A method for calculating thrust envelope of solid rail control engine servo uncertainty

Abstract

This application discloses a method for calculating the thrust envelope of a solid rocket motor based on servo uncertainty, relating to the field of solid rocket motor technology. This method focuses on the gas valve servo system of a throat-operated solid rocket motor, performing uncertainty modeling of the motor drive system and transmission system, analyzing the main influencing parameters of servo system uncertainty, including transmission clearance, eccentric shaft friction coefficient, and other uncertainty parameters and their probability distributions; generating random parameter samples based on the uncertainty model, and using the servo system control model to solve for the actual throat displacement response under random samples, obtaining the engine thrust time history under single-valve and multi-valve cooperative working modes; and fitting the thrust uncertainty envelope by calculating the mean and standard deviation of the thrust response through Monte Carlo simulation. This application quantitatively characterizes the degree of influence of internal factors of the servo mechanism on thrust performance, providing a reference for ensuring precise thrust control of solid rocket motors.

Description

Technical Field

[0001] This application generally relates to the field of solid rocket motor technology, and specifically to a method for calculating the thrust envelope of a solid rocket motor based on servo uncertainty. Background Technology

[0002] Solid rocket motors, due to their simple structure, high reliability, and rapid response, have become a key power source for high-speed, high-maneuverability aircraft to achieve orbit changes and attitude corrections. Thrust adjustment is typically achieved by a servo mechanism driving a throat-type gas valve, altering the throat area of ​​the gas flow path. Therefore, the control accuracy and dynamic characteristics of the servo system directly determine the engine's thrust output performance, thus affecting the aircraft's orbital control accuracy.

[0003] Currently, the analysis of thrust performance and the design of control systems for solid rocket motors primarily employ methods based on deterministic physical and mathematical models. These methods typically ignore or simplify the nonlinear factors actually present in the servo system during modeling, treating all parameters as deterministic values. However, these nonlinear factors are prevalent in practical engineering and exhibit significant stochastic uncertainties. Ignoring these uncertainties leads to deviations between the established simulation model and the real physical system, making it difficult for the thrust prediction results to accurately reflect the possible thrust distribution range during actual operation. Consequently, it becomes challenging to support the design of high-precision, high-reliability orbit control tasks. Summary of the Invention

[0004] In view of the above-mentioned defects or deficiencies in the prior art, it is desirable to provide a method for calculating the thrust envelope of servo uncertainty of solid rocket motors.

[0005] This application provides a method for calculating the thrust envelope of a solid rocket motor based on servo uncertainty. The solid rocket motor includes a gas valve, and by controlling the operation of the gas valve, the variable thrust output of the solid rocket motor can be achieved. The method includes: The key uncertainty parameters affecting thrust performance in the solid rocket motor servo mechanism and their probability distribution information are set; and the action commands of the gas valve are set. A preset number of random samples are generated based on the probability distribution information, and the random samples correspond to combinations of key uncertainty parameters composed of different key uncertainty parameters; A servo system control model is constructed, and the actual displacement response time sequence of the gas valve corresponding to the action command under the combination of key uncertainty parameters is obtained by solving the servo system control model and the random sample. Based on each actual displacement response time sequence, the engine thrust time history corresponding to all random samples is calculated using the engine thrust model. Statistical analysis is performed on the engine thrust time history of all the random samples to calculate the thrust mean and standard deviation of the thrust response, so as to quantify the thrust uncertainty of the solid rocket motor. The thrust uncertainty is used to guide the adjustment and optimization of the thrust performance of the solid rocket motor.

[0006] According to the technical solution provided in this application, the gas valve is a throat-plug type gas valve, and there are multiple such valves, each of which has a throat plug; the key uncertainty parameters include at least: transmission clearance, phase-to-phase resistance, phase-to-phase inductance, eccentric shaft friction coefficient, static friction force, and dynamic friction force.

[0007] According to the technical solution provided in this application, a servo system control model is constructed, and the actual displacement response time sequence of the gas valve corresponding to the action command under the corresponding key uncertainty parameter combination is obtained by solving the servo system control model and the random sample, including: A servo system control model is constructed, which is a three-closed-loop PID control model containing current loop, speed loop and position loop, built on the Simulink platform. Each random sample is input into the servo system control model, and a simulation experiment of the solid rocket motor is performed based on the servo system control model; the simulation experiment is set with the working time of the solid rocket motor, and the action commands are set according to the preset working mode of the solid rocket motor; Through the simulation experiment, the throat displacement response time sequence of each gas valve during the working time is obtained under different combinations of the key uncertainty parameters, and the throat displacement response time sequence corresponding to all the throats is taken as the actual displacement response time sequence of the gas valve under each combination of the key uncertainty parameters.

[0008] According to the technical solution provided in this application, based on each actual displacement response time series, the engine thrust time history corresponding to all the random samples is calculated using the engine thrust model, including: The zero-dimensional internal ballistic equations are solved using the classical fourth-order Runge-Kutta method, and the thrust of a single gas valve is calculated by combining it with a solid rocket motor thrust calculation model. Based on the thrust of all the gas valves, the engine thrust time history under different combinations of the key uncertainty parameters is calculated; the engine thrust time history is used to reflect the changes in the total thrust magnitude and thrust direction angle over time.

[0009] According to the technical solution provided in this application, the zero-dimensional internal ballistic equations are solved using the classical fourth-order Runge-Kutta method, and combined with the thrust calculation model of a solid rocket motor, the thrust of a single gas valve is calculated, including: The actual displacement response time sequence of the gas valve is converted into an equivalent throat area time sequence through a preset displacement-area geometric mapping relationship; The step size, initial time, and initial combustion chamber pressure of the solid rocket motor are set for the classical fourth-order Runge-Kutta method. The combustion chamber pressure time series of the solid rocket motor is calculated by solving the zero-dimensional internal ballistic equation containing the time series of the equivalent throat area. The combustion chamber pressure time series and the equivalent throat area time series are input into the solid rocket motor thrust calculation model to calculate the thrust of each gas valve.

[0010] According to the technical solution provided in this application, based on the thrust of all the gas valves, the engine thrust time history under different combinations of the key uncertainty parameters is calculated, including: Under different combinations of the aforementioned key uncertainty parameters, the thrust of each gas valve is obtained; Based on the thrust of each of the gas valves, vector synthesis is performed according to the spatial layout to calculate the total thrust of the solid rocket motor. Based on the thrust magnitude of each gas valve, the thrust direction angle of the solid rocket motor is calculated as a function of time.

[0011] According to the technical solution provided in this application, the total thrust of the solid rocket motor is calculated, including: During the iteration process, if the current calculation time has not reached the working time of the solid orbit control engine, the time variable is updated and the iteration continues to solve for the combustion chamber pressure and its corresponding total thrust at the next time point. If the current calculation time has reached the operating time of the solid rocket motor, then the total thrust calculation of the solid rocket motor under the current combination of key uncertainty parameters is completed.

[0012] According to the technical solution provided in this application, statistical analysis is performed on the engine thrust time history of all the random samples to calculate the thrust mean and standard deviation of the thrust response, so as to quantify the thrust uncertainty of the solid rocket motor, including: After completing the calculation of one of the random samples, determine whether all the random samples have been calculated. If all the random samples have not been calculated, a new random sample is selected, and the calculation process to obtain the engine thrust time history is repeated. If all the random samples have been calculated, the engine thrust time history corresponding to all random samples is summarized, and the statistical moments and confidence intervals of the total thrust value at each time point during the working time are calculated, thereby outputting probability information for quantifying thrust uncertainty.

[0013] In summary, this technical solution specifically discloses a method for calculating the thrust envelope of a solid rocket motor's servo uncertainty, including: setting multiple key uncertainty parameters affecting thrust performance in the solid rocket motor's servo mechanism and their probability distribution information; setting the action command of the gas valve; generating a preset number of random samples based on the probability distribution information, where each random sample corresponds to a combination of key uncertainty parameters composed of different key uncertainty parameters; constructing a servo system control model, and solving the servo system control model and random samples to obtain the actual displacement response time sequence of the gas valve corresponding to the action command under the corresponding combination of key uncertainty parameters; calculating the engine thrust time history corresponding to all random samples based on each actual displacement response time sequence using the engine thrust model; performing statistical analysis on the engine thrust time history of all random samples, calculating the thrust mean and standard deviation of the thrust response to quantify the thrust uncertainty of the solid rocket motor, and using the thrust uncertainty analysis to guide the regulation and optimization of the solid rocket motor's thrust performance.

[0014] Beneficial Effects: This invention effectively overcomes the limitations of existing deterministic analysis techniques. On one hand, by establishing a servo system control model for key uncertainty parameters of the servo mechanism and employing a combination of Monte Carlo sampling and the servo system control model, it achieves a quantitative characterization of the variable thrust output of a solid rocket motor. On the other hand, it not only outputs the statistical moments and confidence intervals of the thrust response, clarifying the possible range of thrust fluctuations, but also reflects the transmission law of multi-source uncertainties in the servo mechanism-motor system. This provides a direct and reliable quantitative basis for evaluating track control errors, designing robust control systems, and optimizing servo mechanism parameters, thereby supporting the improvement of thrust accuracy and performance optimization of solid rocket motors. Attached Figure Description

[0015] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart illustrating a method for calculating the thrust envelope of a solid rocket motor based on servo uncertainty.

[0016] Figure 2 This is a schematic diagram of the unfolded process of step S300 in a method for calculating the thrust envelope of a solid orbit control engine servo uncertainty.

[0017] Figure 3This is a schematic diagram of the unfolded process of step S400 in a method for calculating the thrust envelope of a solid orbit control engine servo uncertainty. Figure 4 This is a schematic diagram of the servo system control model.

[0018] Figure 5 This is a schematic diagram of the gas valve geometry in a solid rocket motor.

[0019] Figure 6 This is a comparison diagram of the action commands and displacement responses of the four laryngeal plugs.

[0020] Figure 7 The curve shows the average thrust output over time.

[0021] Figure 8 The curve showing the change of the standard deviation of thrust output over time.

[0022] Figure 9 This is a comparison chart of the mean thrust and the 95% confidence interval under multi-valve coordinated regulation.

[0023] Figure 10 This is a comparison chart of the thrust direction angle and the 95% confidence interval under multi-valve coordinated regulation. Detailed Implementation

[0024] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] Example 1 To make the technical solutions of the embodiments of this application clearer and easier to understand, the application background of the embodiments of this application is introduced below.

[0027] Solid-propellant orbit control engines possess advantages such as simple structure, strong environmental adaptability, and fast response speed, providing power for orbit changes in high-speed, highly maneuverable aircraft. Their structure consists of a gas generator, gas valves, a servo mechanism, and a controller. The gas generator produces high-temperature gas, which, in conjunction with the gas valves, generates orbit control force. The throat-type gas valve, as a core component of the solid-propellant orbit control engine, controls the movement of the throat to achieve variable thrust output. Its servo control accuracy has a crucial impact on the overall performance of the orbit control propulsion system. Therefore, conducting research on the response characteristics of the solid-propellant orbit control engine servo system and exploring the influence of thrust adjustment accuracy is of significant engineering importance for achieving precise orbit control of aircraft.

[0028] Currently, commonly used methods for modeling and quantitatively analyzing the thrust of solid rocket motor control systems include: methods for modeling and quantitatively analyzing the thrust of solid rocket motor control systems under deterministic conditions. Specifically, this involves constructing a physical and mathematical model of the solid rocket motor, designing the control system, formulating a control strategy, and designing a controller to quantify the thrust based on deterministic results. However, this type of method neglects the influence of the coupling effects of multiple uncertainties on thrust performance, leading to significant errors between the thrust simulation model and the actual response, and the flow field simulation cannot accurately reflect the actual thrust performance of the engine.

[0029] In view of this, the purpose of this invention is to provide a method for calculating the thrust envelope of a solid rocket motor's servo uncertainty, thereby solving the technical problem that existing deterministic analysis methods cannot quantify the impact of servo system uncertainties on the thrust output of a solid rocket motor. Specifically, the method includes: setting multiple key uncertainty parameters affecting thrust performance in the solid rocket motor's servo mechanism and their probability distribution information; setting the action command for the gas valve; generating a preset number of random samples based on the probability distribution information, where each random sample corresponds to a combination of key uncertainty parameters; constructing a servo system control model, and solving for the actual displacement response time sequence of the gas valve corresponding to the action command under the corresponding combination of key uncertainty parameters using the servo system control model and the random samples; calculating the engine thrust time history corresponding to all random samples based on each actual displacement response time sequence using the engine thrust model; and performing statistical analysis on the engine thrust time history of all random samples to calculate the thrust mean and standard deviation of the thrust response, thereby quantifying the thrust uncertainty of the solid rocket motor and facilitating the optimization and control of the solid rocket motor's thrust performance.

[0030] As can be seen, this invention addresses the challenge of unclear transmission mechanisms of servo mechanism uncertainties in the thrust adjustment process of solid rocket motors by proposing a method for uncertainty modeling and quantitative thrust analysis of the engine control system. It elevates thrust analysis from deterministic prediction to uncertainty quantification, effectively overcoming the limitations of existing deterministic analysis techniques. By establishing probabilistic models of key uncertainty parameters of the servo mechanism and employing a combination of Monte Carlo sampling and servo system control models, quantitative characterization of the thrust output characteristics of solid rocket motors is achieved. This method not only outputs the statistical moments and confidence intervals of the thrust response, clarifying the possible range of thrust fluctuations, but also reveals the transmission laws of multi-source uncertainties in the servo mechanism-engine system. This provides a direct and reliable quantitative basis for evaluating track control errors, designing robust control systems, and optimizing servo mechanism parameters, thereby supporting the improvement of thrust accuracy and performance optimization of solid rocket motors.

[0031] Please refer to the following. Figure 1 The flowchart shown in this embodiment illustrates a method for calculating the thrust envelope of a solid rocket motor based on servo uncertainty. The execution entity of this embodiment can be the servo control system of the solid rocket motor, without specific limitations. Firstly, based on the foregoing description of the solid rocket motor, its structure includes a gas valve, and the servo control system, by controlling the action of the gas valve, can achieve variable thrust output from the solid rocket motor, thereby generating track control force. Based on this description, the steps of this invention will be further explained below. The method includes the following steps: S100: Set the key uncertainty parameters and their probability distribution information that affect the thrust performance of the solid rocket motor servo mechanism; and set the action commands for the gas valves. Based on the working principle, structural characteristics, and engineering experience of solid rocket motor servo mechanisms (typically including motor drivers, reducers, transmission mechanisms, and throat actuators), physical parameters that have a significant impact on the final thrust adjustment accuracy and are subject to manufacturing tolerances, wear, or environmental drift are systematically identified.

[0032] Preferably, these key uncertainty parameters include at least: transmission clearance (reflecting mechanical assembly errors), interphase resistance and interphase inductance (reflecting the dispersion of motor electrical characteristics), eccentric shaft friction coefficient, static friction and dynamic friction (reflecting the randomness of the contact state of the kinematic pair). After these parameters are confirmed, based on historical data, test results, or engineering experience, probability distribution information is set for each parameter, that is, the probability distribution type (such as normal distribution, uniform distribution, etc.) and corresponding distribution parameters (such as mean and standard deviation) of each parameter are specified, as shown in Table 1 below; for example, the transmission clearance can be set to follow a normal distribution with a mean of 0.5 mm and a coefficient of variation of 5%.

[0033] Table 1. Examples of probability distribution information for uncertainty parameters

[0034] Setting the actuation commands for the gas valves requires planning the operating modes of the solid rocket motor (such as no-thrust idling, unidirectional thrust, multi-valve differential regulation, performance mode switching, etc.) based on the needs of the aircraft's orbital control mission. This generates standardized actuation commands to drive the gas valves (throat plugs). These commands serve as the input benchmark for subsequent evaluation of the servo system's tracking performance and thrust response characteristics. If the solid rocket motor has multiple gas valves, it is also necessary to set the motion commands for each valve separately to analyze the impact on engine thrust uncertainty when the throat plug moves according to the specified commands, thus completing the variable thrust uncertainty analysis of the solid rocket motor.

[0035] As can be seen, unlike traditional methods that treat the aforementioned key uncertainty parameters as fixed values, leading to model distortion, this invention describes the randomness of these parameters through probability distributions, establishing a probability space model for solid rocket motors that encompasses multi-source uncertainties. Simultaneously, explicit action commands define the specific tasks the system needs to complete. The combination of these two aspects facilitates subsequent probability-based, task-oriented performance simulations and analyses.

[0036] S200. Generate a preset number of random samples based on probability distribution information. The random samples correspond to combinations of key uncertainty parameters composed of different key uncertainty parameters. Specifically, this invention employs the Monte Carlo simulation method to independently and randomly generate a large number (preset quantity, such as 10) of key uncertainty parameters based on their probability distribution information. 3 Up to 10 5 The parameters are a combination of magnitude (on the order of magnitude), each combination is called a random sample, that is, each random sample corresponds to a key uncertainty parameter combination, and each key uncertainty parameter combination also represents a set of statistically possible physical states of the servo mechanism.

[0037] It should be noted that the size of the random sample needs to be balanced between computational accuracy and computational cost to ensure the convergence and reliability of the statistical results. No special restrictions are imposed here.

[0038] As can be seen, this step discretizes the continuous probability distribution into a large number of concrete and computable scenarios, and generates a massive number of random samples to cover all possible cooperative changes in the uncertainty parameters, providing sufficient data samples for a comprehensive and statistical assessment of the overall impact of uncertainty on system performance.

[0039] S300. Construct a servo system control model, and obtain the actual displacement response time sequence of the gas valve under the action command under the combination of key uncertainty parameters by solving the servo system control model and random samples. In order to establish the correlation between key uncertainty parameters and system dynamic response, and thus accurately simulate how uncertainty affects the actual performance of the servo mechanism, this invention solves the actual displacement response time series of the gas valve based on the combination of key uncertainty parameters contained in each random sample.

[0040] It should be noted that a solid rocket motor has multiple gas valves. In this embodiment of the invention, there are four gas valves, all of which are throat-type gas valves, meaning that each gas valve has a movable throat. The thrust adjustment of the solid rocket motor is usually achieved by driving the throat-type gas valves through a servo mechanism to change the throat area of ​​the gas flow channel. Therefore, the actual displacement response time series of the gas valve essentially records the true trajectory of the throat position changing over time, including tracking errors, delays, and vibrations caused by uncertainties.

[0041] Specifically, see Figure 2 The aforementioned step S300 includes the following steps: S301. Construct a servo system control model. The servo system control model is a three-closed-loop PID control model based on the Simulink platform, which includes a current loop, a speed loop, and a position loop. This invention uses the Simulink simulation platform to simulate the thrust of a solid rocket motor and constructs a three-closed-loop PID control model including a current loop, a velocity loop, and a position loop. This servo system control model integrates the electromagnetic equations of the motor and the mechanical transmission equations, and embeds a nonlinear contact model describing transmission clearance and a Stribeck friction model describing complex friction phenomena, thereby enabling high-fidelity simulation of the dynamic behavior of actual servo systems.

[0042] Specifically, the electromagnetic equations of the motor are as follows: (1)-(3) (1) (2) (3) In the formula, This is the driving voltage; , The back electromotive force coefficient, The torque constant; This is the motor damping coefficient; This refers to the rotor angular velocity; The moment of inertia of the DC motor rotor; For motor load.

[0043] Next, setting the initial position of the laryngeal plug as the midpoint of the entire laryngeal plug's stroke, and taking the right side as the positive direction for translation, the equation of motion of the laryngeal plug can be expressed as the following formula (4): (4) In the formula, This is due to laryngeal plug displacement; The eccentricity radius is the radius of the eccentric axis. The angle of rotation of the eccentric shaft. This is the course of the laryngeal plug.

[0044] The torque balance equation for the transmission mechanism is as follows (5): (5) In the formula, For contact force; For driving torque; The transmission efficiency of the mechanism ranges from 70% to 90%.

[0045] The mathematical expressions for the transmission backlash in the servo mechanism are as follows: Formula (6) and Formula (7): (6) (7) In the formula, These are interaction forces; The position of the slider; The upper boundary contact stiffness; This is the lower boundary contact stiffness; This is the upper limit of the damping coefficient; This is the initial gap between the slider and the upper boundary; This represents the initial gap between the slider and the lower bound.

[0046] The frictional phenomenon between the laryngeal plug and the sealing ring is described using the Stribeck friction model, and its expression is as follows: The formula is as follows (8): (8) In the formula, It is static friction; It is kinetic friction; It is the coefficient of viscous friction; The relative velocity between the laryngeal plug and the sealing ring; Stribeck speed; This is an empirical parameter, usually taken as 2, i.e., the Gaussian exponential model.

[0047] Ultimately, the pneumatic force of the laryngeal plug fThe calculation formula is as follows (9): (9) In the formula, The pressure indicated by the laryngeal plug; This represents the surface area of ​​the laryngeal plug.

[0048] The principle equations represented by formulas (1) to (9) above are connected together in the form of Simulink modules. Precise control of the laryngeal plug displacement is achieved through three closed-loop control. The established servo system control model is as follows: Figure 4 As shown.

[0049] S302. Input each random sample into the servo system control model, and conduct a simulation experiment of the solid rocket motor based on the servo system control model; the simulation experiment sets the working time of the solid rocket motor, and the action commands are set according to the preset working mode of the solid rocket motor. S303. Through simulation experiments, the throat displacement response time sequence of each gas valve during the working time is obtained under different combinations of key uncertainty parameters, and the throat displacement response time sequence corresponding to all throats is taken as the actual displacement response time sequence of the gas valve under each combination of key uncertainty parameters.

[0050] After the servo system control model is established, the solution step size of the Simulink solver also needs to be set. Simulation time Furthermore, after the parameters are set, by using random samples as input and running the program of the servo system control model, the time series of throat valve displacement response under different combinations of key uncertainty parameters for each gas valve can be obtained.

[0051] For example, in practical applications, the operating time of the solid rocket motor can be set to 8 seconds. During the 0-3 second phase, the motor's operating modes are: no-thrust idle mode → unidirectional thrust mode → no-thrust idle mode. During the 3-5 second phase, the motor operates with four sets of sinusoidal signals with an offset of 1 mm, an amplitude of 1 mm, and a frequency of 2 Hz. The initial phase difference between the commands of throat plugs 1 and 3 is 180°, and the initial phase difference between the commands of throat plugs 2 and 4 is also 180°, which is the differential mode. During the 5-8 second phase, the motor's operating modes are: no-thrust idle mode → performance mode → no-thrust idle mode. Based on this, the throat plug displacement response time series obtained through the servo system control model is used to reflect the throat plug displacement during the motor's operating time. For details, please refer to... Figure 6 The figure shows the relationship between the throat valve action command and the actual throat valve displacement of the four gas valves during the working time.

[0052] Ultimately, for a set of key uncertainty parameters, the four throat plug displacement response time series corresponding to it constitute the actual displacement response time series of the gas valve under that key uncertainty parameter combination, which is output by the constructed servo system control model.

[0053] S400. Based on each actual displacement response time series, the engine thrust time history corresponding to all random samples is calculated through the engine thrust model. In order to transmit the dynamic response uncertainty of the servo link to the core performance of the system—thrust—through the physical processes inside the engine, it is necessary to calculate the engine thrust time history by combining the engine thrust model after obtaining the actual displacement response time series corresponding to each random sample. The engine thrust time history here is the engine thrust at each time point during the working time, which is used to reflect the possible range of thrust fluctuations and describe the transmission law of multi-source uncertainty in the servo mechanism-engine system.

[0054] Specifically, see Figure 3 The above step S400 includes the following steps: S401. Solve the zero-dimensional internal ballistic equations using the classical fourth-order Runge-Kutta method, and calculate the thrust of a single gas valve by combining it with the thrust calculation model of a solid rocket motor. The specific processing steps of step S401 are further divided into the following steps: Step 1: Based on the geometric configuration of the laryngeal plug, establish the geometric mapping relationship between the laryngeal plug displacement and the effective laryngeal area of ​​the nozzle; substitute the solved laryngeal plug displacement response time series into the geometric mapping relationship to obtain the equivalent laryngeal area time series. First, based on the fixed geometric configuration of the throat-type gas valve, a geometric mapping relationship between the throat displacement and the effective throat area of ​​the nozzle is established. Substituting the solved throat displacement response time series into the geometric mapping relationship yields the equivalent throat area time series. The equivalent throat area time series is the fundamental variable determining the gas mass flow rate, thereby driving the pressure change in the combustion chamber.

[0055] Combination Figure 5 The schematic diagram of the gas valve's geometric configuration shown illustrates how establishing the geometric mapping relationship between the throat plug displacement and the effective throat area of ​​the nozzle, based on the throat plug's geometry, relies on the inherent and definite mechanical geometry of the throat plug-type gas valve itself. For example, its... Figure 5 The diameter of the laryngeal plug is shown in the formula. Length of the laryngeal plug head Radius of the converging segment Laryngeal plug displacement Generally, the throat plug has a specific profile, forming a variable annular flow gap with the fixed nozzle throat seat. As the throat plug moves axially, the width of this annular gap changes, resulting in a corresponding change in the minimum cross-sectional area for flow through this gap (i.e., the effective throat area). Therefore, for any given valve design drawing, each axial position of the throat plug uniquely corresponds to a theoretical throat area, a relationship determined by the valve's geometry (such as the throat plug diameter mentioned above). Radius of the converging segment (etc.) can be determined directly through geometric principles, or a lookup table can be formed through prior numerical calculations or experimental calibration for complex surfaces, which will not be elaborated further here.

[0056] Step 2: Set the step size, initial time, and initial combustion chamber pressure of the solid rocket motor for the classical fourth-order Runge-Kutta method. Calculate the combustion chamber pressure time series of the solid rocket motor by solving the zero-dimensional internal ballistic equation containing the time series of the equivalent throat area. To solve the zero-dimensional internal ballistic equations describing the dynamic balance between combustion chamber gas generation and ejection, this application employs the classical fourth-order Runge-Kutta method.

[0057] Specifically, the zero-dimensional internal ballistic equation of the solid rocket motor is first expressed as the following formula (10): (10) In the formula, This refers to the combustion chamber pressure of a solid rocket motor. For time; Characteristic velocity of the propellant; The volume of the combustion chamber; For propellant density; The surface area of ​​the burning surface; This is the combustion rate coefficient; The pressure index; It is the sum of the equivalent throat areas, that is, the total equivalent throat area of ​​the engine's main nozzle formed by the combined action of all throat plugs at a certain moment. For specific heat ratio k The function of is specifically expressed as the following formula (11): (11) Based on the above principle, the specific solution process is as follows: Step 1: Set the step size for solving the classic fourth-order Runge-Kutta method Simulation time and the initial combustion chamber pressure of the solid rocket motor ; Step 2: Solve for the real-time combustion chamber pressure and time using the classical fourth-order Runge-Kutta method, where the classical fourth-order Runge-Kutta method is given by the following formula (12): (12) In the formula, The relationship between combustion chamber pressure and time is a function of the zero-dimensional internal ballistic equation. This is the fourth-order Long-Kutaf in the interval. Within, four slope (rate of change) values ​​were estimated using different strategies; In the first k Each numerical calculation step (corresponding time) The combustion chamber pressure; For the next calculation step (the first step) k+1 Each numerical calculation step, corresponding to time The combustion chamber pressure is the combustion chamber pressure time series that needs to be output in this iteration calculation.

[0058] Step 3: Input the combustion chamber pressure time series and the equivalent throat area time series into the solid rocket motor thrust calculation model to calculate the thrust of each gas valve.

[0059] The combustion chamber pressure time series obtained by solving formula (12) is obtained. Then, based on the real-time combustion chamber pressure and time values, the thrust of the solid rocket motor at the current time can be obtained through the solid rocket motor thrust calculation model.

[0060] Specifically, the thrust of a single gas valve can be expressed as the following formula (13): (13) In the formula, For the first i ( i The magnitude of the thrust of gas valves (1, 2, 3, 4) This is the thrust coefficient; For the first i The equivalent throat area of ​​a gas valve.

[0061] Below, thrust coefficient The following formula (14): (14) In the formula, This refers to the nozzle exit pressure. Environmental pressure; This represents the nozzle exit area.

[0062] S402. Based on the thrust of all gas valves, calculate the engine thrust time history under different combinations of key uncertainty parameters; the engine thrust time history is used to reflect the changes in the total thrust magnitude and thrust direction angle over time.

[0063] Based on the actual spatial installation position and orientation of each valve on the engine (e.g.) Figure 5 By combining the thrust vectors of each valve at the same moment (configuration), the engine thrust time history can be generated, which is a complete curve showing the change of thrust magnitude and thrust direction angle over time.

[0064] Specifically, the calculation process of the engine thrust time history in step S402 is as follows: under different combinations of key uncertainty parameters, the thrust of each gas valve is obtained; based on the thrust of each gas valve, vector synthesis is performed according to the spatial layout to calculate the total thrust of the solid rocket motor; based on the thrust of each gas valve, the change of the thrust direction angle of the solid rocket motor with time is calculated.

[0065] Furthermore, the overall force on the solid rocket motor can be expressed as follows (15): (15) In the formula, and Engine y Xianghe z Towards the force; This refers to the overall force distribution of the solid rocket motor. , , and These represent the thrust of the four gas valves.

[0066] Next, the total thrust of the solid rocket motor can be calculated using the following formula (16): (16) The direction angle of the total thrust of the solid rocket motor can be calculated using the following formula (17): (17) In the formula, The direction angle of the total thrust.

[0067] As can be seen, this step achieves an improvement in the evaluation of the performance of individual components to the overall system performance. For the orbit control engine, its final execution of the orbit control task depends on the resultant force vector generated by multiple valves. This step not only quantifies the uncertainty of the magnitude of the resultant force, but also the uncertainty of the thrust direction angle, which is crucial for evaluating the accuracy of orbit control.

[0068] It should be noted that calculating the total thrust using the classic fourth-order Runge-Kutta method is essentially an iterative process. Its aim is to calculate the continuous history of thrust change over time during the entire preset operating period, from engine start-up to shutdown. The iterative process includes: if the current calculation time has not yet reached the operating time of the solid rocket motor, the time variable is updated and the iteration continues to solve for the combustion chamber pressure and its corresponding total thrust at the next time point; if the current calculation time has reached the operating time of the solid rocket motor, the total thrust calculation for the solid rocket motor under the current combination of key uncertainty parameters is completed.

[0069] At the beginning of each iteration step, the algorithm performs a complete calculation process of the fourth-order Runge-Kutta method based on the known state at the current time (mainly the current combustion chamber pressure) and the current equivalent throat area determined by the current servo response. Then, the combustion chamber pressure at the next time point is calculated by the algorithm, and the total engine thrust at that time point is calculated immediately according to the thrust calculation formula (formula (13)-formula (17) above) using the combustion chamber pressure at the next time point and the equivalent throat area at the next time point.

[0070] Throughout the iteration process, to ensure the complete operational time history is calculated, the following convergence check is performed after each time point calculation: It checks whether the current calculation time has reached or exceeded the preset total operational time of the solid rocket motor. If the operational time has not been reached, the time variable is updated and iteration continues, setting the calculated new state as the initial state for the next iteration. Simultaneously, the program flow returns to the starting point of the single-step iteration, using the updated initial state as the new starting point, and reads the throat equivalent area of ​​each throat plug at the corresponding time point to begin calculating the combustion chamber pressure and total thrust for the next time point. Otherwise, the iteration stops and proceeds to the next step; this will not be elaborated further here.

[0071] S500 performs statistical analysis on the engine thrust time history of all random samples, calculates the thrust mean and standard deviation of the thrust response, and quantifies the thrust uncertainty of the solid rocket motor. The thrust uncertainty is used to guide the adjustment and optimization of the thrust performance of the solid rocket motor.

[0072] Specifically, this embodiment of the invention calculates the thrust mean and standard deviation curves of the thrust response over time using Monte Carlo simulation (MCS). Monte Carlo simulation is a numerical calculation method based on probability and statistics theory. Its basic principle is to obtain the probability distribution of the problem under study through a large number of random sampling experiments. Monte Carlo simulation is applicable not only to discrete systems but also to continuous systems, and can handle problems in the simulation of thrust control processes of solid rocket motors that are difficult to solve analytically.

[0073] Furthermore, the mean and standard deviation of the thrust estimated by the Monte Carlo simulation method can be calculated using formulas (18) and (19): (18) (19) In the formula, For the average thrust, The number of sample points For the first Calculated thrust values ​​at each sample point This represents the standard deviation of thrust.

[0074] After calculating the thrust mean and standard deviation for a random sample, another convergence check is performed: whether all random samples have been calculated. If all random samples have not been calculated, a new random sample that has not been calculated is selected, and the calculation process for obtaining the engine thrust time history is repeated. If all random samples have been calculated, the engine thrust time history corresponding to all random samples is summarized, and the statistical moments and confidence intervals of the total thrust value at each time point during the working time are calculated, thereby outputting probability information for quantifying thrust uncertainty.

[0075] In practical applications, after obtaining the engine thrust time history corresponding to all random samples, these are summarized and analyzed. The uncertainty of dynamic thrust during solid rocket motor operation is analyzed in the form of the first second moment. Furthermore, the mean and standard deviation of thrust over time are calculated using Monte Carlo simulation, yielding the following results: Figures 7-10 The mean and standard deviation of thrust shown in the figure change over time, thereby quantifying the thrust uncertainty of the solid rocket motor.

[0076] In practical applications, the thrust mean and standard deviation refer to the two most basic and important statistical characteristics calculated when performing statistical analysis on a large number of Monte Carlo simulation results. They are used to quantitatively describe the distribution of thrust uncertainty. Specifically, the first moment is the mean, and the second moment is the standard deviation. It should be noted that this invention does not impose special limitations on the specific probability characteristics used. For example, skewness and other data can also be used to further analyze the distribution of thrust uncertainty.

[0077] Since multiple random samples have already been obtained as curves of engine thrust time history, the mean can be obtained by averaging the total thrust values ​​of all curves at each specific time point during engine operation. The standard deviation can be obtained by calculating the dispersion of multiple thrust values ​​at each specific time point relative to the mean at that point. The specific process will not be elaborated here.

[0078] In addition, step S500 performs statistical analysis on the engine thrust time history of all random samples. Besides calculating the thrust mean and standard deviation, it can further calculate the confidence interval at a specific confidence level (e.g., 95%) to provide a more intuitive envelope of thrust uncertainty. This confidence interval represents the probability that it covers the true expected thrust value under repeated experiments, and can directly quantify the upper and lower limits of the possible fluctuation of the thrust mean at a given probability (e.g., ...). Figure 9 (As shown). For example, the 95% confidence interval provides a key probabilistic boundary for designing the robustness of control systems and evaluating trajectory control errors, meaning that the thrust output has a very high probability of falling within this boundary.

[0079] Ultimately, the above calculations can be performed for each point in time during the working period, thereby obtaining the curves of the mean thrust over time, the standard deviation of thrust over time, and the upper and lower envelopes of the thrust confidence interval over time. These curves together constitute complete and quantitative probabilistic information on the dynamic thrust uncertainty of the solid rocket motor, which can be used to guide the adjustment and optimization of the thrust performance of the solid rocket motor.

[0080] by Figures 7-10 Taking the obtained probability information images as an example, the uncertainty analysis of the present invention will be briefly explained according to the curve represented by each image: During the 0~3 s phase, by Figure 7 It can be seen that the average thrust jumps to 0.974 at 1 s. Under the control of the controller, the average thrust fluctuates slightly and fails to stabilize at a certain thrust value. At 2 s, the throat changes abruptly, and the engine transitions from a unidirectional operating mode to a thrustless idling model. The average thrust jumps to 0.006, and again, under the control of the controller, the average thrust fluctuates slightly. Figure 8 It can be seen that the thrust standard deviation at the valve step response also shows a step change, with the thrust standard deviation stepping to 0.041 at 2 s.

[0081] During the 3-5 second phase, the engine operates in differential mode. Figure 7 It can be seen that the average thrust fluctuates periodically within the range [0 N, 982.7 N]. Figure 8 It can be seen that during the sinusoidal motion, the standard deviation of the thrust fluctuates back and forth in the interval [0.001, 0.013], and the maximum value of the standard deviation of the multi-valve combined thrust during this stage is 0.013.

[0082] During the 5-8 s phase, each valve undergoes a step response transition at 6 s. Before the step response, the engine is affected by uncertainties in the servo control process, resulting in slight fluctuations in the average thrust. After the transition, the valve opening increases, leading to a decrease in combustion chamber pressure. This reduces the impact of parameter uncertainties on the thrust, causing the thrust to stabilize in the subsequent process. Figure 8 It can be seen that the thrust standard deviation at the valve step response also exhibits a step change.

[0083] Figure 9 The thrust confidence interval is adjusted by multi-valve coordinated control. After the throat plug's step response, the thrust confidence interval widens. As the throat plug stabilizes, the thrust confidence interval gradually narrows, with the maximum thrust confidence interval [0.894, 0.927] in the 1-2 s stage. In the 3-5 s stage, during the throat plug's reciprocating motion, the thrust confidence interval is relatively large at the peaks and troughs, and relatively narrow in the rising and falling phases, with the maximum thrust confidence interval [0.003, 0.034]. In the 5-8 s stage, after the stage transition, the impact of the servo mechanism parameter uncertainty on thrust performance decreases due to the reduced combustion chamber pressure, resulting in a narrower confidence interval throughout the process.

[0084] Figure 10 This represents the change in the 95% confidence interval of the thrust angle (i.e., the thrust direction angle) under multi-valve coordinated regulation. In the 0-1 s stage, the thrust direction angle is uniformly distributed between [-200°, 200°]. In the 1-2 s stage, after switching to unidirectional thrust mode, the thrust angle is around 90°, at which point the confidence interval is narrow, indicating that the thrust direction angle fluctuates little in unidirectional thrust mode and is less affected by uncertainty parameters. In the 3-5 s stage, the thrust angle switches between 45° and -135°, and the confidence interval for the thrust direction angle is largest during the thrust angle step.

[0085] Based on the above description, this application addresses the technical challenge of unclear transmission mechanisms of servo mechanism uncertainties in the thrust adjustment process of solid rocket motors by proposing a method for uncertainty modeling and thrust quantitative analysis of servo control systems. This invention is based on Monte Carlo simulation and a servo system control model of a solid rocket motor, considering the probability distribution information of key uncertainty parameters of the solid rocket motor's servo mechanism to solve for the time-varying behavior of thrust performance information. Specifically, firstly, the key uncertainty parameters of the influencing factors of the solid rocket motor's servo mechanism are obtained, the engine operating mode is set, and throat commands are generated; secondly, the throat displacement response time series of each gas valve under three-loop PID control is solved using the fourth-order Runge-Kutta method; then, the engine thrust variation curve (engine thrust time history) is calculated based on the obtained throat displacement response time series, and the thrust at a specific time point for each random sample is calculated; finally, the thrust uncertainty is quantified using the first two moments to provide probabilistic information for the thrust performance uncertainty analysis of the solid rocket motor.

[0086] This method effectively overcomes the limitations of existing deterministic analysis techniques. Firstly, by establishing a servo system control model of key uncertainty parameters of the servo mechanism and employing a combination of Monte Carlo sampling and the servo system control model, it achieves a quantitative characterization of the variable thrust output of a solid rocket motor. Secondly, it not only outputs the statistical moments and confidence intervals of the thrust response, clarifying the possible range of thrust fluctuations, but also reflects the transmission law of multi-source uncertainties in the servo mechanism-motor system. This provides a direct and reliable quantitative basis for evaluating track control errors, designing robust control systems, and optimizing servo mechanism parameters, thereby supporting the improvement of thrust accuracy and performance optimization of solid rocket motors.

[0087] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for calculating the thrust envelope of a solid rocket motor with servo uncertainty, characterized in that, The solid rocket motor includes a gas valve, and by controlling the operation of the gas valve, the solid rocket motor can achieve variable thrust output; the method includes: The key uncertainty parameters affecting thrust performance in the solid rocket motor servo mechanism and their probability distribution information are set; and the action commands of the gas valve are set. A preset number of random samples are generated based on the probability distribution information, and the random samples correspond to combinations of key uncertainty parameters composed of different key uncertainty parameters; A servo system control model is constructed, and the actual displacement response time sequence of the gas valve corresponding to the action command under the combination of key uncertainty parameters is obtained by solving the servo system control model and the random sample. Based on each actual displacement response time sequence, the engine thrust time history corresponding to all random samples is calculated using the engine thrust model. Statistical analysis is performed on the engine thrust time history of all the random samples to calculate the thrust mean and standard deviation of the thrust response, so as to quantify the thrust uncertainty of the solid rocket motor. The thrust uncertainty is used to guide the adjustment and optimization of the thrust performance of the solid rocket motor.

2. The method for calculating the thrust envelope of a solid rocket motor servo uncertainty according to claim 1, characterized in that, The gas valve is a throat-plug type gas valve, and there are multiple such valves, each of which has a throat plug; the key uncertainty parameters include at least: transmission clearance, phase-to-phase resistance, phase-to-phase inductance, eccentric shaft friction coefficient, static friction, and dynamic friction.

3. The method for calculating the thrust envelope of a solid rocket motor servo uncertainty according to claim 2, characterized in that, A servo system control model is constructed, and the actual displacement response time series of the gas valve corresponding to the action command under the corresponding key uncertainty parameter combination is obtained by solving the servo system control model and the random sample, including: A servo system control model is constructed, which is a three-closed-loop PID control model containing current loop, speed loop and position loop, built on the Simulink platform. Each random sample is input into the servo system control model, and a simulation experiment of the solid rocket motor is performed based on the servo system control model; the simulation experiment is set with the working time of the solid rocket motor, and the action commands are set according to the preset working mode of the solid rocket motor; Through the simulation experiment, the throat displacement response time sequence of each gas valve during the working time is obtained under different combinations of the key uncertainty parameters, and the throat displacement response time sequence corresponding to all the throats is taken as the actual displacement response time sequence of the gas valve under each combination of the key uncertainty parameters.

4. The method for calculating the thrust envelope of a solid rocket motor servo uncertainty according to claim 1, characterized in that, Based on each actual displacement response time series, the engine thrust time history corresponding to all the random samples is calculated using the engine thrust model, including: The zero-dimensional internal ballistic equations are solved using the classical fourth-order Runge-Kutta method, and the thrust of a single gas valve is calculated by combining it with a solid rocket motor thrust calculation model. Based on the thrust of all the gas valves, the engine thrust time history under different combinations of the key uncertainty parameters is calculated; the engine thrust time history is used to reflect the changes in the total thrust magnitude and thrust direction angle over time.

5. The method for calculating the thrust envelope of a solid rocket motor servo uncertainty according to claim 4, characterized in that, The zero-dimensional internal ballistic equations are solved using the classical fourth-order Runge-Kutta method, and combined with a solid rocket motor thrust calculation model, the thrust of a single gas valve is calculated, including: Based on the geometric configuration of the throat plug, a geometric mapping relationship between the throat plug displacement and the effective throat area of ​​the nozzle is established; the solved throat plug displacement response time series is substituted into the geometric mapping relationship to obtain the equivalent throat area time series. The step size, initial time, and initial combustion chamber pressure of the solid rocket motor are set for the classical fourth-order Runge-Kutta method. The combustion chamber pressure time series of the solid rocket motor is calculated by solving the zero-dimensional internal ballistic equation containing the time series of the equivalent throat area. The combustion chamber pressure time series and the equivalent throat area time series are input into the solid rocket motor thrust calculation model to calculate the thrust of each gas valve.

6. The method for calculating the thrust envelope of a solid rocket motor servo uncertainty according to claim 4, characterized in that, Based on the thrust of all the aforementioned gas valves, the engine thrust time history under different combinations of the aforementioned key uncertainty parameters is calculated, including: Under different combinations of the aforementioned key uncertainty parameters, the thrust of each gas valve is obtained; Based on the thrust of each of the gas valves, vector synthesis is performed according to the spatial layout to calculate the total thrust of the solid rocket motor. Based on the thrust magnitude of each gas valve, the thrust direction angle of the solid rocket motor is calculated as a function of time.

7. The method for calculating the thrust envelope of a solid rocket motor servo uncertainty according to claim 5, characterized in that, The total thrust of the solid rocket motor was calculated, including: During the iteration process, if the current calculation time has not reached the working time of the solid orbit control engine, the time variable is updated and the iteration continues to solve for the combustion chamber pressure and its corresponding total thrust at the next time point. If the current calculation time has reached the operating time of the solid rocket motor, then the total thrust calculation of the solid rocket motor under the current combination of key uncertainty parameters is completed.

8. The method for calculating the thrust envelope of a solid rocket motor servo uncertainty according to claim 3, characterized in that, Statistical analysis was performed on the engine thrust time histories of all the aforementioned random samples to calculate the thrust mean and standard deviation of the thrust response, in order to quantify the thrust uncertainty of the solid rocket motor, including: After completing the calculation of one of the random samples, determine whether all the random samples have been calculated. If all the random samples have not been calculated, a new random sample is selected, and the calculation process to obtain the engine thrust time history is repeated. If all the random samples have been calculated, the engine thrust time history corresponding to all random samples is summarized, and the statistical moments and confidence intervals of the total thrust value at each time point during the working time are calculated, thereby outputting probability information for quantifying thrust uncertainty.

Images