Two-stage cascaded power management control method for electric thruster of ultra-low earth orbit satellite

Abstract

This application discloses a two-stage cascaded power control method for ultra-low orbit (ULE) satellite electric thrusters, relating to the field of satellite electric thruster technology. The method includes: constructing a thrust-RF power matching model; conducting research on dynamic estimation technology of RF source power using the extended Kalman filter algorithm, and constructing a state observer; based on the thrust-RF power matching model and the state observer, constructing an adaptive predictive power control framework based on measured data and dynamic state estimation; determining the power coupling mechanism between the helical wave RF source and the ion cyclotron resonance heating RF source, and constructing a mathematical model of the power linkage relationship between the preceding and following stages; based on the preceding and following stage power linkage mathematical model, establishing a dynamic power optimization allocation method with optimal efficiency, thrust, and specific impulse under power constraints, and constructing a feedback controller based on delay-compensated linear quadratic Gaussian control. This application enables two-stage cascaded power control of ULE satellite electric thrusters, thereby optimizing the performance of ULE satellite electric thrusters.

Description

Technical Field

[0001] This application relates to the field of satellite electric thruster technology, and in particular to a method for unified power control of a two-stage cascaded electric thruster for ultra-low orbit satellites. Background Technology

[0002] In ultra-low Earth orbit (UEO) satellite electric propulsion systems, the integrated design of two stages—spiral wave ionization and ion cyclotron resonant heating—while possessing relatively mature individual technologies, the electric propulsion device itself is complex and not simply a superposition of individual technologies. Electromagnetic thrust is proportional to the total radio frequency power, while specific impulse primarily depends on the ionization rate and ion energy of the working fluid. Therefore, increasing the plasma ion temperature and the ionization rate of the working fluid gas effectively increases both thrust and specific impulse. To achieve optimal performance, power distribution between the two stages needs to be optimized. Summary of the Invention

[0003] The purpose of this application is to provide a two-stage cascaded power control method for ultra-low orbit satellite electric thrusters, which can perform two-stage cascaded power control on ultra-low orbit satellite electric thrusters, thereby optimizing the performance of ultra-low orbit satellite electric thrusters.

[0004] To achieve the above objectives, this application provides the following solution: This application provides a method for unified power control of a two-stage cascaded electric thruster for ultra-low Earth orbit satellites, the method comprising: A thrust-RF power matching model is constructed; this model is used to learn the nonlinear characteristics of plasma dynamic loads. Based on the thrust-RF power matching model, the extended Kalman filter algorithm is used to study the dynamic estimation technology of RF source power and to construct a state observer. Based on the thrust-RF power matching model and the state observer, an adaptive predictive power control framework based on measured data and dynamic state estimation is constructed. The power coupling mechanism between the spiral wave radio frequency source and the ion cyclotron resonance heating radio frequency source was determined, and a mathematical model of the power linkage between the front and rear stages was constructed. Based on the mathematical model of power linkage between the front and rear stages, a dynamic power optimization allocation method with optimal efficiency, thrust, and specific impulse under power constraints is established, and the optimal dynamic power optimization allocation strategy for the spiral wave radio frequency source and the ion cyclotron resonance heating radio frequency source is obtained. Based on the optimal dynamic power optimization allocation strategy, a feedback controller based on delay-compensated linear quadratic Gaussian control is constructed. The feedback controller uses the optimal power command output by the adaptive predictive power control framework as the setpoint and the real-time system state provided by the state observer as feedback to generate power adjustment commands through a multi-loop control architecture.

[0005] Optionally, a thrust-RF power matching model is constructed, specifically including: A systematic three-dimensional parameter space experiment was conducted on the electric thruster of a very low Earth orbit (ULE) satellite to obtain a dataset. The dataset includes key state parameters of the ULE satellite electric thruster under different parameter combinations. The parameter combinations include: input power of the helical wave radio frequency source, input power of the ion cyclotron resonance heating radio frequency source, and working fluid flow rate. The key state parameters include thrust, electron density, electron temperature, and equivalent impedance. Using the parameter combination as input and the thrust as output, an end-to-end machine learning model is trained to obtain a thrust-RF power matching model; the end-to-end machine learning model is a gradient boosting decision tree or a shallow neural network.

[0006] Optionally, based on the thrust-RF power matching model, research on dynamic estimation technology of RF source power is carried out using the extended Kalman filter algorithm, and a state observer is constructed, specifically including: Define a state vector and an observation vector; the state vector includes key state parameters; the observation vector includes measured data from multiple sources; the measured data from multiple sources includes: thrust sensor measurements, RF source output power, RF port voltage and current amplitudes, and RF port voltage and current phase differences. Based on the thrust-RF power matching model and the state vector, a state transition equation considering process noise is constructed. Based on the state vector and the observation vector, an observation equation considering observation noise is constructed; Based on the state transition equation considering process noise and the observation equation considering observation noise, the extended Kalman filter algorithm is executed to construct the state observer; Executing the state observer includes a prediction step and an update step; In the prediction step, the current state and error covariance are estimated a priori using the state transition equation and its Jacobian matrix. In the update step, after acquiring the observation data at the current time, the Kalman gain is calculated, and the prior state is corrected using the observation residuals to obtain the final posterior state estimate and update the error covariance.

[0007] Optionally, the state transition equation considering process noise is: in, This is the current state vector; This is the state vector from the previous moment; For the control input of the previous moment; f (·) represents a nonlinear function; The process noise of the previous time step is used to characterize the uncertainty of the model, w∼N(0,Q), where Q is the process noise covariance matrix; The observation equation considering observation noise is as follows: in, This is the observation vector at the current moment; h (.) represents the observation function; The current observation noise is used to reflect the sensor's measurement error, v∼N(0,R), where R is the observation noise covariance matrix.

[0008] Optionally, the adaptive predictive power control framework includes: a state-aware stage that is executed cyclically, a multi-step prediction stage, a rolling optimization stage, and a parameter update stage; In the state perception stage, based on measured multi-source sensor data, the state observer is used to estimate key state parameters in real time at a preset update frequency. In the multi-step prediction stage, the prediction time domain is divided into a preset number of discrete time steps, and each discrete time step is used as a control cycle. The thrust-RF power matching model is called with the current state estimate as the initial condition, and the fourth-order Runge-Kutta numerical integration method is used to determine the thrust output trajectory under different power control sequences in different control cycles. In the rolling optimization stage, a constrained quadratic programming problem is constructed based on the predicted output of the thrust-RF power matching model. The constrained quadratic programming problem is solved online using the effective set algorithm to obtain the optimal power control sequence. The constrained quadratic programming problem includes constraints and a cost function. The constraints are upper and lower power limits and a power change rate limit. The cost function is the sum of the weighted sum of squares of the thrust tracking error and the penalty term for the power increment change, minimizing the thrust tracking error in the prediction time domain. In the parameter update stage, by continuously monitoring the deviation between the model prediction value and the actual measurement value, when the root mean square error of the thrust prediction continuously exceeds the preset root mean square error threshold, the online parameter identification mechanism is triggered, and the ionization efficiency coefficient and power coupling coefficient in the matching model are corrected in real time using the recursive least squares method with a forgetting factor; the forgetting factor is set to 0.95.

[0009] Optionally, the power coupling mechanism between the helical wave radio frequency source and the ion cyclotron resonance heating radio frequency source is determined, and a mathematical model of the power linkage between the preceding and following stages is constructed, specifically including: A multi-factor experiment was designed using the response surface methodology. Multiple power combinations were selected within the operating range of the helical wave RF source and the ion cyclotron resonance heating RF source, and the key state parameters corresponding to each power combination were measured. The power combinations included the input power of the helical wave RF source and the input power of the ion cyclotron resonance heating RF source. Based on the key state parameters, determine the overall system efficiency and specific impulse for each power combination; The first experimental dataset is the overall system efficiency corresponding to each power combination. The thrust and specific impulse corresponding to each power combination are used as the second experimental dataset; Using the power combination as the independent variable and the overall system efficiency as the dependent variable, a multinomial regression model including interaction terms is constructed. Using the first experimental dataset, the coefficients in the multinomial regression model containing interaction terms are determined to obtain the power coupling mechanism; Using the power combination as input and the synchronous prediction values ​​of thrust and specific impulse as output, a three-layer feedforward neural network model with dual output nodes is constructed. The three-layer feedforward neural network is trained using the second experimental dataset and the backpropagation algorithm to construct a thrust-specific impulse prediction model. The power coupling mechanism and the thrust-specific impulse prediction model are used as mathematical models for the power linkage between the front and rear stages.

[0010] Optionally, the power coupling mechanism is as follows: in, For overall system efficiency, , , , , and All are coefficients; Input power to the helical wave radio frequency source; The input is the radio frequency source for ion cyclotron resonance heating.

[0011] Optionally, based on the mathematical model of power linkage between the front and rear stages, a dynamic power optimization allocation method is established to achieve optimal efficiency, thrust, and specific impulse under power constraints. This yields the optimal dynamic power optimization allocation strategy for the helical wave RF source and the ion cyclotron resonance heating RF source, specifically including: Construct a weighted multi-objective function; The weighting coefficients in the weighted multi-objective function are dynamically adjusted according to the phases of the spacecraft mission. According to the sampling period, the weighted multi-objective function is solved by the improved particle swarm optimization method to obtain the optimal dynamic power optimization allocation strategy; the sampling period is synchronized with the control period in the multi-step prediction link under the adaptive predictive power control framework. The improved particle swarm optimization method is as follows: Initialize the population size and maximum number of iterations; Calculate the fitness function value for each particle in the population; the fitness function is a power coupling mechanism. The particle corresponding to the optimal fitness function value is determined as the solution vector; Substitute the solution vector into the weighted multi-objective function to obtain the weighted multi-objective function value; When the solution vector meets the penalty condition, the weighted multi-objective function value is updated using the penalty function; The penalty condition is: the solution vector violates any one of the following constraints: total power constraint, radio frequency source power limit constraint, or plasma stability constraint; the total power constraint is: P ion + P ICR ≤5kW; of which, P ion Input power to the helical wave radio frequency source; P ICR The input power of the ion cyclotron resonance heating radio frequency source is specified; the power limit constraint of the radio frequency source is as follows: P ion ∈[1,3]kW; P ICR ∈[0.5,2]kW; the plasma stability constraint is: n e ≤5×10 17 m -3 ; T e ≤12eV; where, n e Electron density; T e For electron temperature; The penalty function is: in, The updated weighted multi-objective function value; and The power and plasma stability constraint penalty coefficient; and This represents the violation of power and plasma stability constraints. The population is updated using an inertial weighted velocity update formula, and the fitness function of the updated population is determined. The inertial weighted velocity update formula is as follows: in, for The first in the population at a given time i The velocity of each particle; ω Inertial weights; c 1 represents the cognitive factor; c 2 represents social factors; v i ( t) represents the i-th digit in the population at time t. i The velocity of each particle; r 1 and r 2 is a random number uniformly distributed in the range [0,1], used to introduce randomness in the search; pbest i Let be the optimal position of the i-th particle found so far. x i ( t )for t Time of the first i The current position vector of each particle; gbest This is the globally optimal position found so far for the entire population; The population with the largest fitness function before and after the update is retained, and the process returns to the step "Calculate the fitness function value of each particle in the population" until the maximum number of iterations is reached. The particle corresponding to the optimal fitness function value is the optimal dynamic power optimization allocation strategy.

[0012] Optionally, the weighting coefficients in the weighted multi-objective function are dynamically adjusted according to the mission phase described by the spacecraft, specifically including: The spacecraft is in the orbital transfer phase, and the weighting coefficients of the weighted multi-objective function are: [ α , β , γ = [0.7, 0.2, 0.1]; The spacecraft is in the deep space cruise phase, and the weighting coefficients of the weighted multi-objective function are: [ α , β , γ = [0.2, 0.3, 0.5]; During the spacecraft's maneuvering and evasive phase, the weighting coefficients of the weighted multi-objective function are: [ α , β , γ = [0.6, 0.2, 0.2].

[0013] Optionally, based on the optimal dynamic power allocation strategy, a feedback controller based on delay-compensated linear quadratic Gaussian control is constructed, specifically including: Based on the state-space model derived from the thrust-power matching model; At the nominal operating point, the nonlinear state-space model is Jacobian linearized to obtain the system's state matrix, input matrix, and output matrix. The core of the controller adopts a linear quadratic Gaussian architecture, and the optimal state feedback gain matrix is ​​obtained by solving the algebraic Riccati equation. Based on the optimal state feedback gain matrix, the state estimate is obtained through an extended Kalman filter to form the output feedback control law; The feedback controller integrates a multi-level compensation mechanism; The multi-level compensation mechanism includes: In the feedback loop, a minimum variance filter is used to preprocess the thrust sensor signal; A Smith predictor structure is introduced, which uses the nominal model of the system to calculate the system output in parallel under no-delay conditions, and corrects the control quantity by comparing the difference between the predicted output and the actual output.

[0014] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a two-stage cascaded power control method for ultra-low orbit satellite electric thrusters. Based on the nonlinear characteristics of plasma dynamic load, a matching model between thruster thrust and the power of each stage of radio frequency (RF) source is constructed. Research on dynamic estimation technology of RF source power is carried out, and an adaptive predictive power control framework based on measured data and dynamic state estimation is constructed. The power linkage relationship of each stage is analyzed, a mathematical model of power linkage between the preceding and following stages is constructed, and a dynamic power optimization allocation method with optimal efficiency, thrust, and specific impulse under power constraints is established. Based on minimum variance filtering technology and delay-compensated linear quadratic Gaussian controller method, combined with extended Kalman filtering method, a robust coordinated feedback controller is designed to achieve unified power control of helical wave RF source and heating RF source. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of a two-stage cascaded power control method for an ultra-low orbit satellite electric thruster according to one embodiment of this application; Figure 2 This is a diagram showing the composition of a two-stage coordinated control module for the thruster in one embodiment of this application; Figure 3 This is a diagram illustrating the overall architecture of a satellite electric propulsion system and data acquisition in one embodiment of this application. Figure 4 This is a schematic diagram of the plasma currents of each part when only a helical wave radio frequency source power is applied for ionization in one embodiment of this application; Figure 5 This is a schematic diagram of the plasma currents of each part when the power of the helical wave radio frequency source and the power of the ion cyclotron resonance heating radio frequency source are applied simultaneously in one embodiment of this application. Detailed Implementation

[0017] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0018] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] In one exemplary embodiment, such as Figure 1 As shown, a method for unified power control of a two-stage cascaded electric thruster for ultra-low Earth orbit satellites is provided. The method includes: Step 101: Construct the thrust-RF power matching model. The thrust-RF power matching model is used to learn the nonlinear characteristics of plasma dynamic loads.

[0020] Step 101 specifically includes: Step 101-1: Conduct a systematic three-dimensional parameter space experiment on the ultra-low orbit satellite electric thruster to obtain a dataset. The overall architecture diagram of the satellite electric thruster system and data acquisition is shown below. Figure 3 As shown, the dataset includes key state parameters of a VLEO satellite electric thruster under different parameter combinations. Parameter combinations include: helical wave RF source input power, ion cyclotron resonant heating RF source input power, and propellant flow rate. Key state parameters include thrust, electron density, electron temperature, and equivalent impedance.

[0021] Step 101-2: Using the parameter combination as input and thrust as output, train the end-to-end machine learning model to obtain the thrust-RF power matching model. The end-to-end machine learning model is a gradient boosting decision tree or a shallow neural network.

[0022] First, considering the nonlinear characteristics of the plasma load, a matching model between the thrust and the power of each stage of the radio frequency source needs to be constructed. The core of this model is to quantify the mapping relationship between the power input of the helical wave radio frequency source and the heating radio frequency source to the thrust output, while also considering the influence of their power coupling on the plasma state. The core of this method lies in establishing a model that can completely map the power of the helical wave radio frequency source (…). P ion ), ion cyclotron resonance heating radio frequency source power ( P ICR A comprehensive mathematical model is developed to integrate the working gas mass flow rate (Q) with the thrust output. This model aims to quantify the coupling effect between three key input parameters and how they collaboratively influence plasma properties and ultimately determine the thrust magnitude. The model is constructed based on a systematic three-dimensional parameter space experiment. The experimental design needs to cover…P ion , P ICR And the full operating range of the working fluid flow rate Q. Specifically, under the baseline condition of keeping other parameters constant, systematically change: 1) P ion and P ICR The power combinations form a two-dimensional power scan plane; 2) the working fluid flow rate Q is repeated at multiple discrete flow rates (e.g., 5, 10, 15 sccm). At each stable ( P ion , P ICR Under the parameter combination of Q, the final steady-state thrust T is accurately measured, and key plasma state parameters (such as electron density) are recorded simultaneously. n e Electronic temperature T e Equivalent impedance Z (This serves as supplementary information for understanding physical mechanisms and model diagnostics.) Figure 4 and Figure 5 This is a typical data example collected in this experiment, visually demonstrating the distribution of plasma current under different power input combinations. Among them, P A Represents total input power. P HEL Represents the power of the helical wave radio frequency source. P ICRH Power of the radio frequency source for ion cyclotron resonance heating. A 0 represents the plasma current generated by the discharge after helical wave ionization excitation. A 1 represents the plasma current under the combined effect of ionization power and resonant heating power. A 2 represents the plasma current under the combined effect of ionization power and secondary resonant heating power. Figure 4 Corresponding to only applying the power of the helical wave radio frequency source ( P HEL The baseline operating condition of the plasma was used to record the plasma current A0 generated at that time. Figure 5 Corresponding to the simultaneous application of helical wave radio frequency source power and ion cyclotron resonance heating radio frequency source power ( P ICRH The two figures, representing the combined operation of the two systems, record the plasma current A1 under primary resonant heating and the plasma current A2 under secondary resonant heating. Essentially, these figures visualize the abstract variable of "power input" as the observable physical quantity of "plasma current"—they record, through concrete examples, the plasma current under different conditions (i.e., under different conditions). P ion, P ICR The differentiated plasma state responses under power combinations provide an intuitive physical picture for subsequent analysis of power coupling effects. These plasma current data, as an important component of key state parameters, directly reflect the modulation effect of power input on the plasma, thus linking abstract power parameters with the final thrust output through the intermediate link of plasma state changes. Based on the collected complete dataset, an end-to-end machine learning method is used to construct the model. The model's input feature vector is [ P ion , P ICR The output is the target thrust T, where Q is the input variable. Algorithms capable of handling complex nonlinear relationships can be selected, such as gradient boosting decision trees or shallow neural networks. During training, the model will automatically learn the interaction between these three input variables; for example, learning the interaction under different flow rates Q. P ion and P ICR The optimal ratio of the propellant is varied to implicitly capture the profound impact of the working fluid flow rate on ionization and heating efficiency. The performance of the final model is verified by calculating the error between predicted and measured thrust on independent test sets. When the model's average absolute percentage error in prediction remains stable within 5% over a wide operating range covering different flow levels, the integrated model is considered to have met engineering application standards. This model provides a more comprehensive optimization basis for power control strategies, enabling optimal thruster performance under different working fluid flow conditions.

[0023] Step 102: Based on the thrust-RF power matching model, conduct research on dynamic estimation technology of RF source power using the extended Kalman filter algorithm, and construct a state observer.

[0024] Step 102: Specifically includes: Step 102-1: Define the state vector and observation vector. The state vector includes key state parameters. The observation vector includes measured data from multiple sensors. The measured data from multiple sensors includes: thrust sensor measurements, RF source output power, RF port voltage and current amplitudes, and RF port voltage and current phase differences.

[0025] Step 102-2: Based on the thrust-RF power matching model and state vector, construct the state transition equation considering process noise. The state transition equation considering process noise is: in, This is the current state vector; This is the state vector from the previous moment; For the control input of the previous moment;f (·) represents a nonlinear function; The process noise of the previous time step is used to characterize the uncertainty of the model, w∼N(0,Q), where Q is the process noise covariance matrix; Step 102-3: Based on the state vector and observation vector, construct the observation equation considering observation noise. The observation equation considering observation noise is: in, This is the observation vector at the current moment; h (.) represents the observation function; The noise observed at the current moment reflects the sensor's measurement error. v ∼N(0,R), where R is the observation noise covariance matrix.

[0026] Step 102-4: Based on the state transition equation considering process noise and the observation equation considering observation noise, execute the extended Kalman filter algorithm to construct the state observer.

[0027] The execution state observer includes a prediction step and an update step. In the prediction step, the current state and error covariance are estimated a priori using the state transition equation and its Jacobian matrix. In the update step, the Kalman gain is calculated after acquiring the observation data at the current time, and the prior state is corrected using the observation residuals to obtain the final posterior state estimate and update the error covariance.

[0028] Based on the established thrust and radio frequency power matching model, further research on dynamic power estimation technology is needed to achieve accurate perception and closed-loop control of the system's operating state. Under actual on-orbit operating conditions, the plasma state parameters inside the thruster of a VLEO spacecraft fluctuate dynamically due to internal factors such as attitude adjustment and fuel consumption, as well as external factors such as changes in the space environment. Directly measuring these parameters usually involves time delays or systematic errors. Therefore, this paper proposes a dynamic state estimation method based on Extended Kalman Filter (EKF), which uses measurable sensor data to infer the system's key state parameters in real time. This method first defines a state vector. It includes key state variables such as plasma density, electron temperature, thrust, and equivalent impedance of the radio frequency port; observation vector It consists of directly obtainable physical quantities such as thrust sensor measurements, RF source output power, RF port voltage and current amplitudes, and their phase differences. State transition equations. This is derived from the aforementioned thrust-power matching model, where the control input... Given two types of RF power and working fluid flow rate, the nonlinear function f(·) specifically describes how the state variables evolve with the control input and the previous time step. The process noise w∼N(0,Q) is used to characterize the uncertainty of the model; the observation equation A physical relationship was established between state variables and observed quantities. The thrust observation directly corresponds to the thrust F in the state. Radio frequency power is correlated with voltage, current, and phase difference through a function established by circuit theory. The observation noise v∼N(0,R) reflects the sensor's measurement error. The EKF algorithm is executed in two recursive steps: prediction and update. In the prediction step, the state transition equation f(·) and its Jacobian matrix are used. For the current state and error covariance Perform prior estimation; in the update step, when new observation data is obtained... Then, calculate the Kalman gain. And utilize the observation residuals The prior states are corrected to obtain the final posterior state estimate. And update the error covariance This observer possesses parameter adaptive capabilities. When system parameters change, it adjusts model parameters online by analyzing the persistent deviation between the thrust estimate and sensor readings. Simultaneously, to achieve real-time operation within the spacecraft's embedded system, the algorithm is optimized, including pre-calculating the Jacobian matrix, determining the optimal noise covariance matrix parameters through offline simulation, and employing scalar updates to simplify matrix operations and reduce computational complexity. Through this design, this dynamic state estimation technique can provide accurate and real-time state feedback for subsequent power allocation and thrust control strategies, ensuring stable system operation under various conditions.

[0029] Step 103: Based on the thrust-RF power matching model and state observer, construct an adaptive predictive power control framework based on measured data and dynamic state estimation.

[0030] 5. The adaptive predictive power control framework includes: a state-aware stage that executes cyclically, a multi-step prediction stage, a rolling optimization stage, and a parameter update stage.

[0031] In the state perception stage, key state parameters are estimated in real time using a state observer at a preset update frequency, based on measured multi-source sensor data.

[0032] In the multi-step prediction stage, the prediction time domain is divided into a preset number of discrete time steps, and each discrete time step is used as a control cycle. The thrust-RF power matching model is called with the current state estimate as the initial condition, and the fourth-order Runge-Kutta numerical integration method is used to determine the thrust output trajectory under different power control sequences in different control cycles.

[0033] In the rolling optimization phase, a constrained quadratic programming problem is constructed based on the predicted output of the thrust-RF power matching model. The optimal power control sequence is obtained by solving the constrained quadratic programming problem online using the effective set algorithm. The constrained quadratic programming problem includes constraints and a cost function. The constraints are upper and lower power limits and a power change rate limit. The cost function is the sum of the weighted sum of squares of the thrust tracking error and the penalty term for the power increment change, minimizing the time domain of the prediction.

[0034] During the parameter update phase, the deviation between the model's predicted values ​​and the actual measured values ​​is continuously monitored. When the root mean square error (RMSE) of the thrust prediction continuously exceeds the preset RMSE threshold, an online parameter identification mechanism is triggered. A recursive least squares method with a forgetting factor is used to correct the ionization efficiency coefficient and power coupling coefficient in the matching model in real time. The forgetting factor is set to 0.95.

[0035] Based on the established thrust-power matching model and dynamic state estimation technology, this invention constructs an adaptive predictive power control framework. This framework achieves precise and forward-looking control of radio frequency power through a closed-loop architecture of "state perception - multi-step prediction - rolling optimization - parameter update". Specifically, in the state perception stage, by integrating multi-source sensor data such as thrust sensor, radio frequency power monitoring unit, electrical characteristic acquisition module and magnetic field sensor, and using a state observer based on extended Kalman filter, and based on the aforementioned established state transition equation and observation equation, key state parameters such as plasma density, electron temperature, instantaneous thrust and equivalent impedance are estimated in real time at an update frequency of 100Hz, providing accurate system state information for subsequent control decisions. In the multi-step prediction stage, using the current state estimate as the initial condition, the experimentally calibrated thrust-power matching model is invoked, and the fourth-order Runge-Kutta numerical integration method is used to predict the thrust output trajectory under different power control sequences within a time range of 5-10 seconds. The prediction time domain is divided into 500 discrete time steps, each step corresponding to a 10ms control cycle. In the rolling optimization phase, a constrained optimization problem is constructed based on the model's predicted output. Its cost function comprehensively considers thrust tracking accuracy and control smoothness. Specifically, it minimizes the sum of the weighted squares of the thrust tracking error and the penalty term for power increment changes within the prediction time domain, while simultaneously satisfying upper and lower power limits and power change rate constraints. This quadratic programming problem is solved online using the effective set algorithm to obtain the optimal power control sequence. In the parameter update phase, the deviation between the model's predicted values ​​and the actual measured values ​​is continuously monitored. When the root mean square error of the thrust prediction continuously exceeds a preset threshold of 3%, an online parameter identification mechanism is triggered. A recursive least squares method with a forgetting factor is used to correct the ionization efficiency coefficient and power coupling coefficient in the matching model in real time. The forgetting factor is set to 0.95 to ensure the stability of parameter updates. This framework forms a self-learning control system through the cyclical execution of the above four phases. The total processing time for each control cycle is controlled within 15ms, with state estimation taking 5ms, multi-step prediction taking 6ms, and optimization solving taking 4ms, ensuring continuous real-time control performance. In particular, the model predictive controller in the framework uses real-time linearization technology to handle nonlinear optimization problems, which significantly reduces computational complexity while ensuring control accuracy. Ultimately, it achieves real-time optimal control with limited computing resources, ensuring that the system maintains the accuracy and stability of thrust control throughout the entire mission cycle.

[0036] Step 104: Determine the power coupling mechanism between the helical wave radio frequency source and the ion cyclotron resonance heating radio frequency source, and construct a mathematical model of the power linkage relationship between the front and rear stages.

[0037] Step 104 specifically includes: Step 104-1: Design a multi-factor experiment using the response surface methodology. Select multiple power combinations within the operating range of the helical wave RF source and the ion cyclotron resonance heating RF source, and measure the key state parameters corresponding to each power combination. The power combinations include: the input power of the helical wave RF source and the input power of the ion cyclotron resonance heating RF source.

[0038] Step 104-2: Determine the overall system efficiency and specific impulse for each power combination based on key state parameters. The overall system efficiency is defined as the ratio of the jet kinetic energy power output by the thruster to the total input electrical power, calculated using the following formula: m For the working fluid mass flow rate, v e For equivalent exhaust velocity, P ion and P ICR These represent the input power of the helical wave radio frequency source and the ion cyclotron resonance heating radio frequency source, respectively.

[0039] Step 104-3: Use the overall system efficiency corresponding to each power combination as the first experimental dataset.

[0040] Step 104-4: Use the thrust and specific impulse corresponding to each power combination as the second experimental dataset.

[0041] Step 104-5: Construct a multinomial regression model with interaction terms, using power combination as the independent variable and overall system efficiency as the dependent variable.

[0042] Step 104-6: Using the first experimental dataset, determine the coefficients in the multinomial regression model containing interaction terms to obtain the power coupling mechanism. The power coupling mechanism is as follows: in, For overall system efficiency, , , , , and All are coefficients; Input power to the helical wave radio frequency source; The input is the radio frequency source for ion cyclotron resonance heating.

[0043] Step 104-7: Using the power combination as input and the synchronous prediction values ​​of thrust and specific impulse as output, construct a three-layer feedforward neural network model with dual output nodes. Train the three-layer feedforward neural network using the second experimental dataset and backpropagation algorithm to construct a thrust-specific impulse prediction model.

[0044] Step 104-8: Use the power coupling mechanism and thrust-specific impulse prediction model as a mathematical model for the power linkage relationship between the front and rear stages.

[0045] To further improve the power utilization efficiency of electric propulsion systems, it is necessary to systematically analyze the power coupling mechanism between the helical wave radio frequency source and the heating radio frequency source, and establish a precise mathematical model of their linkage. Helical wave radio frequency source ( It is mainly responsible for the ionization process of the working gas; its increased power will increase the plasma density. n e ; while ion cyclotron resonance heating radio frequency source ( The energy is transferred to the ions through a resonance mechanism, and its heating efficiency is strongly dependent on the plasma density parameter. A nonlinear coupling relationship exists between the two: when... As the concentration increases, the plasma density rises. The energy absorption efficiency increases accordingly; however, when the density exceeds a certain critical value, the plasma frequency approaches the operating frequency of the radio frequency source, causing wave propagation cutoff. Simultaneously, the ion cyclotron resonance condition is disrupted, and the energy absorption efficiency decreases significantly. The construction of the linkage mathematical model is based on experimental data from the system design. A multi-factor experiment is designed using the response surface methodology. (1-3kW) and Representative power combinations were selected within the operating range of 0.5-2kW, and the experiment was repeated three times for each power point to ensure data reliability. Experimental measurements included key parameters such as thrust output, plasma density ne, electron temperature Te, and ion temperature Ti. Based on the experimental data, a multinomial regression model including interaction terms was used to quantify the coupling effect between the two, the basic form of which is: , where η represents the overall system efficiency. To handle highly nonlinear relationships, a three-layer feedforward neural network can also be used, with […]. , Using [value] as input and thrust efficiency and specific impulse as output, the network weights are trained through backpropagation. The established linkage model can clearly define the optimal operating range under different power combinations. During the spacecraft cruise phase, the optimization objective is to maximize specific impulse, which is achieved by solving [function name]. Isp ( , Find the corresponding optimal power ratio; during the acceleration maneuver phase, the objective is to maximize thrust, and solve for max. T ( , This linkage model provides a key theoretical foundation for subsequent dynamic power optimization allocation, enabling the system to intelligently adjust the power allocation strategy according to different task requirements, thereby achieving overall performance optimization.

[0046] Step 105: Based on the mathematical model of power linkage between the front and rear stages, establish a dynamic power optimization allocation method with optimal efficiency, thrust, and specific impulse under power constraints, obtain the optimal dynamic power optimization allocation strategy for the helical wave RF source and the ion cyclotron resonance heating RF source, and thus construct a feedback controller.

[0047] Step 105 specifically includes: Step 105-1: Construct a weighted multi-objective function.

[0048] Step 105-2: Dynamically adjust the weight coefficients in the weighted multi-objective function according to the spacecraft mission phase.

[0049] During the orbital transfer phase, the weighting coefficients of the weighted multi-objective function are: [α,β,γ]=[0.7,0.2,0.1]. During the deep space cruise phase, the weighting coefficients of the weighted multi-objective function are: [α,β,γ]=[0.2,0.3,0.5]. During the maneuvering and evasive phase, the weighting coefficients of the weighted multi-objective function are: [α,β,γ]=[0.6,0.2,0.2].

[0050] Step 105-3: Based on the sampling period, solve the weighted multi-objective function using the improved particle swarm optimization method to obtain the optimal dynamic power allocation strategy. The sampling period is synchronized with the control period in the multi-step prediction stage under the adaptive predictive power control framework.

[0051] The improved particle swarm optimization method is as follows: Initialize the population size and maximum number of iterations.

[0052] Calculate the fitness function value for each particle in the population. The fitness function is a power coupling mechanism.

[0053] The particle corresponding to the optimal fitness function value is determined as the solution vector.

[0054] Substituting the solution vector into the weighted multi-objective function yields the weighted multi-objective function value.

[0055] When the solution vector meets the penalty condition, the weighted multi-objective function value is updated using the penalty function.

[0056] The penalty condition is that the solution vector violates any of the following constraints: total power constraint, radio frequency source power limit constraint, or plasma stability constraint.

[0057] The total power constraint is: + ≤5kW.

[0058] in, Input power to the helical wave radio frequency source. Input power for the ion cyclotron resonance heating radio frequency source.

[0059] The power limit constraint for the radio frequency source is: ∈[1,3]kW. ∈[0.5,2]kW.

[0060] The plasma stability constraint is: n e ≤5×10 17 m -3 . T e ≤12eV.

[0061] in, n e This represents the electron density. T e It represents the electron temperature.

[0062] The penalty function is: in, The updated weighted multi-objective function value; and The power and plasma stability constraint penalty coefficient; and The violation of power and plasma stability constraints The population is updated using an inertial weighted velocity update formula, and the fitness function of the updated population is determined. The inertial weighted velocity update formula is as follows: in, for The first in the population at a given time i The velocity of each particle; ω Inertial weights; c 1 represents the cognitive factor; c 2 represents social factors; v i ( t )for t The first in the population at a given time i The velocity of each particle; r 1 and r 2 is a random number uniformly distributed in the range [0,1], used to introduce randomness in the search; pbest i For the first i The optimal position of each individual particle found so far; x i ( t )for t Time of the first i The current position vector of each particle; gbestThis is the globally optimal position found so far for the entire population; The population with the largest fitness function before and after the update is retained, and the process returns to the step "Calculate the fitness function value of each particle in the population" until the maximum number of iterations is reached. The particle corresponding to the optimal fitness function value is the optimal dynamic power optimization allocation strategy.

[0063] Based on the established power linkage model, a dynamic power optimization allocation method is needed to achieve optimal efficiency, thrust, and specific impulse under power constraints. The core of this method is to achieve multi-objective coordinated optimization of thrust, efficiency, and specific impulse under multiple physical constraints, including the maximum power limit of the radio frequency source, the upper limit of plasma temperature, and total power constraints. Specifically, the mathematical expression of the optimization problem adopts a weighted multi-objective function form: The weighting coefficients are dynamically adjusted according to different mission phases of the spacecraft. During the orbital transfer phase, […]. α , β , γ The initial weighting is set to [0.7, 0.2, 0.1], with thrust maximization as the primary objective. During deep-space cruise, a weighting of [0.2, 0.3, 0.5] is used, focusing on specific impulse optimization. In the maneuvering and evasion phase, a weighting combination of [0.6, 0.2, 0.2] is used to balance thrust and maneuverability. The optimization algorithm employs an improved particle swarm optimization method, setting the population size to 40 particles and the maximum number of iterations to 100. The position vector of each particle is represented as […]. , The velocity update uses a standard formula with inertial weights: Inertia weight ω The cognitive factor decreased linearly from 0.9 to 0.4. c 1 and social factors c Both are set to 1.5. The fitness function is directly calculated using the power linkage model to evaluate the overall system performance for each particle. Constraint handling employs a penalty function method; if the solution vector violates the total power constraint... + ≤5kW, power limits for each radio frequency source ( ∈[1,3]kW, ∈[0.5,2]kW) or plasma stability constraint ( n e ≤5×10 17 m -3 , T e When the value of the objective function is ≤12eV, the objective function value is adjusted to Among them, the power constraint penalty coefficient Set to 10, temperature constraint penalty coefficient. Take 20. Dynamic characteristics are achieved through real-time status monitoring. When a sudden change in system parameters (such as |Δ) is detected, n e | / n e In the event of a 5% error or sudden disturbance, the optimizer can reconverge within 50ms, adjusting power allocation to prevent plasma confinement failure. This optimization method is executed every 100ms, synchronized with the control system's sampling period, ensuring optimal performance of the propulsion system throughout the entire mission cycle by online balancing of multiple competing objectives.

[0064] Step 106: Based on the aforementioned optimal dynamic power allocation strategy, construct a feedback controller based on delay-compensated linear quadratic Gaussian control. The feedback controller uses the optimal power command output by the adaptive predictive power control framework as the setpoint and the real-time system state provided by the state observer as feedback, generating power adjustment commands through a multi-loop control architecture.

[0065] Step 106 includes: Step 106-1: Based on the state-space model derived from the thrust-power matching model, f(·) is a nonlinear vector function. , which correspond to electron density, electron temperature, thrust and equivalent impedance respectively; the spiral wave power and heating power are u(t).

[0066] Step 106-2: Perform Jacobi linearization on the nonlinear state-space model at the nominal operating point to obtain the system's state matrix, input matrix, and output matrix. Then, construct an optimal control problem based on the state matrix and input matrix to solve for the state feedback gain, and construct a state observer based on the state matrix and output matrix for real-time estimation.

[0067] Step 106-3: The core of the controller adopts a linear quadratic Gaussian architecture, and the optimal state feedback gain matrix is ​​obtained by solving the algebraic Riccati equation.

[0068] Step 106-4: Based on the optimal state feedback gain matrix, obtain the state estimate through an extended Kalman filter to form the output feedback control law.

[0069] The feedback controller integrates a multi-level compensation mechanism.

[0070] The multi-level compensation mechanism includes: preprocessing the thrust sensor signal using a minimum variance filter in the feedback loop; introducing a Smith predictor structure to calculate the system output under no-delay conditions in parallel using the system's nominal model; and correcting the control input by comparing the difference between the predicted output and the actual output.

[0071] Finally, to achieve precise coordinated control of the helical wave RF source and the ion cyclotron resonance heating RF source, a robust coordinated feedback controller based on a delay-compensated linear quadratic Gaussian controller was designed. This controller uses the optimal power command output by the dynamic power optimization allocation module as the setpoint and the real-time system state provided by the extended Kalman filter state observer as feedback, generating precise power adjustment commands through a multi-loop control architecture. The controller design is based on a state-space model derived from the thrust-power matching model. At the nominal operating point (… =3kW, The nonlinear model is Jacobian linearized at (=2kW) to obtain the system's state matrix A, input matrix B, and output matrix C. The state variables are chosen as [Δ n e ,Δ T e ,ΔF]^T, representing the deviations of plasma density, electron temperature, and thrust relative to their nominal values, respectively; the control input is [Δ ,Δ ]^T represents the adjustment amount of the two-stage RF power. To address the sensor noise and time-varying delay in the system, the controller integrates a multi-stage compensation mechanism. In the feedback loop, a minimum variance filter is used to preprocess the thrust sensor signal. This filter is designed with optimal gain based on noise statistics, effectively suppressing the influence of measurement noise. To compensate for the inherent delays in RF power response and plasma setup, a Smith predictor structure is introduced. The system output under no-delay conditions is calculated in parallel using the system's nominal model, and the control quantity is corrected by comparing the difference between the predicted output and the actual output. The core of the controller adopts a linear quadratic Gaussian architecture, obtaining the optimal state feedback gain matrix K by solving the algebraic Riccati equation. The selection of weight matrices Q and R comprehensively considers thrust tracking accuracy and power adjustment costs, with matrix Q focusing on thrust tracking performance and matrix R limiting drastic changes in the control quantity. When the state cannot be directly measured, an extended Kalman filter is used to obtain the state estimate, forming the output feedback control law. To enhance system robustness, the H∞ design concept was introduced into the LQG framework. Uncertainties in model parameters and disturbances in the space environment were uniformly modeled as additive disturbances, and the stability of the system under disturbances was ensured by solving the H∞ optimization problem. When encountering sudden disturbances (such as abrupt changes in plasma parameters caused by solar wind), this composite control structure can quickly adjust the power distribution, maintaining thrust tracking accuracy while ensuring stability. The controller's performance was verified using a hardware-in-the-loop simulation platform, simulating various extreme conditions including plasma quenching and sensor failure. Test results show that the controller can effectively suppress disturbances within 50ms, with the thrust tracking error remaining within ±2%, demonstrating good dynamic performance and robust stability.

[0072] like Figure 2 This application studies the phase and power measurement technology of helical wave radio frequency source and ion cyclotron resonance heating radio frequency source. The detector is arranged at the output end of the radio frequency power supply and the incident power and reflected power are detected by directional coupler respectively. The phase detector is arranged at the feed port of the coupled antenna and the matching network port respectively to collect the phase signal. The collected phase and power signals are transmitted to the signal acquisition and control core FPGA via high-speed AD conversion module. The FPGA realizes communication with the host computer through phase and power fitting calculation, ADC and DAC drive control, control algorithm implementation and communication protocol decoding.

[0073] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for two-stage cascade power management control of an electric thruster of an ultra-low earth orbit satellite, characterized in that, The method includes: A thrust-RF power matching model is constructed; this model is used to learn the nonlinear characteristics of plasma dynamic loads. Based on the thrust-RF power matching model, the extended Kalman filter algorithm is used to study the dynamic estimation technology of RF source power and to construct a state observer. Based on the thrust-RF power matching model and the state observer, an adaptive predictive power control framework based on measured data and dynamic state estimation is constructed. The power coupling mechanism between the spiral wave radio frequency source and the ion cyclotron resonance heating radio frequency source was determined, and a mathematical model of the power linkage between the front and rear stages was constructed. Based on the mathematical model of power linkage between the front and rear stages, a dynamic power optimization allocation method with optimal efficiency, thrust, and specific impulse under power constraints is established, and the optimal dynamic power optimization allocation strategy for the spiral wave radio frequency source and the ion cyclotron resonance heating radio frequency source is obtained. Based on the optimal dynamic power optimization allocation strategy, a feedback controller based on delay-compensated linear quadratic Gaussian control is constructed. The feedback controller uses the optimal power command output by the adaptive predictive power control framework as the set value and the real-time system state provided by the state observer as feedback to generate power adjustment commands through a multi-loop control architecture. Based on the thrust-RF power matching model, research is conducted on dynamic estimation technology of RF source power using the extended Kalman filter algorithm, and a state observer is constructed, specifically including: Define a state vector and an observation vector; the state vector includes key state parameters; the observation vector includes measured data from multiple sources; the measured data from multiple sources includes: thrust sensor measurements, RF source output power, RF port voltage and current amplitudes, and RF port voltage and current phase differences. Based on the thrust-RF power matching model and the state vector, a state transition equation considering process noise is constructed. Based on the state vector and the observation vector, an observation equation considering observation noise is constructed; Based on the state transition equation considering process noise and the observation equation considering observation noise, the extended Kalman filter algorithm is executed to construct the state observer; Executing the state observer includes a prediction step and an update step; In the prediction step, the current state and error covariance are estimated a priori using the state transition equation and its Jacobian matrix. In the update step, after acquiring the observation data at the current time, the Kalman gain is calculated, and the prior state is corrected using the observation residuals to obtain the final posterior state estimate and update the error covariance.

2. The method of claim 1, wherein the method further comprises: Constructing a thrust-RF power matching model specifically includes: A systematic three-dimensional parameter space experiment was conducted on the electric thruster of a very low Earth orbit (ULE) satellite to obtain a dataset. The dataset includes key state parameters of the ULE satellite electric thruster under different parameter combinations. The parameter combinations include: input power of the helical wave radio frequency source, input power of the ion cyclotron resonance heating radio frequency source, and working fluid flow rate. The key state parameters include thrust, electron density, electron temperature, and equivalent impedance. Using the parameter combination as input and the thrust as output, an end-to-end machine learning model is trained to obtain a thrust-RF power matching model; the end-to-end machine learning model is a gradient boosting decision tree or a shallow neural network.

3. The method for unified power control of a two-stage cascaded ultra-low orbit satellite electric thruster according to claim 2, characterized in that, The state transition equation considering process noise is: wherein, is the current time state vector; is the previous time state vector; is the previous time control input; f(·) is a nonlinear function; is the previous time process noise, used to represent the uncertainty of the model, w ~ N(0, Q), Q is the process noise covariance matrix; The observation equation considering observation noise is as follows: wherein is the observation vector at the current time instant; h(.) is the observation function; is the observation noise at the current time instant, which is used to reflect the measurement error of the sensor, v ~ N(0, R), where R is the observation noise covariance matrix.

4. The method of claim 3, wherein the method further comprises: The adaptive predictive power control framework includes: a state-aware stage that executes cyclically, a multi-step prediction stage, a rolling optimization stage, and a parameter update stage; In the state perception stage, based on measured multi-source sensor data, the state observer is used to estimate key state parameters in real time at a preset update frequency. In the multi-step prediction stage, the prediction time domain is divided into a preset number of discrete time steps, and each discrete time step is used as a control cycle. The thrust-RF power matching model is called with the current state estimate as the initial condition, and the fourth-order Runge-Kutta numerical integration method is used to determine the thrust output trajectory under different power control sequences in different control cycles. In the rolling optimization stage, a constrained quadratic programming problem is constructed based on the predicted output of the thrust-RF power matching model. The constrained quadratic programming problem is solved online using the effective set algorithm to obtain the optimal power control sequence. The constrained quadratic programming problem includes constraints and a cost function. The constraints are upper and lower power limits and a power change rate limit. The cost function is the sum of the weighted sum of squares of the thrust tracking error and the penalty term for the power increment change, minimizing the thrust tracking error in the prediction time domain. In the parameter update stage, by continuously monitoring the deviation between the model prediction value and the actual measurement value, when the root mean square error of the thrust prediction continuously exceeds the preset root mean square error threshold, the online parameter identification mechanism is triggered, and the ionization efficiency coefficient and power coupling coefficient in the matching model are corrected in real time using the recursive least squares method with a forgetting factor; the forgetting factor is set to 0.

95.

5. The method of claim 1, wherein, The power coupling mechanism between the helical wave radio frequency source and the ion cyclotron resonance heating radio frequency source was determined, and a mathematical model of the power linkage between the preceding and following stages was constructed, specifically including: A multi-factor experiment was designed using the response surface methodology. Multiple power combinations were selected within the operating range of the helical wave RF source and the ion cyclotron resonance heating RF source, and the key state parameters corresponding to each power combination were measured. The power combinations included the input power of the helical wave RF source and the input power of the ion cyclotron resonance heating RF source. Based on the key state parameters, determine the overall system efficiency and specific impulse for each power combination; The overall system efficiency corresponding to each power combination is used as the first experimental dataset; The thrust and specific impulse corresponding to each power combination are used as the second experimental dataset; Using the power combination as the independent variable and the overall system efficiency as the dependent variable, a multinomial regression model including interaction terms is constructed. Using the first experimental dataset, the coefficients in the multinomial regression model containing interaction terms are determined to obtain the power coupling mechanism; Using the power combination as input and the synchronous prediction values ​​of thrust and specific impulse as output, a three-layer feedforward neural network model with dual output nodes is constructed. The three-layer feedforward neural network is trained using the second experimental dataset and the backpropagation algorithm to construct a thrust-specific impulse prediction model. The power coupling mechanism and the thrust-specific impulse prediction model are used as mathematical models for the power linkage between the front and rear stages.

6. The method of claim 5, wherein the method further comprises: The power coupling mechanism is as follows: wherein, is the system integrated efficiency, , , , , and are coefficients; is the helicon wave radio frequency source input power; is the ion cyclotron resonance heating radio frequency source input.

7. The method of claim 1, wherein the method further comprises: Based on a mathematical model of power linkage between the front and rear stages, a dynamic power optimization allocation method is established to optimize efficiency, thrust, and specific impulse under power constraints. This yields the optimal dynamic power optimization allocation strategy for the helical wave RF source and the ion cyclotron resonance heating RF source, specifically including: Construct a weighted multi-objective function; The weighting coefficients in the weighted multi-objective function are dynamically adjusted according to the phases of the spacecraft mission. According to the sampling period, the weighted multi-objective function is solved by the improved particle swarm optimization method to obtain the optimal dynamic power optimization allocation strategy; the sampling period is synchronized with the control period in the multi-step prediction link under the adaptive predictive power control framework. The improved particle swarm optimization method is as follows: Initialize the population size and maximum number of iterations; Calculate the fitness function value for each particle in the population; the fitness function is a power coupling mechanism. The particle corresponding to the optimal fitness function value is determined as the solution vector; Substitute the solution vector into the weighted multi-objective function to obtain the weighted multi-objective function value; When the solution vector meets the penalty condition, the weighted multi-objective function value is updated using the penalty function; The penalty condition is: the solution vector violates any one of the following constraints: total power constraint, radio frequency source power limit constraint, or plasma stability constraint; the total power constraint is: Pion + PICR ≤ 5 kW; where Pion is the input power of the helical wave radio frequency source; PICR is the input power of the ion cyclotron resonance heating radio frequency source; the radio frequency source power limit constraint is: Pion ∈ [1, 3] kW; PICR ∈ [0.5, 2] kW; the plasma stability constraint is: ne ≤ 5 × 10¹⁷ m⁻³; Te ≤ 12 eV; where ne is the electron density; Te is the electron temperature; The penalty function is: wherein, is the updated weighted multi-objective function value; and is a power and plasma stability constraint penalty coefficient; and is a violation of the power and plasma stability constraint; The population is updated using an inertial weighted velocity update formula, and the fitness function of the updated population is determined. The inertial weighted velocity update formula is as follows: wherein, is is the velocity of the i-th particle in the population at time t; ω is the inertia weight; c1 is the cognitive factor; c2 is the social factor; vi(t) is the velocity of the i-th particle in the population at time t; r1 and r2 are random numbers uniformly distributed in the range [0, 1] for introducing search randomness; pbesti is the individual best position searched so far by the i-th particle; xi(t) is the current position vector of the i-th particle at time t; gbest is the global best position searched so far by the entire population. The population with the largest fitness function before and after the update is retained, and the process returns to the step "Calculate the fitness function value of each particle in the population" until the maximum number of iterations is reached. The particle corresponding to the optimal fitness function value is the optimal dynamic power optimization allocation strategy.

8. The method of claim 7, wherein the method further comprises: The weighting coefficients in the weighted multi-objective function are dynamically adjusted according to the mission phase described by the spacecraft, specifically including: The spacecraft is in the orbital transfer phase, and the weighting coefficients of the weighted multi-objective function are: [α,β,γ]=[0.7,0.2,0.1]; The spacecraft is in the deep space cruise phase, and the weighting coefficients of the weighted multi-objective function are: [α,β,γ]=[0.2,0.3,0.5]; During the maneuvering and evasion phase of the spacecraft, the weighting coefficients of the weighted multi-objective function are: [α,β,γ]=[0.6,0.2,0.2].

9. The method for unified power control of a two-stage cascaded ultra-low orbit satellite electric thruster according to claim 1, characterized in that, Based on the aforementioned optimal dynamic power allocation strategy, a feedback controller based on delay-compensated linear quadratic Gaussian control is constructed, specifically including: Based on the state-space model derived from the thrust-power matching model; At the nominal operating point, the nonlinear state-space model is Jacobian linearized to obtain the system's state matrix, input matrix, and output matrix. The core of the controller adopts a linear quadratic Gaussian architecture, and the optimal state feedback gain matrix is ​​obtained by solving the algebraic Riccati equation. Based on the optimal state feedback gain matrix, the state estimate is obtained through an extended Kalman filter to form the output feedback control law; The feedback controller integrates a multi-level compensation mechanism; The multi-level compensation mechanism includes: In the feedback loop, a minimum variance filter is used to preprocess the thrust sensor signal; A Smith predictor structure is introduced, which uses the nominal model of the system to calculate the system output in parallel under no-delay conditions, and corrects the control quantity by comparing the difference between the predicted output and the actual output.

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