CN110618608B - Composite guidance tracking control method and device - Google Patents

Abstract

The invention relates to a composite guidance tracking control method and a device, which mainly aim at a guided missile direct force/aerodynamic force composite control system, consider the influence of a nonlinear function and external interference, and firstly estimate the system state by constructing a state observer; and secondly, uncertainty in a missile composite control system is eliminated through a designed integral sliding mode surface and a state observer, the stability of a closed-loop system is guaranteed, the response speed of the missile can be effectively improved, and the stability and overload capacity of the missile are increased.

Description

A composite guidance tracking control method and device

technical field

The invention belongs to the technical field of aerospace, and in particular relates to a composite guidance tracking control method and device.

Background technique

With the advancement of science and technology, traditional aerodynamic guidance can no longer meet the needs of modern warfare. Therefore, the new generation of missile control technology generally adopts the direct/air composite control method to improve the guidance accuracy of the missile. A lot of research has been done at home and abroad for the straight/gas composite control system. Among them, the French Aster and the American Patriot missiles have successfully completed interception experiments. Compared with conventional aerodynamic missiles, the control guidance has a faster response speed. High stability is an effective way to achieve "zero off-target amount".

The missile straight/air composite control system has strong nonlinearity and uncertainty, so it brings great difficulty to the modeling and control of the composite control system. In recent years, researchers at home and abroad have used sliding mode control, adaptive theory, fuzzy control, optimal control and other theories to study composite control systems, but most of these have ignored the influence of nonlinear factors and external disturbances in the control system. , resulting in instability of the existing composite guidance tracking control.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a composite guidance tracking control method and device, which is used to solve the problem of instability of the control system caused by ignoring nonlinear factors and external disturbances in the existing "using sliding mode variable structure for composite guidance control" in modeling .

In order to solve the above-mentioned technical problems, the present invention proposes a composite guidance tracking control method, which includes the following steps:

1) According to the set nonlinear function and external disturbance, establish the missile dynamics model of the missile composite control system as follows:

α_j(j＝1…5)为导弹动力学参数，f(x,t)是非线性函数，d(·)是外部干扰，C是给定矩阵，u₁是系统综合控制率，u₁＝σ_z+A₁B⁺F，σ_z是舵偏角，

l为导弹质心到脉冲发动机的距离，J_z是导弹气动力参数中的转动惯量，

m为弹体质量，v是导弹在末节制导时速度，F是侧喷发动机最大推力值，B⁺是系数B的广义逆；where x(t) is the state variable of the missile dynamics model, y(t) is the output variable of the missile dynamics model,

α _j (j=1...5) is the missile dynamics parameter, f(x, t) is the nonlinear function, d( ) is the external disturbance, C is the given matrix, u ₁ is the comprehensive control rate of the system, u ₁ = σ _z +A ₁ B ⁺ F, σ _z is the rudder deflection angle,

l is the distance from the center of mass of the missile to the pulse engine, J _z is the moment of inertia in the aerodynamic parameters of the missile,

m is the mass of the projectile, v is the speed of the missile when it is guided at the distal end, F is the maximum thrust value of the side-jet engine, and B ⁺ is the generalized inverse of the coefficient B;

2) Construct a state observer according to the comprehensive control rate u ₁ of the system, the output variable y(t) of the missile dynamics model and the sliding mode dynamic equation, and obtain the state variable of the state observer and the estimation function of the output variable; The sliding mode dynamic equation described above is obtained through the following steps:

S1) Design an integral sliding mode surface according to the state variable of the state observer;

S2) make a difference between the state variable of the missile dynamics model and the state variable of the state observer to obtain an error estimate;

S3) Using the error estimation and combining the output variable y(t) of the missile dynamics model, the sliding mode dynamic equation is obtained.

Because the system state is not completely measurable in the process of compound guidance and tracking control, there are uncertainties of nonlinearity and disturbance. The present invention takes into account the influence of nonlinear functions and external disturbances. First, the system state is estimated by constructing a state observer; secondly, the uncertainty in the missile composite control system is eliminated through the designed integral sliding mode surface and state observer. , which ensures the stability of the closed-loop system, can effectively improve the response speed of the missile, and increase the stability and overload capacity of the missile.

As a further definition of the nonlinear function, the nonlinear function satisfies the following constraints:

||f(x,t)||≤α+β||y(t)||

In the formula, α>0, β>0 are unknown parameters.

As a further definition of external interference, the external interference satisfies the following constraints:

||d(·)||<d, where d is an unknown scalar.

As a further definition of the state observer, the state observer is as follows:

为x(t)的估计值，u_e是设定的函数，并用于衰减非线性函数和外部干扰的影响，C是给定矩阵，L是观测器增益。In the formula,

is the estimated value of x(t), _ue is the set function and is used to attenuate the influence of nonlinear functions and external disturbances, C is the given matrix, and L is the observer gain.

As a further definition of the integral sliding mode surface, the integral sliding mode surface is as follows:

In the formula, s(t) is the function of the integral sliding mode surface, K is the coefficient matrix, and K is selected so that A+BK is a Hurwitz matrix, Q is a symmetric positive definite matrix, and B is a non-singular matrix.

As a further limitation of the error estimate, the obtained error estimate is as follows:

where e(t) is the error estimate.

Further, the derivative of the integral sliding mode surface function is:

Setting this derivative to zero and solving for it yields:

是所述积分滑模面的函数的导数，L是观测器增益，C是给定矩阵，e(t)是所述误差估计，u_e是设定的函数，并用于衰减非线性函数和外部干扰的影响。In the formula,

is the derivative of the function of the integral sliding mode surface, L is the observer gain, C is the given matrix, e(t) is the error estimate, u _e is the set function and is used to attenuate nonlinear functions and external the effect of interference.

Further, _ue adopts the following calculation formula:

其中，S_e(t)＝B^TXe(t)，X＞0且满足B^TX＝NC，N是给定矩阵。In the formula,

Wherein, Se (t)=B ^T _Xe (t), X>0 and satisfy B ^T X=NC, N is a given matrix.

As a further definition of the sliding mode dynamic equation, the sliding mode dynamic equation is as follows:

where e(t) is the error estimate, L is the observer gain, and I is the identity matrix.

In order to solve the above-mentioned technical problems, the present invention also proposes a composite guidance and tracking control device, comprising a processor for implementing the instructions for executing the following steps:

1) According to the set nonlinear function and external disturbance, establish the missile dynamics model of the missile composite control system as follows:

α_j(j＝1…5)为导弹动力学参数，f(x,t)是非线性函数，d(·)是外部干扰，C是给定矩阵，u₁是系统综合控制率，u₁＝σ_z+A₁B⁺F，σ_z是舵偏角，

l为导弹质心到脉冲发动机的距离，J_z是导弹气动力参数中的转动惯量，

m为弹体质量，v是导弹在末节制导时速度，F是侧喷发动机最大推力值，B⁺是系数B的广义逆；where x(t) is the state variable of the missile dynamics model, y(t) is the output variable of the missile dynamics model,

α _j (j=1...5) is the missile dynamics parameter, f(x, t) is the nonlinear function, d( ) is the external disturbance, C is the given matrix, u ₁ is the comprehensive control rate of the system, u ₁ = σ _z +A ₁ B ⁺ F, σ _z is the rudder deflection angle,

l is the distance from the center of mass of the missile to the pulse engine, J _z is the moment of inertia in the aerodynamic parameters of the missile,

m is the mass of the projectile, v is the speed of the missile when it is guided at the distal end, F is the maximum thrust value of the side-jet engine, and B ⁺ is the generalized inverse of the coefficient B;

2) Construct a state observer according to the comprehensive control rate u ₁ of the system, the output variable y(t) of the missile dynamics model and the sliding mode dynamic equation, and obtain the state variable of the state observer and the estimation function of the output variable; The sliding mode dynamic equation described above is obtained through the following steps:

S1) Design an integral sliding mode surface according to the state variable of the state observer;

S2) make a difference between the state variable of the missile dynamics model and the state variable of the state observer to obtain an error estimate;

S3) Using the error estimation and combining the output variable y(t) of the missile dynamics model, the sliding mode dynamic equation is obtained.

As a further definition of the nonlinear function, the nonlinear function satisfies the following constraints:

||f(x,t)||≤α+β||y(t)||

In the formula, α>0, β>0 are unknown parameters.

As a further definition of external interference, the external interference satisfies the following constraints:

||d(·)||<d, where d is an unknown scalar.

As a further definition of the state observer, the state observer is as follows:

为x(t)的估计值，u_e是设定的函数，并用于衰减非线性函数和外部干扰的影响，C是给定矩阵，L是观测器增益。In the formula,

is the estimated value of x(t), _ue is the set function and is used to attenuate the influence of nonlinear functions and external disturbances, C is the given matrix, and L is the observer gain.

As a further definition of the integral sliding mode surface, the integral sliding mode surface is as follows:

In the formula, s(t) is the function of the integral sliding mode surface, K is the coefficient matrix, and K is selected so that A+BK is a Hurwitz matrix, Q is a symmetric positive definite matrix, and B is a non-singular matrix.

As a further limitation of the error estimate, the obtained error estimate is as follows:

where e(t) is the error estimate.

Further, the derivative of the function of the integral sliding mode surface is:

Setting this derivative to zero and solving for it yields:

是所述积分滑模面的函数的导数，L是观测器增益，C是给定矩阵，e(t)是所述误差估计，u_e是设定的函数，并用于衰减非线性函数和外部干扰的影响。In the formula,

is the derivative of the function of the integral sliding mode surface, L is the observer gain, C is the given matrix, e(t) is the error estimate, u _e is the set function and is used to attenuate nonlinear functions and external the effect of interference.

Further, _ue adopts the following calculation formula:

其中，S_e(t)＝B^TXe(t)，X＞0且满足B^TX＝NC，N是给定矩阵。In the formula,

Wherein, Se (t)=B ^T _Xe (t), X>0 and satisfy B ^T X=NC, N is a given matrix.

As a further definition of the sliding mode dynamic equation, the sliding mode dynamic equation is as follows:

where e(t) is the error estimate, L is the observer gain, and I is the identity matrix.

Description of drawings

Fig. 1 is the flow chart of the composite guidance tracking control method of the present invention;

Figure 2 is the output response curve of overload tracking when the attack angle command is 10 and the attack angle command is 8;

Fig. 3 is the output response curve of the pitch angular velocity when the attack angle command is 10 and the attack angle command is 8;

Figure 4 is the output response curve of the overload tracking error when the attack angle command is 10 and the attack angle command is 8;

Fig. 5 is the output response curve diagram of the comprehensive control rate u ₁ when the attack angle command is 10 and the attack angle command is 8;

Fig. 6 is the output response curve diagram of the pitch angle velocity tracking error e(t) when the attack angle command is 10 and the attack angle command is 8;

Fig. 7 is the output response curve of the angle of attack tracking when the command of the angle of attack is 10 and the command of the angle of attack is 8;

Figure 8 is a schematic diagram of the system sliding mode motion trajectory.

Detailed ways

The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

Example 1:

The present invention provides a composite guidance tracking control method, comprising the following steps:

1) According to the set nonlinear function and external disturbance, establish the missile dynamics model of the missile composite control system as follows:

α_j(j＝1…5)为导弹动力学参数，f(x,t)是非线性函数，d(·)是外部干扰，C是给定矩阵，u₁是系统综合控制率，u₁＝σ_z+A₁B⁺F，σ_z是舵偏角，

l为导弹质心到脉冲发动机的距离，J_z是导弹气动力参数中的转动惯量，

m为弹体质量，v是导弹在末节制导时速度，F是侧喷发动机最大推力值，B⁺是系数B的广义逆；where x(t) is the state variable of the missile dynamics model, y(t) is the output variable of the missile dynamics model,

α _j (j=1...5) is the missile dynamics parameter, f(x, t) is the nonlinear function, d( ) is the external disturbance, C is the given matrix, u ₁ is the comprehensive control rate of the system, u ₁ = σ _z +A ₁ B ⁺ F, σ _z is the rudder deflection angle,

l is the distance from the center of mass of the missile to the pulse engine, J _z is the moment of inertia in the aerodynamic parameters of the missile,

m is the mass of the projectile, v is the speed of the missile when it is guided at the distal end, F is the maximum thrust value of the side-jet engine, and B ⁺ is the generalized inverse of the coefficient B;

2) According to the comprehensive control rate u ₁ of the system, the output variable y(t) of the missile dynamics model and the sliding mode dynamic equation, the state observer is constructed, and the estimated functions of the state variable and output variable of the state observer are obtained; the sliding mode dynamic equation is Obtained by the following steps:

S1) Design the integral sliding mode surface according to the state variable of the state observer;

S2) make the difference between the state variable of the missile dynamics model and the state variable of the state observer to obtain an error estimate;

S3) Using the error estimation, combined with the output variable y(t) of the missile dynamics model, the sliding mode dynamic equation is obtained.

Because the system state is not completely measurable in the process of compound guidance and tracking control, there are uncertainties of nonlinearity and disturbance. The present invention considers the influence of nonlinear functions and external disturbances: firstly, the system state is estimated by constructing a state observer; secondly, the uncertainty in the missile composite control system is eliminated through the designed integral sliding mode surface and state observer , which ensures the stability of the closed-loop system, can effectively improve the response speed of the missile, and increase the stability and overload capacity of the missile.

As a further limitation of the nonlinear function, the nonlinear function satisfies the following constraints:

||f(x,t)||≤α+β||y(t)||

In the formula, α>0, β>0 are unknown parameters.

As a further definition of external interference, the external interference satisfies the following constraints:

||d(·)||<d, where d is an unknown scalar.

As a further definition of the state observer, the state observer is as follows:

为x(t)的估计值，u_e是设定的函数，并用于衰减非线性函数和外部干扰的影响，C是给定矩阵，L∈R^n×p，L是观测器增益。In the formula,

is the estimated value of x(t), _ue is the set function and is used to attenuate the influence of nonlinear functions and external disturbances, C is the given matrix, L∈Rn ^×p , L is the observer gain.

In order to ensure that the entire composite guidance control system moves on the entire sliding surface, as a further definition of the integral sliding surface, the integral sliding surface is as follows:

In the formula, s(t) is the function of the integral sliding mode surface, Q∈R ^n×m is a constant matrix, K∈R ^n×m is a coefficient matrix, and K is selected so that A+BK is a Hurwitz matrix , Q is a symmetric positive definite matrix, and B is a nonsingular matrix.

As a further qualification of the error estimate, the resulting error estimate is as follows:

where e(t) is the error estimate.

Further, the derivative of the function integrating the sliding mode surface is:

Setting this derivative to zero and solving for it yields:

是积分滑模面的函数的导数，L是观测器增益，C是给定矩阵，e(t)是误差估计，u_e是设定的函数，并用于衰减非线性函数和外部干扰的影响。In the formula,

is the derivative of the function integrating the sliding mode surface, L is the observer gain, C is the given matrix, _e (t) is the error estimate, ue is the set function and is used to attenuate the effects of nonlinear functions and external disturbances.

Further, _ue adopts the following calculation formula:

其中，S_e＝B^TXe(t)，X＞0且满足B^TX＝NC，N是给定矩阵，表示过载，其中N可达到的最大值为N_y。In the formula,

Wherein, S _e =B ^T Xe(t), X>0 and B ^T X=NC is satisfied, N is a given matrix, representing overload, wherein the maximum value that N can reach is N _y .

As a further definition of the sliding mode dynamic equation, the sliding mode dynamic equation is as follows:

where e(t) is the error estimate, L is the observer gain, and I is the identity matrix.

Based on the above tracking control method, correspondingly, the present invention also proposes a composite guidance tracking control device, comprising a processor for implementing an instruction for executing the following steps:

1) According to the set nonlinear function and external disturbance, establish the missile dynamics model of the missile composite control system as follows:

α_j(j＝1…5)为导弹动力学参数，f(x,t)是非线性函数，d(·)是外部干扰，C是给定矩阵，u₁是系统综合控制率，u₁＝σ_z+A₁B⁺F，σ_z是舵偏角，

l为导弹质心到脉冲发动机的距离，J_z是导弹气动力参数中的转动惯量，

m为弹体质量，v是导弹在末节制导时速度，F是侧喷发动机最大推力值，B⁺是系数B的广义逆；where x(t) is the state variable of the missile dynamics model, y(t) is the output variable of the missile dynamics model,

α _j (j=1...5) is the missile dynamics parameter, f(x, t) is the nonlinear function, d( ) is the external disturbance, C is the given matrix, u ₁ is the comprehensive control rate of the system, u ₁ = σ _z +A ₁ B ⁺ F, σ _z is the rudder deflection angle,

l is the distance from the center of mass of the missile to the pulse engine, J _z is the moment of inertia in the aerodynamic parameters of the missile,

m is the mass of the projectile, v is the speed of the missile when it is guided at the distal end, F is the maximum thrust value of the side-jet engine, and B ⁺ is the generalized inverse of the coefficient B;

2) According to the comprehensive control rate u ₁ of the system, the output variable y(t) of the missile dynamics model and the sliding mode dynamic equation, the state observer is constructed, and the estimated functions of the state variable and output variable of the state observer are obtained; the sliding mode dynamic equation is Obtained by the following steps:

S1) Design the integral sliding mode surface according to the state variable of the state observer;

S2) make the difference between the state variable of the missile dynamics model and the state variable of the state observer to obtain an error estimate;

S3) Using the error estimation, combined with the output variable y(t) of the missile dynamics model, the sliding mode dynamic equation is obtained.

The composite guidance and tracking control device referred to in the above embodiment is actually a computer solution based on the method process of the present invention, that is, a software framework, which can be applied to a computer, and the above device is corresponding to the method process. process. Since the introduction of the above method is sufficiently clear and complete, it will not be described in detail.

Embodiment 2:

The invention provides a composite guidance and tracking control method. The missile composite guidance and tracking control method involves the design of a state observer and the design of an adaptive sliding mode control. An integral sliding mode surface is designed according to the state estimation function obtained by the state observer. Make sure that the system moves over the entire sliding surface.

As shown in Figure 1, the missile dynamics model of the missile composite guidance and tracking control system is designed as follows:

l为导弹质心到脉冲发动机的距离，令u₁＝σ_z+A₁B+F，

y(t)为系统输出，F是侧喷发动机最大推力值。α is the angle of attack of the missile, ω _z is the pitch angular velocity of the missile, m is the mass of the missile, V is the speed of the missile at the end of the guidance, and α _j (j=1…5) is the missile dynamic parameter. in,

l is the distance from the missile center of mass to the pulse engine, let u ₁ =σ _z +A ₁ B+F,

y(t) is the system output, and F is the maximum thrust value of the side injection engine.

According to the nonlinear function f(x,t) and external disturbance d(·), the following improved missile dynamics model is established:

d(·) satisfies ||d(·)||<d, where d is an unknown scalar.

The above-mentioned unknown nonlinear function f(x,t) satisfies ||f(x,t)||≤α+β||y(t)||, where α>0 and β>0 are unknown parameters.

Constructing a state observer, the state observer is equivalent to the difference between the actual object and the nominal model caused by external disturbances and changes in model parameters to the control input, that is, the equivalent disturbance is observed, and equivalent compensation is introduced into the control. , to achieve complete control over interference. The design representation of the state observer is as follows:

为x(t)的估计值，L∈R^n×p，

u₁是系统综合控制率，控制器u_e用来衰减未知非线性函数f(x,t)和外部干扰d(·)的影响，令S_e＝B^TXe(t)，假设X＞0且满足B^TX＝NC；

u_e是通过上述建立的数学模型的输出y(t)与构造的S_e得到的。在实际应用过程中，非线性和外部干扰的精确信息通常是不可测的。因此，本发明采用

和

分别来估计三个未知参数α，β和d。各参数的估计误差分别被定义为

和

in,

is the estimated value of x(t), L∈R ^n×p ,

u ₁ is the overall control rate of the system, the controller u _e is used to attenuate the influence of the unknown nonlinear function f(x,t) and the external disturbance d(·), let Se =B ^T _Xe (t), assuming X>0 And satisfy B ^T X=NC;

_ue is obtained through the output y(t) of the mathematical model established above and the constructed _Se . In practical applications, the precise information of nonlinearity and external disturbances is usually unmeasurable. Therefore, the present invention adopts

and

to estimate the three unknown parameters α, β and d, respectively. The estimation error of each parameter is defined as

and

in,

u_ic是点火规则的控制率，

其中l₁满足，l₁≥0，η(t)是一个正定常数，由下式表示：The design of the system comprehensive control rate u ₁ in the state observer is for the accessibility of the state observer's state trajectory to ensure that the system moves on the entire sliding surface, u ₁ =u _ib +u _ic , u _ib is the rudder link control rate,

u _ic is the control rate of the ignition rule,

where l ₁ satisfies, l ₁ ≥ 0, η(t) is a positive definite constant, expressed by the following formula:

In the formula, ρ is a known value, and it can be seen from the Lyapunov theorem that the system state can reach the system sliding mode surface in a finite time.

According to the state observer, the estimated functions of the state variables and output variables are obtained, and the integral sliding mode surface is designed according to the estimated function of the state variables. The integral sliding mode surface is designed as follows:

Among them, Q∈R ^n×m is a constant matrix, K∈R ^n×m is a coefficient matrix, K is selected to satisfy A+BK is a Hurwitz matrix, Q is a symmetric positive definite matrix, and B is a non-singular matrix.

To find the derivative of the function of the integral sliding mode surface, the derivative of the function of the integral sliding mode surface is:

得到的解为：make

The obtained solution is:

是积分滑模面的函数的导数，L是观测器增益，C是给定矩阵，e(t)是误差估计，u_e是设定的函数，并用于衰减非线性函数和外部干扰的影响。In the formula,

is the derivative of the function integrating the sliding mode surface, L is the observer gain, C is the given matrix, _e (t) is the error estimate, ue is the set function and is used to attenuate the effects of nonlinear functions and external disturbances.

Combining the obtained solution with the state observer, the sliding mode dynamic equation is obtained. The sliding mode dynamic equation is as follows:

where e(t) is the error estimate, L is the observer gain, and I is the identity matrix.

的估计函数做差，得到误差估计，误差估计如下：Compare the state variable x(t) of the missile dynamics model with the state variable obtained by the state observer

The estimated function of , and the error estimate is obtained. The error estimate is as follows:

where e(t) is the error estimate.

The stability analysis is performed according to the following two formulas:

Positive definite matrix X∈R n ^×n , matrix Y∈R ^n×p , N∈R ^m×p , L∈R ^n×p constraint matrix are not equal as follows:

X(A+BK)+(A+BK) ^T X+X≥0 (3)

A ^T X+XA-YC-C ^T Y ^T +X≥0 (4)

B ^T X(i)=NC (5)

ξ＝I-B(QB)^-1Q，

Δ₁₁＝X(A+BK)+(A+BK)^TX，Δ₂₂＝A^TX+XA-YC-C^TY^T，Δ₃＝diag{-X,0,0}，由李雅普诺夫定理证得此系统稳定。in,

ξ=IB(QB) ^-1 Q,

Δ ₁₁ =X(A+BK)+(A+BK) ^T X , Δ ₂₂ =A ^T X+XA-YC-C ^T Y ^T , Δ ₃ =diag{-X,0,0}, by Lyapuno The theorem proves that the system is stable.

The meaning of the system motion of the present invention in the entire sliding surface is: for each component of the system x ₁ (t), x ₂ (t)...x _n (t), when an initial value (x ₁ (0) , x ₂ (0)) and a u, with the increase of time t, the point (x ₁ , x ₂ ) will move according to a certain trajectory. A suitable sliding surface s(x ₁ , x ₂ )=0 is designed on the (x ₁ , x ₂ ) plane. When (x ₁ , x ₂ ) moves to a certain point (x ₁ (t _p ), x ₂ (t _p )) at a certain time t _p , it is found that s(x ₁ (t _p ), x ₂ (t _p ))=0, then, (x ₁ , x ₂ ) is said to reach the sliding surface.

得到的u_1eq即是趋近运动的趋近律。系统一旦到达滑模面，控制律u_e将保证系统沿滑模面达到原点，进而使得系统稳定，如图8所示。Sliding mode motion includes two processes: approach motion and sliding mode motion. The system tends to the sliding mode surface from any state until it reaches the sliding mode surface. The motion is called the approach motion, that is, the process of the approach motion is s→0, where, the present invention

The obtained u _1eq is the reaching law of the reaching motion. Once the system reaches the sliding mode surface, the control law _ue will ensure that the system reaches the origin along the sliding mode surface, thereby making the system stable, as shown in Figure 8.

In Figure 1, the rudder link refers to the link including the rudder system, which is referred to here as abbreviated, and the rudder system is usually translated as an operating mechanism or called a servo system. According to the command generated by the guidance system, the rudder surface is driven to overcome the aerodynamic force to deflect it according to a certain rule, and the attitude control torque is generated, so that the missile generates the corresponding angle of attack, and the angle of attack generates overload, so as to adjust the missile to the required attitude.

Pulse engine, also called pulse detonation engine, is a new concept engine based on detonation combustion. Its principle is different from that of common rocket engines or aviation jet engines. This kind of engine directly uses the detonation wave generated by the detonation combustion in the combustion chamber to compress the gas to generate power. The detonation wave produced by the detonation combustion rapidly increases the pressure and temperature of the detonable fuel (the pressure can be as high as 100 atmospheres and the temperature can reach 2000°C). Therefore, the detonation combustion engine can achieve the purpose of compressing the gas without the traditional compressor and turbine components, which greatly simplifies the structure and greatly reduces the cost. The output of the pulse engine is F in the missile dynamics model.

The output of the rudder link is the rudder deflection angle, the rudder deflection angle is the deflection angle of the steering gear, and the steering gear is the actuator of the missile control system. , Control the maneuvering flight of the missile. Simply put, the steering gear is the action mechanism, which is used to change the flight line of defense of the missile and realize maneuverability. In Figure 1, the rudder link is applied to the missile dynamics model through u _ib .

The ignition rule in Figure 1 is also called ignition logic, which is to form a library of the conditions that need to be satisfied for ignition. When the ignition conditions are satisfied, the serial number of the ignition pulse engine is determined, and then the ignition command is issued. Of course, there are many existing algorithm researches on ignition logic (not much introduction here), and reasonable pulse engine ignition logic can consume less engine.

The ignition rule acts on the pulse engine, which can improve the utilization rate of the pulse engine. When the ignition conditions are met, the serial number of the ignition pulse engine is determined, and then the ignition command is issued. Studying reasonable pulse engine ignition logic can consume less engine. In Figure 1, _ue is the control rate of this link of the ignition rule.

α_j(j＝1…5)为导弹动力学参数，

根据末阶制导过程中导弹质量m和速度v求取

a₁＝a₂＝a₃＝0.15，a₄＝-38.454，a₅＝0.156，σ_z＝u₁-A₁B⁺F，F取最大推力,将上述数据代入导弹动力学模型，代入根据非线性函数和外部干扰建立的数学模型。In order to verify the effectiveness of this method, Simulink software is used to simulate and verify the composite guidance tracking control method. The maximum thrust of the solid motor is F _max = 2500N, the dynamic response time is τ = 0.05s, N _y represents the maximum value that N can achieve, The overload command of the missile is set as N _y =20, the distance from the pulse engine to the center of mass of the missile is l = 1m,

α _j (j=1…5) is the missile dynamics parameter,

According to the missile mass m and velocity v in the final guidance process

a ₁ = a ₂ = a ₃ = 0.15, a ₄ = -38.454, a ₅ = 0.156, σ _z = u ₁ -A ₁ B ⁺ F, F takes the maximum thrust, substitute the above data into the missile dynamics model, and substitute the basis Mathematical model established by nonlinear functions and external disturbances.

The above data is combined with the data given below and substituted into the state observer. The data given are as follows:

The set nonlinear function f(x,t) and external disturbance d(·) are as follows:

f(x,t)=0.28+0.2sin(200t)x ₁ (t)

Substitute the following data into the function for the sliding surface above:

K=[-7.5445-6.6562], p=0.1, Q=[0.47620.9524], l ₁ =85.

在实际进行运算的时候，先根据不等式(1)-(5)，利用matlab解出不等式得到观测器增益L，再将L带入状态观测器

中，即可求出

进而得出

Estimated value of x(t) of the present invention

In the actual operation, according to the inequalities (1)-(5), use matlab to solve the inequalities to obtain the observer gain L, and then bring L into the state observer

, it can be found

to get

The angle of attack commands are set to 10 and 8 respectively. Figure 2 is the output response curve of overload tracking, Figure 3 is the output response curve of the pitch angular velocity, Figure 4 is the output response curve of the overload tracking error, and Figure 5 is the comprehensive control rate u ₁ Figure 6 is the output response curve of the pitch angle velocity tracking error e, Figure 7 is the output response curve of the attack angle tracking when the attack angle command is 10 and the attack angle command is 8. It can be seen from the above figures that the designed composite guidance and tracking control method can realize the global asymptotic stability of the closed-loop control system.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims (6)

1. a composite guidance tracking control method, is characterized in that, comprises the following steps: 1) According to the set nonlinear function and external disturbance, establish the missile dynamics model of the missile composite control system as follows:

x(t) is the state variable of the missile dynamics model, y(t) is the output variable of the missile dynamics model,

α _j is the missile dynamics parameter, j=1...5, f(x, t) is the nonlinear function, d( ) is the external disturbance, C is the given matrix, u ₁ is the comprehensive control rate of the system, u ₁ =σ _z + A ₁ B ⁺ F, σ _z is the rudder deflection angle,

l is the distance from the center of mass of the missile to the pulse engine, J _z is the moment of inertia in the aerodynamic parameters of the missile,

m is the mass of the projectile, v is the speed of the missile when it is guided at the distal end, F is the maximum thrust value of the side-jet engine, and B ⁺ is the generalized inverse of the coefficient B; 2) Construct a state observer according to the comprehensive control rate u ₁ of the system, the output variable y(t) of the missile dynamics model and the sliding mode dynamic equation, and obtain the state variable of the state observer and the estimation function of the output variable; The sliding mode dynamic equation described above is obtained through the following steps: S1) Design an integral sliding mode surface according to the state variable of the state observer; S2) make a difference between the state variable of the missile dynamics model and the state variable of the state observer to obtain an error estimate; S3) using the error estimation, combined with the output variable y(t) of the missile dynamics model, to obtain the sliding mode dynamic equation; The nonlinear function satisfies the following constraints: ||f(x,t)||≤α+β||y(t)|| In the formula, α>0, β>0 are unknown parameters; The state observer is as follows:

In the formula,

is the estimated value of x(t), _ue is the set function, and is used to attenuate the influence of nonlinear functions and external disturbances, C is the given matrix, and L is the observer gain; The integral sliding surface is as follows:

In the formula, s(t) is the function of the integral sliding mode surface, K is the coefficient matrix, and K is selected so that A+BK is a Hurwitz matrix, Q is a symmetric positive definite matrix, and B is a non-singular matrix; The resulting error estimate is as follows:

where e(t) is the error estimate; The derivative of the function of the integral sliding mode surface is:

Setting this derivative to zero and solving for it yields:

In the formula,

is the derivative of the function of the integral sliding mode surface, L is the observer gain, C is the given matrix, e(t) is the error estimate, u _e is the set function and is used to attenuate nonlinear functions and external the effect of interference; u _e adopts the following calculation formula:

In the formula,

Wherein, Se (t)=B ^T _Xe (t), X>0 and satisfy B ^T X=NC, N is a given matrix; The sliding mode dynamic equation is as follows:

where e(t) is the error estimate, L is the observer gain, and I is the identity matrix. 2. The composite guidance and tracking control method according to claim 1, wherein the external disturbance satisfies the following constraints: ||d(·)||<d, where d is an unknown scalar. 3. The composite guidance and tracking control method according to claim 1, wherein the external disturbance satisfies the following constraints: ||d(·)||<d, where d is an unknown scalar. 4. A composite guidance and tracking control device, characterized in that it comprises a processor for implementing an instruction that executes the following steps: 1) According to the set nonlinear function and external disturbance, establish the missile dynamics model of the missile composite control system as follows:

where x(t) is the state variable of the missile dynamics model, y(t) is the output variable of the missile dynamics model,

α _j is the missile dynamics parameter, j=1...5, f(x, t) is the nonlinear function, d( ) is the external disturbance, C is the given matrix, u ₁ is the comprehensive control rate of the system, u ₁ =σ _z + A ₁ B ⁺ F, σ _z is the rudder deflection angle,

l is the distance from the center of mass of the missile to the pulse engine, J _z is the moment of inertia in the aerodynamic parameters of the missile,

m is the mass of the projectile, v is the speed of the missile when it is guided at the distal end, F is the maximum thrust value of the side-jet engine, and B ⁺ is the generalized inverse of the coefficient B; 2) Construct a state observer according to the comprehensive control rate u ₁ of the system, the output variable y(t) of the missile dynamics model and the sliding mode dynamic equation, and obtain the state variable of the state observer and the estimation function of the output variable; The sliding mode dynamic equation described above is obtained through the following steps: S1) Design an integral sliding mode surface according to the state variable of the state observer; S2) make a difference between the state variable of the missile dynamics model and the state variable of the state observer to obtain an error estimate; S3) using the error estimation, combined with the output variable y(t) of the missile dynamics model, to obtain the sliding mode dynamic equation; The nonlinear function satisfies the following constraints: ||f(x,t)||≤α+β||y(t)|| In the formula, α>0, β>0 are unknown parameters; The state observer is as follows:

In the formula,

is the estimated value of x(t), _ue is the set function, and is used to attenuate the influence of nonlinear functions and external disturbances, C is the given matrix, and L is the observer gain; The integral sliding surface is as follows:

In the formula, s(t) is the function of the integral sliding mode surface, K is the coefficient matrix, and K is selected so that A+BK is a Hurwitz matrix, Q is a symmetric positive definite matrix, and B is a non-singular matrix; The resulting error estimate is as follows:

where e(t) is the error estimate; The derivative of the function of the integral sliding mode surface is:

Setting this derivative to zero and solving for it yields:

In the formula,

is the derivative of the function of the integral sliding mode surface, L is the observer gain, C is the given matrix, e(t) is the error estimate, u _e is the set function and is used to attenuate nonlinear functions and external the effect of interference; u _e adopts the following calculation formula:

In the formula,

Wherein, Se (t)=B ^T _Xe (t), X>0 and satisfy B ^T X=NC, N is a given matrix; The sliding mode dynamic equation is as follows:

where e(t) is the error estimate, L is the observer gain, and I is the identity matrix. 5. The composite guidance and tracking control device according to claim 4, wherein the external disturbance satisfies the following constraints: ||d(·)||<d, where d is an unknown scalar. 6. The composite guidance and tracking control device according to claim 4, wherein the external disturbance satisfies the following constraints: ||d(·)||<d, where d is an unknown scalar.

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