CN113496062A - Method for designing motion time sequence of throat bolt of attitude and orbit control engine under stable pressure constraint - Google Patents
Method for designing motion time sequence of throat bolt of attitude and orbit control engine under stable pressure constraint Download PDFInfo
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Abstract
The application relates to a method for designing the motion time sequence of a throat plug of a posture and orbit control engine under the stable constraint of pressure intensity, which comprises the following steps: setting the sum of equivalent throat areas of valves of each orbit control spray pipe of the attitude and orbit control engine as a fixed value, and setting a valve area coefficient as the product of a sine amplitude modulation function of each valve and a sine frequency modulation function of each valve; establishing a traversal index representing the position combination state of the laryngeal suppository; determining a design variable and a target function according to the motion frequency of each laryngeal plug in the sinusoidal frequency modulation function of each valve; and solving a real number optimization problem formed by substituting the ergodic indexes of the sample points after normalization by adopting a particle swarm optimization, outputting various design variables corresponding to an optimal result, substituting a sinusoidal frequency modulation function, and solving a throat plug motion scheme under the stable constraint of output pressure and the magnitude and direction of a thrust vector of the engine at each moment by adopting an interpolation method. The aim of accurately regulating and controlling the thrust by an easily-controlled mechanism is fulfilled.
Description
Technical Field
The application relates to the technical field of solid attitude and orbit control engines, in particular to a method for designing the motion time sequence of a throat plug of a lower attitude and orbit control engine with stable pressure.
Background
The solid attitude and orbit control engine is one of the core subsystems of a kinetic energy weapon, is mainly used for intercepting ballistic missiles, attacking satellites and the like, and can be arranged in weapon systems with higher requirements on safety, such as air bases, sea bases and the like. The solid attitude and orbit control engine has the working principle that the opening and closing of a valve or the displacement of a throat plug are controlled by controlling a servo control system, and the equivalent throat area is changed to control the flow of high-temperature gas, so that the adjustment of the direction and the size of thrust is realized. The motion scheme design of the throats is a crucial step for performance evaluation of the solid attitude and orbit control engine under the condition of different throats position combinations, and the main task is to enable the combination of the four valves to cover all working conditions as far as possible by determining the motion laws of the four throats so as to obtain a more representative and universal test result.
Aiming at the laryngeal suppository movement scheme, the traditional systematic design method is less, and more, an empirical design method is adopted, namely, the laryngeal suppository movement scheme is manually set and adjusted based on the existing design case so as to meet the requirement of thrust. However, in the process of implementing the invention, the inventor finds that the traditional method for designing the movement scheme of the laryngeal plug has the technical problem that the designed movement scheme of the laryngeal plug cannot accurately regulate and control the thrust.
Disclosure of Invention
Therefore, in order to solve the above technical problems, it is necessary to provide a method for designing a motion sequence of a throat plug of a posture-controlled engine under stable pressure constraint, which is easy for a control mechanism to accurately regulate and control thrust.
In order to achieve the above purpose, the embodiment of the invention adopts the following technical scheme:
the embodiment of the invention provides a method for designing the motion time sequence of a throat bolt of a posture and orbit control engine under the stable constraint of pressure, which comprises the following steps:
setting the sum of equivalent throat areas of valves of each orbit control spray pipe of the attitude and orbit control engine as a fixed value, and setting a valve area coefficient as the product of a sine amplitude modulation function of each valve and a sine frequency modulation function of each valve;
establishing a ergodic index representing the position combination state of the laryngeal suppository according to the position combination state of the laryngeal suppository in the movement process of the laryngeal suppository; the sample points of the ergodic index comprise the displacement of the four laryngeal plugs at different moments within the effective working time;
determining a design variable and a target function according to the motion frequency of each laryngeal plug in the sinusoidal frequency modulation function of each valve;
solving a real number optimization problem formed by substituting the ergodic indexes of the sample points after normalization by adopting a particle swarm optimization, and outputting each design variable corresponding to an optimal result;
substituting each design variable corresponding to the optimal result into a sine frequency modulation function of each valve, solving a throat plug motion scheme under the stable constraint of output pressure by adopting an interpolation method, and calculating the magnitude and direction of a thrust vector of the output attitude and orbit control engine at each moment.
The technical scheme has the following advantages and beneficial effects:
the method for designing the motion time sequence of the throat plug of the attitude and orbit control engine under the stable pressure constraint comprises the steps of firstly setting the sum of equivalent throat areas of the valves of all orbit control spray pipes of the attitude and orbit control engine to be a fixed value, setting a valve area coefficient to be the product of a sine amplitude modulation function of each valve and a sine frequency modulation function of each valve, establishing a calculation equation of the equivalent throat area of each valve, then establishing a ergodic index representing the position combination state of the throat plug in the motion process of the throat plug, secondly determining the motion frequency of each throat plug in the sine frequency modulation function of each valve as a design variable and determining a corresponding target function, substituting the ergodic index of each sample point after normalization and the target function to form a real number optimization problem in the motion design of the throat plug. And then, solving the real number optimization problem by adopting a particle swarm algorithm, substituting each design variable corresponding to the optimal result obtained and output into the sinusoidal frequency modulation function of each valve for solving, processing by adopting an interpolation method, outputting an optimal laryngeal suppository motion scheme, and calculating and outputting the magnitude and direction of the thrust vector of the engine at each moment.
The scheme obtained covers all working conditions as far as possible under the condition that the pressure of the combustion chamber is stable, is representative, and is convenient for more accurate and effective engine thrust adjustment. Compared with the traditional design method, excessive engineering experience is not needed, meanwhile, complicated manual iterative calculation is avoided, the optimal scheme can be directly tested, and a large number of unrepresentative invalid schemes are filtered, so that the test times are reduced, and the test cost is saved; the pressure of the combustion chamber is stable, so that the aim of more accurate and effective thrust regulation is fulfilled.
Drawings
FIG. 1 is a schematic flow chart of a method for designing a timing sequence of movement of a throat plug of an attitude and orbit control engine with a stable pressure constraint in one embodiment;
FIG. 2 is a schematic diagram of an equivalent throat area calculation coordinate system in one embodiment;
FIG. 3 is a diagram illustrating an amplitude modulation function and a location of a fiducial point in one embodiment;
FIG. 4 is a schematic diagram illustrating an application of the method for designing the timing sequence of the movement of the throat plug of the attitude and orbit control engine with a steady pressure constraint according to an embodiment;
FIG. 5 is a schematic illustration of a posture and orbit control engine configuration, according to an embodiment;
FIG. 6 is a schematic view of a nozzle throat pattern in one embodiment;
FIG. 7 is a graphical illustration of the trend of the position of the laryngeal plug with the equivalent laryngeal area of the laryngeal plug in one embodiment;
FIG. 8 is a graph illustrating equivalent throat coefficients for each valve in one embodiment;
FIG. 9 is a schematic diagram of the equivalent throat profile of each valve after experimental design in one embodiment;
FIG. 10 is a schematic diagram showing the displacement curves of the throats of the valves after experimental design in one embodiment;
FIG. 11 is a schematic diagram of thrust scatter after experimental design in one embodiment;
FIG. 12 is a schematic diagram of the two-dimensional distribution of displacement sample points of the laryngeal plug after experimental design in one embodiment;
FIG. 13 is a schematic diagram of a two-dimensional distribution of equivalent throat area sample points after experimental design in one embodiment;
FIG. 14 is a block diagram of an apparatus for timing movement of a throat plug of a steady pressure low attitude control engine according to an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein in the description of the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
In addition, the technical solutions in the embodiments of the present invention may be combined with each other, but it must be based on the realization of those skilled in the art, and when the technical solutions are contradictory or cannot be realized, such a combination of technical solutions should be considered to be absent and not within the protection scope of the present invention.
In practice, the inventor finds that the currently commonly used thrust matching design method has the following disadvantages: the existing laryngeal suppository movement scheme is given by engineers through personal experience, lacks of theoretical basis and needs a great deal of experience support. The method is not comprehensive in performance assessment of the target engine, the obtained test result is not representative, and hundreds of tests are usually carried out to obtain a representative test result covering most of laryngeal suppository movement schemes. The design efficiency is low, the time cost is high, the waste of resources is caused, the obtained motion scheme of the throat plug cannot ensure that the sum change rate of the equivalent throat area is zero, the pressure of the combustion chamber is a constraint of a constant value, and the accurate regulation and control of the thrust cannot be carried out.
Therefore, the invention provides a posture-orbit-control engine throat plug motion time sequence design method under the condition of stable pressure based on the solid engine ballistic and experimental design method aiming at the technical problem that the throat plug motion scheme designed in the traditional throat plug motion scheme design method cannot accurately regulate and control the thrust, so that the problem that the throat plug motion scheme without scientific basis and unreasonable pressure is manually provided is avoided, the ideal motion scheme of the throat plug under the known configuration can be rapidly and accurately calculated, and the scientific parameter determination of the throat plug motion equation under the condition of stable pressure is realized. The movement scheme of the laryngeal plug obtained by the method is implemented, most working conditions can be covered under the pressure restriction domain, the representative test result is obtained, the control mechanism is easy to accurately adjust the thrust, and performance assessment and key parameter identification can be conveniently carried out on the engine in the later period.
Referring to fig. 1, in one embodiment, the present invention provides a method for designing a timing sequence of motion of a throat plug of a posture-controlled engine under stable pressure constraint, including the following steps S12 to S20:
s12, setting the sum of equivalent throat areas of the valves of each orbit control nozzle of the attitude and orbit control engine as a fixed value, and setting the valve area coefficient as the product of the sine amplitude modulation function of each valve and the sine frequency modulation function of each valve.
It will be appreciated that the profile function y for a given laryngeal plug2And profile function y of the nozzle1As shown in formula (1):
wherein x isnlThe left end point, x, of the nozzle curvenuRepresenting the right-hand end point, x, of the nozzle curveplCoordinates representing the distal end of the laryngeal plug, s represents the displacement of the apex of the laryngeal plug, x1Coordinates, x, representing points on the profile curve of the nozzle2Coordinates representing points on the laryngeal plug profile curve.
A coordinate system for calculating the effective stroke interval of the laryngeal plug and the equivalent laryngeal area for different positions of movement of the laryngeal plug is shown in fig. 2. For a single valve, as the laryngeal plug moves from left to right, the equivalent throat area is calculated by adopting the formula (2), and the equivalent throat area gradually decreases along with the movement of the laryngeal plug and reaches the minimum value when the laryngeal plug completely penetrates. Starting point x of effective stroke interval of laryngeal suppositorybegThe initial position of the displacement of the laryngeal plug, which affects the equivalent laryngeal area, is the endpoint x of the laryngeal plug strokeendIs the furthest position that can be reached during movement of the laryngeal plug.
At a displacement s, a profile function f at the nozzle1(x1) A point (x) at any position1,y1) Function f (x) of profile of the laryngeal plug2S) at any point (x)2,y2) Then its laryngeal plug is equivalent to throat area AtiIs as follows;
the sum A of the equivalent throat areas of the valves of the orbit control nozzles of the attitude and orbit control enginet0Set to a constant value, the sum of the equivalent throat areas of the valves At0Equivalent throat area A of each valvetiThe relationship of (t) is characterized by formula (3), (i ═ 1,2,3, 4).
At0＝At1(t)+At2(t)+At3(t)+At4(t)＝C (3)
Wherein A ist1(t)，At2(t)，At3(t) and At4(t) represents the equivalent throat areas of the four valves, respectively, t represents the current time, and C represents a constant.
And setting the valve area coefficient function as the product of the amplitude modulation function and the frequency modulation function so as to meet the requirements of constant equivalent throat and cover the states of single valve opening and three valves fully closing.
In one embodiment, the sinusoidal amplitude modulation function for each valve is:
wherein q is1(t)，q2(t)，q3(t) and q4(t) amplitude modulation functions of the four valves, ai、bi、ciAnd diEach represents the ith valve amplitude modulation function coefficient, (i ═ 1,2,3,4), and t represents the current time. A can be derived by solving for a fixed pointi、bi、ciAnd diThe value of (c).
Specifically, as shown in fig. 3, the maximum and minimum values of the ordinary sine function only occur once in one cycle, and the maximum value of the function is regarded as the maximum state of the single valve opening degree, and the minimum value of the function is regarded as the minimum state of the single valve opening degree. The reference point of the sine amplitude modulation function of each valve is a point at which the sine function value is 1, namely, the limit state of single-valve opening and three-valve closing appears at the point, and the state only appears once in working time, so that the position of each curve reference point is fixed.
In a four-valve engine, the limit states of each valve occur once, namely, the four positions and states of the single-valve amplitude modulation function are known, and the opening degree of each valve at a specific moment is shown in a normalized space state in table 1. And solving the quaternary equation set through the four-point coordinates to obtain the amplitude modulation function coefficient in the curve equation.
Selecting four moments t in the time period1、t2、t3And t4Taking 10 seconds as an example of the time when the four valves reach the limit states of single-valve opening and three-valve closing respectively, 0s, 3.3333s, 6.6667s and 10s are selected according to the equipartition method and are substituted into the formula (5), and a is calculatedi、bi、ciAnd diAnd obtaining the amplitude modulation functions of the four valves.
TABLE 1
In one embodiment, the sinusoidal chirp function for each valve is:
wherein, g1(t)，g2(t)，g3(t) and g4(t) denotes the frequency modulation function, ω, of the four valves, respectively1、ω2、ω3And ω4Each of the four sinusoidal frequency modulation curves has a frequency (i ═ 1,2,3,4), t1、t2、t3And t4Respectively representing the moment at which the respective valve reaches a limit condition, j1、j2、j3And j4Respectively representing the position of each valve datum point; u and v represent the amplitude and mean of the sinusoidal chirp, respectively, and are calculated as shown in equation (7):
wherein, wmaxRepresenting the upper bound of the normalized space, wminRepresenting the lower bound of the normalized space.
It can be understood that the frequency modulation function is adopted to limit the interval of the motion equation of the laryngeal plug to the space of [0,1], as shown in formula (6).
In one embodiment, at any one time, each valve equivalent throat area is equal to the product of a valve area ratio coefficient and the sum of the valve equivalent throat areas, the valve area ratio coefficient being the proportion of the valve area coefficient within the total valve area coefficient, and therefore the equation for calculating each valve equivalent throat area based on the sinusoidal amplitude modulation function of each valve and the sinusoidal frequency modulation function of each valve is:
wherein A ist1(t)、At2(t)、At3(t) and At4(t) represents equivalent throat areas of the four valves, At0Is the sum of equivalent throat areas, q1(t)，q2(t)，q3(t) and q4(t) represents the amplitude modulation function of the four valves, g1(t)，g2(t)，g3(t) and g4(t) denotes the frequency modulation function of each of the four valves, and t denotes the current time. The equivalent throat areas of the four valves can be obtained through the formula (8), and the equivalent throat areas of the valves and the displacement rule interpolation of the throats can be carried out, so that the displacement x of the four throats at the current moment can be obtained1(t)，x2(t)，x3(t) and x4(t)。
S14, establishing a ergodic index representing the position combination state of the laryngeal plug according to the position combination state of the laryngeal plug in the movement process of the laryngeal plug; the sample points of the ergodic index include the displacement of the four laryngeal plugs at different times within the effective working time.
In some embodiments, the following substeps S142 to S148 may be specifically included:
s142, establishing a pressure variation curve of the gas generator in the movement process of the throat plug by adopting a zero-dimensional internal trajectory model;
s144, the displacement of the throats of the four valves in the effective working time is respectively used as four dimensions of the sample;
s146, performing discrete processing on the four-dimensional samples according to the set time step to obtain different time displacements of the four laryngeal plugs in the effective working time;
and S148, establishing a ergodic index by taking the displacement at different moments as sample points.
Specifically, a zero-dimensional internal trajectory model is adopted to establish a pressure variation curve of the gas generator in the movement process of the throat plug; and (3) calculating the zero-dimensional internal trajectory of the attitude and orbit control engine, and solving the formula (9) by adopting a four-order Runge-Kutta method to obtain a pressure variation curve of the gas generator.
The zero-dimensional internal ballistic model is:
wherein p iscIs the combustion chamber pressure, t is time, Γ is a function of the specific heat ratio k, c*Is a characteristic velocity, VcIs the combustion chamber volume, ppIs the density of the propellant, AbIs the burning surface area of the charge, a is the burning rate coefficient, n is the pressure index, e is the grain thickness, r0Is the radius of charge, L is the length of the cavity, R is the gas constant of the gas, TfIs the constant pressure combustion temperature, k is the specific heat ratio, At0Is the total throat area.
After obtaining the pressure variation curve of the gas generator, the displacement x of the throats of the four valves in the effective working time1(t)，x2(t)，x3(t) and x4(t) as four dimensions of the sample, respectively. And dispersing four curves corresponding to the four dimensions according to the time step delta t to obtain displacement and pressure matrixes at different moments and using the displacement and pressure matrixes as sample points. Based on ergodic index phipThe ergodic index is established for the combination of different positions and pressures of the laryngeal plugs.
In one embodiment, the established ergodicity index is as shown in equation (10):
wherein (x)·j-x·(j-1))pRepresenting the Euclidean distance between a previous time sample point and a next time sample point in different dimensions, n represents the number of all sample points, p is a constant, x1jRepresents the displacement of the first laryngeal plug at the jth sample, x1(j-1)Denotes the displacement of the first laryngeal plug at time j-1, x2jRepresents the displacement of the second laryngeal plug at the jth sample, x2(j-1)Denotes the displacement of the second laryngeal plug at time j-1, x3jRepresents the displacement of the third laryngeal plug at the jth sample, x3(j-1)Represents the displacement of the third laryngeal plug at time j-1, x4jRepresents the displacement of the fourth laryngeal plug at the jth sample, x4(j-1)The displacement of the fourth laryngeal plug at time j-1 is shown.
And S16, determining a design variable and an objective function according to the movement frequency of each laryngeal plug in the sinusoidal frequency modulation function of each valve.
It will be appreciated that the frequencies of motion (ω) of the sinusoidal motion profile of the FM function of the four valves are selected1、ω2、ω3And ω4) As a design variable. To ensure the reasonability of the movement of the laryngeal suppository, the frequency variation range is limited to [5,50 ]]. Selecting phipEvaluating the spatial uniformity of the sample according to a criterion, normalizing the four-dimensional sample points and calculating phi according to the formula (10)pThe value is obtained.
In one embodiment, the objective function is:
f(x)＝min(Φp(ω1,ω2,ω3,ω4)) (11)
wherein phipRepresenting the ergodic index, ω1、ω2、ω3And ω4Respectively represents the motion frequencies of four laryngeal suppository sinusoidal motion curves, and the variation range of the motion frequencies is [5,50 ]]。
It will be appreciated that the objective function is shown as equation (11) at ΦpThe goal of minimizing the maximum distance is achieved when the value reaches a minimum value.
And S18, solving a real number optimization problem formed by substituting the ergodic indexes of the sample points after normalization by adopting a particle swarm optimization, and outputting each design variable corresponding to the optimal result.
In some embodiments, the following substeps S182 to S184 may be specifically included:
s182, in the solving process, convergence judgment is carried out on solving calculation by adopting a set convergence criterion; the convergence criterion includes:
abs(Fa-Fb)≤e (12)
or
iter≥Nmax (13)
Wherein, abs (F)a-Fb) Represents the optimum value FaWith a sub-optimum value FbError between eRepresents the upper limit of acceptable error set, iter represents the number of iteration steps, NmaxRepresenting the maximum value of the iteration steps;
and S184, if any one of the convergence criteria is met, jumping out of the solution loop and outputting each design variable corresponding to the optimal result.
Specifically, the real number optimization problem is solved by using a particle swarm algorithm, and convergence determination is performed by using equations (12) and (13). If the optimal value FaWith a sub-optimum value FbAnd other values are within a given acceptable range or the iteration step iter reaches the maximum given step number, the error is considered to be converged, the loop is jumped out, and each design variable corresponding to the optimal result is output, namely the motion frequency omega obtained by solving1、ω2、ω3And ω4。
In some embodiments, the maximum given number of steps may optionally be taken to be 5000. Better optimal results can be obtained under the condition of relatively less solving time consumption, so that the efficiency of design processing is better improved.
In some embodiments, the following sub-step S185 may be specifically included:
s185, if the convergence criterion is not met, returning to execute the step S14 until any one of the convergence criteria is met; at this time, the motion frequency ω is obtained by solving the design variables corresponding to the optimal result, namely the convergence, the cycle jump and the output of the optimal result1、ω2、ω3And ω4。
And S20, substituting each design variable corresponding to the optimal result into the sinusoidal frequency modulation function of each valve, solving the motion scheme of the throat plug under the stable constraint of the output pressure by adopting an interpolation method, and calculating the magnitude and direction of the thrust vector of the output attitude and orbit control engine at each moment.
It can be understood that the optimal solution is substituted into the laryngeal-plug motion formula (6) to obtain a laryngeal-plug motion scheme, and the magnitude and direction of the thrust vector of the attitude and orbit control engine at each moment are solved.
In one embodiment, the magnitude of the thrust vector of the attitude and orbit control engine at each moment is calculated by the following formula:
Fi(t)＝CF(t)pc(t)Ati(t)(i＝1,2,3,4) (14)
the direction of the thrust vector of the attitude and orbit control engine at each moment is calculated by the following formula:
wherein, FiRepresenting single valve thrust, t representing the current time, i representing the valve number, CFRepresenting the thrust coefficient, pcRepresenting the combustion chamber pressure, AtiRepresenting the equivalent throat area of a single valve, Γ represents a function of the specific heat ratio k, k represents the specific heat ratio, peIndicating the pressure of the gas at the outlet of the nozzle, paDenotes atmospheric pressure, AeDenotes the cross-sectional area of the nozzle outlet, At0Denotes the sum of the equivalent throat areas of the valves, FyAnd FzAxial forces of thrust in the y-direction and the z-direction, respectively, are represented, and θ represents a thrust vector angle.
Wherein, FyAnd FzThe following relationships exist:
as shown in fig. 4, the method for designing the motion time sequence of the throat plug of the attitude and orbit control engine under the stable pressure constraint includes the steps of firstly setting the sum of equivalent throat areas of the valves of each orbit control nozzle of the attitude and orbit control engine to be a fixed value, setting a valve area coefficient to be the product of a sine amplitude modulation function of each valve and a sine frequency modulation function of each valve, establishing a calculation equation of the equivalent throat area of each valve, then establishing a traversal index representing the position combination state of the throat plug in the motion process of the throat plug, secondly determining the motion frequency of each throat plug in the sine frequency modulation function of each valve as a design variable and determining a corresponding target function, substituting the traversal index of each sample point after normalization and the target function to form a real number optimization problem in the motion design of the throat plug. And then, solving the real number optimization problem by adopting a particle swarm algorithm, substituting each design variable corresponding to the optimal result obtained and output into the sinusoidal frequency modulation function of each valve for solving, processing by adopting an interpolation method, outputting an optimal laryngeal suppository motion scheme, and calculating and outputting the magnitude and direction of the thrust vector of the engine at each moment.
The scheme obtained covers all working conditions as far as possible under the condition that the pressure of the combustion chamber is stable, is representative, and is convenient for more accurate and effective engine thrust adjustment. Compared with the traditional design method, excessive engineering experience is not needed, meanwhile, complicated manual iterative calculation is avoided, the optimal scheme can be directly tested, and a large number of unrepresentative invalid schemes are filtered, so that the test times are reduced, and the test cost is saved; the pressure of the combustion chamber is stable, so that the aim of more accurate and effective thrust regulation is fulfilled.
It should be understood that although the steps in the flowcharts of fig. 1 and 4 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps of fig. 1 and 4 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
In one embodiment, as shown in fig. 4, in order to more intuitively and fully illustrate the above method for designing the motion sequence of the attitude and orbit control engine throat plug under the pressure stability constraint, an example of application and verification of the design method provided by the present invention is given below as an example of experimental design of a timing sequence of a certain four-nozzle orbit control engine.
It should be noted that the embodiment given in this specification is only illustrative and not the only limitation of the specific embodiment of the present invention, and those skilled in the art can adopt the above method for designing the motion sequence of the throat plug of the attitude and orbit control engine under the stable constraint of pressure to realize the rapid design of the throat plug motion schemes of the different attitude and orbit control engines.
Attitude and orbit control motor layout as shown in fig. 5, the attitude and orbit control motor can generate orbit control forces along the body Oy axis and the Oz axis, and the valves are numbered as valves 1,2,3 and 4 in the clockwise direction. The nozzle throat plug profile is shown in fig. 6, and the configuration parameters are shown in table 2, and are set according to actual engine parameters. The experimental design method aims to improve the reliability and effectiveness of a single test result by scientifically and reasonably designing the motion scheme of the laryngeal plug on the premise of keeping the pressure of the combustion chamber stable. And finally, the full inspection of the actual performance of the target engine under each laryngeal plug motion combination is realized.
TABLE 2
Aiming at the case, a solid attitude and orbit control engine time sequence experimental design method under the constraint of pressure stability is applied to complete the motion scheme design of the throat plug, and the specific steps are as follows:
(1) initially setting the algorithm, setting the dimension of the sample to 4, the number of particle populations to 20, the maximum iteration number to 5000, and giving an upper bound U of the variablebAnd a lower bound Lb，ω∈[5,50]An initial population is randomly generated in a design variable domain, and the velocity of each particle is assigned to an initial value. And circularly solving according to the time step within the defined working time, and calculating to the final time 10s by taking the time 0s as the initial time and superposing according to the time step 0.01 s.
(2) And setting initial parameters of the engine to obtain a laryngeal plug motion equation. Based on the known throat plug generatrix and the nozzle generatrix, the equivalent throat area-throat plug displacement change shown in FIG. 7 is given by calculationAnd (4) relationship. Simultaneously, the maximum value of the equivalent throat area of the single valve is determined to be 5.3093E-4m2And a minimum value of 3.6488E-9m2And the initial position of the effective stroke of the corresponding laryngeal suppository is 0m and the final position is 0.0500 m. The sum of the valve equivalent throat areas is defined as the maximum value of the single valve equivalent throat area.
(3) Time is dispersed into 1001 times according to the time step of 0.01s, and the sum A of equivalent throat areas is obtainedt0Set as the maximum opening 5.3093E-4m of the single valve2Calculating the combustion chamber pressure p at the initial momentcAnd performing zero-dimensional internal trajectory calculation by adopting a fourth-order Runge Kutta method. Will be at time tiSubstituting the corresponding positions into the amplitude modulation function to calculate the frequency modulation function coefficient a of each valvei,bi,ci,di(i ═ 1,2,3,4), and the current amplitude modulation function q of the valve is obtained1(t)，q2(t)，q3(t) and q4(t) of (d). Selecting limit time of each valve as reference time, and substituting the reference time into a frequency modulation function g1(t)，g2(t)，g3(t) and g4(t), calculating the valve area ratio coefficient to obtain the equivalent throat area A of each valve at presentt1(t)，At2(t)，At3(t) and At4(t), interpolating the relation between the known equivalent throat area and the displacement of the laryngeal plug to obtain the current displacement x of the laryngeal plug of the valve1(t)，x2(t)，x3(t) and x4(t) of (d). And after zero-dimensional internal trajectory calculation, equivalent throat areas, throat bolt displacements and combustion chamber pressure of the four valves at corresponding moments after dispersion according to time steps can be obtained.
(4) Selecting four valve throat plug displacement x1(t)，x2(t)，x3(t) and x4(t) four dimensions of the sample, normalizing the output parameters according to phipAnd calculating the space uniformity of the target function value according to the criterion, wherein the value of p is 2, and the target function value is obtained through calculation.
(5) And (5) performing convergence judgment on the data, and jumping out of the loop if the convergence condition is reached. Outputting four sine function frequencies omega corresponding to the optimal solution under the current condition1，ω2，ω3And ω4. If not, repeating the steps (3) - (5).
(6) And substituting the optimal solution into a valve area coefficient equation (8) to obtain a corresponding optimal motion scheme of the laryngeal suppository. The magnitude F and the direction theta of the thrust vector of the engine at each moment are obtained.
The change of the equivalent throat area along with the displacement of the laryngeal plug is shown in fig. 7, the effective movement range of the laryngeal plug is [0,0.0500] meter, the change range of the equivalent throat area of the single valve is [3.6488E-9,5.3093E-4] square meter, the equivalent throat area is gradually reduced along with the progression of the laryngeal plug from left to right, and the equivalent throat area reaches the minimum value when the laryngeal plug moves to the final position. In the actual working process, the throat plug changes according to the motion rule, the equivalent throat area can change the pressure change of the combustion chamber, and the equivalent throat areas of the four valves are limited to be a fixed value in order to ensure the constant pressure of the combustion chamber. The engine operating parameters are shown in table 3. The simulation model initialization parameters in step (2) are set according to tables 2 and 3.
TABLE 3
Will be at time tiSubstituting the corresponding positions into the amplitude modulation function to calculate the frequency modulation function coefficient a of each valvei,bi,ci,di(i ═ 1,2,3,4), and the current amplitude modulation function q of the valve is obtained1(t)，q2(t), q3(t) and q4 (t). The value of the equivalent throat area coefficient for each valve can be derived from the value of the amplitude modulation function at each time, as shown in FIG. 8.
Taking the extreme state time of each valve in Table 1 as a reference time, i.e. t in each valve frequency modulation functioniAre each t1，t2，t3And t4The frequency modulation function is shown as equation (18).
Four parameters of a frequency modulation function in a four-valve solid attitude and orbit control engine valve area coefficient equation are used as design variables, the motion scheme parameters are selected by adopting the experimental design method, and the obtained results are shown in table 4.
TABLE 4
The equivalent throat change curve of each valve is shown in FIG. 9, and the displacement change curve of each valve throat plug is shown in FIG. 10. The diagram result shows that the experimental design of the movement scheme of the laryngeal suppository fully considers the displacement combination of the laryngeal suppository under various conditions and covers the limit states of single valve opening and three valve closing.
The pressure of the combustion chamber obtained by using the parameter calculation is constant at 10.6507MPa, the thrust range is [556.8577,19138] N, the corresponding thrust scatter diagram is shown in FIG. 11, almost all angles and sizes in the thrust design space are covered, the directions and sizes of thrust vectors are uniform, and the thrust performance in all directions can be fully considered.
The effect of the experimental design method is obvious through the two-dimensional distribution diagram of the sample points in fig. 12 and 13, and the obtained sample points can be uniformly distributed in a low-dimensional space. The self-adaptive particle swarm optimization method is applied to the time sequence experimental design, and the dispersivity of sample points in a high-dimensional space and a low-dimensional space can be ensured. The results after experimental design can fully examine most of combination schemes of the four spray pipes, and the thrust in each direction of the maximum proportion limit can be tested in a single test. The test cost and the time cost can be greatly reduced by applying the experimental design method to design the motion scheme of the laryngeal suppository, and the conclusion of more scientificity and reliability is obtained.
The design method is applied to the design of various different solid attitude and orbit control engine throat plug motion schemes, compared with the existing method, the manual participation process is less, the test times are reduced, the design variables obtained by the experimental design method are simulated to cover most of working conditions, and the obtained result is more representative and more reliable.
Those skilled in the art can understand that the present application is designed for the throats of four-valve solid attitude control engines as an example, and on the basis of the design concept of the present application, those skilled in the art can implement rapid design of other numbers of valve throats according to the same principle of the design concept.
Referring to fig. 14, a timing sequence design apparatus 100 for a posture and orbit control engine throat plug motion under pressure stability constraint is further provided, and includes an equivalence establishing module 13, a characterization establishing module 15, an objective determining module 17, an optimization solving module 19, and a plan outputting module 21. The equivalent establishing module 13 is configured to set a sum of equivalent throat areas of valves of each orbit control nozzle of the attitude and orbit control engine to a fixed value, and set a valve area coefficient to a product of a sinusoidal amplitude modulation function of each valve and a sinusoidal frequency modulation function of each valve. The representation establishing module 15 is used for establishing a traversal index representing the combined state of the positions of the laryngeal plugs according to the combined state of the positions of the laryngeal plugs in the movement process of the laryngeal plugs; the sample points of the ergodic index include the displacement of the four laryngeal plugs at different times within the effective working time. The target determination module 17 is used to determine the design variables and the target function according to the motion frequency of each laryngeal plug in the sinusoidal chirp function of each valve. The optimization solving module 19 is configured to solve a real number optimization problem formed by substituting the ergodic indexes of the normalized sample points into a simultaneous objective function by using a particle swarm algorithm, and output design variables corresponding to an optimal result. The scheme output module 21 is used for substituting each design variable corresponding to the optimal result into a sinusoidal frequency modulation function of each valve, solving a throat plug motion scheme under the stable constraint of output pressure by adopting an interpolation method, and calculating the magnitude and direction of a thrust vector of the output attitude and orbit control engine at each moment.
The attitude and orbit control engine throat plug motion time sequence design device 100 under the stable pressure constraint firstly sets the sum of equivalent throat areas of the valves of the orbit control nozzles of the attitude and orbit control engine to be a fixed value, sets the valve area coefficient to be the product of the sine amplitude modulation function of each valve and the sine frequency modulation function of each valve, establishes a calculation equation of the equivalent throat area of each valve, then establishes a ergodic index representing the position combination state of the throat plug in the motion process, secondly determines the motion frequency of each throat plug in the sine frequency modulation function of each valve as a design variable and determines a corresponding target function, substitutes the ergodic index of each sample point after normalization and the target function to form a real number optimization problem in the throat plug motion design in a simultaneous mode. And then, solving the real number optimization problem by adopting a particle swarm algorithm, substituting each design variable corresponding to the optimal result obtained and output into the sinusoidal frequency modulation function of each valve for solving, processing by adopting an interpolation method, outputting an optimal laryngeal suppository motion scheme, and calculating and outputting the magnitude and direction of the thrust vector of the engine at each moment.
The scheme obtained covers all working conditions as far as possible under the condition that the pressure of the combustion chamber is stable, is representative, and is convenient for more accurate and effective engine thrust adjustment. Compared with the traditional design method, excessive engineering experience is not needed, meanwhile, complicated manual iterative calculation is avoided, the optimal scheme can be directly tested, and a large number of unrepresentative invalid schemes are filtered, so that the test times are reduced, and the test cost is saved; the pressure of the combustion chamber is stable, so that the aim of more accurate and effective thrust regulation is fulfilled.
In an embodiment, in each module of the pressure stable constraint lower attitude and orbit control engine throat plug motion timing sequence designing apparatus 100, a part of the modules may be further specifically used to implement corresponding steps or sub-steps added in each embodiment of the pressure stable constraint lower attitude and orbit control engine throat plug motion timing sequence designing method.
For specific limitations of the apparatus 100 for designing the motion timing sequence of the throat plug of the attitude and orbit control engine under the stable pressure constraint, reference may be made to the corresponding limitations of the above method for designing the motion timing sequence of the throat plug of the attitude and orbit control engine under the stable pressure constraint, and details thereof are not repeated herein. The modules in the above-described pressure stability constraint lower attitude and orbit control engine throat plug motion timing design apparatus 100 may be implemented wholly or partially by software, hardware, and combinations thereof. The modules can be embedded in hardware or independent of a device with specific data processing functions, or can be stored in a memory of the device in a software form, so that a processor can call and execute operations corresponding to the modules, and the device can be, but is not limited to, a computer device or a computing system for designing a solid-state orbit attitude control engine.
In still another aspect, a computer device is provided, which includes a memory and a processor, the memory stores a computer program, and the processor executes the computer program to implement the following steps: setting the sum of equivalent throat areas of valves of each orbit control spray pipe of the attitude and orbit control engine as a fixed value, and setting a valve area coefficient as the product of a sine amplitude modulation function of each valve and a sine frequency modulation function of each valve; establishing a ergodic index representing the position combination state of the laryngeal suppository according to the position combination state of the laryngeal suppository in the movement process of the laryngeal suppository; the sample points of the ergodic index comprise the displacement of the four laryngeal plugs at different moments within the effective working time; determining a design variable and a target function according to the motion frequency of each laryngeal plug in the sinusoidal frequency modulation function of each valve; solving a real number optimization problem formed by substituting the ergodic indexes of the sample points after normalization by adopting a particle swarm optimization, and outputting each design variable corresponding to an optimal result; substituting each design variable corresponding to the optimal result into a sine frequency modulation function of each valve, solving a throat plug motion scheme under the stable constraint of output pressure by adopting an interpolation method, and calculating the magnitude and direction of a thrust vector of the output attitude and orbit control engine at each moment.
In one embodiment, the processor when executing the computer program may further implement the additional steps or substeps of the above-described pressure plateau constraint lower attitude control engine throat plug motion timing design method embodiments.
In yet another aspect, there is also provided a computer readable storage medium having a computer program stored thereon, the computer program when executed by a processor implementing the steps of: setting the sum of equivalent throat areas of valves of each orbit control spray pipe of the attitude and orbit control engine as a fixed value, and setting a valve area coefficient as the product of a sine amplitude modulation function of each valve and a sine frequency modulation function of each valve; establishing a ergodic index representing the position combination state of the laryngeal suppository according to the position combination state of the laryngeal suppository in the movement process of the laryngeal suppository; the sample points of the ergodic index comprise the displacement of the four laryngeal plugs at different moments within the effective working time; determining a design variable and a target function according to the motion frequency of each laryngeal plug in the sinusoidal frequency modulation function of each valve; solving a real number optimization problem formed by substituting the ergodic indexes of the sample points after normalization by adopting a particle swarm optimization, and outputting each design variable corresponding to an optimal result; substituting each design variable corresponding to the optimal result into a sine frequency modulation function of each valve, solving a throat plug motion scheme under the stable constraint of output pressure by adopting an interpolation method, and calculating the magnitude and direction of a thrust vector of the output attitude and orbit control engine at each moment.
In one embodiment, the computer program, when executed by the processor, further implements the additional steps or sub-steps of the above-described pressure plateau constraint lower attitude control engine throat plug motion timing design method in various embodiments.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware related to instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), synchronous link DRAM (Synchlink) DRAM (SLDRAM), Rambus DRAM (RDRAM), and interface DRAM (DRDRAM).
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above examples only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the spirit of the present application, and all of them fall within the scope of the present application. Therefore, the protection scope of the present patent should be subject to the appended claims.
Claims (10)
1. A method for designing the motion time sequence of a throat plug of a posture and orbit control engine under the stable constraint of pressure intensity is characterized by comprising the following steps:
setting the sum of equivalent throat areas of valves of each orbit control spray pipe of the attitude and orbit control engine as a fixed value, and setting a valve area coefficient as the product of a sine amplitude modulation function of each valve and a sine frequency modulation function of each valve;
establishing a ergodic index representing the position combination state of the laryngeal suppository according to the position combination state of the laryngeal suppository in the movement process of the laryngeal suppository; the sample points of the ergodic index comprise different time displacements of four laryngeal plugs in effective working time;
determining a design variable and a target function according to the movement frequency of each laryngeal plug in the sinusoidal frequency modulation function of each valve;
solving a real number optimization problem formed by combining the ergodic indexes of the sample points subjected to substitution normalization with the objective function by adopting a particle swarm optimization, and outputting each design variable corresponding to an optimal result;
substituting each design variable corresponding to the optimal result into the sinusoidal frequency modulation function of each valve, solving a throat plug motion scheme under the stable constraint of output pressure by adopting an interpolation method, and calculating and outputting the magnitude and direction of the thrust vector of the attitude and orbit control engine at each moment.
2. The pressure stability constraint lower attitude and orbit control engine larynx plug motion time sequence design method according to claim 1, characterized in that the step of establishing a ergodic index representing the larynx plug position combination state according to the larynx plug position combination state in the larynx plug motion process comprises:
establishing a pressure variation curve of the gas generator in the movement process of the throat plug by adopting a zero-dimensional internal trajectory model;
the displacement of the throats of the four valves in the effective working time is respectively used as four dimensions of the sample;
performing discrete processing on the samples with four dimensions according to a set time step to obtain different time displacements of the four laryngeal plugs in the effective working time;
and establishing the ergodicity index by taking the displacement of each different moment as a sample point.
3. The pressure stability constraint lower attitude and orbit control engine throat plug motion time sequence design method according to claim 1 or 2, characterized in that the ergodic index is as follows:
wherein (x)·j-x·(j-1))pRepresenting the Euclidean distance between a previous time sample point and a next time sample point in different dimensions, n represents the number of all sample points, p is a constant, x1jRepresents the displacement of the first laryngeal plug at the jth sample, x1(j-1)Denotes the displacement of the first laryngeal plug at time j-1, x2jRepresents the displacement of the second laryngeal plug at the jth sample, x2(j-1)Denotes the displacement of the second laryngeal plug at time j-1, x3jRepresents the displacement of the third laryngeal plug at the jth sample, x3(j-1)Represents the displacement of the third laryngeal plug at time j-1, x4jRepresents the displacement of the fourth laryngeal plug at the jth sample, x4(j-1)The displacement of the fourth laryngeal plug at time j-1 is shown.
4. The pressure stability constraint lower attitude control engine throat plug motion timing design method of claim 3, wherein the objective function is:
f(x)＝min(Φp(ω1,ω2,ω3,ω4))
wherein phipRepresenting said ergodic index, ω1、ω2、ω3And ω4Respectively represents the motion frequencies of four laryngeal suppository sinusoidal motion curves, and the variation range of the motion frequencies is [5,50 ]]。
5. The pressure stability constraint under-attitude and orbit control engine throat plug motion time sequence design method according to claim 1, characterized in that the step of solving a real number optimization problem formed by the ergodic indexes of each sample point after substitution normalization and the objective function in conjunction by using a particle swarm algorithm and outputting each design variable corresponding to an optimal result comprises:
in the solving process, convergence judgment is carried out on solving calculation by adopting a set convergence criterion; the convergence criterion includes:
abs(Fa-Fb) E is less than or equal to e or iter is more than or equal to Nmax
Wherein, abs (F)a-Fb) Represents the optimum value FaWith a sub-optimum value FbE represents the upper limit value of the acceptable error, iter represents the number of iteration steps, NmaxRepresenting the maximum value of the iteration steps;
and if any one of the convergence criteria is met, jumping out of a solving cycle and outputting each design variable corresponding to the optimal result.
6. The pressure stability constraint under-attitude and orbit control engine throat plug motion time sequence design method of claim 5, wherein the step of solving a real number optimization problem formed by the ergodic indexes of each sample point after substitution normalization and the objective function in conjunction by using a particle swarm algorithm and outputting each design variable corresponding to an optimal result further comprises:
and if the convergence criterion is not met, returning to the step of executing the step of establishing the ergodic index representing the position combination state of the laryngeal plug according to the position combination state of the laryngeal plug in the movement process until any one of the convergence criteria is met.
7. The pressure stability constrained lower attitude control engine throat plug motion timing design method of claim 1, wherein the sinusoidal amplitude modulation function for each valve is:
wherein q is1(t)，q2(t)，q3(t) and q4(t) amplitude modulation functions of the four valves, ai、bi、ciAnd diEach represents the ith valve amplitude modulation function coefficient, (i ═ 1,2,3,4), and t represents the current time.
8. The pressure stability constraint lower attitude control engine throat plug motion timing design method of claim 7, wherein the sine frequency modulation function of each valve is:
wherein, g1(t)，g2(t)，g3(t) and g4(t) denotes the frequency modulation function, ω, of the four valves, respectively1、ω2、ω3And ω4Each of the four sinusoidal frequency modulation curves has a frequency (i ═ 1,2,3,4), t1、t2、t3And t4Respectively representing the moment at which the respective valve reaches a limit condition, j1、j2、j3And j4Respectively representing the position of each valve datum point; u and v represent the amplitude and mean of the sinusoidal frequency modulation curve, respectively, and the calculation method is as follows:
wherein, wmaxRepresenting the upper bound of the normalized space, wminRepresenting the lower bound of the normalized space.
9. The pressure stability-constrained attitude control engine throat plug motion timing design method of claim 8, wherein the calculated equation for each valve equivalent throat area based on the sinusoidal amplitude modulation function of each valve and the sinusoidal frequency modulation function of each valve is:
wherein A ist1(t)、At2(t)、At3(t) and At4(t) represents equivalent throat areas of the four valves, At0Is the sum of equivalent throat areas, q1(t)，q2(t)，q3(t) and q4(t) represents the amplitude modulation function of the four valves, g1(t)，g2(t)，g3(t) and g4(t) denotes the frequency modulation function of each of the four valves, and t denotes the current time.
10. The method for designing the motion sequence of the throat plug of a posture and orbit controlled engine under the stable constraint of pressure according to claim 1, wherein the magnitude of the thrust vector of the posture and orbit controlled engine at each moment is calculated by the following formula:
Fi(t)＝CF(t)pc(t)Ati(t)(i＝1,2,3,4)
the direction of the thrust vector of the attitude and orbit control engine at each moment is calculated by the following formula:
wherein, FiRepresenting single valve thrust, t representing the current time, i representing the valve number, CFRepresenting the thrust coefficient, pcRepresenting the combustion chamber pressure, AtiRepresenting the equivalent throat area of a single valve, Γ represents a function of the specific heat ratio k, k represents the specific heat ratio, peIndicating the pressure of the gas at the outlet of the nozzle, paDenotes atmospheric pressure, AeDenotes the cross-sectional area of the nozzle outlet, At0Denotes the sum of the equivalent throat areas of the valves, FyAnd FzAxial forces of thrust in the y-direction and the z-direction, respectively, are represented, and θ represents a thrust vector angle.
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