CN116301028A - Multi-constraint online flight trajectory planning mid-section guidance method based on air-breathing hypersonic platform - Google Patents

Abstract

The invention belongs to the technical field of hypersonic aircraft middle section guiding, and relates to a multi-constraint online flight track planning middle section guiding method based on an air suction hypersonic platform. The invention firstly designs the flight track on line based on the air-pushing coupling characteristic of the air suction type platform. In the transverse plane, the transverse plane turns based on a fixed roll angle, and the track design is performed by eliminating the lead angle. In the longitudinal plane, a principle that the fuel consumption is low and the dynamic pressure state can be kept for a long time is adopted to design a longitudinal flight strategy. The method has great advantages in oil consumption, and can effectively enlarge the area of an interception airspace. After the nominal track is obtained, track section tracking guidance is realized by adopting a track linearization control method, and the effectiveness of the method is verified. The method is suitable for middle section guidance based on the suction type super platform and has wide application prospect.

Description

Multi-constraint online flight trajectory planning midsection guidance based on air-breathing hypersonic platform cited method

technical field

The invention belongs to the technical field of mid-section guidance of hypersonic aircraft, and relates to a multi-constraint online flight trajectory planning mid-section guidance method based on an air-breathing hypersonic platform.

Background technique

The task of mid-course guidance is to guide the air-breathing hypersonic platform to within the working distance of the infrared seeker. In recent years, a variety of mid-course guidance schemes have been developed for conventional hypersonic vehicles. Among them, sliding mode guidance, proportional guidance and optimal control theory are more and more widely used in the design of mid-section guidance law.

In the published research, the middle guidance law of the sliding mode can make the guidance system converge to the sliding mode surface in a limited time, and ensure that the line-of-sight angle converges to the expected value when the mid-term guidance is switched over, and the line-of-sight angular rate is close to zero. On this basis, considering the requirements of interception performance, the quadratic optimal control method is used to solve the mid-section guidance including constraint conditions and optimal control problems. This guidance law has the advantage of optimal control energy, but it also has the problems of mathematical complexity and large amount of calculation. It is not acceptable to take into account complex flight calculations. Therefore, the guidance system puts forward higher requirements for the design method of the mid-section guidance law. Other studies use neural networks to approximate the optimal feedback strategy suitable for real-time implementation. The suboptimal midcourse guidance law is obtained through the neural network model trained offline, which has a better approximation effect on the optimal flight trajectory. The algorithm has the characteristics of high computational efficiency, high precision, and is suitable for airborne guidance.

The above-mentioned research methods and research contents are still mainly applied to traditional hypersonic vehicles. The scramjet engine used in the air-breathing hypersonic platform can extract oxygen from the atmosphere during flight, without carrying oxidant, which reduces the load quality. This means that, for the same mass of propellant, a scramjet can produce more thrust than a rocket engine. In addition, the scramjet engine has strict dynamic pressure constraints, and exceeding the limit may cause the engine to stall, resulting in interception failure. However, the existing design methods for mid-section guidance cannot effectively utilize the working characteristics of scramjet engines, which brings difficulties to the design of mid-section guidance methods based on air-breathing platforms.

Contents of the invention

Since the scramjet equipped on the air-breathing hypersonic platform has special requirements for operating conditions, the dynamic pressure is required to strictly meet the constraints. In addition, considering the different fuel consumption patterns between rocket power and scramjet engines, the traditional guidance method is not applicable, and the optimal midcourse guidance has the problem of long calculation time in long-range interception. Based on this, the online trajectory planning method is redesigned for the dynamic characteristics of the air-breathing hypersonic platform. The present invention designs a multi-constraint mid-section guidance strategy method based on the air-breathing hypersonic platform, and online planning new predictions based on the remaining time estimation method The hit point, combined with the characteristics of the platform, designs online the flight trajectory that meets the state constraints based on the relative position model, and completes the online guidance according to the trajectory tracking control, and completes the online trajectory planning and guidance quickly and accurately. So as to provide relevant technical approaches for the mid-section guidance law design of the air-breathing hyper-ultra-hypersonic platform.

Technical scheme of the present invention:

A multi-constraint online flight trajectory planning mid-section guidance method based on an air-breathing hypersonic platform, specifically as follows:

(1) Online flight trajectory planning method based on predicted hit points

(1.1) Air-breathing hypersonic platform flight strategy

After the launch of the air-breathing hypersonic platform, it has experienced two flight states: booster stage and scramjet power cruise stage.

(a) Boosting section: The boosting section adopts the command generation rule of the rising section. This method divides the ascent process of the aircraft into several flight stages, and sets fixed program angle commands for each segment, and these commands are determined by a limited number of parameters. These parameters and their corresponding program commands are obtained by offline optimization according to mission requirements, and are bound in the booster. In the controller system, the attitude control system can be used to realize the program instructions during the ascent flight. In order to seek the rapid generation of flight trajectory, the entire ascent segment is divided into three segments, including the vertical ascent segment (0≤t≤T ₁₁ ), the negative angle of attack turning segment (T ₁₁ ≤t≤T ₁₂ ), and the gravity turning segment (T ₁₂ ≤ t ≤ _{T 13} ).

The approximate formula for the full flight angle of air-breathing hypersonic platform is:

Where: 1/v ₀ is the thrust-to-weight ratio. α _m is the amplitude of the maximum negative angle of attack, t _m is the moment of maximum negative angle of attack, T ₁₂ is the turning section of negative angle of attack, which can be set freely; T ₁₃ is the exhaustion time of solid rocket fuel.

(b) Scramjet power cruising stage: For the air-breathing hypersonic platform, the thrust provided by the scramjet engine can be obtained by data interpolation:

In the formula, Q is the dynamic pressure; ρ is the air density at the height of the air-breathing hypersonic platform; k _r is the opening of the thrust regulating valve; C is the speed of sound; Ma is the Mach number; T is the thrust of the engine. V is the air-breathing hypersonic platform velocity.

(b.1) Valve opening: Since the cruising speed is greater than the speed at the end of the boost phase, this requires the air-breathing hypersonic platform to first accelerate to the specified speed, and then turn into a constant speed flight state. During the accelerated flight, the thrust is the maximum value that the scramjet engine can provide, that is, the valve opening k _r =1, that is:

T = T _max

即：In the state of constant speed flight, in order to keep the speed constant, it is necessary to use

Right now:

In the formula: θ, δ, m, r, x, y, z, α represent the air-breathing hypersonic platform ballistic inclination angle, ballistic deflection angle, mass, distance from the center of the earth, the three components of the launch system, and the angle of attack; T, D Respectively represent engine thrust and resistance; g is surface gravitational acceleration.

The valve opening is:

(b.2) Angle of attack: the cruising segment considers the flight characteristics of the air-breathing hypersonic platform, and requires the hypersonic platform to be in a flight state of constant altitude and constant speed as much as possible. In order to meet the interception requirements, the flight trajectory can be divided into a level flight segment and a climb segment based on the flight altitude. The angle of attack command is obtained according to the program command of different flight states.

(b.2.1) Level flight segment

由于：The level flight section requires the rate of change of the height of the air-breathing hypersonic platform to be constant, so the aircraft's

because:

h=rR _e

In the formula: h and Re represent the flying height of the hypersonic platform and the radius of the earth, respectively.

The derivatives of x, y, and z can be derived and then derived from the three components V _x , V _y , and V _z of the velocity of the launch system to obtain the second-order derivative change rate of the altitude with respect to the angle of attack:

与升、阻力有关，而升、阻力又与攻角有关，通过设置攻角的迭代初值α₀、攻角小量△α，通过迭代/>

的方式获得攻角。because

It is related to the lift and resistance, and the lift and resistance are related to the angle of attack. By setting the iterative initial value of the angle of attack α ₀ and the small amount of the angle of attack △α, through the iteration />

way to obtain the angle of attack.

In the formula: α _k is the angle of attack value after k iterations, λ is the optimal step size factor of the damped Newton method, which can make:

In the formula: d _k is the search direction, then let

Right now:

in:

是攻角为α_k时的发射坐标系各轴加速度，/>

是攻角为α_k+Δα时的发射坐标系各轴加速度，设置截止条件|α_k+1-α_k|<ε，ε为小量，则迭代至截止条件满足，即可获得平飞段攻角值。In the formula:

is the acceleration of each axis of the launch coordinate system when the angle of attack is α _k , />

is the acceleration of each axis of the launch coordinate system when the angle of attack is α _k + Δα, set the cut-off condition |α _k+1 -α _k |<ε, ε is a small amount, then iterate until the cut-off condition is satisfied, and the level flight section can be obtained Angle of attack value.

(b.2.2) Climb segment

The climb section refers to a flight process in which the hypersonic platform climbs to a specified altitude, which can be subdivided into three parts: the constant angle of attack climb section, the straight climb section, and the smooth transition section.

First of all, the hypersonic platform can change the inclination angle of the flight trajectory by increasing the lift force at a large angle of attack during the climbing section of the fixed angle of attack, so that the hypersonic platform has the ability to climb.

When the inclination angle of the flight path reaches the preset value, it climbs to a certain height in a straight line. In order to keep the interception flight trajectory straight up, the rate of change of the inclination of the flight trajectory is required to be constant at 0°/s, and the rate of change of the inclination of the flight trajectory is:

The iterative initial value α ₀ of the angle of attack can be set through Newton iteration, namely:

作为迭代终止条件获得飞行攻角α，积分获得直线爬升飞行轨迹。Through loop iteration angle of attack α _k , to

The flight angle of attack α is obtained as the iteration termination condition, and the straight-line climbing flight trajectory is obtained by integral.

Finally, through the smooth transition section, the program command of the flight path inclination is obtained through the transition function with the flight height as the independent variable and the flight path inclination as the dependent variable.

θ _d (h)＝φ(h)*θ ₁ +(1-φ(h))θ ₀

In the formula: h _max is the intercept height, h _min is the initial height of the specified smooth section, h is the actual height, θ ₀ is the inclination angle of the initial flight trajectory of the smooth section, and θ ₁ is the inclination angle of the expected flight trajectory. Requirements, at the smooth end, the expected flight trajectory inclination angle θ ₁ =0° in the flight trajectory coordinate system, the flight trajectory inclination angle instruction can be simplified as:

θ _d (h)=(1-φ(h))θ ₀

Therefore, in order to convert the flight trajectory inclination command in the flight trajectory coordinate system into the flight trajectory inclination command in the launch system, it is necessary to use the coordinate transformation matrix to obtain:

In the formula: δ _d is the deflection angle of the flight trajectory under the flight trajectory system, since any standard flight trajectory family only exists in the vertical plane, so υ = δ _d ≡ 0°. After obtaining the flight trajectory inclination angle θ′ in the launch coordinate system, the change rate of the flight trajectory inclination angle can be obtained based on the iterative step size Δt by subtracting the flight trajectory inclination angle θ from the current actual launch coordinate system:

The rate of change of flight trajectory inclination angle in the launch coordinate system can also be expressed as:

The iteration of the angle of attack is completed by the rate of change of the inclination angle of the flight trajectory, and the flight trajectory of the smooth segment is obtained by substituting it into the integral of the dynamic model. The specific method is the same as that of the level flight segment.

(1.2) Design of Online Flight Trajectory Planning Method

The flight trajectory is designed online based on the air-push coupling characteristics of the air-breathing platform, and the control parameters are angle of attack, roll angle and engine throttle.

In the transverse plane, consider the yaw channel, the yaw channel turns based on a fixed roll angle, the trajectory design is performed by eliminating the lead angle, and the roll angle command is given based on the direction of the lead angle:

Among them, η _zmin is the allowable maximum deviation of line-of-sight angle, and γ ₀ is the set fixed roll angle amplitude.

In the longitudinal plane, considering that the optimal working state of the scramjet engine used in the air-breathing hypersonic platform is the isodynamic pressure flight state, the flight altitude has a great influence on the fuel consumption rate. Here, the longitudinal flight strategy is designed based on the principle of less fuel consumption and maintaining the constant pressure state for a long time.

It is known that the dynamic pressure is related to the flight speed and altitude. For an air-breathing hypersonic platform flying at a constant speed, the dynamic pressure is only related to the flight altitude, so the constant pressure state can be maintained by keeping the altitude constant. In terms of fuel consumption rate, considering that the flight altitude has a greater impact on the contrast, the use of a low flight trajectory can effectively reduce fuel consumption, which is more conducive to subsequent interception. Based on the above principles, the flight trajectory is designed based on the predicted hit point height h _f , the height of the hypersonic platform at the current moment h ₀ , and the height deviation.

(a) If the current flight altitude h is greater than the height of the predicted hit point, in order to take advantage of the characteristics of low flight trajectory specific impulse height, first use the downward pressure flight trajectory to reduce to the height of the predicted hit point, and then use the cruising flight mode to fly to the predicted hit point .

(b) If the current flight altitude h is lower than the predicted hit point altitude, in order to avoid premature climb, resulting in a decrease in specific impulse and uneconomical fuel consumption, first fly at the current flight altitude, and climb to intercept after the remaining flight time is less than the preset value altitude, and resumes cruise flight mode again.

(2) Nominal trajectory tracking guidance method design

The nominal trajectory is obtained by step (1). Trajectory-following guidance can be described as designing an appropriate guidance law after designing the nominal trajectory based on the online flight trajectory planning method based on the predicted hit point, so that the actual flight trajectory in the middle guidance section can better track the nominal trajectory.

Taking speed, height and lateral position as state variables, the trajectory dynamics model is dimensionally extended, and its state space is expressed as

In the formula, x(t) is the state quantity during the flight of the middle guidance section; u(t) is the control variable.

suppose

为标称轨迹状态量；/>

为标称轨迹控制量；e为实际飞行轨迹与标称轨迹状态量的差值，/>

为实际飞行过程中控制量与标称轨迹控制量的差值。则有In the formula,

is the nominal trajectory state quantity; />

is the nominal trajectory control quantity; e is the difference between the actual flight trajectory and the nominal trajectory state quantity, />

It is the difference between the control quantity in the actual flight process and the nominal trajectory control quantity. then there is

线性化，可得along e(t)=0,

Linearized, we can get

In the formula,

For the above-mentioned system, a time-varying controller is adopted, and its form is as follows:

In the formula,

In the formula, K(t) is the control parameter, a 3×6 matrix. The closed-loop system matrix can be obtained by substituting the above formula into the time-varying controller.

Let the expected closed-loop matrix be

In the formula, λ _i , (i=1,...,6) is the expected characteristic root.

Let the closed-loop system matrix be equal to the closed-loop system matrix obtained above, and each control parameter in the desired closed-loop matrix can be obtained

In the formula,

The above control parameters are determined by the expected characteristic root, so the required control parameters need to select the appropriate expected characteristic root.

The three subspaces can be described as second-order systems, described in the form of characteristic equations, as follows:

The solution can be obtained:

为自然频率，ω₁(t),ω₂(t),ω₃(t)为阻尼比，通过需求性能来确定期望系统的/>

和ω₁(t),ω₂(t),ω₃(t)，从而设计出满足性能需求的控制器参数。In the formula,

is the natural frequency, ω ₁ (t), ω ₂ (t), ω ₃ (t) are the damping ratios, and determine the desired system's /> through the demand performance

And ω ₁ (t), ω ₂ (t), ω ₃ (t), so as to design the controller parameters that meet the performance requirements.

For an underdamped second-order linear system, the rise time and overshoot estimation formulas of its step response are as follows:

From the above formula, not only the rise time and overshoot of the system can be obtained, but also the damping ratio and frequency of the desired system can be obtained, and then the characteristic root of the desired system matrix can be determined to obtain the controller parameters.

Beneficial results of the present invention:

The present invention first needs to design the flight trajectory online based on the air-push coupling characteristics of the air-breathing platform, wherein the control parameters are angle of attack, roll angle and engine throttle. In the yaw channel, the yaw channel performs turns based on a fixed roll angle, performs trajectory design by eliminating the lead angle, and gives a roll angle command based on the direction of the lead angle. In the longitudinal plane, the longitudinal flight strategy is designed based on the principle of less fuel consumption and the ability to maintain an isodynamic pressure state for a long time. Compared with the traditional mid-section guidance method of proportional guidance, the online flight trajectory planning mid-section guidance method of the present invention limits the flight height of the platform, thereby ensuring that the dynamic pressure meets the working conditions of the scramjet engine. In terms of fuel consumption, the mid-section guidance of online flight trajectory planning plans the most fuel-efficient trajectory under the conditions of equal altitude and constant speed. On this basis, combined with the relative position model, the guidance command to ensure that the hypersonic platform is on the most fuel-efficient trajectory most of the time is designed to reduce fuel consumption. Therefore, online flight trajectory planning mid-section guidance has a great advantage in terms of fuel consumption, and can effectively expand the interception airspace area. This method is suitable for midsection guidance based on an air-breathing hyperplatform, and has broad application prospects.

Description of drawings

Fig. 1 is a flow chart of a mid-section guidance method based on an air-breathing hypersonic platform based on multi-constraint online flight trajectory planning;

Fig. 2 is a schematic diagram of the trajectory planning of the vertical flight strategy;

Fig. 3 is a guide map in the middle section of online trajectory planning;

Fig. 4 is the angle-of-attack-time graph of trajectory online planning method;

Fig. 5 is the trajectory roll angle-time graph of trajectory online planning method;

Fig. 6 is the thrust adjustment valve opening-time graph of trajectory online planning method;

Fig. 7 is the gravity, lift-time graph of trajectory online planning method;

Fig. 8 is the thrust, resistance-time graph of trajectory online planning method;

Fig. 9 is the height-time curve of trajectory online planning method;

Fig. 10 is the specific impulse-time curve of trajectory online planning method;

Fig. 11 is the quality-time curve of trajectory online planning method;

Fig. 12 is the angle of attack-time graph of trajectory linearization guidance control;

Fig. 13 is the roll angle-time graph of trajectory linearization guidance control;

Fig. 14 is the throttle-time graph of trajectory linearization guidance control.

Detailed ways

The specific implementation manners of the present invention will be further described below in conjunction with the accompanying drawings and technical solutions.

A multi-constraint online flight trajectory planning mid-section guidance method based on an air-breathing hypersonic platform, including the design of an online flight trajectory planning method based on predicted hit points and a nominal trajectory tracking guidance method. The flowchart of the mid-section guidance method is shown in FIG. 1 .

This embodiment is specifically as follows:

(1) Input the initial state and give the target state

Assuming that the initial position of the interception position is (-3.9°, 79.8°), the initial predicted hit point of the air-breathing hypersonic platform is (3.19°, 79.18°, 29Km), the initial launch azimuth is -5°, and the flight speed is 1800m/s. Using the cruise + climb + cruise flight mode, after 105s, 350s, and 400s of launch, the predicted flight trajectory is refreshed, and the predicted hit point is changed to (3.00°, 80.00°, 28Km), (2.90°, 79.90°, 29Km), (2.95 °, 79.95°, 29.5Km), the straight-line distance of position change is greater than 100Km, 10Km, 5Km respectively.

(2) Design of online flight trajectory planning method based on predicted hit point

After obtaining the predicted hit point, it is necessary to design the flight trajectory online based on the air-push coupling characteristics of the air-breathing platform. In the yaw channel, the yaw channel performs turns based on a fixed roll angle, performs trajectory design by eliminating the lead angle, and gives a roll angle command based on the direction of the lead angle. In the longitudinal plane, the longitudinal flight strategy is designed based on the principle of less fuel consumption and maintaining the constant pressure state for a long time. The schematic diagram of the trajectory planning of the longitudinal flight strategy is shown in Figure 2. The superiority of the mid-course guidance method based on online flight trajectory planning is verified by comparing the terminal position error, line-of-sight angular rate, remaining fuel, and whether the dynamic pressure exceeds the state constraints with the proportional guidance.

Firstly, using the simulation conditions of online trajectory planning simulation, the performance analysis of mid-section guidance based on proportional guidance is carried out. Among them, the schematic diagram of online trajectory planning mid-section guidance is shown in Figure 3; from Figure 3, it can be seen that the online trajectory planning mid-section guidance method can correct the course within a specified time and reach the predicted hit point, which has certain use value.

Fig. 4 is the angle of attack-time curve diagram of trajectory online planning method; Fig. 5 is the trajectory roll angle-time curve diagram of trajectory online planning method; Fig. 6 is the thrust adjustment valve opening degree-time curve diagram of trajectory online planning method; Fig. 7 is the gravity, lift-time curve diagram of the trajectory online planning method; Figure 8 is the thrust, resistance-time curve diagram of the trajectory online planning method; it can be seen from the above figure that during the entire flight process, the angle of attack changes smoothly, and the thrust adjustment valve The opening floats within a reasonable range, lift and gravity can reach balance after the predicted hit point changes, thrust and drag can also reach balance after the predicted hit point changes, and the aircraft can move towards the target after the predicted hit point changes. cruise flight. and successfully guide to the target

In order to further prove the performance superiority of the online flight trajectory planning mid-section guidance method, the fuel consumption and dynamic pressure are compared here. It can be seen from the height-time curve in Fig. 9 that the guidance in the middle section of the online flight trajectory planning limits the flight height of the platform, thus ensuring that the dynamic pressure meets the working conditions of the scramjet engine. From the specific impulse-time curve in Figure 10, it can be seen that the specific impulse of the aircraft is maintained at a very high level during the flight, indicating that the engine has high efficiency, and the propellant can produce more speed increments under the same conditions. large, indicating that this method can give full play to the advantages of the scramjet engine of the air-breathing platform.

In terms of fuel consumption, the mid-section guidance of online flight trajectory planning plans the most fuel-efficient trajectory under the conditions of equal altitude and constant speed. On this basis, combined with the relative position model, the guidance command to ensure that the hypersonic platform is on the most fuel-efficient trajectory most of the time is designed to reduce fuel consumption. The quality-time curve is shown in Figure 11. Therefore, online flight trajectory planning mid-section guidance has a great advantage in terms of fuel consumption, and can effectively expand the interception airspace area. Table 1 is the comparison between the online flight trajectory planning mid-section guidance method and the proportional guidance method in terms of terminal error, line-of-sight angle rate, remaining fuel and dynamic pressure constraints.

Table 1 Data comparison table

It can be seen from Table 1 that proportional guidance has the problem of excessive line-of-sight rotation rate, while the guidance method in the middle section of online flight trajectory planning can ensure that the line-of-sight rotation rate is eliminated to zero, providing better interception conditions for the subsequent final interception . To sum up, the evaluation indicators of the online flight trajectory planning mid-section guidance are better than the proportional guidance, and the online flight trajectory planning mid-section guidance can effectively improve the interception performance of the platform.

(3) Nominal trajectory tracking guidance method design

After obtaining the nominal trajectory, in order to verify the effectiveness of the trajectory linearization guidance law, a guidance simulation analysis considering the lift force pulling 10% is carried out here to verify the effectiveness of the method. The available attack angle range of the aircraft is α∈[-4°, 6°], and the available roll angle range is γ∈[-50°, 50°].

From the angle of attack-time graph in Figure 12, the roll angle-time graph in Figure 13, and the thrust adjustment valve opening in Figure 14-time graph, it can be seen that the angle of attack, roll angle, and throttle command of the trajectory linearization guidance control method of the present invention It has achieved good tracking effect, and the control parameters change relatively smoothly, and has strong anti-interference ability, which can effectively reduce the control burden of the aircraft. Trajectory linear guidance has higher guidance accuracy. The visible trajectory linearization guidance method of the invention is suitable for on-line guidance of superb platforms.

Claims (1)

1. A multi-constraint on-line flight path planning middle section guiding method based on an air suction hypersonic speed platform is characterized by comprising the following specific steps:

(1) Online flight trajectory planning method based on predicted hit point

(1.1) air-breathing hypersonic platform flight strategy

After the air suction type hypersonic speed platform is launched, the air suction type hypersonic speed platform is subjected to two flight states of a boosting section and a scramjet power cruising section;

(a) Boosting section: the boosting section adopts a single-stage carrier rocket ascending section instruction generation rule; dividing the ascending process of the aircraft into a plurality of flight stages, setting fixed program angle instructions in each stage, determining the instructions by a limited number of parameters, performing off-line optimization according to task requirements to obtain the parameters and corresponding program instructions, and binding the parameters and the corresponding program instructions in a booster system, wherein the program instructions can be realized by using a gesture control system in the ascending stage flight process; to seek rapid generation of flight trajectory, the entire ascending segment is divided into 3 segments including vertical ascending segment 0.ltoreq.t.ltoreq.t ₁₁ Negative angle of attack turning section T ₁₁ ≤t≤T ₁₂ Gravity turning section T ₁₂ ≤t≤T ₁₃ ；

The whole-course flight attack angle approximation formula of the suction hypersonic speed platform is as follows:

wherein: 1/v ₀ Is the thrust-weight ratio; alpha _m Is the maximum negative angle of attack magnitude, t _m At the maximum moment of negative attack angle value, T ₁₂ The negative attack angle turning section can be freely arranged; t (T) ₁₃ The fuel exhaustion time of the solid rocket;

(b) Scramjet power cruise section: for an air suction type air suction hypersonic speed platform, the thrust provided by the scramjet engine is obtained through data interpolation:

wherein Q is dynamic pressure; ρ is the air density at the height of the aspirated hypersonic platform; k (k) _r The opening of the valve is regulated for thrust; c is the sound velocity; ma is Mach number; t is engine thrust; v is the speed of the suction hypersonic speed platform;

(b.1) valve opening: because the cruising speed is higher than the speed at the end of the boosting section, the air suction type hypersonic speed platform is required to accelerate to a specified speed at first and then to be in a constant-speed flight state; the thrust is the maximum value provided by the scramjet engine in the accelerating flight process, namely the valve opening k _r =1, i.e.:

T＝T _max

in order to maintain a constant speed in a constant speed flight state, it is necessary to make

Namely:

wherein: θ, δ, m, r, x, y, z, α represent three components of the ballistics dip angle, ballistics deflection angle, mass, centroid distance and emission system of the aspiration hypersonic platform, respectively, and the attack angle; t, D the engine thrust and drag, respectively; g is the earth surface gravity acceleration;

the opening of the valve is as follows:

(b.2) angle of attack: dividing a flight track into a flat flight section and a climbing section based on the flight altitude; the attack angle instruction is obtained according to program instructions of different flight states;

(b.2.1) Flat fly section

The flat flight section requires the change rate of the altitude of the suction hypersonic platform to be unchanged, so that an aircraft is required

As a result of:

h＝r-R _e

wherein: h. r is R _e Respectively representing the flying height and the earth radius of the suction hypersonic platform;

deriving x, y, z and then summing the three components V of the transmission system speed _x 、V _y 、V _z Deriving to obtain the second derivative change rate of the attack angle:

due to

Related to rise and resistance, which in turn are related to angle of attack, by setting an initial iteration value alpha of angle of attack ₀ Small angle of attack Δα by iteration +.>

Obtaining an angle of attack by way of (a);

wherein: alpha _k Is the attack angle value after iterating k times, and lambda is the optimal step factor of the damping Newton method, so that:

wherein: d, d _k Is the search direction, order

Namely:

wherein:

wherein:

is the attack angle alpha _k Acceleration of each axis of the emission coordinate system at the moment, +.>

Is the attack angle alpha _k Acceleration of each axis of emission coordinate system at +Δα, setting cutoff condition |α _k+1 -α _k |<Epsilon, epsilon is small, then theObtaining the attack angle value of the flat flight segment when the cut-off condition is met;

(b.2.2) climbing section

The climbing section refers to a flight process of the suction hypersonic platform climbing to a designated height, and is divided into three parts, namely a fixed attack angle climbing section, a linear climbing section and a smooth transition section;

firstly, the suction hypersonic platform changes the inclination angle of a flight track by increasing lift force at a fixed attack angle climbing section, so that the suction hypersonic platform has climbing capacity;

when the inclination angle of the flight track reaches a preset value, the flight track ascends to a certain height in a linear climbing mode; in order to keep the intercepted flight path to climb straight, the inclination angle change rate of the flight path is required to be constant at 0 degrees/s, and the inclination angle change rate of the flight path is as follows:

setting an iteration initial value alpha of attack angle ₀ By newton's iteration, namely:

by cyclic iteration of angle of attack alpha _k To

Obtaining a flight attack angle alpha as an iteration termination condition, and obtaining a linear climbing flight track through integration;

finally, through a smooth transition section, a program instruction of the inclination angle of the flight track is obtained by taking the flight height as an independent variable and taking the inclination angle of the flight track as an excessive function of the dependent variable;

θ _d (h)＝φ(h)*θ ₁ +(1-φ(h))θ ₀

wherein: h is a _max To intercept the height, h _min For a given smooth segment start height, h is the actual height, θ ₀ To smooth the initial flight path inclination angle theta ₁ To expect the inclination angle of the flight track, the inclination angle theta of the flight track is expected under the coordinate system of the flight track at the smooth tail end due to the design requirement of equal height and constant speed ₁ =0°, the flight trajectory inclination command is reduced to:

θ _d (h)＝(1-φ(h))θ ₀

therefore, in order to convert the flight trajectory inclination angle instruction in the flight trajectory coordinate system into the flight trajectory inclination angle instruction in the emission system, it is necessary to obtain by conversion through the coordinate conversion matrix:

wherein: delta _d As any one standard flight track group exists only in the longitudinal plane, so that v=delta _d 0 deg. ≡0 °; after the flight track inclination angle theta' under the emission coordinate system is obtained, the variation rate of the flight track inclination angle is obtained based on the iteration step delta t by subtracting the flight track inclination angle theta of the current actual emission coordinate system from the flight track inclination angle theta of the current actual emission coordinate system:

the change rate of the inclination angle of the flight trajectory under the emission coordinate system is expressed as follows:

iteration of attack angles is completed through the change rate of the inclination angle of the flight track, and the attack angles are substituted into the dynamic model integration to obtain the flight track of the smooth section, and the specific method is the same as that of the flat flight section;

(1.2) design of on-line flight trajectory planning method

On-line design of a flight track based on the air-pushing coupling characteristic of the air-sucking platform, wherein control parameters are attack angle, tilting angle and engine throttle;

in the transverse plane, considering a yaw path, the yaw path turns based on a fixed roll angle, performs track design by eliminating a lead angle, and gives a roll angle instruction based on the direction of the lead angle:

wherein the method comprises the steps of

To allow maximum deviation of line of sight angle, gamma ₀ For a set fixed roll angle magnitude;

in the longitudinal plane, a longitudinal flight strategy is designed based on the principle that fuel consumption is low and an equal dynamic pressure state can be maintained for a long time, and specifically comprises the following steps:

if the current flight height h is larger than the predicted hit point height, the characteristic of low flight track specific impulse is utilized, firstly, a downward flight track is adopted, the height of the predicted hit point is reduced, and then a cruise flight mode is adopted to fly against the predicted hit point;

if the current flight height h is smaller than the predicted hit point height, in order to avoid premature climbing, specific impact is reduced, fuel consumption is uneconomical, the aircraft flies at the current flight height, climbs to the interception height after the remaining flight time is smaller than a preset value, and returns to the cruising flight mode again;

(2) Nominal track tracking guidance method design

Obtaining a nominal track through the step (1), and then designing a proper guidance rule so that the actual flight track of the middle guide section well tracks the nominal track; the method comprises the following steps:

the trajectory dynamics model is dimensionally expanded by taking the speed, the altitude and the transverse position as state variables, and the state space is expressed as

Wherein x (t) is the state quantity of the middle guide section in the flight process; u (t) is a control variable;

assume that

In the method, in the process of the invention,

is a nominal track state quantity; />

Is a nominal trajectory control quantity; e is the difference between the actual flight trajectory and the nominal trajectory state quantity, +.>

The difference value between the control quantity and the nominal track control quantity in the actual flight process is obtained; then

Has the following components

Along with

Linearization, can obtain

In the method, in the process of the invention,

for the above system, a time-varying controller is used, which takes the form:

in the method, in the process of the invention,

wherein K (t) is a control parameter, a 3×6 matrix; substituting the above into a time-varying controller to obtain a closed-loop system matrix;

let the desired closed-loop matrix be

Wherein lambda is _i (i=1, …, 6) is the desired feature root;

the closed-loop system matrix is equal to the closed-loop system matrix obtained above, and each control parameter in the expected closed-loop matrix can be obtained

In the method, in the process of the invention,

the control parameters are determined by the expected characteristic roots, so that proper expected characteristic roots need to be selected when the control parameters are required;

the three subspaces can be described as a second order system, described in terms of a characteristic equation, as follows:

the solution can be obtained:

in the method, in the process of the invention,

is natural frequency omega ₁ (t),ω ₂ (t),ω ₃ (t) damping ratio, by demand performance to determine the desired system +.>

And omega ₁ (t),ω ₂ (t),ω ₃ (t) thereby designing controller parameters that meet performance requirements;

for an underdamped second order linear system, the step response rise time and overshoot estimation formulas are as follows:

the rising time and overshoot of the system can be obtained by the above formula, and meanwhile, the damping ratio and the frequency of the expected system can be obtained, so that the characteristic root of the expected system matrix can be determined, and the controller parameters can be obtained.

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