An energy management method for correcting additional induced drag with online prediction

Abstract

The application discloses an energy management method for correcting additional induced drag by online prediction, which comprises the following steps: firstly, online prediction of terminal velocity is realized by using multi-stage variable step length integral parallel calculation; secondly, the additional induced drag is calculated by using the difference between the predicted terminal velocity and the expected terminal velocity; finally, the additional guidance command is determined by using the existing guidance law to realize deceleration. The method has the advantages of strong universality, long action time, high calculation precision and strong engineering practice ability.

Description

Technical Field

[0001] This invention belongs to the field of rocket technology, specifically relating to an energy management method that uses online prediction and correction of additional induced drag. Background Technology

[0002] Existing guided rocket energy management technologies are based on drag-velocity profile methods, requiring a pre-set energy baseline trajectory for bang-bang deceleration control. This method suffers from low energy management accuracy and a fixed trajectory, failing to meet the requirements of rapid rocket launch and versatility. Therefore, a simple, widely applicable, and highly versatile energy management method is needed. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, this invention provides an energy management method that employs online prediction and correction of additional induced drag. First, it uses multi-stage variable-step-size integral parallel calculation to achieve online prediction of terminal velocity. Second, it calculates the additional induced drag using the difference between the predicted and desired terminal velocities. Finally, it determines the additional guidance command using existing guidance laws to achieve deceleration. This method is highly versatile, has a long response time, high computational accuracy, and strong engineering practical application capabilities.

[0004] The technical solution adopted by this invention to solve its technical problem is as follows:

[0005] Step 1: Calculate the expected acceleration;

[0006] Step 1-1: The guidance equations are divided into three stages: mid-guidance stage, terminal guidance stage, and overload zeroing stage, which correspond to multiple different guidance strategies and motion equations.

[0007] set up These are longitudinal demand overload and lateral demand overload, with different expressions corresponding to the three stages;

[0008] Steps 1-2: The longitudinal and lateral overload requirements for the mid-guided section are as follows:

[0009] (1)

[0010] in All are guidance proportional differential coefficients, designed using the gain scheduling method, and represent the effects of altitude deviation, altitude change rate deviation, and trajectory tilt angle deviation on acceleration, respectively. These are the height and the height derivative, respectively. These are the nominal height and the derivative of the nominal height, respectively. These are the ballistic deviation angle and the expected ballistic deviation angle, respectively.

[0011] Steps 1-3: The longitudinal and lateral overload requirements for the final guidance section are as follows:

[0012] (2)

[0013] in, These are the rocket's flight speed, gravitational acceleration, and local trajectory inclination angle, respectively. , Let be the derivatives of the desired trajectory inclination angle and the desired trajectory deflection angle, respectively, and their expressions are:

[0014] (3)

[0015] in All of these are guidance proportional differential coefficients, determined by the proportional guidance law; These are the line-of-sight inclination angle, line-of-sight inclination velocity, line-of-sight deflection angle, and line-of-sight deflection velocity, respectively. These are the desired line of sight tilt angle and the desired line of sight deflection angle, respectively. Remaining flight time;

[0016] Steps 1-4: The longitudinal and lateral overload requirements for the overload zeroing stage are as follows:

[0017] (4)

[0018] Steps 1-5: Based on longitudinal overload requirements And lateral overload required The drag acceleration was calculated. The calculation process is as follows:

[0019] (5)

[0020] in For the angle of attack and sideslip angle The function, through Obtain the corresponding angle of attack and sideslip angle. Since it is a function of the angle of attack and the sideslip angle, the drag acceleration is ultimately obtained. ;

[0021] Step 2: Terminal velocity prediction;

[0022] The ballistic equations are:

[0023] (6)

[0024] in These are the rocket's range, altitude, and lateral velocity, respectively.

[0025] During flight, a variable-step-size integral operation is performed on equation (6), and the termination condition is: ,in The target altitude is calculated repeatedly during flight, and the predicted speed is sent out in real time. ;

[0026] Step 3: Add induced resistance;

[0027] Let the speed difference ,in The desired speed; when the speed difference exceeds the preset limit. ,Right now The strategy of implementing additional induced drag is employed when necessary; otherwise, normal guided flight is maintained. The expected additional induced drag coefficient is:

[0028] (7)

[0029] in These are the rocket's mass, dynamic pressure, and reference area, respectively.

[0030] Step 4: Desired guidance command;

[0031] The process for solving the expected additional lateral force coefficient is as follows:

[0032] (8)

[0033] in This is the nominal drag coefficient. This represents the expected resistance coefficient.

[0034] Since the drag coefficient is a function of the desired angle of attack, the desired angle of attack can be obtained by solving for it. ;

[0035] Since the lateral force coefficient is The function is then used to solve for the desired lateral force coefficient. ;

[0036] set up Additional lateral force coefficient:

[0037] (9)

[0038] in, This indicates the longitudinal acceleration measured by the accelerometer. This indicates the lateral angular velocity measured by the accelerometer;

[0039] Let the maximum lateral overload and the maximum normal overload be respectively , The remaining additional overloads are respectively longitudinal and lateral, expressed as:

[0040] (10)

[0041] The actual expected overload command is obtained by combining the additional induced drag calculation. They are respectively:

[0042] (11)

[0043] in, It is a symbolic function;

[0044] Step 5: Use the actual expected overload command Replace longitudinal overload And lateral overload required As the desired overload command that the controller needs to track, tracking this overload command can ensure that the end velocity converges to the desired velocity. .

[0045] The beneficial effects of this invention are as follows:

[0046] The method of this invention ensures that the missile decelerates throughout the mid-course and terminal guidance phases, and this method has broad application prospects. Attached Figure Description

[0047] Figure 1 This is a flowchart of the method of the present invention.

[0048] Figure 2 This is a schematic diagram of the terminal velocity distribution range in Monte Carlo shooting according to an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of the statistical distribution of terminal velocity in Monte Carlo shooting according to an embodiment of the present invention.

[0050] Figure 4 This is a schematic diagram of the miss distance distribution in Monte Carlo shooting according to an embodiment of the present invention.

[0051] Figure 5 This is a schematic diagram of the probability distribution of miss distance in Monte Carlo shooting according to an embodiment of the present invention. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0053] To address the general energy management problem of guided rockets, it is necessary to research a terminal velocity control method applicable to various guidance strategies and ballistic types. This method should ensure high deceleration accuracy and strong deceleration capability while maintaining versatility and meeting the requirements of rapid computation by the onboard computer. This invention provides an online predictive correction method for additional induced drag applicable to various guidance strategies.

[0054] like Figure 1 As shown, the steps of the embodiments of the present invention are described as follows:

[0055] Step 1: Calculate the expected acceleration;

[0056] Guidance equations are generally divided into several stages, including the mid-course guidance stage, the terminal guidance stage, and the overload zeroing stage, each corresponding to different guidance strategies and motion equations. Ballistic prediction only uses the guidance strategy to obtain the required overload command closed loop, without calculating the inner loop, i.e., the attitude loop.

[0057] set up These are the required overloads in the longitudinal and lateral directions, respectively, and their expressions differ for each of the three guidance stages. The required overloads for the three stages are as follows:

[0058] Overload is required in the mid-guidance phase:

[0059] (1)

[0060] in The specific values ​​are determined by the guidance and control system design strategy.

[0061] Overload is required in the final guidance phase:

[0062] (2)

[0063] in , Let be the derivatives of the desired trajectory inclination angle and the desired trajectory deflection angle, respectively, and their specific expressions are as follows:

[0064] (3)

[0065] in The specific values ​​are determined by the guidance and control system design strategy.

[0066] Overload reset requires overload:

[0067] (4)

[0068] Based on longitudinal and lateral overload The drag acceleration can be calculated. The calculation process is as follows:

[0069] (5)

[0070] in For the angle of attack and sideslip angle The function, through Obtain the corresponding angle of attack and sideslip angle. Since it is a function of the angle of attack and the sideslip angle, the drag acceleration can ultimately be obtained. ; The specific functional expression is the aerodynamic characteristics of the rocket, which are determined by its aerodynamic shape.

[0071] Step 2, terminal velocity prediction;

[0072] The ballistic equations are:

[0073] (6)

[0074] During flight, a parallel computing core is used to perform variable-step-size integration on the equation, with the calculation termination condition being... ,in The target height. Integral result. The state at the moment of impact. This prediction process repeatedly calculates during flight, sending out the predicted velocity in real time. .

[0075] Step 3: Add induced resistance;

[0076] Let the speed difference ,in The desired speed. When the speed error exceeds the preset limit. ,Right now When the flight path is under certain conditions, the strategy of additional induced drag is implemented; otherwise, normal guidance flight is maintained. The expected additional induced drag coefficient is:

[0077] (7)

[0078] Step four, desired guidance command;

[0079] The process for solving the expected additional lateral force coefficient is as follows:

[0080] (8)

[0081] in This is the nominal drag coefficient. Let be the desired drag coefficient. Since the drag coefficient is a function of the desired angle of attack, the desired angle of attack can be obtained by solving for it. Because the lateral force coefficient is The function of , therefore the desired lateral force coefficient can be obtained. .set up Additional lateral force coefficient:

[0082] (9)

[0083] The additional lateral force coefficient is applied to the desired overload for additional deceleration, requiring the acceleration guidance command to be decomposed into longitudinal and lateral directions. Let the maximum lateral and maximum normal overloads be respectively... ; The remaining additional overloads are respectively longitudinal and lateral, and their expressions are:

[0084] (10)

[0085] Therefore, by combining the calculation of additional induced drag, the true expected overload command is obtained. They are respectively:

[0086] (11)

[0087] This instruction replaces the longitudinal overload requirement. And lateral overload required As the desired overload command that the controller needs to track, tracking this overload command can satisfy the condition that the end velocity converges to... .

[0088] Example:

[0089] The invention will be further described using a case study of a guided rocket weapon system. The guided rocket launch point is at an altitude of 0m, and the target altitude is... m, for vertical attack on targets at a range of 1000km, with required drop velocity. m / s, mass kg.

[0090] Step 1: Calculate the expected acceleration;

[0091] Ballistic reference altitude Given the pre-installed value, taking its derivative yields... ,parameter , Based on the expected overload expressions for different stages, the nominal expected acceleration is calculated as follows: .

[0092] Step 2, terminal velocity prediction;

[0093] nominal expected acceleration Substitute into the prediction equation:

[0094]

[0095] By integration, we can calculate the result when... Predicted terminal velocity .

[0096] Step 3: Add induced resistance;

[0097] set up

[0098]

[0099] Step four, desired guidance command;

[0100] Let the drag coefficient be Lift coefficient The expected angle of attack is expressed as:

[0101]

[0102] Expected additional lift:

[0103] (12)

[0104] Let the measured normal force overloads be respectively The additional lateral force is:

[0105] (13)

[0106] Let the maximum lateral and maximum normal accelerations be respectively According to the desired acceleration command in equations (14) and (15) By superimposing additional lateral acceleration, an acceleration command that satisfies the final velocity control is generated.

[0107] Figure 2 The horizontal axis represents the terminal velocity distribution range, which is divided into 5 ranges: <700m / s, 700~720m / s, 720~780m / s, 780~800m / s, and >800m / s. The numbers on the vertical axis of the bar chart represent the number of 500 ballistic trajectories in the Monte Carlo target shooting where the terminal velocity falls within the corresponding range.

[0108] Figure 3 The horizontal axis represents the terminal velocity (Vf), and the vertical axis represents the probability density function. As can be seen from the figure, the standard terminal velocity of 750 m / s has the highest probability of occurring. The 1σ interval is approximately between 740 m / s and 760 m / s, meaning that 68.27% of the terminal velocities fall within this interval.

[0109] Figure 4 The horizontal and vertical axes represent the x-axis and z-axis positions, respectively, with the target point at the center. The distribution of the miss distance can be seen from the figure.

[0110] Figure 5 The horizontal axis represents the miss distance, and the vertical axis represents the probability distribution. As can be seen from the graph, a miss distance of 1.5m from the target is a high-probability event, with a probability of approximately 30%; miss distances of more than 4m from the target are low-probability events, with a probability of less than 5%.

[0111] To verify the feasibility of this invention, 500 Monte Carlo target practice simulations were conducted using the energy management method proposed in this invention, and the required sideslip angle was tracked using the 6-DOF missile dynamics equations. The mathematical simulation results are as follows: Figures 2-5The curve is shown. Simulation results show that the missile energy management method designed in this invention uses a missile-borne computer to perform real-time prediction of terminal velocity through parallel calculation, obtains the current required sideslip angle through iterative calculation, and achieves energy management by responding to the required sideslip angle through the inner loop of missile control. This enables lateral random maneuvering in high-precision energy management and mid-course guidance of the missile, increasing the probability of missile penetration.

Claims

1. An energy management method employing online prediction correction of additional induced drag, characterized by, Includes the following steps: Step 1: Calculate the expected acceleration; Step 1-1: The guidance equations are divided into three stages: mid-guidance stage, terminal guidance stage, and overload zeroing stage, which correspond to multiple different guidance strategies and motion equations. Let respectively longitudinal and lateral required overloads, corresponding to different expressions in the three phases; Steps 1-2: The longitudinal and lateral overload requirements for the mid-guided section are as follows: （1） in All are guidance proportional differential coefficients, designed using the gain scheduling method, and represent the effects of altitude deviation, altitude change rate deviation, and trajectory tilt angle deviation on acceleration, respectively. These are the height and the height derivative, respectively. These are the nominal height and the derivative of the nominal height, respectively. These are the ballistic deviation angle and the expected ballistic deviation angle, respectively. Steps 1-3: The longitudinal and lateral overload requirements for the final guidance phase are as follows: （2） in, These are the rocket's flight speed, gravitational acceleration, and local trajectory inclination angle, respectively. , Let be the derivatives of the desired trajectory inclination angle and the desired trajectory deflection angle, respectively, and their expressions are: （3） in All of these are guidance proportional differential coefficients, determined by the proportional guidance law; These are the line-of-sight inclination angle, line-of-sight inclination velocity, line-of-sight deflection angle, and line-of-sight deflection velocity, respectively. These are the desired line of sight tilt angle and the desired line of sight deflection angle, respectively. Remaining flight time; Steps 1-4: The longitudinal and lateral overload requirements for the overload zeroing stage are as follows: （4） Steps 1-5: Based on longitudinal overload requirements And lateral overload required The drag acceleration was calculated. The calculation process is as follows: （5） in For the angle of attack and sideslip angle The function, through Obtain the corresponding angle of attack and sideslip angle. Since it is a function of the angle of attack and the sideslip angle, the drag acceleration is ultimately obtained. ; Step 2: Terminal velocity prediction; The ballistic equations are: （6） wherein respectively the range, altitude, and lateral range of the rocket; During flight, a variable-step-size integral operation is performed on equation (6), and the termination condition is: ,in The target altitude is calculated repeatedly during flight, and the predicted speed is sent out in real time. ; Step 3: Add induced resistance; Let the speed difference ,in The desired speed; when the speed difference exceeds the preset limit. ,Right now The strategy of implementing additional induced drag is employed when necessary; otherwise, normal guided flight is maintained. The expected additional induced drag coefficient is: （7） in These are the rocket's mass, dynamic pressure, and reference area, respectively. Step 4: Desired guidance command; The process for solving the expected additional lateral force coefficient is as follows: （8） wherein C D is the nominal state drag coefficient, C D is the desired drag coefficient; Since the drag coefficient is a function of the desired combined attack angle, the desired combined attack angle is solved as ; Because the lateral force coefficient is The function is then used to solve for the desired lateral force coefficient. ; Let is the additional side force coefficient: （9） wherein, denotes the longitudinal acceleration measured by the accelerometer, denotes the lateral angular velocity measured by the accelerometer; Let the maximum lateral and normal overloads be respectively , respectively the longitudinal and lateral residual additional overloads, expressed by the formulae: （10） Real desired overload command is calculated in combination with additional induced drag respectively: （11） in, It is a symbolic function; Step 5: Use the actual expected overload command Replace longitudinal overload And lateral overload required As the desired overload command that the controller needs to track, tracking this overload command can ensure that the end velocity converges to the desired velocity. .

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