阅读说明：本技术 一种基于伪谱法修正的过重补制导方法和弹道整形制导方法 (Over-emphasis guidance method and trajectory shaping guidance method based on pseudo-spectrum correction ) 是由 陈万春 黄鹂鸣 于 2020-02-07 设计创作，主要内容包括：本发明提供了一种基于伪谱弹道优化结果修正的过重补制导方法和弹道整形制导方法,属于航天技术、武器技术、制导控制领域。具体包括：一、建立交战模型,确定导弹气动参数和大气模型参数；二、建立导弹运动方程组并建立最优控制问题；三、使用伪谱法对最优控制问题进行求解；四、通过多项式拟合等方式拟合伪谱最优结果；五、根据伪谱最优结果修正典型弹道整形制导律和典型重力补偿制导律。优点在于：提升导弹的末速,大大增强导弹的攻击效能；通过对伪谱最优结果的拟合,将制导律分段,前一段提升导弹飞行高度,后一段调整制导参数使其满足落角约束；解决了典型重力补偿制导律的“黑洞”现象,对实际应用有重要意义。(The invention provides an over-retraining guidance method and a trajectory shaping guidance method based on pseudo-spectrum trajectory optimization result correction, and belongs to the fields of aerospace technology, weapon technology and guidance control. The method specifically comprises the following steps: firstly, establishing a combat model, and determining missile pneumatic parameters and atmospheric model parameters; secondly, establishing a missile motion equation set and establishing an optimal control problem; thirdly, solving the optimal control problem by using a pseudo-spectrum method; fourthly, fitting the optimal result of the pseudo spectrum in a polynomial fitting mode and the like; and fifthly, correcting a typical ballistic shaping guidance law and a typical gravity compensation guidance law according to the pseudo-spectrum optimal result. Has the advantages that: the final speed of the missile is improved, and the attack efficiency of the missile is greatly enhanced; by fitting the pseudo-spectrum optimal result, segmenting a guidance law, wherein the front section promotes the flying height of the missile, and the rear section adjusts the guidance parameters to enable the guidance parameters to meet the falling angle constraint; the problem of 'black holes' in a typical gravity compensation guidance law is solved, and the method has important significance for practical application.)

1. An overcomplete guidance method and a ballistic reshaping guidance method based on pseudo-spectral method correction are characterized in that: the guidance method fits the optimal result in a short time after the missile is launched, so that the trajectory height is improved, the drop angle of the missile can be adjusted by adjusting the guidance parameters, and the guidance capability of a typical guidance law is greatly improved. The method comprises the following specific steps:

the method comprises the following steps: building empty bomb kinematics model

In the middle guide section of the air-to-air missile, the motion of the middle guide section can be decomposed into two planes, namely a lateral plane and a longitudinal plane. For the lateral plane, because the atmospheric parameters at the same height are the same and no component of gravity in the horizontal direction exists, the transverse motion only depends on the terminal position of the missile target, and the proportional guidance method is generally adopted, the flight trajectory of the missile target is straight and the motion amplitude is not large. The height variation in the longitudinal plane is mainly taken into account, thus limiting the movement of the projectile in the plumb plane. The kinematic equation of the system is shown as formula (1),

where r is the horizontal position, h is the height, v is the velocity, γ is the ballistic inclination, T is the thrust, α is the angle of attack, L and D are the lift and drag experienced by the missile, for a dipulse air-to-air missile, the mass flow and thrust of the missile can be written as piecewise functions that vary with time,

step two: establishing optimal control problem and resolving using pseudo-spectral method

A series of optimal trajectories for the secondary ignition problem can be obtained using pseudo-spectroscopy, where the trajectory optimization problem is a multi-segment optimal control problem due to the multi-pulse form of thrust. The selection state quantity is written as equation (4).

X＝[x₁x₂x₃x₄x₅x₆]^T＝[r h V γ m α]^T(4)

According to the dynamic modeling of the missile, a differential equation is written as an equation (5).

Since the optimization problem is a multi-segment optimal control problem, it is necessary to constrain the connection conditions of state quantities between different segments, and to impose constraints on control variables. In order to ensure the flight quality and operability, path constraint is required to be added as rudder deflection angle constraint.

The selection of the objective function has a decisive influence on the trajectory, usually considering the shortest flight time or the maximum terminal velocity, which are contradictory to each other and need to be chosen, so that a weighting coefficient k is designed to observe the effects of different objective functions,

min J＝k*t_f-v(t_f) (6)

the value of k determines the emphasis of the objective function on two factors: k is 0, corresponding to the maximum end speed index; k is more than 0 and less than 1, the end speed index is emphasized, and the variation range of the end speed is larger, so that the condition is basically equal to the maximum end speed condition at the moment; k > 1, more emphasizing the flight time index; k → ∞, corresponding to the shortest flight time index.

Step three: fitting optimal guidance law

And changing the initial state of the bullet, and solving the optimal guidance law by using a pseudo-spectral method. And observing a curve graph of the change of the attack angle along with the time, finding that the attack angle shows a linear change rule within 10s after the emission, and the initial attack angle changes along with the change of the range, and improving the typical guidance law according to the rule.

The typical guidance law is segmented, the overload value of the control quantity at the moment is deduced in the first 10s according to the linear change rule of the attack angle, the formula (7) of the improved trajectory shaping guidance law is obtained as follows,

equation (8) for improving the gravity compensated guidance law is as follows,

wherein, C_Lα is a coefficient of gravity₀Is an initial attack angle, k is the change law of the attack angle with time, T is time, m is mass, g is gravity acceleration, T is current thrust, V is_cFor the relative speed of the projectile, γ is the ballistic dip and λ is the viewing angle, as shown in FIG. 8, λ_fTo preset the end view angle, t_goFor the remaining time of flight, N' is the proportional guidance coefficient and c is the gravity compensation coefficient.

For improving trajectory shaping guidance law, preset terminal sight angle lambda is adjusted_fControlling the size of the drop angle of the missile; for improving the gravity compensation guidance law, the falling angle of the missile is controlled by adjusting the gravity compensation coefficient c.

Step four: selecting guidance parameters for a typical guidance law

Improved trajectory shaping guidance law andinitial angle of attack α in modified gravity compensated guidance law₀And the attack angle change law k along with time can be adjusted according to the pseudo-spectrum optimal result in different missile initial states, so that the simulation result of the improved typical guidance law is as close as possible to the pseudo-spectrum optimal result, as shown in the formula (9).

Under the condition of loose constraint on the falling angle, along with the change of the initial condition, the simulation result shows that the optimal falling angle is not necessarily the maximum falling angle, and the change of the falling angle can be fitted according to the change of the initial condition in the same way, as shown in formula (10), wherein gamma is_f,minThe angle of fall is restricted according to the actual condition, such as-50 degrees and gamma_f,opFor pseudo-spectral optimum results without corner-of-fall constraints, gamma_fThen for the final selected fall angle, the guidance parameters may be adjusted to bring the missile fall angle to γ_f。

γ_f＝max(γ_f,op,γ_f,min)

In practical application, the guidance parameter gamma can be calculated through off-line simulation fitting_fAnd c, a relational expression between the initial condition and the current state, thereby realizing the online application of the guidance law.

So far, the control law provided by the invention can be applied in a simulation way.

The simulation method of the control law is described by a simulated pseudo code as follows:

a) initial state information including the speed, position, attitude, etc. of the projectile is acquired.

b) Calculating an initial angle of attack α based on the initial state of the projectile₀And the angle of attack change law k over time.

c) Deducing a guidance parameter gamma according to the current state quantity_fAnd c, judging whether the current flight time is more than 10s or not, and calculating according to different rules according to the flight timeAnd (5) controlling the quantity.

d) And performing dynamic simulation on the given control quantity by using a four-step Runge Kutta method, judging whether the target is hit or missed, if the target is hit or missed, finishing the program operation, and if the target is missed or missed, continuing.

e) Go back to step c) until the target is hit or missed.

In conclusion, the method is deduced through the four steps, namely the over-retraining guidance method and the trajectory shaping guidance method based on pseudo-spectrum correction, and the example simulation result shows that the method can improve the trajectory height by fitting the optimal result of the pseudo-spectrum, can restrict the missile falling angle by adjusting the guidance parameters, greatly improves the range of the missile, eliminates the 'black hole' phenomenon of the typical gravity compensation guidance law, and has excellent comprehensive performance.

Technical Field

The invention provides an over-retraining guidance method and a trajectory shaping guidance method based on pseudo-spectrum trajectory optimization result correction, and belongs to the fields of aerospace technology, weapon technology and guidance control.

Background

The problem of guidance of the double-pulse medium-distance air-to-air missile needs to be solved is energy management, the speed curve of the missile needs to be reasonably controlled, and meanwhile, the flying height of the missile is improved, so that the missile is in a high-altitude area with thin air and small density in most of the flying time. In order to achieve the striking of high-value and high-risk targets, the modern precision guidance aircraft needs to further improve the operational capacity, so that higher requirements such as missile falling angle limitation are put on the precision guidance aircraft in engineering. Therefore, there is a need to develop guidance laws that can increase the missile trajectory height while allowing the missile drop angle to be adjusted by some means.

Typical guidance laws that are common today for elevated missile trajectory heights include: the trajectory shaping guidance law, the overweight compensation guidance law and the like belong to the augmentation proportion guidance methods. Compared with an offline pseudo-spectrum optimal simulation result and a typical guidance law simulation result, the missile guided by using the typical guidance law cannot reach a higher height after a certain drop angle constraint is met, and the gravity compensation guidance law can not hit a target within a certain range. Therefore, there is a need for improvements to the typical guidance law that can increase the ballistic height while controlling the missile fall angle by adjusting the guidance parameters.

Disclosure of Invention

Aiming at the problems of the medium-distance air-to-air missile, the invention provides an overcomplete guidance method and a trajectory shaping guidance method based on pseudo-spectrum correction based on the existing typical guidance law and according to the optimal result of pseudo-spectrum off-line calculation.

The method comprises the following specific steps:

the method comprises the following steps: building empty bomb kinematics model

In the middle guide section of the air-to-air missile, the motion of the middle guide section can be decomposed into two planes, namely a lateral plane and a longitudinal plane. For the lateral plane, because the atmospheric parameters at the same height are the same and no component of gravity in the horizontal direction exists, the transverse motion only depends on the terminal position of the missile target, and the proportional guidance method is generally adopted, the flight trajectory of the missile target is straight and the motion amplitude is not large. The height variation in the longitudinal plane is mainly taken into account, thus limiting the movement of the projectile in the plumb plane. The kinematic equation of the system is shown as formula (1),

where r is the horizontal position, h is the height, v is the velocity, γ is the ballistic inclination, T is the thrust, α is the angle of attack, L and D are the lift and drag experienced by the missile, for a dipulse air-to-air missile, the mass flow and thrust of the missile can be written as piecewise functions that vary with time,

step two: establishing optimal control problem and resolving using pseudo-spectral method

A series of optimal trajectories for the secondary ignition problem can be obtained using pseudo-spectroscopy, where the trajectory optimization problem is a multi-segment optimal control problem due to the multi-pulse form of thrust. The selection state quantity is written as equation (4).

X＝[x₁x₂x₃x₄x₅x₆]^T＝[r h V γ m α]^T(4)

According to the dynamic modeling of the missile, a differential equation is written as an equation (5).

Since the optimization problem is a multi-segment optimal control problem, it is necessary to constrain the connection conditions of state quantities between different segments, and to impose constraints on control variables. In order to ensure the flight quality and operability, path constraint is required to be added as rudder deflection angle constraint.

The selection of the objective function has a decisive influence on the trajectory, usually considering the shortest flight time or the maximum terminal velocity, which are contradictory to each other and need to be chosen, so that a weighting coefficient k is designed to observe the effects of different objective functions,

minJ＝k*t_f-v(t_f) (6)

the value of k determines the emphasis of the objective function on two factors: k is 0, corresponding to the maximum end speed index; k is more than 0 and less than 1, the end speed index is emphasized, and the variation range of the end speed is larger, so that the condition is basically equal to the maximum end speed condition at the moment; k > 1, more emphasizing the flight time index; k → ∞, corresponding to the shortest flight time index.

Step three: fitting optimal guidance law

And changing the initial state of the bullet, and solving the optimal guidance law by using a pseudo-spectral method. And observing a curve graph of the change of the attack angle along with the time, finding that the attack angle shows a linear change rule within 10s after the emission, and the initial attack angle changes along with the change of the range, and improving the typical guidance law according to the rule.

The typical guidance law is segmented, the overload value of the control quantity at the moment is deduced in the first 10s according to the linear change rule of the attack angle, the formula (7) of the improved trajectory shaping guidance law is obtained as follows,

equation (8) for improving the gravity compensated guidance law is as follows,

wherein, C_Lα is a coefficient of gravity₀Is the initial angle of attack, k is the angle of attack change with time law, T is time, m is mass, g is acceleration of gravity, T is the current thrustForce, V_cGamma is the ballistic inclination angle, lambda is the viewing angle, lambda is the relative speed of the projectile, gamma is the ballistic inclination angle_fTo preset the end view angle, t_goFor the remaining time of flight, N' is the proportional guidance coefficient and c is the gravity compensation coefficient.

For improving trajectory shaping guidance law, preset terminal sight angle lambda is adjusted_fControlling the size of the drop angle of the missile; for improving the gravity compensation guidance law, the falling angle of the missile is controlled by adjusting the gravity compensation coefficient c.

Step four: selecting guidance parameters for a typical guidance law

Improving ballistic reshaped guidance law and improving initial angle of attack α in gravity compensated guidance law₀And the attack angle change law k along with time can be adjusted according to the pseudo-spectrum optimal result in different missile initial states, so that the simulation result of the improved typical guidance law is as close as possible to the pseudo-spectrum optimal result, as shown in the formula (9).

Under the condition of loose constraint on the falling angle, along with the change of the initial condition, the simulation result shows that the optimal falling angle is not necessarily the maximum falling angle, and the change of the falling angle can be fitted according to the change of the initial condition in the same way, as shown in formula (10), wherein gamma is_f,minThe angle of fall is restricted according to the actual condition, such as-50 degrees and gamma_f,opFor pseudo-spectral optimum results without corner-of-fall constraints, gamma_fThen for the final selected fall angle, the guidance parameters may be adjusted to bring the missile fall angle to γ_f。

γ_f＝max(γ_f,op,γ_f,min)

In practical application, the guidance parameter gamma can be calculated through off-line simulation fitting_fAnd c, a relational expression between the initial condition and the current state, thereby realizing the online application of the guidance law.

So far, the control law provided by the invention can be applied in a simulation way.

The simulation method of the control law is described by a simulated pseudo code as follows:

1. initial state information including the speed, position, attitude, etc. of the projectile is acquired.

2. Calculating an initial angle of attack α based on the initial state of the projectile₀And the angle of attack change law k over time.

3. Deducing a guidance parameter gamma according to the current state quantity_fAnd c, judging whether the current flight time is more than 10s, and calculating the control quantity according to the flight time according to different rules.

4. And performing dynamic simulation on the given control quantity by using a four-step Runge Kutta method, judging whether the target is hit or missed, if the target is hit or missed, finishing the program operation, and if the target is missed or missed, continuing.

5. Go back to step 3 until the target is hit or missed.

In conclusion, the method is deduced through the four steps, namely the over-retraining guidance method and the trajectory shaping guidance method based on pseudo-spectrum correction, and the example simulation result shows that the method can improve the trajectory height by fitting the optimal result of the pseudo-spectrum, can restrict the missile falling angle by adjusting the guidance parameters, greatly improves the range of the missile, eliminates the 'black hole' phenomenon of the typical gravity compensation guidance law, and has excellent comprehensive performance.

The invention has the advantages that:

(1) the over-retraining guidance method and the trajectory shaping guidance method based on pseudo-spectrum correction are provided, the final speed of the missile can be improved, and the attack efficiency of the missile is greatly enhanced.

(2) And by fitting the pseudo-spectrum optimal result, the guidance law is segmented, the flight height of the missile is improved in the former segment, and the guidance parameters are adjusted in the latter segment to meet the falling angle constraint.

(3) The problem of 'black holes' in a typical gravity compensation guidance law is solved, and the method has important significance for practical application.

Drawings

Fig. 1 is an abstract drawing.

Fig. 2 is a schematic diagram of the force analysis of the empty bomb in the longitudinal plane.

Figure 3 is a pseudo-spectral optimal ballistic curve at different ranges.

FIG. 4 is a pseudo-spectral optimum velocity profile at different ranges.

Figure 5 is a pseudo-spectral optimal ballistic dip curve at different ranges.

FIG. 6 is a pseudo-spectral optimal angle of attack curve at different ranges.

Fig. 7 is a pseudo-spectral optimum dynamic pressure curve at different ranges.

Fig. 8 is a schematic view of the ammunition engagement in the plumb surface.

FIG. 9 is a comparison of terminal velocities of different guidance law missiles.

FIG. 10 is a comparison of different guidance law time of flight.

FIG. 11 is a comparison of maximum heights for different guidance laws.

Figure 12 is a comparison of different guidance law ballistic curves.

FIG. 13 is a comparison of different guide law velocity curves.

Figure 14 is a comparison of different guidance law ballistic inclination curves.

FIG. 15 is a comparison of different guidance law angle of attack curves.

FIG. 16 is a comparison of different guidance law pressure curves.

Fig. 17 is a ballistic graph of the black hole phenomenon.

FIG. 18 is a graph showing the velocity change of the black hole phenomenon

FIG. 19 is a flow diagram of a simulation of an improved exemplary guidance method that improves ballistic height based on pseudo-spectral optimization results.

In the above figures, the symbols and symbols are as follows:

in FIG. 2, L, D, G and T are respectively the lift, drag, gravity and thrust experienced by the missile, V is the missile velocity vector, α, gamma and psi are respectively the angle of attack, ballistic inclination and pitch, the same applies to FIG. 9, lambda is the line of sight angle, and in FIG. 18, C is the angle of gravity_Lα is a coefficient of gravity₀Is the initial angle of attack, k is the angle of attack change with time law, t is time, m is mass, g is acceleration of gravity, V_cIs in the form of bullet eyesFor velocity, λ_fTo preset the end view angle, t_goFor the remaining time of flight, N' is the proportional guidance coefficient and c is the gravity compensation coefficient.

Detailed Description

The invention will be further explained in detail with reference to the drawings and the embodiments.

Aiming at the problems of the medium-distance air-to-air missile, the invention provides an overcomplete guidance method and a trajectory shaping guidance method based on pseudo-spectrum correction based on the existing typical guidance law and according to the optimal result of pseudo-spectrum off-line calculation.

The method comprises the following specific steps:

the method comprises the following steps: building empty bomb kinematics model

In the middle guide section of the air-to-air missile, the motion of the middle guide section can be decomposed into two planes, namely a lateral plane and a longitudinal plane. For the lateral plane, because the atmospheric parameters at the same height are the same and no component of gravity in the horizontal direction exists, the transverse motion only depends on the terminal position of the missile target, and the proportional guidance method is generally adopted, the flight trajectory of the missile target is straight and the motion amplitude is not large. The height change in the longitudinal plane is mainly considered, so that the movement of the missile is limited in the plumb surface, and the force analysis schematic diagram of the missile in the plumb surface is shown in figure 2. The kinematic equation of the system is shown as formula (1),

where r is the horizontal position, h is the height, v is the velocity, γ is the ballistic inclination, T is the thrust, α is the angle of attack, L and D are the lift and drag experienced by the missile, for a dipulse air-to-air missile, the mass flow and thrust of the missile can be written as piecewise functions that vary with time,

step two: establishing optimal control problem and resolving using pseudo-spectral method

A series of optimal trajectories for the secondary ignition problem can be obtained using pseudo-spectroscopy, where the trajectory optimization problem is a multi-segment optimal control problem due to the multi-pulse form of thrust. The selection state quantity is written as equation (4).

X＝[x₁x₂x₃x₄x₅x₆]^T＝[r h V γ m α]^T(4)

According to the dynamic modeling of the missile, a differential equation is written as an equation (5).

Since the optimization problem is a multi-segment optimal control problem, it is necessary to constrain the connection conditions of state quantities between different segments, and to impose constraints on control variables. In order to ensure the flight quality and operability, path constraint is required to be added as rudder deflection angle constraint.

The selection of the objective function has a decisive influence on the trajectory, usually considering the shortest flight time or the maximum terminal velocity, which are contradictory to each other and need to be chosen, so that a weighting coefficient k is designed to observe the effects of different objective functions,

minJ＝k*t_f-v(t_f) (6)

the value of k determines the emphasis of the objective function on two factors: k is 0, corresponding to the maximum end speed index; k is more than 0 and less than 1, the end speed index is emphasized, and the variation range of the end speed is larger, so that the condition is basically equal to the maximum end speed condition at the moment; k > 1, more emphasizing the flight time index; k → ∞, corresponding to the shortest flight time index.

Step three: fitting optimal guidance law

Solving the optimal guidance problem by using a pseudo-spectrum method, changing the initial position of a target, solving the optimal guidance law by using the pseudo-spectrum method, wherein a simulated ballistic curve, a velocity curve, a ballistic dip curve, an attack angle curve and a dynamic pressure curve are shown in figures 3-7. And observing a curve graph of the change of the attack angle along with the time, finding that the attack angle approximately shows a linear change rule within 10s after the emission, and the initial attack angle changes along with the change of the range, and improving the typical guidance law according to the rule.

The typical guidance law is segmented, the overload value of the control quantity at the moment is deduced in the first 10s according to the linear change rule of the attack angle, the formula (7) of the improved trajectory shaping guidance law is obtained as follows,

equation (8) for improving the gravity compensated guidance law is as follows,

wherein, C_Lα is a coefficient of gravity₀Is an initial attack angle, k is the change law of the attack angle with time, T is time, m is mass, g is gravity acceleration, T is current thrust, V is_cFor the relative speed of the projectile, γ is the ballistic dip and λ is the viewing angle, as shown in FIG. 8, λ_fTo preset the end view angle, t_goFor the remaining time of flight, N' is the proportional guidance coefficient and c is the gravity compensation coefficient.

For improving trajectory shaping guidance law, preset terminal sight angle lambda is adjusted_fControlling the size of the drop angle of the missile; for improving the gravity compensation guidance law, the falling angle of the missile is controlled by adjusting the gravity compensation coefficient c.

Step four: selecting guidance parameters for a typical guidance law

Improving ballistic reshaped guidance law and improving initial angle of attack α in gravity compensated guidance law₀The attack angle change law k along with time can be adjusted according to the pseudo-spectrum optimal results in different initial states of the missile, so that the typical guidance law is improvedThe simulation result of (2) is as close as possible to the optimal result of the pseudo spectrum, as shown in formula (9).

Under the condition of loose constraint on the falling angle, along with the change of the initial condition, the simulation result shows that the optimal falling angle is not necessarily the maximum falling angle, and the change of the falling angle can be fitted according to the change of the initial condition in the same way, as shown in formula (10), wherein gamma is_f,minThe angle of fall is restricted according to the actual condition, such as-50 degrees and gamma_f,opFor pseudo-spectral optimum results without corner-of-fall constraints, gamma_fThen for the final selected fall angle, the guidance parameters may be adjusted to bring the missile fall angle to γ_f。

γ_f＝max(γ_f,op,γ_f,min)

In this example, only the initial position r of the target is present under the initial condition_t0There are variations, therefore α₀And gamma_fCan be fitted to follow_t0A varying polynomial, k being-1.8, as in formula (13), in which r_t0Unit is kilometer km]，α₀In units of degrees [ ° ]]，

And simulating and comparing a pseudo-spectrum optimal result, improving a trajectory shaping guidance law, improving guidance effects of a gravity compensation guidance law, a trajectory shaping guidance law and a gravity compensation guidance law. Wherein the guidance parameter is a predetermined end-of-line-of-sight angle λ for both the modified trajectory shaping guidance law and the typical trajectory shaping guidance law_fThe gravity compensation coefficient c is used for the improved gravity compensation guidance law and the typical gravity compensation guidance law.

And comparing simulation results of different guidance laws, such as comparison graphs of the terminal speed, the flight time and the maximum height of the missile shown in the figures 9-11, wherein points with excessive miss distance are not drawn and have no comparative significance. The trajectory contrast curve, the speed contrast curve, the trajectory inclination angle contrast curve, the attack angle contrast curve and the dynamic pressure contrast curve with the attack distance of 150km are shown in fig. 12-16, the guidance effect of improving the typical guidance law is greatly improved compared with the typical guidance law, and the trajectory is closer to the pseudospectral optimal result. The maximum height of the improved typical guidance law is close to the optimal result of a pseudo spectrum, the flight time is slightly long, and the final speed of the missile is slightly small.

For the gravity compensation guidance law, the improved gravity compensation guidance law eliminates the phenomenon of 'black holes' of the typical gravity compensation guidance law, wherein the 'black holes' are the phenomenon that only missiles can hit the target under the conditions of small and large range, and the middle range cannot hit the target due to the over-small falling speed. As shown in fig. 17-18. With increasing range, in order for the missile to hit the target, the typical gravity compensation guidance law needs to increase the ballistic height by increasing the re-compensation coefficient, the higher the ballistic height, the lower the air resistance due to the lower air density, but at the same time, the increase in range causes a non-linear relationship between the energy loss and the ballistic height. And the improved gravity compensation guidance law can enable the missile to fly in a better airspace due to fitting of a pseudo-spectrum optimal result after launching, thereby eliminating the phenomenon of 'black holes'.

In practical application, the guidance parameter gamma can be calculated through off-line simulation fitting_fAnd c, a relational expression between the initial condition and the current state, thereby realizing the online application of the guidance law.

So far, the control law provided by the invention can be applied in a simulation way. The following describes the simulation method of the control law by a simulated pseudo code, and the flow chart is shown in fig. 19:

1. initial state information including the speed, position, attitude, etc. of the projectile is acquired.

2. Calculating an initial angle of attack α based on the initial state of the projectile₀And the angle of attack change law k over time.

3. Deducing a guidance parameter gamma according to the current state quantity_fAnd c, judging whether the current flight time is more than 10s, and calculating the control quantity according to the flight time according to different rules.

4. And performing dynamic simulation on the given control quantity by using a four-step Runge Kutta method, judging whether the target is hit or missed, if the target is hit or missed, finishing the program operation, and if the target is missed or missed, continuing.

5. Go back to step 3 until the target is hit or missed.

In conclusion, the method is deduced through the four steps, namely the over-retraining guidance method and the trajectory shaping guidance method based on pseudo-spectrum correction, and the example simulation result shows that the method can improve the trajectory height by fitting the optimal result of the pseudo-spectrum, can restrict the missile falling angle by adjusting the guidance parameters, greatly improves the range of the missile, eliminates the 'black hole' phenomenon of the typical gravity compensation guidance law, and has excellent comprehensive performance.