CN114815888B - Affine form guidance control integrated control method - Google Patents
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Abstract
An affine form guidance control integrated control method belongs to the field of missile model automatic control. In order to solve the problems that the existing guidance control integration is a non-affine model, the guidance loop and the control loop cannot realize synchronous control within one simulation step length, and the control precision is low. Establishing an affine form guidance control integrated model according to a missile target relative kinematics model, a missile attitude dynamics model, system interference caused by aerodynamic parameter deviation, system interference caused by steering engine installation deviation and system interference caused by missile inertial navigation equipment measurement error; controlling u, d 'in an integrated model by controlling the guidance in affine form' 1 、d 2 And d 3 Obtaining x in affine form guidance control integrated model 1 、x 2 And x 3 By x 1 、x 2 And x 3 Is controlling the true missile. The method is used for acting on a real missile to realize smaller off-target quantity.
Description
Technical Field
The invention relates to a control method for a model, and belongs to the field of missile model automatic control.
Background
In recent years, with the rapid development of hypersonic aircrafts, research on hypersonic aircrafts control at home and abroad is also endangered. Conventional guided munitions typically design a guidance circuit separately from a control circuit in order to reduce the complexity of model construction and meet the design requirements of the control algorithm. Wherein the inner loop is an autopilot control loop that generates a desired flight procedure angle by changing rudder deflection commands; the outer loop is the guidance loop that generates the acceleration command. However, hypersonic weapons generally have flight speeds above mach 5, especially at terminal guidance stages, which are characterized by fast time-varying, strong coupling, strong nonlinearity, and strong uncertainty, which cause conventional design methods to fail to meet the requirements for their fast response miss distance and even cause instability of the missile.
Guidance control integration (Integrated guidance and control, IGC) design ideas were originally proposed by Williams. By considering the guidance loop and the control loop as a whole to carry out controller design, the coupling influence between the two loops and the interaction influence between the movement of the mass center of the aircraft and the movement around the mass center are considered, and the whole response speed and control performance are greatly improved. In the terminal guidance stage, the IGC method can directly calculate the rudder deflection control instruction of the missile through the missile-mesh relative information, and the guidance loop output overload instruction is not required to be transmitted to the control loop, so that the system response time can be greatly reduced, and the influence caused by the coupling uncertainty between the two loops can be eliminated.
Aiming at the strong coupling characteristic of hypersonic aircrafts, many scholars at home and abroad consider the aircrafts as rigid bodies, establish a full-state coupling model comprising all states in guidance and control loops, construct a cascade system by a mass center motion equation and a mass center surrounding kinematic equation, and directly obtain rudder deflection control instructions by using information such as line of sight angles, line of sight angular speeds, flight attitude angles and the like through methods such as sliding mode control, self-adaptive control, optimal control and the like. However, the above-mentioned studies cannot completely eliminate the coupling influence between the two systems, and the methods based on the optimal control all have the drawbacks that the calculation load is heavy, it is difficult to reproduce the application, and the like. Furthermore, since IGC methods based on BTT missiles are not well studied, the coupling effect between the yaw circuit and the roll circuit of BTT missiles is rarely considered.
The 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 intersection and butt joint 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 buffeting problem, and the output performance of an actuator is seriously damaged.
Disclosure of Invention
The invention aims to solve the problems that the existing integrated guidance control is a non-affine model, the guidance loop and the control loop cannot realize synchronous control within one simulation step length, and the control precision is low, and provides an integrated affine form guidance control method.
An affine form guidance control integrated control method, comprising the steps of:
an affine form of the guided control integration model is expressed as:
in the method, in the process of the invention,
θ L is the inclination angle of the sight line phi L To achieve the declination, x 2 ＝[α β γ v ] T ，γ V The roll angle of the missile, alpha is attack angle, beta is sideslip angle, and x 3 ＝[ω x ω y ω z ] T ，ω x ω y ω z Representing the angular velocity of the missile body coordinate system relative to the ground coordinate system, u= [ delta ] x δ y δ z ] T U is the desired rudder deflection angle, delta z For yaw rudder deflection angle, delta y For pitching rudder deflection angle, delta x For steering rudder deflection angle d 1 、d 2 And d 3 The system interference caused by pneumatic parameter deviation, the system interference caused by steering engine installation deviation and the system interference caused by missile inertial navigation equipment measurement error are respectively,
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 mass of the missile, g is gravity acceleration, θ is ballistic inclination angle, and phi V Representing the deflection angle of trajectory, q is dynamic pressure, S is the reference area of missile, L is lift force, L is coordination constant required to be designed, J y J x J z Representing the moment of inertia of the three axes of the missile, m x ，m y ，m z Respectively represent the steering moment of the three axes of the missile,
for the lift coefficient c y The deviation of the attack angle alpha, R is the relative distance between the missile and the target;
The beneficial effects of the invention are as follows:
aiming at a BTT missile IGC model, the application provides a novel modeling method: the differential stratosphere of the state variable is not required to be constructed and is directly converted into an affine system model. In addition, aiming at the saturation phenomenon of an actuator, an auxiliary system is designed, the input saturation phenomenon is ensured to be processed, the state of the auxiliary system can enter a small boundary under the condition of no singularity, the self-adaptive technology is applied to estimate 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 error) acting on a BTT missile, and the convergence of a terminal sight angle tracking error and a sight angle rate and the consistent final limitation of the system are strictly proved by applying Lyapunov stability theory.
Therefore, the present application corresponds to controlling u and d in the affine form of guidance control integrated model by designing the controller and controlling the controller 1 、d 2 And d 3 Obtaining x in affine form guidance control integrated model 1 、x 2 And x 3 Is proved to be when x 1 、x 2 And x 3 When approaching the limit of 0, x at this time 1 、x 2 And x 3 Acting on a real missile, the target is easier to hit, and smaller off-target quantity is realized.
The affine form guidance control integrated model designed by the application integrates the control loop and the guidance loop together, so that the guidance loop and the control loop realize synchronous control within one simulation step length, and the control precision is high, for example, in the affine form guidance control integrated model
Indicating a guidance circuit->
And->
Representing the control loop and also designing the unknown quantity d in the affine form of the guided control integrated model by designing the unknown quantity u in the affine form of the guided control integrated model by designing the adaptive rate 1 、d 2 And d 3 Also by designing the virtual control quantity, designing the first filteringThe controller, the second-order backstepping control rate, the auxiliary system and the second filter are designed to complete the control and realize the function of the controller, thereby controlling and obtaining x 1 、x 2 And x 3 。
Drawings
FIG. 1 is a flow chart of an affine form guidance control integrated control method;
FIG. 2 is a three-dimensional view of an integrated guidance law glider attack trajectory;
fig. 3 (1) is a graph of variation of the ballistic tilt angle, in which theta represents the ballistic tilt angle, and fig. 3 (2) is a graph of variation of the ballistic deflection angle, in which fai represents the ballistic deflection angle;
fig. 4 (1) is a line-of-sight inclination angle change graph, and fig. 4 (2) is a line-of-sight deflection angle change graph;
FIG. 5 (1) is a graph of variation of the derivative of the dip angle of trajectory, where dTotal represents the derivative of dip angle of trajectory, and FIG. 5 (2) is a graph of variation of the derivative of the deflection angle of trajectory, where dFail represents the derivative of deflection angle of trajectory;
FIG. 6 (1) is ω x Is shown in FIG. 6 (2) as ω y Is shown in FIG. 6 (3) as ω z A graph of the variation of (2);
FIG. 7 (1) is S 1,1 The change curve is shown in FIG. 7 (2) as S 1,2 A variation graph;
fig. 8 (1), 8 (2) and 8 (3) are S respectively 2 A variation graph of three components;
fig. 9 (1), 9 (2) and 9 (3) are S respectively 3 A variation graph of three components;
fig. 10 (1) is a rudder deflection angle variation chart of the x-axis, wherein detax represents the rudder deflection angle of the x-axis; fig. 10 (2) is a rudder deflection angle variation map of the y-axis, wherein detay represents the rudder deflection angle of the y-axis; fig. 10 (3) is a rudder deflection angle change chart of the z-axis, in which detaz represents the rudder deflection angle of the z-axis.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention is further described below with reference to the drawings and specific examples, which are not intended to be limiting.
The first embodiment is as follows: a guidance control integrated control method of affine form according to the present embodiment will be described with reference to fig. 1, and includes the steps of:
an affine form of the guided control integration model is expressed as:
in the method, in the process of the invention,
θ L is the inclination angle of the sight line phi L To achieve the declination, x 2 ＝[α β γ v ] T ，γ V The roll angle of the missile, alpha is attack angle, beta is sideslip angle, and x 3 ＝[ω x ω y ω z ] T ，ω x ω y ω z Representing the angular velocity of the missile body coordinate system relative to the ground coordinate system, u= [ delta ] x δ y δ z ] T U is the desired rudder deflection angle, delta z For yaw rudder deflection angle, delta y For pitching rudder deflection angle, delta x For steering rudder deflection angle d 1 、d 2 And d 3 The system interference caused by pneumatic parameter deviation, the system interference caused by steering engine installation deviation and the system interference caused by missile inertial navigation equipment measurement error are respectively,
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 mass of the missile, g is gravity acceleration, θ is ballistic inclination angle, and phi V Representing the deflection angle of trajectory, q is dynamic pressure, S is the reference area of missile, L is lift force, L is coordination constant required to be designed, J y J x J z Representing the moment of inertia of the three axes of the missile, m x ，m y ，m z Respectively represent the steering moment of the three axes of the missile,
for the lift coefficient c y The deviation of the attack angle alpha, R is the relative distance between the missile and the target;
In the present embodiment, in the case of the present embodiment,
1. coordinate system establishment
For ease of analysis, the following coordinate system definitions are given here:
(1) Geocentric inertial coordinate system (o I x I y I z I ): origin o of coordinate system I Is the earth center, o I z I The axis being perpendicular to the equatorial plane of the earth and pointing to the north pole, o I x I Shaft and o I y I With axis in equatorial plane o I x I Along the intersection of the equatorial plane with 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 centroid, ox of the aircraft 1 The axis coincides with the longitudinal axis of the aircraft body, the directional head is positive, oy 1 Is positioned in the longitudinal symmetrical plane of the aircraft body and is corresponding to ox 1 The axis is vertical, pointing positively, and oz 1 Is determined by right-hand rule
(7) Velocity coordinate system (ox) v y v z v ): the origin o of coordinates is the mass center of the aircraft, ox v Axis is along the direction of aircraft velocity, oy v The axis is located in the main plane of symmetry of the aircraft and is perpendicular to ox v The axis pointing upwards oz v Axis and ox v y v The faces are perpendicular and form a right hand coordinate system.
(8) Ballistic coordinate system (ox) 2 y 2 z 2 ): the origin o of coordinates is the mass center of the aircraft, ox 2 Axis is along the direction of aircraft velocity, oz 2 The shaft being located in a plumb face containing a velocity vectorPerpendicular to ox 2 A shaft directed downward; oy (Oy) 2 Axis and ox 2 y 2 The faces are perpendicular and form a right hand coordinate system.
2. Model building
Giving a guided integrated missile target relative kinematics and dynamics model. The integrated guidance control is essentially to combine the missile tracking control system and the missile stability control system, and firstly, without losing generality, a missile attack target model is established under a sight line coordinate system as follows:
wherein R is the relative distance between the missile and the target, theta 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, similarly, a ti (i=r, θ, Φ) is an acceleration component of the target on the velocity coordinate system. For a fixed target scene of missile attack ground, a ti ＝0。
In the terminal guidance section, the aerodynamic acceleration of the missile is provided by aerodynamic force, so that the relation between the aerodynamic acceleration of the missile and the aerodynamic force is established by considering the relation between the aerodynamic acceleration of the missile and the aerodynamic force as follows:
wherein m is the mass of the missile, ρ is the air density, V m Is the speed of the missile, q is dynamic pressure, S is the reference area of the missile, and alpha, beta and delta z ，δ y The attack angle, the sideslip angle, the yaw rudder deflection angle and the pitch rudder deflection angle are respectively.
And carrying out stress analysis on the missile, and obtaining projection under a trajectory system:
Y′＝Y cosγ V -Z sinγ V -mg cosθ
Z′＝Y sinγ V +Z cosγ V
the following relation can be obtained by defining the coordinate system and projecting the pneumatic acceleration of the missile on the speed system under the sight coordinate system:
wherein, the liquid crystal display device comprises a liquid crystal display device,
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 )
the new missile target relative kinematics equation can be obtained by arranging the formulas 3 and 4:
the kinematic equations for the ballistic tilt and the ballistic deflection 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 lift force generated by tilting the fuselage turns in a lateral component, and the sideslip angle is 0 through attitude control, so that the three-dimensional guidance control integrated model can be written as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
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 of the three-dimensional guidance and control integrated model. d, d 1 、d 2 And d 3 The system is the total interference 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 Are all disturbances caused by the relevant state errors in the system, so that it can be assumed that the total disturbance is bounded, i.e. the following:
|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 liquid crystal display device comprises a liquid crystal display device,
the functions in the system equation are:
however, in the above-mentioned guidance circuit formula 45, the control amount thereof
Is x 2 Is not affine, resulting in the need for advanced passage of control loop state quantities alpha, beta, gamma in the design of the subsequent control loop v Calculate->
The guidance loop and the control loop cannot realize synchronous control in one simulation step length, and certain influence is caused on control precision and dynamic performance.
In order to deal with this problem, the guidance control integrated model is converted into an affine system model, and the guidance loop and the control loop are uniformly proven. Equation 45, equation 46 and equation 47 are converted into the following forms:
wherein, the liquid crystal display device comprises a liquid crystal display device,
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 of the three-dimensional guidance and control integrated model.
The functions in the system equation are:
where l is the coordination constant that needs to be designed.
And (3) designing a controller:
the application designs a self-adaptive sliding mode guidance rate based on a back-stepping method to realize the stabilization of a model and ensure the system state x 1 ，x 2 ，x 3 Practical stabilization is achieved in the case of unknown disturbances and input saturation.
To solve the problem of unknown disturbance upper bound, the disturbance term d 'in the model (formula 1) is firstly calculated' 1 ，d 2 ，d 3 One assumption is made:
let 1 be the set d 'of all disturbances in model (1)' 1 ，d 2 ，d 3 Is bounded and 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 Is a slip form surface S 1 ：
S 1 ＝[S 1,1 S 1,2 ] T
Lyapunov equation
And (3) deriving:
therefore, when the designed slip form surface converges to zero,
can be converted into
Wherein ρ is 1 ＝min{2k 11 ,2k 12 }. Then to ensure the slip plane S 1 Convergence, designing the following virtual control amount:
wherein k is 1 Is a positive diagonal matrix and k 1 ＝[k 1,1 k 1,2 ] T ，k 2 Is a positive constant which is used for the control of the power supply,
to disturbance d' 1 The estimation of the upper limit is carried out and the estimation error is set up>
Let Lyapunov equation be
The derivation can be obtained:
wherein S is 2 ＝x 2 -x 2c -y 1 ，
Wherein k is c1 > 0. Substituting equation 20 into the virtual control amount yields:
to ensure that the virtual state quantity is bounded, a second-order backstepping control rate is designed for S 2 Stabilization is carried out:
wherein k is 3 Is a positive constant which is used for the control of the power supply,
to disturbance d 2 The estimation of the upper limit is carried out and the estimation error is set up>
Let Lyapunov equation be
/>
The derivation can be obtained:
wherein S is 3 ＝x 3 -x 3c -y 2 - ζ, the filtering error of the second filter
ζ is the state of the designed auxiliary system
Wherein k is c2 ,k ξ ＞0，Δu＝[Δu 1 Δu 2 Δu 3 ] T Representing controller output bias due to input saturation
Δu i ＝u i -u c,i (i＝1,2,3)
Substituting the equation 22, the equation 23 and the second-order backstepping virtual control amount into the equation 31 to obtain
The following guidance rate and adaptation rate can be designed to ensure that all states are stable in the presence of external disturbances in the position
Wherein k is 4 Is a positive constant.
The following theorem is given later;
theorem 1: under the condition that the assumption 1 is established, the improved affine form BTT missile guidance control integrated model (formula 1) is utilized, and the designed guidance rate, the auxiliary system, the first filter, the second filter and the self-adaptive rate are applied to ensure S 1 ,S 2 ,S 3 Are all practically stable, and x 1 ,x 2 ,x 3 Can also realize actual stability
And (3) proving:
design of lyapunov function:
the above is derived and substituted into the controller (formula 24) to obtain:
note that: by means of the designed auxiliary system, it can be seen in the derivation of the above formula: representing actuator output difference terms due to input saturation
Can be compensated by the auxiliary system, thus enabling the state x of the system model (equation 1) to be compensated in the presence of input saturation 1 ,x 2 ,x 3 Stabilization is performed.
Substitution of the adaptive equation
In (1) to obtain
The application of the young's inequality is available:
substitution 35 can be obtained:
due to the nature of the low pass filter it is known that: y is 1 ,y 2 Are all bounded. And according to b 1 And b 2 Definition of (2)
Can obtain b 1 y 1 Sum of I b 2 y 2 The l is bounded. />
It is assumed here that their upper bounds are:
equation 38 can be converted into
Wherein c=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 Estimate error of the disturbance upper limit
Are consistent and stable.
1. When S is 1 If there is a limit, then according to its definition
The method can obtain:
2. when S is 2 If there is a limit, then according to its definition (S 2 ＝x 2 -x 2c -y 1 ) The method can obtain:
||x 2 ||≤||S 2 +y 1 +x 2c ||≤φ s +||y 1 ||+||x 2c ||
thus, the first and second substrates are bonded together, ||x 2 I is also bounded.
3. When S is 3 If there is a limit, then according to its definition (S 3 ＝x 3 -x 3c -y 2 - ζ) is available:
||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 Is bounded, and can directly derive that the auxiliary system state ζ is bounded.
Then it can obtaining ||x 3 I is also bounded.
Based on the above analysis, it can be obtained that: all states x 1 ,x 2 ,x 3 Are all bounded.
Simulation analysis
And performing simulation analysis on the designed integrated guidance law, and similarly, taking the projection of the missile at the terminal guidance starting moment on the ground as an origin, establishing a coordinate system, and setting terminal guidance simulation initial conditions as follows:
the initial positions of the missile and the target are as follows: x is x m0 ＝0km，y m0 ＝20km，z m0 ＝0km，x t0 ＝16km，y t0 ＝0km，z t0 ＝0km；
The speed of the missile terminal guidance starting moment is as follows: v m0 The ballistic tilt angle θ= -6 °, the ballistic deflection angle ψ=5° is =1200 m/s; the initial attitude angle is: alpha 0 ＝5°，β 0 ＝0°，γ 0 =10°; the desired end attack angle is: θ f ＝-72°，ψ f -2 °. The end guidance trajectory simulation results are shown in fig. 2 to 10. The final off-target amount was 1.16m. As can be seen from the simulation results described above: slip plane S 1 Virtual error S 2 ,S 3 Can ensure convergence to a small boundary near zero, and under the condition that the input saturation external disturbance exists, the state quantity x of the system 1 ,x 2 ,x 3 Can converge to a small boundary around zero. The final line of sight inclination and line of sight offset can both converge to the desired line of sight inclination and line of sight offset.
Therefore, the application designs the terminal attack guidance law for the scene of the assisted gliding rocket projectile attacking the low-speed moving target, and firstly gives an affine form guidance control integrated model designed in consideration of the coupling factors between the guidance system and the control system; then, based on a sliding mode control theory, designing a guidance law with end sight angle constraint; and designing an auxiliary system according to the adaptive theory, wherein the disturbance existing in the model can be proved, and the stability of the system can be ensured when input saturation exists. Finally, the effectiveness of the designed guidance laws is verified by simulation analysis.
The second embodiment is as follows: the present embodiment is further defined by the affine form guidance control integrated control method according to the first embodiment, wherein in step 1, the missile attack target model is expressed as:
wherein a is tR 、a tθ And a tφ Representing three acceleration components, a, of a target in a velocity coordinate system mR 、a mθ And a mφ Representing three acceleration components of the missile in the velocity coordinate system,
for the second derivative of R>
For theta of L Is used for the first derivative of (c),
the projection equation of the aerodynamic acceleration of the missile on the velocity system to the sight coordinate system is expressed as:
wherein a is my ,a mz For the pneumatic acceleration of the missile at the velocity train,
Z′＝Y sinγ V +Z cosγ V ，Y′＝Y cosγ V -Z sinγ V -mg cosθ，/>
for the lift coefficient c y Deviation of attack angle alpha +.>
For the lift coefficient c y Deviation of sideslip angle beta +.>
For the lateral force coefficient c z Deviation of attack angle alpha +.>
For the lateral force coefficient c z Deviation of sideslip angle beta +.>
For the lateral force coefficient c z For the deflection angle delta of pitching rudder y Is a bias guide of (2);
the missile target relative kinematic model is expressed as:
the kinematic equations for the ballistic tilt and the ballistic deflection are expressed as:
wherein V is m Is missile speed;
the attitude dynamics model of the missile is expressed as:
and a third specific embodiment: in this embodiment, in step 3, u and d 'in the affine form of the integrated model of the integrated control of the guided control are controlled' 1 、d 2 And d 3 Obtaining x in affine form guidance control integrated model 1 、x 2 And x 3 The specific process is as follows:
step 31, obtaining a derivative of a first Lyapunov equation according to the sliding film surface, the affine form guidance control integrated model and the first Lyapunov equation;
controlling an integrated model according to the guidance of the sliding film surface and affine form, and setting a first-order virtual error S 2 And a second Lyapunov equation, the derivative of the second Lyapunov equation being obtained;
according to the slide film surface, affine form guidance control integrated model and first-order virtual error S 2 Second order virtual error S 3 And a third Lyapunov equation, resulting in a derivative of the third Lyapunov equation,
step 32, obtaining new derivative of the second Lyapunov equation according to the virtual control quantity 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 for u and the guidance rate for d' 1 、d 2 And d 3 Obtaining the derivative of the Lyapunov function;
step 34, obtaining new derivative of Lyapunov function according to derivative of Lyapunov function and Young's inequality, combining with synovial surface to obtain x in affine form guidance control integrated model 1 、x 2 And x 3 Is defined in the specification.
The specific embodiment IV is as follows: the present embodiment is further defined by the affine form guidance control integrated control method according to the third embodiment, wherein in the step 32, the virtual control amount x 2c The method comprises the following steps:
let d' 1 ，d 2 ，d 3 Is bounded and unknown, 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
let d%' 1 ||≤d 1m ，||d 2 ||≤d 2m ，||d 3 ||≤d 3m ；
x 2c Expressed as:
wherein k is 1 Is a positive diagonal matrix and k 1 ＝[k 1,1 k 1,2 ] T ，k 1,1 And k 1,2 Is k 1 Is 2 components of k 2 Is a positive constant which is used for the control of the power supply,
to pair d 1m Is determined by the estimation of (a);
the first filter designed is:
wherein k is c1 Is constant, k c1 ＞0，
For the first filter output, +.>
A derivative of the output of the first filter;
the designed second-order backstepping control rate is as follows:
wherein k is 3 Is a positive constant which is used for the control of the power supply,
to pair d 2m Is based on the estimation of S 2 ＝x 2 -x 2c -y 1 ，/>
S 1 Is a sliding film surface;
the second filter was designed as:
wherein k is c2 ＞0，x 3c For the other virtual control quantity,
for the second filter output, +.>
A derivative of the output of the second filter;
the designed auxiliary system is as follows:
wherein k is ξ ＞0，Δu＝[Δu 1 Δu 2 Δu 3 ] T ，Δu i ＝u i -u c,i (i＝1,2,3)，u i To the ith component of the desired rudder deflection angle u, u c,i Is the actual rudder deflection angle u c Is used to determine the (i) th component of the (c),
u max the maximum rudder deflection angle is output, and xi is the state of the auxiliary system; />
The designed guidance rate is as follows:
in the method, in the process of the invention,
to pair d 3m Is k 4 Is a normal number S 3 ＝x 3 -x 3c -y 2 -ξ，/>
The self-adaption rate of the design is as follows:
wherein k is θ1 、k θ2 、k θ3 、k θ4 、k θ5 、k θ6 Are all normal S 2 And S is 3 Representing 2 virtual errors.
Fifth embodiment: the present embodiment is further defined by an affine form guidance control integrated control method according to the fourth embodiment, wherein in the present embodiment, in step 31, a derivative of the first lyapunov equation is obtained, and the specific process is as follows:
first, design a control method for theta L And phi L Is a slip form surface S 1 ：
Wherein S is 1,1 And S is 1,2 Representing the slide surface S 1 Component, k of 11 k 12 Is the normal number of the two groups of the,
let the first Lyapunov equation
The first lyapunov equation is derived according to equations 26 and 1:
when the sliding die surface S 1 To converge to zero, equation 27 transitions to:
wherein ρ is 1 ＝min{2k 11 ,2k 12 }。
Specific embodiment six: the present embodiment is further defined by an affine form guidance control integrated control method according to the fifth embodiment, wherein in the present embodiment, in step 31, a derivative of the second lyapunov equation is obtained, and the specific process is as follows:
let the second Lyapunov equation be
According to equation 26, equations 1 and S 2 ＝x 2 -x 2c -y 1 Deriving a second Lyapunov equation:
wherein y is 1 For the filtering error of the first filter,
seventh embodiment: the present embodiment is further defined by the affine form guidance control integrated control method according to the sixth embodiment, wherein in the step 32, a new derivative of the second lyapunov equation is obtained, specifically:
the virtual control quantity formula is brought into formula 29 to obtain the new second derivative of Lyapunov equation as:
eighth embodiment: the present embodiment is further defined by the affine form guidance control integrated control method according to the seventh embodiment, wherein in the present embodiment, in step 31, a derivative of the third lyapunov equation is obtained, specifically:
let the third Lyapunov equation be
According to formula 26, formulas 1, S 2 ＝x 2 -x 2c -y 1 And S is 3 ＝x 3 -x 3c -y 2 ζ, deriving the third Lyapunov equation:
wherein y is 2 For the filtering error of the second filter,
in step 33, a new third derivative of the lyapunov equation is obtained, specifically:
bringing equations 20, 21, 22 and 23 into equation 31 yields the new third derivative of Lyapunov equation:
detailed description nine: the present embodiment is further defined by an affine form guidance control integrated control method according to the eighth embodiment, wherein in the present embodiment, in step 33, a derivative of the lyapunov function is obtained, and the specific procedure is as follows:
the lyapunov function was designed as:
in the method, in the process of the invention,
is d 1m Error of estimation of ∈10->
And deriving the formula 33 according to the preparation rate, 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 method, in the process of the invention,
is d 2m Error of estimation of ∈10->
Is d 3m Error of estimation of ∈10->
The equation 34 is taken into the adaptive rate equation to obtain the derivative of the lyapunov function:
detailed description ten: in this embodiment, in step 34, x in the affine-form integrated guidance control model is obtained, which is a further limitation of the affine-form integrated guidance control method according to the ninth embodiment 1 、x 2 And x 3 The specific process is as follows:
the young inequality is:
bringing equations 36 and 37 into equation 35 yields:
from the properties of the first filter and the second filter, it is known that: y is 1 ,y 2 Are all bounded and according to b 1 And b 2 Definition of (b) yields |b 1 y 1 Sum of I b 2 y 2 The l is bounded, here it is assumed that their upper bound is:
in the method, in the process of the invention,
and->
2 positive constants;
according to equation 39, equation 38 is converted into:
where c=min { k } 2 ,k 3 ,2k 4 ,k θ2 k θ1 ,k θ3 k θ4 ,k θ5 k θ6 }，
According to equation 40, we get:
wherein i=1, 2,3, t is time,
when S is 1 If there is a limit, then according to S 1 Is defined by (1), resulting in:
when S is 2 In the case of limitation, according to S 2 Is defined by (1), resulting in:
||x 2 ||≤||S 2 +y 1 +x 2c ||≤φ s +||y 1 ||+||x 2c i, equation 43
Thus, the first and second substrates are bonded together, ||x 2 It is also bounded that it is,
when S is 3 In the case of limitation, according to S 3 Is defined by (1), resulting in:
||x 3 ||≤||S 3 +y 2 +x 3c +ξ||≤φ s +||y 1 ||+||x 2c +|ζ|, equation 44
Since the xi is a finite number of times, obtaining ||x 3 I is also bounded;
thus, x in the affine form of the guidance control integrated model is obtained 1 、x 2 And x 3 Is defined in the specification.
In the present 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 the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.
Claims (10)
1. An affine form guidance control integrated control method, characterized by comprising the steps of:
step 1, according to a missile attack target model and a projection equation for projecting the pneumatic acceleration of the missile on a speed system to a sight line coordinate system, a missile target relative kinematics model, a trajectory dip angle and a trajectory deflection angle kinematics equation and a missile attitude dynamics model are obtained;
step 2, establishing an affine form guidance control integrated model according to a missile target relative kinematics model, a missile attitude dynamics model, system interference caused by aerodynamic parameter deviation, system interference caused by steering engine installation deviation and system interference caused by missile inertial navigation equipment measurement error;
an affine form of the guided control integration model is expressed as:
in the method, in the process of the invention,
θ L is the inclination angle of the sight line phi L To achieve the declination, x 2 ＝[α β γ v ] T ，γ V The roll angle of the missile, alpha is attack angle, beta is sideslip angle, and x 3 ＝[ω x ω y ω z ] T ，ω x ω y ω z Represents the angular velocity of the missile body coordinate system relative to the ground coordinate system, u= [ delta ] x δ y δ z ] T U is the desired rudder deflection angle, delta z For yaw rudder deflection angle, delta y For pitching rudder deflection angle, delta x For steering rudder deflection angle d 1 、d 2 And d 3 The system interference caused by pneumatic parameter deviation, the system interference caused by steering engine installation deviation and the system interference caused by missile inertial navigation equipment measurement error are respectively,
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 mass of the missile, g is gravity acceleration, θ is ballistic inclination angle, and phi V Representing the deflection angle of trajectory, q is dynamic pressure, S is the reference area of missile, L is lift force, and L is the coordination needed to be designedConstant, J y J x J z Representing the moment of inertia of the three axes of the missile, m x ，m y ，m z Respectively represent the steering moment of the three axes of the missile,
for the lift coefficient c y Deviation of attack angle alpha, R is the relative distance between missile and target, V m For missile speed, +.>
For the lift coefficient c y Deviation of attack angle alpha +.>
For the lateral force coefficient c z Deviation of the sideslip angle beta;
step 3, controlling u and d in the integrated model by controlling affine form guidance 1 ′、d 2 And d 3 Obtaining x in affine form guidance control integrated model 1 、x 2 And x 3 By x 1 、x 2 And x 3 Is controlling the true missile.
2. The affine form guidance control integrated control method according to claim 1, wherein in step 1, the missile attack target model is expressed as:
wherein a is tR 、a tθ And a tφ Representing three acceleration components, a, of a target in a velocity coordinate system mR 、a mθ And a mφ Representing three acceleration components of the missile in the velocity coordinate system,
for the second derivative of R>
For theta of L Is used for the first derivative of (c),
the projection equation of the aerodynamic acceleration of the missile on the velocity system to the sight coordinate system is expressed as:
wherein a is my ,a mz For the pneumatic acceleration of the missile at the velocity train,
Z′＝Ysinγ V +Zcosγ V ，Y′＝Ycosγ V -Zsinγ V -mgcosθ，/>
for the lift coefficient c y Deviation of attack angle alpha +.>
For the lift coefficient c y For yaw rudder deflection angle delta z Is of the type of (A) and (B)>
For the lateral force coefficient c z Deviation of attack angle alpha +.>
For the lateral force coefficient c z Deviation of sideslip angle beta +.>
For the lateral force coefficient c z For the deflection angle delta of pitching rudder y Is a bias guide of (2);
the missile target relative kinematic model is expressed as:
the kinematic equations for the ballistic tilt and the ballistic deflection are expressed as:
wherein V is m Is missile speed;
the attitude dynamics model of the missile is expressed as:
3. the affine form guidance control integrated control method according to claim 2, wherein in step 3, u, d in the affine form guidance control integrated model are controlled 1 ′、d 2 And d 3 Obtaining x in affine form guidance control integrated model 1 、x 2 And x 3 The specific process is as follows:
step 31, obtaining a derivative of a first Lyapunov equation according to the sliding film surface, the affine form guidance control integrated model and the first Lyapunov equation;
controlling an integrated model according to the guidance of the sliding film surface and affine form, and setting a first-order virtual error S 2 And a second Lyapunov equation, the derivative of the second Lyapunov equation being obtained;
according to the slide film surface, affine form guidance control integrated model and first-order virtual error S 2 Second order virtual error S 3 And a third Lyapunov equation, resulting in a derivative of the third Lyapunov equation,
step 32, obtaining new derivative of the second Lyapunov equation according to the virtual control quantity 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, derivative of the first Lyapunov equation, derivative of the new second Lyapunov equation, derivative of the new third Lyapunov equation, guidance rate for u and guidance rate for d according to the designed Lyapunov function 1 ′、d 2 And d 3 Obtaining the derivative of the Lyapunov function;
step 34, obtaining new derivative of Lyapunov function according to derivative of Lyapunov function and Young's inequality, combining with synovial surface to obtain x in affine form guidance control integrated model 1 、x 2 And x 3 Is defined in the specification.
4. An affine form guidance control integrated control method according to claim 3, wherein in step 32, the virtual control amount x 2c The method comprises the following steps:
suppose d 1 ′，d 2 ，d 3 Is bounded and unknown, satisfies:
let d'd less than d 1m ，||d 2 ||≤d 2m ，||d 3 ||≤d 3m ；
x 2c Expressed as:
wherein k is 1 Is a positive diagonal matrix and k 1 ＝[k 1,1 k 1,2 ] T ，k 1,1 And k 1,2 Is k 1 Is 2 components of k 2 Is a positive constant which is used for the control of the power supply,
to pair d 1m Is determined by the estimation of (a);
the first filter designed is:
wherein k is c1 Is constant, k c1 ＞0，
For the first filter output, +.>
A derivative of the output of the first filter;
the designed second-order backstepping control rate is as follows:
wherein k is 3 Is a positive constant which is used for the control of the power supply,
to pair d 2m Is based on the estimation of S 2 ＝x 2 -x 2c -y 1 ，/>
S 1 Is a sliding film surface;
the second filter was designed as:
wherein k is c2 ＞0，x 3c For the other virtual control quantity,
for the second filter output, +.>
A derivative of the output of the second filter;
the designed auxiliary system is as follows:
wherein k is ξ ＞0，Δu＝[Δu 1 Δu 2 Δu 3 ] T ，Δu i ＝u i -u c,i (i＝1,2,3)，u i To the ith component of the desired rudder deflection angle u, u c,i Is the actual rudder deflection angle u c Is used to determine the (i) th component of the (c),
u max the maximum rudder deflection angle is output, and xi is the state of the auxiliary system;
the designed guidance rate is as follows:
in the method, in the process of the invention,
to pair d 3m Is k 4 Is a normal number S 3 ＝x 3 -x 3c -y 2 -ξ，/>
The self-adaption rate of the design is as follows:
wherein k is θ1 、k θ2 、k θ3 、k θ4 、k θ5 、k θ6 Are allPositive constant, S 2 And S is 3 Representing 2 virtual errors.
5. The affine form guidance control integrated control method according to claim 4, wherein in step 31, the derivative of the first lyapunov equation is obtained by:
first, design a control method for theta L And phi L Is a slip form surface S 1 ：
Wherein S is 1,1 And S is 1,2 Representing the slide surface S 1 Component, k of 11 k 12 Is the normal number of the two groups of the,
let the first Lyapunov equation
The first lyapunov equation is derived according to equations 26 and 1:
when the sliding die surface S 1 To converge to zero, equation 27 transitions to:
wherein ρ is 1 ＝min{2k 11 ,2k 12 }。
6. The affine form guidance control integrated control method according to claim 5, wherein in step 31, the derivative of the second lyapunov equation is obtained by:
let the second Lyapunov equation be
According to equation 26, equations 1 and S 2 ＝x 2 -x 2c -y 1 Deriving a second Lyapunov equation:
wherein y is 1 For the filtering error of the first filter,
7. the affine form guidance control integrated control method according to claim 6, wherein in step 32, the derivative of the new second lyapunov equation is obtained, specifically:
the virtual control quantity formula is brought into formula 29 to obtain the new second derivative of Lyapunov equation as:
8. the affine form guidance control integrated control method according to claim 7, wherein in step 31, the derivative of the third lyapunov equation is obtained, specifically:
let the third Lyapunov equation be
According to formula 26, formulas 1, S 2 ＝x 2 -x 2c -y 1 And S is 3 ＝x 3 -x 3c -y 2 ζ, deriving the third Lyapunov equation:
wherein y is 2 For the filtering error of the second filter,
in step 33, a new third derivative of the lyapunov equation is obtained, specifically:
bringing equations 20, 21, 22 and 23 into equation 31 yields the new third derivative of Lyapunov equation:
9. the affine form guidance control integrated control method according to claim 8, wherein in step 33, the derivative of the lyapunov function is obtained by the following steps:
the lyapunov function was designed as:
in the method, in the process of the invention,
is d 1m Error of estimation of ∈10->
And deriving the formula 33 according to the preparation rate, 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 method, in the process of the invention,
is d 2m Error of estimation of ∈10->
Is d 3m Error of estimation of ∈10->
The equation 34 is taken into the adaptive rate equation to obtain the derivative of the lyapunov function:
10. the affine form guidance control integrated control method according to claim 9, wherein in step 34, x in the affine form guidance control integrated model is obtained 1 、x 2 And x 3 The specific process is as follows: the young inequality is:
bringing equations 36 and 37 into equation 35 yields:
from the properties of the first filter and the second filter, it is known that: y is 1 ,y 2 Are all bounded and according to b 1 And b 2 Definition of (b) yields b 1 y 1 And b 2 y 2 Is bounded, and it is assumed here that their upper bound is:
in the method, in the process of the invention,
and->
2 positive constants;
according to equation 39, equation 38 is converted into:
where c=min { k } 2 ,k 3 ,2k 4 ,k θ2 k θ1 ,k θ3 k θ4 ,k θ5 k θ6 }，
According to equation 40, we get:
wherein i=1, 2,3, t is time,
when S is 1 If there is a limit, then according to S 1 Is defined by (1), resulting in:
when S is 2 In the case of limitation, according to S 2 Is defined by (1), resulting in:
x 2 ≤S 2 +y 1 +x 2c ≤φ s +y 1 +x 2c equation 43
Thus, x 2 It is also a matter of course that,
when S is 3 In the case of limitation, according to S 3 Is defined by (1), resulting in:
x 3 ≤S 3 +y 2 +x 3c +ξ≤φ s +y 1 +x 2c +ζ, equation 44
Since ζ is bounded, we obtain x 3 Is also bounded;
thus, x in the affine form of the guidance control integrated model is obtained 1 、x 2 And x 3 Is defined in the specification.
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