Gas flow control method and system applied to solid working medium electric propulsion system

Abstract

The invention provides a gas flow control method and system applied to a solid-state working medium electric propulsion system, and the method comprises the steps: firstly constructing a second-order nonlinear prediction model from heating power to output flow in order to solve the problems of strong nonlinearity, multivariable coupling and strict safety constraints in a solid-state iodine sublimation process; the model accurately depicts a complete physical process of heating sheet thermal inertia, contact thermal resistance, iodine phase change dynamics and pipeline gas dynamics. And on the basis, rolling optimization is executed in each control cycle: a future flow trajectory is predicted based on a current state and a model, and an optimization problem with constraints is solved online to obtain an optimal heating power sequence. According to the method, high-precision and overshoot-free tracking of the flow is achieved, it is strictly guaranteed that the system operates within safety constraints, and the performance and reliability of the solid-state electric propulsion system are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of aerospace propulsion technology, and in particular to a gas flow control method and system for solid propellant electric propulsion systems. Background Technology

[0002] Solid propellant electric propulsion systems are a revolutionary technology developed in recent years for micro and nano satellite platforms. Taking iodine propellant thrusters as an example, they store iodine propellant in solid form. When working, they are heated to sublimate it into gas, which is then ionized and accelerated by electrostatics to generate thrust.

[0003] Compared to traditional high-pressure gas propulsion systems such as xenon, solid-state working propellant electric propulsion systems have significant advantages such as small size, dry launch, high safety, and high integration. However, their performance is highly dependent on the stability and control precision of the gas flow rate. Fluctuations in the flow rate directly affect the plasma density, beam quality, and final thrust in the ionization chamber. Therefore, achieving high-precision and high-dynamic-response control of the gas flow rate is one of the core challenges of this system.

[0004] Currently, most engineering applications employ classic PID control, which indirectly stabilizes gas flow by adjusting heater power. However, this method has significant limitations: 1. As a linear controller, PID has difficulty handling the inherent strong nonlinear relationship between heating power and gas flow rate (including latent heat of phase change, nonlinearity of gas flow, etc.). 2. PID controllers cannot explicitly handle multiple safety and performance constraints such as heater temperature, working fluid temperature, and power change rate. They can only passively cut off the circuit after the limit is exceeded, which can easily lead to overshoot or oscillation. 3. The system involves dynamic processes at multiple time scales (such as the thermal inertia of the heating element and the establishment of pipeline pressure), making it difficult for PID parameters to remain optimal under all operating conditions.

[0005] Nonlinear Model Predictive Control (NMPC) is an advanced closed-loop optimization control strategy and is theoretically the most suitable framework for iodine-based electric propulsion systems. The core of this framework is to establish a nonlinear dynamic mathematical model for the controlled object and to make predictions and optimizations based on it. However, the successful application of this framework depends heavily on the accuracy of the prediction model. Currently, there is a lack of a nonlinear prediction model that can accurately characterize the physical dynamics of the entire process from electric heating to gas flow output and is suitable for online optimization calculations. Summary of the Invention

[0006] This invention provides a gas flow control method and system for solid working fluid electric propulsion systems. Its model accurately depicts the complete physical processes of heating element thermal inertia, contact thermal resistance, iodine phase transition dynamics, and pipeline gas dynamics, enabling the system to achieve rapid and accurate tracking and control of the target flow rate, reduce overshoot and steady-state error, and greatly improve dynamic performance.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: I. Overall Control Framework A gas flow control method for solid propellant electric propulsion systems includes the following steps: S1: Establish a nonlinear prediction model from the input power of the heating element to the output flow rate of the gas. This model explicitly describes the thermal inertia of the heating element, the contact thermal resistance, the phase transition dynamics of solid iodine, and the gas pressure dynamics of the gas supply pipeline. S2: In each control cycle k, the current status information of the system is obtained through sensors, including at least the surface temperature of the heating element, the surface temperature of the solid iodine, and the pipeline pressure; S3: Using the model described in S1 and the current state obtained in S2 as initial conditions, simulate the candidate heating power sequence for the next N steps to predict the gas flow trajectory within the next N steps. S4: Based on the predicted time domain N, under the constraints of the heating element input power and output flow rate, the optimal power sequence is solved by minimizing the performance function, so that the system can smoothly transition from the current output flow rate to the desired output flow rate; S5: Apply the first value in the optimal power sequence obtained from S4, i.e. the optimal heating power at the current moment, to the system. At the next sampling moment, return to S2 and repeat this rolling optimization process.

[0008] Step S2 also includes a state estimation step, which uses a first-order inertial system combined with a pure time delay element to perform state estimation.

[0009] II. Construction of Nonlinear Prediction Model The nonlinear prediction model is a second-order dynamic model with two time constants, and its input is the electric power of the heating element. The output is the mass flow rate at the thruster inlet. Its transmission relationship is described by the following series of physical processes: S11: Establish the heat balance equation for the heating element, considering the heat capacity of the heating element. The resulting thermal inertia and contact thermal resistance with solid iodine : ,in, The heat is transferred to the iodine by the heating element through the contact thermal resistance. This refers to the heat loss from the heating element to the environment. The surface temperature of the heating element. This refers to the rate of temperature change of the heating element. ,in, This refers to the surface temperature of solid iodine. ,in, The emissivity of the heating element surface, This refers to the exposed area of ​​the heating element that is not in contact with iodine. The surface temperature of the heating element. This is the initial temperature value; S12: Establish the phase transition kinetic equation for iodine. When iodine reaches its melting point, All of it is used to overcome the latent heat of phase transition: If the mass of solid iodine changes slowly, the equation simplifies to ,in, For the heat loss of solid iodine to the storage tank, The evaporation rate of iodine. The latent heat of phase transition of iodine. For the mass of solid iodine involved in heating, The specific heat capacity of solid iodine, That is the melting point of iodine; ,in, To improve the thermal conductivity of the storage tank walls, This refers to the contact area between iodine and the tank wall of the storage and supply tank. The surface temperature of solid iodine. This is the initial temperature value; S13: Establish the dynamic equations for gas pressure and flow output within the pipeline, treating gaseous iodine within the pipeline as an ideal gas, with its pressure... The dynamic change is determined by the evaporation rate With output flow The difference determines: ,in, J / (kg・K) is the gas constant of iodine. The temperature of gaseous iodine inside the pipe. For the volume of the pipe; S14: By combining the above equations, the simplified heating power is derived. To output flow Second-order dynamic model: ,in, The time constant of thermal inertia of the heating element-iodine is... The dynamic time constant of pipeline pressure. For power-flow gain.

[0010] III. Mathematical Description of Rolling Optimization 1. At each time k, define : , Vector D is the thrust control quantity at the current time k. The thrust control quantity sequence then consists of step B-1, where the thrust control quantity refers to the power of the heating element; W represents the output sequence obtained through a nonlinear prediction model based on the current state and vector D, i.e., the predicted output flow sequence. ; 2. The prediction model is derived from the second-order dynamic model: 3. Define the performance function: , Among them, M r The target flow command is defined by Q and R, which are weight matrices, and B is the prediction time domain. Determine the performance index Get the minimum value That is, the optimal power sequence, and the first value in the optimal power sequence is passed to the engine as the thrust control quantity for the next moment; During flow control, the control quantity is subject to the following constraints: △U is the control variable, i.e., heating power, and the two constraints represent the maximum temperature constraint and the upper and lower limits of heating power constraints, respectively.

[0011] IV. Feedback Correction Strategy To improve the robustness of the control system to model mismatch and external disturbances, a feedback correction strategy is introduced on the basis of the basic rolling optimization loop. This strategy compares the actual measured value of the flow sensor with the model prediction value at each sampling time, generates a correction signal, and corrects the optimized control command or the prediction model itself online based on the correction signal, thereby forming a closed-loop correction mechanism with anti-interference capability to ensure that the system output remains stable within the target range for a long time. The preferred method for feedback correction is to use correction instructions: 1. At each new sampling time t+k, the actual flow rate M_meas(t+k) is obtained through the flow sensor, and the deviation between the actual flow rate M_pred(t+k) and the predicted flow rate M_pred(t+k) is calculated as e_corr(t+k) = M_meas(t+k) - M_pred(t+k); 2. The heating power command for the next moment is corrected based on the deviation e_corr(t+k). The correction formula is: U_corr(t+k+1)=U_opt(t+k+1)+B·e_corr(t+k) Wherein, U_opt(t+k+1) is the optimal heating power command generated by NMPC optimization, and B is the correction coefficient (determined according to the characteristics of the storage and supply system and operating experience, which can be a constant or an adjustment parameter related to the operating conditions). This method has a small amount of calculation and is suitable for online real-time execution. 3. The corrected heating power U_corr(t+k+1) is applied to the heating element as the actual control quantity, and the next round of "prediction-optimization-correction" cycle begins with this new state. This strategy can effectively suppress steady-state errors caused by parameter drift, environmental changes, etc., and ensure the accuracy of flow control.

[0012] V. Control System Implementation A gas flow control system for a solid propellant electric propulsion system includes: Sensor module: used to collect the surface temperature of the heating element, the temperature of the storage tank wall, and the pipeline pressure; State estimation module: Based on sensor data and nonlinear prediction models, it uses Kalman filter-type algorithms to estimate the complete state vector of the system in real time; NMPC core computing module: Embedded nonlinear prediction model and optimization algorithm, solves the optimization problem shown by the performance function online; Power drive module: Converts the calculated optimal heating power into a drive signal to control the operation of the heating element.

[0013] VI. Beneficial Effects 1. A nonlinear prediction model was constructed, which can explicitly describe the thermal inertia of the heating element, contact thermal resistance, solid iodine phase change dynamics, and gas pressure dynamics in the gas supply pipeline. Based on the prediction of this high-fidelity physical model, the system can proactively adjust the heating power, effectively compensate for the system's time delay characteristics, achieve rapid and accurate tracking of the target flow rate, and reduce overshoot and steady-state errors. 2. NMPC directly incorporates the physical constraints of the system into the optimization problem, fundamentally avoiding potential limit-breaking behaviors during the control process, ensuring that the system automatically operates within a safe region under any operating condition, and improving the system's safety and reliability. Attached Figure Description

[0014] Figure 1 This is a schematic diagram illustrating the application of the NMPC of the present invention in a solid working fluid electric propulsion flow control system; Figure 2 This is a schematic diagram of the overall scheme of the present invention. Detailed Implementation

[0015] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby providing a clearer and more explicit definition of the scope of protection of the present invention.

[0016] I. Derivation of Nonlinear Prediction Model The derivation is based on the logic chain of heating element thermal equilibrium → phase change kinetics of iodine → flow output dynamics: 1. The thermal balance equation of the heating element (including thermal inertia and contact thermal resistance) Variable and parameter definitions: The input power (W) of the heating element is a control variable determined by the current / voltage output from the power supply module. ,in, The resistance of the heating element; The heat (W) transferred to iodine by the heating element through contact thermal resistance obeys Fourier's law. ,in: The contact thermal resistance (K / W) between the heating element and solid iodine is related to the contact pressure and surface roughness, with a typical value of 0.1~1K / W. : Heating element surface temperature (K), state variable; : Surface temperature (K) of solid iodine, a state variable; The heat loss (W) from the heating element to the environment is mainly due to radiation. , Emissivity of the heating element surface (typical value 0.7~0.9); The exposed area of ​​the heating element that is not in contact with iodine (m²); Heat capacity of heating element (J / K) ( For the quality of the heating element, Its specific heat capacity, such as nickel-chromium alloy c≈450 J / (kg·K) The heating element temperature change rate (K / s) reflects thermal inertia (the heating element temperature does not respond instantaneously after a power change).

[0017] 2. The phase transition kinetics equation for iodine (when iodine reaches its melting point, All of it is used to overcome the latent heat of phase transition. Variable and parameter definitions: Heat loss (W) from solid iodine to the storage tank. , To improve the thermal conductivity of the storage tank walls, This refers to the contact area between iodine and the tank wall of the storage / supply tank; : Evaporation rate of iodine (kg / s); The latent heat of phase transition of iodine; : Mass of solid iodine involved in heating (kg); Specific heat capacity of solid iodine (427 J / (kg・K)); The melting point of iodine; : Temperature change rate of solid iodine (K / s).

[0018] Simplification and physical meaning: If the mass of solid iodine changes slowly ( The second term can be ignored, and the equation simplifies to: This is directly related to the effective heat transfer and evaporation rate of the heating element: heating element power. Add → Increase → Increase (provided that) To maintain contact heat transfer.

[0019] 3. Establish the dynamic equations for gas pressure and flow output within the pipeline (pressure of gaseous iodine within the pipeline). (Pa) satisfies the ideal gas law, and its dynamic change is determined by the difference between the evaporation rate and the output flow rate. Variable and parameter definitions: J / (kg・K) (gas constant of iodine); : Temperature of gaseous iodine inside the pipeline (K, approximately ambient temperature T0≈300 K, or the temperature of the heating element if the pipeline is heated). Pipe volume (m³) , For the length of the pipe, It is the cross-sectional area; Pipeline output flow rate (kg / s), i.e., the final output flow rate of the storage and supply system, is determined by the pressure difference at the pipeline outlet (in molecular flow mode): in, This is the pipeline flow coefficient, with a typical value of 10⁻² Pa.

[0020] 4. By simultaneously solving the above equations and neglecting higher-order terms, we obtain the simplified heating power. To output flow Second-order dynamic model: Variable and parameter definitions: : Thermal inertia time constant (s) of heating element-iodine. (Typical value 3~10 s); : Dynamic time constant of pipeline pressure (s) (Typical value 0.5~2 s); Power-flow gain (kg / (s·W)), typical value 10−9~10−8 kg / (s·W).

[0021] This second-order dynamic model reflects the complete dynamic lag from the change in heating element power to the heating element temperature rise, the iodine phase transition, the establishment of pipeline pressure, and the flow output: Short time scale (<τ2): Flow change is mainly affected by the pipeline pressure response; Long time scale (>τ1): The steady-state flow value is determined by the heating element power. The larger, The higher the steady-state value.

[0022] Its key constraint is: heating element temperature constraint. Iodine temperature constraint: (Iodine decomposition temperature ≈ 873 K); Output flow constraint: (The flow rate adjustment range of the thruster is usually 40% to 150% of the rated flow rate).

[0023] II. Solving the Rolling Optimization Problem The performance function takes the following quadratic form index: Where Mr is the target flow command, Q and R are weight matrices, and B is the prediction time domain; Using the minimum value of this function as an indicator, fuel consumption should be minimized during flow control. During flow control, the control quantity is subject to the following constraints: The performance indicators are obtained online through optimization algorithms. Get the minimum value However, only the first component of D is considered. This information is transmitted to the engine as the thrust control input for the next moment. This process is repeated cyclically, and at each moment, the thrust control input that optimizes the performance indicators for the next B step can always be calculated. .

[0024] For the above quadratic optimization problem with nonlinear constraints, the SQP (Sequential Quadratic Programming) algorithm is used to solve it: The core advantage is that SQP is an efficient method for small- to medium-scale constrained smooth nonlinear optimization, requiring the fewest calculations of the objective function, constraints, and their gradients, and is well-suited to the online real-time control requirements of energy storage and supply systems. Compared with the traditional linear programming (LP) algorithm: In terms of flow tracking accuracy, SQP can better handle the nonlinear coupling relationship between heating power and flow rate, and its accuracy is significantly better than LP; in terms of real-time performance, the calculation time of the two is almost the same, which can meet the sampling period requirements of the storage and supply system (such as second-level or minute-level sampling).

[0025] III. Feedback Correction Strategy The storage and supply system contains nonlinearities (such as nonlinear changes in fluid viscosity with temperature) and uncertainties (such as fluctuations in ambient temperature and changes in resistance caused by scaling in pipelines). The predicted flow rate based solely on a fixed model cannot perfectly match the actual flow rate. Therefore, a feedback correction strategy is adopted to correct the prediction deviation through measured data, thereby ensuring control accuracy and system robustness.

[0026] Calibration execution: At time k, the actual flow rate M_meas(k) is obtained through the flow sensor, and the deviation between the actual flow rate M_pred(k) and the predicted flow rate M_pred(k) is calculated as e_corr(k) = M_meas(k) - M_pred(k); The heating power command for the next moment is corrected based on the deviation e_corr(k). The correction formula is: U_corr(k+1)=U_opt(k+1)+B·e_corr(k), where U_opt(k+1) is the optimal heating power command generated by NMPC optimization, and B is the correction coefficient. The corrected heating power U_corr(k+1) is applied to the heating element as the actual control quantity, and the next round of "prediction-optimization-correction" cycle begins with this new state.

[0027] IV. Control System Implementation A gas flow control system for a solid propellant electric propulsion system includes: Sensor module: used to collect the surface temperature of the heating element, the temperature of the storage tank wall, and the pipeline pressure; State estimation module: Based on sensor data and nonlinear prediction models, it uses Kalman filter-type algorithms to estimate the complete state vector of the system in real time; NMPC core computing module: Embedded nonlinear prediction model and optimization algorithm, solves the optimization problem shown by the performance function online; Power drive module: Converts the calculated optimal heating power into a drive signal to control the operation of the heating element.

[0028] The control system operates on an onboard computer and continuously applies optimized heating power to the system based on a gas flow control method, ensuring that the flow rate remains at the set precision throughout the entire process. Within this system, flow control is completed throughout the entire operational phase.

[0029] The beneficial effects of the gas flow control method and system of the present invention applied to a solid working propellant electric propulsion system are as follows: 1. A nonlinear prediction model was constructed, which can explicitly describe the thermal inertia of the heating element, contact thermal resistance, solid iodine phase change dynamics, and gas pressure dynamics in the gas supply pipeline. Based on the prediction of this high-fidelity physical model, the system can proactively adjust the heating power, effectively compensate for the system's time delay characteristics, achieve rapid and accurate tracking of the target flow rate, and reduce overshoot and steady-state errors. 2. NMPC directly incorporates the physical constraints of the system into the optimization problem, fundamentally avoiding potential limit-breaking behaviors during the control process, ensuring that the system automatically operates in the safe region under any operating conditions, and improving the safety and reliability of the system; 3. The model parameters all have clear physical meanings and can reflect the health status of the system. They can perform health management simultaneously while implementing flow control. 4. The model also reveals the key time constant affecting the flow response speed ( , This information can guide the selection of heating elements and the design of pipelines, thereby optimizing the dynamic performance of the system from the source. 5. By introducing a feedback correction mechanism based on measured flow rate, online compensation for model prediction errors can be achieved, effectively suppressing parameter changes and unknown external disturbances, enabling the system to maintain high-precision flow control even during long-term operation and in complex spatial environments.

[0030] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A gas flow control method applied to a solid working fluid electric propulsion system, characterized in that, Includes the following steps: S1: Establish a nonlinear prediction model from the input power of the heating element to the output flow rate of the gas. This model explicitly describes the thermal inertia of the heating element, the contact thermal resistance, the phase transition dynamics of solid iodine, and the gas pressure dynamics of the gas supply pipeline. S2: In each control cycle k, the current status information of the system is obtained through sensors, including at least the surface temperature of the heating element, the surface temperature of the solid iodine, and the pipeline pressure; S3: Using the model described in S1 and the current state obtained in S2 as initial conditions, simulate the candidate heating power sequence for the next N steps to predict the gas flow trajectory within the next N steps. S4: Based on the predicted time domain N, under the constraints of the heating element input power and output flow rate, the optimal power sequence is solved by minimizing the performance function, so that the system can smoothly transition from the current output flow rate to the desired output flow rate; S5: Apply the first value in the optimal power sequence obtained from S4, i.e. the optimal heating power at the current moment, to the system. At the next sampling moment, return to S2 and repeat this rolling optimization process.

2. The gas flow control method for a solid working fluid electric propulsion system according to claim 1, characterized in that, The nonlinear prediction model is constructed by simultaneously solving the heat balance equation of the heating element, the phase change kinetics equation of iodine, and the dynamics of gas pressure and flow output in the pipeline. Finally, a simplified second-order dynamic model from heating power to output flow is derived. ,in, The time constant of thermal inertia of the heating element-iodine is... The dynamic time constant of pipeline pressure. For power-flow gain.

3. The gas flow control method for a solid working fluid electric propulsion system according to claim 2, characterized in that, The process of constructing the nonlinear prediction model is as follows: S11: Establish the heat balance equation for the heating element: ,in, The heat is transferred to the iodine by the heating element through the contact thermal resistance. This refers to the heat loss from the heating element to the environment. The surface temperature of the heating element. This refers to the rate of temperature change of the heating element. S12: Establish the phase transition kinetic equation for iodine: If the mass of solid iodine changes slowly, the equation simplifies to ,in, For the heat loss of solid iodine to the storage tank, The evaporation rate of iodine. The latent heat of phase transition of iodine. For the mass of solid iodine involved in heating, The specific heat capacity of solid iodine, That is the melting point of iodine; S13: Establish the dynamic equations for gas pressure and flow output within the pipeline: ,in, J / (kg・K) is the gas constant of iodine. The temperature of gaseous iodine inside the pipe. This refers to the pipe volume.

4. The gas flow control method for a solid working fluid electric propulsion system according to claim 1, characterized in that, The performance function described in step S4 is defined as follows: , of which M r The target flow instruction is defined by Q and R, which are weight matrices, and B is the prediction time domain.

5. A gas flow control method for a solid working fluid electric propulsion system according to claim 1 or 4, characterized in that, The constraints mentioned in step S4 include: , representing the maximum temperature constraint and the upper and lower limits of heating power constraints.

6. The gas flow control method for a solid working fluid electric propulsion system according to claim 1, characterized in that, Step S2 also includes a state estimation step, which uses a first-order inertial system combined with a pure time delay element to perform state estimation.

7. The gas flow control method for a solid working fluid electric propulsion system according to claim 1, characterized in that, Step S5 also includes a feedback correction step: S51: At time k, the actual flow rate M_meas(k) is obtained through the flow sensor, and the deviation between the actual flow rate M_pred(k) and the predicted flow rate M_pred(k) is calculated as e_corr(k) = M_meas(k) - M_pred(k); S52: The heating power command for the next moment is corrected based on the deviation e_corr(k). The correction formula is: U_corr(k+1)=U_opt(k+1)+B·e_corr(k), where U_opt(k+1) is the optimal heating power command generated by NMPC optimization, and B is the correction coefficient. S53: The corrected heating power U_corr(k+1) is applied to the heating element as the actual control quantity.

8. A control system for implementing the method of any one of claims 1-7, characterized in that, include: Sensor module: used to collect the surface temperature of the heating element, the temperature of the storage tank wall, and the pipeline pressure; State estimation module: Based on sensor data and nonlinear prediction models, it uses Kalman filter-type algorithms to estimate the complete state vector of the system in real time; NMPC core computing module: Embedded nonlinear prediction model and optimization algorithm, solves the optimization problem shown by the performance function online; Power drive module: Converts the calculated optimal heating power into a drive signal to control the operation of the heating element.

9. The control system according to claim 8, characterized in that, The system is deployed on a spaceborne computer and adopts an explicit model predictive control approach, which means that the optimal control law is pre-stored as a piecewise affine function through offline calculation, and the control command is quickly obtained online through table lookup and interpolation.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-7.

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