteed to be processed, the state of the auxiliary system can enter a very small boundary under the non-singular condition, various unknown interferences (system interference caused by pneumatic parameter deviation, system interference caused by steering engine installation deviation and system interference caused by missile inertial navigation equipment measurement errors) acting on the BTT missile are estimated by using a self-adaptive technology, and the convergence of a terminal line-of-sight angle tracking error and a line-of-sight angular rate and the final bounding property of the consistency of the system are strictly proved by using a Lyapunov stability theory.
Therefore, the method is equivalent to controlling u and d in affine guidance control integrated model by designing the controller 1 、d 2 And d 3 Obtaining x in the guidance control integrated model in the affine form 1 、x 2 And x 3 When x is proved 1 、x 2 And x 3 X at the time of approaching the limit of 0 1 、x 2 And x 3 The target is hit more easily and a smaller miss distance is realized when the missile is acted on a real missile.
The guidance control integrated model in the affine form integrates the control loop and the guidance loop, so that the guidance loop and the control loop can be synchronously controlled in one simulation step length, and the control precision is high, for example, the guidance control integrated model in the affine form integrates the control loop and the guidance loop together, and the control precision is highIn an affine form guidance control integrated model
A guidance loop is shown which is,
and
represents a control loop, and also designs an unknown quantity u in the guidance-control integrated model of the affine form by designing a guidance rate, designs an unknown quantity d in the guidance-control integrated model of the affine form by designing an adaptation rate 1 、d 2 And d 3 The control is completed by designing a virtual control quantity, designing a first filter, designing a second-order backstepping control rate, designing an auxiliary system and designing a second filter, so that the function of the controller is realized, and the controller is controlled to obtain x 1 、x 2 And x 3 。
Drawings
FIG. 1 is a flow chart of an affine guidance control integrated control method;
FIG. 2 is a three-dimensional view of an integrated guidance law gliding mass attack trajectory;
fig. 3(1) is a graph showing a change in ballistic inclination angle, where theta denotes a ballistic inclination angle, and fig. 3(2) is a graph showing a change in ballistic deflection angle, where fai denotes a ballistic deflection angle;
FIG. 4(1) is a view showing the variation of the inclination angle of the visual line, and FIG. 4(2) is a view showing the variation of the declination angle of the visual line;
fig. 5(1) is a graph of the variation of the derivative of the ballistic inclination angle, wherein dthetal denotes the derivative of the ballistic inclination angle, and fig. 5(2) is a graph of the variation of the derivative of the ballistic declination angle, wherein dfail denotes the derivative of the ballistic declination angle;
FIG. 6(1) is ω x FIG. 6(2) is ω y FIG. 6(3) is a graph of ω z A graph of variation of (d);
FIG. 7(1) is S 1,1 Change curve, FIG. 7(2) is S 1,2 A variation graph;
FIG. 8(1), FIG. 8(2) and FIG. 8(3) are S 2 A graph of the variation of the three components of (a);
FIG. 9(1), FIG. 9(2) and FIG. 9(3) are S 3 A graph of the variation of the three components of (a);
fig. 10(1) is a plot of the rudder deflection angle change of the x-axis, where detax represents the rudder deflection angle of the x-axis; fig. 10(2) is a plot of the rudder deflection angle change of the y-axis, where detay represents the rudder deflection angle of the y-axis; fig. 10(3) is a plot of the rudder deflection angle change of the z-axis, where detaz represents the rudder deflection angle of the z-axis.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
The first embodiment is as follows: the embodiment is described with reference to fig. 1, and the method for integrated control of guidance and control in an affine form according to the embodiment includes the following steps:
an affine form guidance control integrated model is expressed as:
in the formula (I), the compound is shown in the specification,
θ L is the inclination angle of the line of sight L To achieve the deflection angle, x 2 ＝[α β γ v ] T ，γ V Is the roll angle of the missile, alpha is the angle of attack, beta is the angle of sideslip, x 3 ＝[ω x ω y ω z ] T ，ω x ω y ω z Denotes the angular velocity of the missile body coordinate system of the missile relative to the ground coordinate system, u ═ delta x δ y δ z ] T U is the desired rudder deflection angle, δ z For yaw rudder angle, delta y For pitching rudder deflection angle, delta x For rolling rudder angle, d 1 、d 2 And d 3 Respectively system interference caused by pneumatic parameter deviation, system interference caused by steering engine installation deviation and system interference caused by missile inertial navigation equipment measurement error,
c 1 ＝cosθ L cosθ+sinθsinθ L cos(φ L -φ V )，c 2 ＝sinθ L sin(φ L -φ V )，c 3 ＝sinθsin(φ V -φ L )，c 4 ＝cos(φ L -φ V ) M is the missile mass, g is the gravitational acceleration, theta is the trajectory inclination angle, phi V Showing the deviation angle of the trajectory, q is dynamic pressure, S is the reference area of the missile, L is lift force, L is a coordination constant to be designed, and J y J x J z Representing the three-axis moment of inertia of the missile, m x ，m y ，m z Respectively represents the three-axis operating moment of the missile,
is coefficient of lift c y For the partial derivative of the angle of attack alpha, R is the relative distance between the missile and the target;
In the present embodiment, it is preferred that,
1. coordinate system establishment
For ease of analysis, the following coordinate system definitions are given herein:
(1) earth's center inertial coordinate system (o) I x I y I z I ): origin o of coordinate system I Is the earth's heart o I z I The axis being perpendicular to the equatorial plane of the earth and pointing in the north pole, o I x I Shaft and o I y I Axis in equatorial plane, o I x I Is along the line of intersection of the equatorial plane and the meridian plane, o I y I The axis is determined by the right hand rule.
(5) Projectile coordinate system (ox) 1 y 1 z 1 ): the origin of the coordinate system is the center of mass, ox, of the aircraft 1 Shaft and aircraftThe longitudinal axes of the bodies are coincident, and the pointing direction of the head is positive, oy 1 Located in the longitudinal symmetrical plane of the aircraft body and connected with ox 1 The axis is vertical, pointing upwards is positive, and oz 1 Is determined by the right-hand rule
(7) Speed coordinate system (ox) v y v z v ): the origin of coordinates o is the aircraft centroid, ox v Axis in aircraft speed direction, oy v The axis lying in the main plane of symmetry of the aircraft, perpendicular to ox v Axis directed upward, oz v Shaft and ox v y v The planes are perpendicular and form a right-hand coordinate system.
(8) Ballistic coordinate system (ox) 2 y 2 z 2 ): the origin of coordinates o is the aircraft centroid, ox 2 Axis in aircraft speed direction, oz 2 The axis lying in the plumb plane containing the velocity vector perpendicular to ox 2 A shaft pointing downward; oy 2 Shaft and ox 2 y 2 The planes are perpendicular and form a right-hand coordinate system.
2. Model building
And giving out a guided missile target relative kinematics and a dynamic model integrated with guidance. The guidance control integration is essentially the joint design of a tracking control system and a missile body stability control system of a missile, firstly, without loss of generality, a model of a missile attack target is established as follows under a sight coordinate system:
where R is the relative distance between the missile and the target, θ L And phi L Is the angle of sight, a mi (i-R, θ, Φ) is the acceleration component of the missile on the velocity coordinate system, and similarly,a ti (i ═ R, θ, Φ) is the acceleration component of the target on the velocity coordinate system. For the missile attacking ground fixed target scene, a ti ＝0。
In the final guiding section, the pneumatic acceleration of the missile is provided by aerodynamic force, so that the relationship between the pneumatic acceleration and the aerodynamic force of the missile is established by taking the relationship between the pneumatic acceleration and the aerodynamic force of the missile into consideration as follows:
wherein m is the missile mass, ρ is the air density, V m Is the missile speed, q is the dynamic pressure, S is the missile reference area, alpha, beta, delta z ，δ y Respectively an attack angle, a sideslip angle, a yaw rudder deflection angle and a pitch rudder deflection angle.
And (3) carrying out stress analysis on the missile, and obtaining the missile by projection under a trajectory system:
Y′＝Y cosγ V -Z sinγ V -mg cosθ
Z′＝Y sinγ V +Z cosγ V
by defining the coordinate system, the aerodynamic acceleration of the missile on the speed system is projected under the sight line coordinate system, and the following relation can be obtained:
wherein the content of the first and second substances,
c 1 ＝cosθ L cosθ+sinθsinθ L cos(φ L -φ V )
c 2 ＝sinθ L sin(φ L -φ V )
c 3 ＝sinθsin(φ V -φ L )
c 4 ＝cos(φ L -φ V )
new missile target relative kinematic equations can be obtained by processing the formulas 3 and 4:
the kinematic equations for ballistic dip and ballistic declination are as follows:
similarly, by carrying out stress analysis and coordinate conversion on the missile, the attitude kinetic equation of the missile can be obtained:
for a BTT missile, the BTT missile turns at a lateral component through lift force generated by a tilting fuselage, and a sideslip angle is 0 through attitude control, so that a three-dimensional guidance control integrated model can be written as follows:
wherein the content of the first and second substances,
x 2 ＝[α β γ v ] T ，x 3 ＝[ω x ω y ω z ] T ，
u＝[δ x δ y δ z ] T and the control input is the control input of the three-dimensional guidance and control integrated model. d 1 、d 2 And d 3 The method is characterized in that the method is total interference of a system caused by pneumatic parameter deviation, steering engine installation deviation, missile inertial navigation equipment measurement error and the like, and specifically comprises the following steps:
due to d 1 、d 2 And d 3 All are disturbances caused by correlated state errors in the system, so it can be assumed that its total disturbance is bounded, i.e. satisfies:
|d 11 |≤d 11m ,|d 12 |≤d 12m
|d 21 |≤d 21m ,|d 22 |≤d 22m ,|d 23 |≤d 23m
|d 31 |≤d 31m ,|d 32 |≤d 32m ,|d 33 |≤d 33m
wherein the content of the first and second substances,
the system equation has the following functions:
however, in the above guidance loop equation 45, the control amount thereof
Is x 2 Lead to the need to advance the design of the control loop through the control loop state quantities α, β, γ in the following v Computing
The guidance loop and the control loop can not realize synchronous control in a simulation step length, and certain influence is caused on control precision and dynamic performance.
In order to deal with the problem, the guidance and control integrated model is converted into an affine system model, and the guidance loop and the control loop are uniformly proved. Equations 45, 46 and 47 are converted to the following forms:
wherein the content of the first and second substances,
x 2 ＝[α β γ v ] T ，x 3 ＝[ω x ω y ω z ] T 。u＝[δ x δ y δ z ] T and the control input is the control input of the three-dimensional guidance and control integrated model.
Then the functions in the system equation are:
where l is a tuning constant that needs to be designed.
Designing a controller:
the application designs a self-adaptation sliding mould conductivity based on backstepping method to realize the stabilization of the model and guarantee the system state x 1 ，x 2 ，x 3 Achieving reality under unknown disturbance and input saturation conditionsAnd (4) the stability is ensured.
To solve the problem that the disturbance upper bound is unknown, firstly, the disturbance term d 'in the model (formula 1) is subjected to' 1 ，d 2 ，d 3 One assumption is made:
suppose 1 all disturbance sets d 'in model (1)' 1 ，d 2 ，d 3 Is bounded and the last is unknown. Let | d' 1 ||≤d m1 ，||d 2 ||≤d m2 ，||d 3 ||≤d m3 。
First, a state quantity theta is designed L And phi L Sliding form surface S 1 ：
S 1 ＝[S 1,1 S 1,2 ] T
Let Lyapunov equation
And (5) obtaining a derivative:
thus, when the designed slip-form surface converges to zero,
can be converted into
Where ρ is 1 ＝min{2k 11 ,2k 12 }. Then in order to ensure the slip form surface S 1 Convergence, the following virtual control quantities are designed:
wherein k is 1 Is a positive definite diagonal matrix and k 1 ＝[k 1,1 k 1,2 ] T ，k 2 Is a normal number which is a positive integer,
is to disturbance d' 1 Estimating the previous time and setting the estimation error
Let Lyapunov equation be
The derivation can be:
wherein S is 2 ＝x 2 -x 2c -y 1 ，
Wherein k is c1 Is greater than 0. Substituting equation 20 into the virtual control amount yields:
in order to ensure that the virtual state quantity is bounded, a second-order backstepping control rate pair S is designed 2 And (3) carrying out stabilization:
wherein k is 3 Is a normal number which is a positive integer,
to a disturbance d 2 Estimating the previous time and setting the estimation error
Let Lyapunov equation be
The derivation can be:
wherein S is 3 ＝x 3 -x 3c -y 2 ξ, filtering error of the second filter
Xi is the state of the designed auxiliary system
Wherein k is c2 ,k ξ ＞0，Δu＝[Δu 1 Δu 2 Δu 3 ] T Indicating controller output deviation due to input saturation
Δu i ＝u i -u c,i (i＝1,2,3)
The formula 22, the formula 23 and the second-order backstepping virtual control amount are substituted into the formula 31 to obtain
The conductance and adaptation rates can be designed to ensure that all states are stable in the presence of site-specific external perturbations
Wherein k is 4 Is a normal number.
The following theorem is given later;
theorem 1: under the condition that 1 is established, the S can be ensured by utilizing the improved affine BTT missile guidance control integrated model (formula 1) and applying the designed guidance rate, the auxiliary system, the first filter, the second filter and the self-adaptive rate 1 ,S 2 ,S 3 Are all practically stable, and x 1 ,x 2 ,x 3 Can also realize practical stability
And (3) proving that:
designing a Lyapunov function:
the derivation of the above equation is substituted into the controller (equation 24) to obtain:
note: by means of the designed auxiliary system, it can be seen in the derivation of the above equation: representing actuator output difference term due to input saturation
Can be compensated by the auxiliary system, thus enabling the state x of the system model (equation 1) to be corrected in the presence of input saturation 1 ,x 2 ,x 3 And (6) stabilizing.
Substituting adaptive equations
In (b) obtaining
The young inequality is applied to obtain:
substitution of formula 35 can be:
due to the nature of the low pass filter: y is 1 ,y 2 Are bounded. And according to b 1 And b 2 Definition of (1)
Can obtain | | b 1 y 1 I and B 2 y 2 | | is bounded.
It is assumed here that their upper bounds are:
equation 38 may be converted to
Wherein, c is min { k ═ min { (k) 2 ,k 3 ,2k 4 ,k θ2 k θ1 ,k θ3 k θ4 ,k θ5 k θ6 }，
Thus, S can be realized 1 ,S 2 ,S 3 And the estimation error of the disturbance
Are consistently stable.
1. When S is 1 When bounded, then according to its definition
The following can be obtained:
2. when S is 2 When bounded, then according to its definition (S) 2 ＝x 2 -x 2c -y 1 ) The following can be obtained:
||x 2 ||≤||S 2 +y 1 +x 2c ||≤φ s +||y 1 ||+||x 2c ||
thus, | | x 2 Also, is bounded.
3. When S is 3 When bounded, then according to its definition (S) 3 ＝x 3 -x 3c -y 2 ξ) can be:
||x 3 ||≤||S 3 +y 2 +x 3c +ξ||≤φ s +||y 1 ||+||x 2c ||+||ξ||
due to the desired controller output u and the actual controller output u c Are bounded, it can be directly derived that the auxiliary system state ξ is bounded.
Then | x can be obtained 3 Also, is bounded.
Based on the above analysis it can be found that: all states x 1 ,x 2 ,x 3 Are bounded.
Simulation analysis
Carrying out simulation analysis on the designed integrated guidance law, establishing a coordinate system by taking the ground projection of the missile at the final guidance starting moment as an origin, and setting the initial conditions of the final guidance simulation as follows:
the initial positions of the missile and the target are: x is the number of m0 ＝0km，y m0 ＝20km，z m0 ＝0km，x t0 ＝16km，y t0 ＝0km，z t0 ＝0km；
The speed of the missile at the starting moment of terminal guidance is as follows: v. of m0 1200m/s, ballistic inclination angle theta-6 degrees, ballistic deflection angle psi-5 degrees; the initial attitude angle is: alpha is alpha 0 ＝5°，β 0 ＝0°，γ 0 10 °; the desired end attack angle is: theta f ＝-72°，ψ f -2 °. The results of the terminal guidance trajectory simulation are shown in fig. 2 to 10. The final miss distance was 1.16 m. It can be seen from the above simulation results that: slip form surface S 1 And a virtual error S 2 ,S 3 Can both ensure convergence to a small bound near zero, and the state quantity x of the system under the condition that input saturation external disturbance exists 1 ,x 2 ,x 3 Can converge to a small bound around zero. And the final sight line inclination angle and the sight line deflection angle can converge to the expected sight line inclination angle and the sight line deflection angle.
Therefore, the terminal attack guidance law design is carried out on the scene that the boosting gliding rocket bomb attacks the low-speed moving target, and an affine form guidance control integrated model designed when the coupling factor between the guidance system and the control system is considered is provided; then designing a guidance law with terminal line-of-sight angle constraint based on a sliding mode control theory; and designing the upper limit of disturbance existing in the model according to the self-adaptive theory, and in addition, designing an auxiliary system can ensure that the stability of the system can be still proved when input saturation exists. And finally, the effectiveness of the designed guidance law is verified through simulation analysis.
The second embodiment is as follows: in this embodiment, the guidance control integrated control method in an affine form described in the first embodiment is further defined, and in this embodiment, in step 1, the missile attack target model is expressed as:
in the formula, a tR 、a tθ And a tφ Representing the three acceleration components of the target on a speed coordinate system, a mR 、a mθ And a mφ Representing the three acceleration components of the missile on the velocity coordinate system,
is the second derivative to R and is,
is to theta L The second derivative of (a) is,
the projection equation of the pneumatic acceleration of the missile on the speed system to the sight line coordinate system is expressed as follows:
in the formula, a my ,a mz Is the pneumatic acceleration of the missile on the speed system,
Z′＝Y sinγ V +Z cosγ V ，Y′＝Y cosγ V -Z sinγ V -mg cosθ，
is coefficient of lift c y For the partial derivatives of the angle of attack alpha,
is coefficient of lift c y For the partial derivatives of the sideslip angle beta,
coefficient of lateral force c z For the partial derivatives of the angle of attack alpha,
coefficient of lateral force c z For the partial derivatives of the sideslip angle beta,
coefficient of lateral force c z For pitch rudder deflection angle delta y Partial derivatives of (a);
the missile target relative kinematics model is represented as:
the kinematic equations for ballistic dip and ballistic declination are expressed as:
in the formula, V m Is the missile velocity;
the attitude dynamics model of the missile is expressed as:
the third concrete implementation mode: in this embodiment, the guidance control integration control method of affine type according to the second embodiment is further defined, and in this embodiment, in step 3, u and d 'in the guidance control integration model of affine type are controlled' 1 、d 2 And d 3 Obtaining x in the guidance control integrated model in the affine form 1 、x 2 And x 3 The specific process is as follows:
31, obtaining a derivative of a first Lyapunov equation according to the slide membrane surface, the guidance control integrated model in the affine form and the first Lyapunov equation;
according to the slide film surface, the affine guidance control integrated model and the set first-order virtual error S 2 And a second lyapunov equation, obtaining a derivative of the second lyapunov equation;
according to the slide film surface, the guidance control integrated model of the affine form, the first order virtual error S 2 Second order virtual error S 3 And a third Lyapunov equation, to obtain a derivative of the third Lyapunov equation,
step 32, obtaining a new derivative of the second Lyapunov equation according to the virtual manipulated variable and the derivative of the second Lyapunov equation,
obtaining a new derivative of a third Lyapunov equation according to the first filter, the second filter, the auxiliary system, the second-order backstepping control rate and the derivative of the third Lyapunov equation;
step 33, according to the designed Lyapunov function, the derivative of the first Lyapunov equation, the derivative of the new second Lyapunov equation, the derivative of the new third Lyapunov equation, the guidance rate with respect to u and the guidance rate with respect to d' 1 、d 2 And d 3 Obtaining the derivative of the Lyapunov function according to the self-adaptive rate of the Lyapunov function;
step 34, obtaining a new derivative of the Lyapunov function according to the derivative and the Young inequality of the Lyapunov function, and obtaining x in the guidance control integrated model in the affine form by combining with the slide membrane surface 1 、x 2 And x 3 The limit of (2).
The fourth concrete implementation mode: in the present embodiment, the integrated guidance control method of affine type described in the third embodiment is further limited, and in the present embodiment, the virtual control amount x is calculated in step 32 2c Comprises the following steps:
let d' 1 ，d 2 ，d 3 Is bounded and the last is unknown, satisfying:
|d 11 |≤d 11m ,|d 12 |≤d 12m
|d 21 |≤d 21m ,|d 22 |≤d 22m ,|d 23 |≤d 23m ，
|d 31 |≤d 31m ,|d 32 |≤d 32m ,|d 33 |≤d 33m
let | d' 1 ||≤d 1m ，||d 2 ||≤d 2m ，||d 3 ||≤d 3m ；
x 2c Expressed as:
in the formula, k 1 Is a positive definite diagonal matrix and k 1 ＝[k 1,1 k 1,2 ] T ，k 1,1 And k 1,2 Is k 1 2 components of, k 2 Is a normal number of the cells,
is a pair of d 1m (ii) an estimate of (d);
the first filter was designed to be:
in the formula, k c1 Is a constant number, k c1 ＞0，
Is the output of the first filter and is,
is the derivative of the first filter output;
the designed second-order backstepping control rate is as follows:
in the formula, k 3 Is a normal number which is a positive integer,
is a pair of d 2m Estimation of (S) 2 ＝x 2 -x 2c -y 1 ，
S 1 Is a slide film surface;
the second filter is designed to be:
in the formula, k c2 ＞0，x 3c In order to be the other of the virtual control quantities,
is the output of the second filter and is,
is the derivative of the second filter output;
the designed auxiliary system is as follows:
in the formula, k ξ ＞0，Δu＝[Δu 1 Δu 2 Δu 3 ] T ，Δu i ＝u i -u c,i (i＝1,2,3)，u i Is the i-th component of the desired rudder deflection angle u, u c,i Is the actual rudder deflection angle u c The (i) th component of (a),
u max the maximum value of the output rudder deflection angle is shown, and xi is the state of the auxiliary system;
the designed guidance ratio is as follows:
in the formula (I), the compound is shown in the specification,
is a pair of d 3m Estimate of (a), k 4 Is a normal number, S 3 ＝x 3 -x 3c -y 2 -ξ，
The designed adaptive rate is as follows:
in the formula, k θ1 、k θ2 、k θ3 、k θ4 、k θ5 、k θ6 Are all normal, S 2 And S 3 2 virtual errors are represented.
The fifth concrete implementation mode: in this embodiment, the guidance control integrated control method in an affine form according to the fourth embodiment is further limited, and in this embodiment, in step 31, a derivative of a first lyapunov equation is obtained, and the specific process is as follows:
firstly, design a relation theta L And phi L Sliding form surface S 1 ：
In the formula, S 1,1 And S 1,2 Representing the slip form surface S 1 Component of (a), k 11 k 12 Are all normal numbers, and are all positive numbers,
let the first Lyapunov equation
The first lyapunov equation is derived from equation 26 and equation 1:
when sliding mode surface S 1 Upon convergence to zero, equation 27 transitions to:
where ρ is 1 ＝min{2k 11 ,2k 12 }。
The sixth specific implementation mode: in this embodiment, the guidance control integrated control method in an affine form described in the fifth embodiment is further limited, and in this embodiment, in step 31, a derivative of a second lyapunov equation is obtained, and the specific process is as follows:
let the second Lyapunov equation be
According to formula 26, formula 1 and S 2 ＝x 2 -x 2c -y 1 And, deriving a second Lyapunov equation:
in the formula, y 1 Is the filtering error of the first filter and,
the seventh embodiment: in this embodiment, a new derivative of the second lyapunov equation is obtained in step 32, specifically:
substituting the formula for the virtual manipulated variable into formula 29, a new second derivative of the Lyapunov equation is obtained:
the specific implementation mode is eight: in this embodiment, in step 31, a derivative of a third lyapunov equation is obtained, specifically:
let the third Lyapunov equation be
According to the formula 26, the formula 1 and the formula S 2 ＝x 2 -x 2c -y 1 And S 3 ＝x 3 -x 3c -y 2 ξ, derived from the third Lyapunov equation:
wherein, y 2 Is the filtering error of the second filter and,
in step 33, a new derivative of the third lyapunov equation is obtained, specifically:
substituting equation 20, equation 21, equation 22, and equation 23 into equation 31 yields a new third derivative of the lyapunov equation:
the specific implementation method nine: in this embodiment, the guidance control integrated control method in an affine form according to the eighth embodiment is further limited, and in this embodiment, in step 33, a derivative of the lyapunov function is obtained, and the specific process is as follows:
the Lyapunov function is designed as:
in the formula (I), the compound is shown in the specification,
is d 1m The error of the estimation of (2) is,
deriving formula 33 according to the permeability, the derivative of the first lyapunov equation, the derivative of the new second lyapunov equation, and the derivative of the new third lyapunov equation to obtain:
in the formula (I), the compound is shown in the specification,
is d 2m The error of the estimation of (2) is,
is d 3m The error of the estimation of (2) is,
substituting the formula 34 into the adaptive rate formula, the derivative of the lyapunov function is obtained:
the detailed implementation mode is ten: in this embodiment, the guidance control integrated control method of affine type described in the ninth embodiment is further defined, and in this embodiment, in step 34, x in the guidance control integrated model of affine type is obtained 1 、x 2 And x 3 The specific process is as follows:
the young inequality is:
substituting equation 36 and equation 37 into equation 35 yields:
from the properties of the first and second filters: y is 1 ,y 2 Are all bounded and according to b 1 And b 2 The definition of (A) gives | | | b 1 y 1 I and B 2 y 2 | | is bounded, where it is assumed that their upper bound is:
in the formula (I), the compound is shown in the specification,
and
2 normal numbers;
from equation 39, equation 38 is converted to:
wherein c is min { k ═ min { (k) 2 ,k 3 ,2k 4 ,k θ2 k θ1 ,k θ3 k θ4 ,k θ5 k θ6 }，
From equation 40, we get:
wherein i is 1,2,3, t is time,
when S is 1 When bounded, according to S 1 To obtain:
when S is 2 When bounded, according to S 2 To obtain:
||x 2 ||≤||S 2 +y 1 +x 2c ||≤φ s +||y 1 ||+||x 2c |, equation 43
Therefore, | | x 2 It is also bounded that,
when S is 3 When bounded, according to S 3 To obtain:
||x 3 ||≤||S 3 +y 2 +x 3c +ξ||≤φ s +||y 1 ||+||x 2c | + | ξ |, equation 44
Since xi is bounded, get | | | x 3 | | is also bounded;
therefore, x in the affine form guidance control integrated model is obtained 1 、x 2 And x 3 The limit of (c).
In this embodiment, e -ct And
representing an exponential function.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.
Claims (10)
1. An affine guidance control integrated control method is characterized by comprising the following steps:
step 1, obtaining a missile target relative kinematics model, a kinematics equation of a trajectory inclination angle and a trajectory deflection angle and a missile attitude dynamics model according to a missile attack target model and a projection equation for projecting the aerodynamic acceleration of a missile on a speed system to a sight coordinate system;
step 2, establishing an affine guidance control integrated model according to a missile target relative kinematics model, a missile attitude dynamics model, system interference caused by pneumatic parameter deviation, system interference caused by steering engine installation deviation and system interference caused by missile inertial navigation equipment measurement error;
an affine guidance control integrated model expressed as:
in the formula (I), the compound is shown in the specification,
θ L is the angle of inclination of the line of sight, phi L To achieve the deflection angle, x 2 ＝[α β γ v ] T ，γ V Is the roll angle of the missile, alpha is the angle of attack, beta is the angle of sideslip, x 3 ＝[ω x ω y ω z ] T ，ω x ω y ω z Representing the angular velocity of the missile's missile body coordinate system relative to the ground coordinate system, u ═ δ x δ y δ z ] T U is the desired rudder deflection angle, δ z For yaw rudder angle, delta y For pitching rudder deflection angle, delta x For rolling rudder angle, d 1 、d 2 And d 3 Respectively system interference caused by pneumatic parameter deviation, system interference caused by steering engine installation deviation and system interference caused by missile inertial navigation equipment measurement error,
c 1 ＝cosθ L cosθ+sinθsinθ L cos(φ L -φ V )，c 2 ＝sinθ L sin(φ L -φ V )，c 3 ＝sinθsin(φ V -φ L )，c 4 ＝cos(φ L -φ V ) M is the missile mass, g is the gravitational acceleration, theta is the trajectory inclination angle, phi V Showing the deviation angle of the trajectory, q is dynamic pressure, S is the reference area of the missile, L is lift force, L is a coordination constant to be designed, and J y J x J z Representing the three-axis moment of inertia of the missile, m x ，m y ，m z Respectively represents the three-axis operating moment of the missile,
is coefficient of lift c y For the partial derivative of the angle of attack alpha, R is the relative distance between the missile and the target;
step 3, controlling u and d 'in the integrated model by controlling guidance in affine form' 1 、d 2 And d 3 Obtaining x in the guidance control integrated model in the affine form 1 、x 2 And x 3 By the limit of x 1 、x 2 And x 3 The limits of (c) control the real missile.
2. The integrated control method for guidance and control in an affine form as claimed in claim 1, wherein in step 1, the missile attack target model is expressed as:
in the formula, a tR 、a tθ And a tφ Representing the three acceleration components of the target on a speed coordinate system, a mR 、a mθ And a mφ Representing the three acceleration components of the missile on the velocity coordinate system,
is the second derivative to R and is,
is to theta L The second derivative of (a) is,
the projection equation of the pneumatic acceleration of the missile on the speed system to the sight line coordinate system is expressed as follows:
in the formula, a my ,a mz Is the pneumatic acceleration of the missile on the speed system,
Z′＝Ysinγ V +Zcosγ V ，Y′＝Ycosγ V -Zsinγ V -mgcosθ，
is coefficient of lift c y For the partial derivatives of the angle of attack alpha,
is coefficient of lift c y For the partial derivatives of the sideslip angle beta,
coefficient of lateral force c z For the partial derivatives of the angle of attack alpha,
coefficient of lateral force c z For the partial derivatives of the sideslip angle beta,
coefficient of lateral force c z For pitch rudder deflection angle delta y Partial derivatives of (a);
the missile target relative kinematics model is represented as:
the kinematic equations for ballistic dip and ballistic declination are expressed as:
in the formula, V m Is the missile velocity;
the missile attitude dynamics model is expressed as:
3. the integrated control method for guidance and control in an affine form as claimed in claim 2, wherein in step 3, u and d 'in the integrated model for guidance and control in an affine form are controlled' 1 、d 2 And d 3 Obtaining x in the guidance control integrated model in the affine form 1 、x 2 And x 3 The specific process is as follows:
31, obtaining a derivative of a first Lyapunov equation according to a set slide film surface, an affine guidance control integrated model and the first Lyapunov equation;
according to the slide film surface, the affine guidance control integrated model and the set first-order virtual error S 2 And a second lyapunov equation, obtaining a derivative of the second lyapunov equation;
according to the slide film surface, the guidance control integrated model of the affine form, the first order virtual error S 2 Second order virtual error S 3 And a third Lyapunov equation, to obtain a derivative of the third Lyapunov equation,
step 32, obtaining a new derivative of the second Lyapunov equation according to the virtual controlled variable and the derivative of the second Lyapunov equation,
obtaining a new derivative of a third Lyapunov equation according to the first filter, the second filter, the auxiliary system, the second-order backstepping control rate and the derivative of the third Lyapunov equation;
step 33, according to the designed Lyapunov function, the derivative of the first Lyapunov equation, the derivative of the new second Lyapunov equation, the derivative of the new third Lyapunov equation, the guidance rate with respect to u and the guidance rate with respect to d' 1 、d 2 And d 3 Obtaining the derivative of the Lyapunov function according to the self-adaptive rate of the Lyapunov function;
step 34, obtaining a new derivative of the Lyapunov function according to the derivative and the Young inequality of the Lyapunov function, and obtaining x in the guidance control integrated model in the affine form by combining with the slide membrane surface 1 、x 2 And x 3 The limit of (2).
4. An affine form guidance control integrated control method according to claim 3, wherein in the step 32, the virtual control quantity x 2c Comprises the following steps:
let d' 1 ，d 2 ，d 3 Is bounded and the last is unknown, satisfying:
let | d' 1 ||≤d 1m ，||d 2 ||≤d 2m ，||d 3 ||≤d 3m ；
x 2c Expressed as:
in the formula, k 1 Is a positive definite diagonal matrix and k 1 ＝[k 1,1 k 1,2 ] T ，k 1,1 And k 1,2 Is k is 1 2 components of, k 2 Is a normal number which is a positive integer,
is a pair of d 1m (ii) is estimated;
the first filter was designed to be:
in the formula, k c1 Is a constant number, k c1 ＞0，
Is the output of the first filter and is,
is the derivative of the first filter output;
the designed second-order backstepping control rate is as follows:
in the formula, k 3 Is a normal number which is a positive integer,
is a pair of d 2m Estimation of (S) 2 ＝x 2 -x 2c -y 1 ，
S 1 Is a slide film surface;
the second filter is designed to be:
in the formula, k c2 ＞0，x 3c In order to be the other of the virtual control quantities,
is the output of the second filter and is,
is the derivative of the second filter output;
the designed auxiliary system xi is:
in the formula, k ξ ＞0，Δu＝[Δu 1 Δu 2 Δu 3 ] T ，Δu i ＝u i -u c,i (i＝1,2,3)，u i Is the ith component of the desired rudder deflection angle u, u c,i Is the actual rudder deflection angle u c The (i) th component of (a),
u max is the maximum value of the rudder deflection angle of the output,
the designed guidance ratio is as follows:
in the formula (I), the compound is shown in the specification,
is to d 3m Estimate of (a), k 4 Is a normal number, S 3 ＝x 3 -x 3c -y 2 -ξ，
The designed adaptive rate is as follows:
in the formula, k θ1 、k θ2 、k θ3 、k θ4 、k θ5 、k θ6 Are all normal, S 2 And S 3 2 virtual errors are represented.
5. The integrated control method for affine type guidance control as claimed in claim 4, wherein in the step 31, a derivative of a first lyapunov equation is obtained, and the specific process is as follows:
firstly, design a relation theta L And phi L Sliding form surface S 1 ：
In the formula, S 1,1 And S 1,2 Surface S of the slip form 1 Component of (a), k 11 k 12 Are all normal numbers, and are all positive numbers,
let the first Lyapunov equation
The first lyapunov equation is derived from equation 26 and equation 1:
when sliding mode surface S 1 Upon convergence to zero, equation 27 transitions to:
where ρ is 1 ＝min{2k 11 ,2k 12 }。
6. An affine form guidance control integrated control method according to claim 5, wherein in the step 31, a derivative of a second lyapunov equation is obtained by the following specific process:
let the second Lyapunov equation be
According to formula 26, formula 1 and S 2 ＝x 2 -x 2c -y 1 And, deriving a second Lyapunov equation:
in the formula, y 1 Is the filtering error of the first filter and,
7. an integrated control method for affine type guidance control as claimed in claim 6, wherein in step 32, a new derivative of the second lyapunov equation is obtained, specifically:
substituting the formula for the virtual manipulated variable into equation 29, a new derivative of the second Lyapunov equation is obtained as:
8. the integrated control method for affine type guidance control as claimed in claim 7, wherein in step 31, a derivative of a third lyapunov equation is obtained, specifically:
let the third Lyapunov equation be
According to the formula 26, the formula 1 and the formula S 2 ＝x 2 -x 2c -y 1 And S 3 ＝x 3 -x 3c -y 2 ξ, derived from the third Lyapunov equation:
wherein, y 2 Is the filtering error of the second filter and,
in step 33, a new derivative of the third lyapunov equation is obtained, specifically:
substituting equation 20, equation 21, equation 22, and equation 23 into equation 31 yields a new third derivative of the lyapunov equation:
9. the integrated control method for affine type guidance control as claimed in claim 8, wherein in step 33, a derivative of the lyapunov function is obtained by the specific process:
the Lyapunov function is designed as:
in the formula (I), the compound is shown in the specification,
is d 1m The error of the estimation of (2) is,
deriving formula 33 according to the permeability, the derivative of the first lyapunov equation, the derivative of the new second lyapunov equation, and the derivative of the new third lyapunov equation to obtain:
in the formula (I), the compound is shown in the specification,
is d 2m The error of the estimation of (2) is,
is d 3m The error of the estimation of (2) is,
substituting the formula 34 into the adaptive rate formula, the derivative of the lyapunov function is obtained:
10. the integrated control method for guidance and control in an affine form as claimed in claim 9, wherein in step 34, x in the integrated model for guidance and control in an affine form is obtained 1 、x 2 And x 3 The specific process is as follows: the young inequality is:
substituting equation 36 and equation 37 into equation 35 yields:
from the properties of the first and second filters: y is 1 ,y 2 Are all bounded and according to b 1 And b 2 The definition of (A) gives | | | b 1 y 1 I and B 2 y 2 | | is bounded, where it is assumed that their upper bound is:
from equation 39, equation 38 is converted to:
wherein c is min { k ═ min { (k) 2 ,k 3 ,2k 4 ,k θ2 k θ1 ,k θ3 k θ4 ,k θ5 k θ6 }，
From equation 40, we get:
wherein i is 1,2,3, t is time,
when S is 1 When bounded, according to S 1 To obtain:
when S is 2 When bounded, according to S 2 To obtain:
||x 2 ||≤||S 2 +y 1 +x 2c ||≤φ s +||y 1 ||+||x 2c |, equation 43
Therefore, | | x 2 It is also bounded that,
when S is 3 When bounded, according to S 3 To obtain:
||x 3 ||≤||S 3 +y 2 +x 3c +ξ||≤φ s +||y 1 ||+||x 2c | + | ξ |, equation 44
Since xi is bounded, get | | | x 3 | | is also bounded;
therefore, x in affine form integrated model of guidance control is obtained 1 、x 2 And x 3 The limit of (c).
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