Isolated conductor surface potential active disturbance rejection control method based on rbf neural network and info optimization algorithm

Abstract

This invention relates to an active disturbance rejection control method for the surface potential of an isolated conductor based on an RBF neural network and the INFO optimization algorithm, belonging to the field of charge control technology for space inertial sensors. The invention addresses the problems of insufficient accuracy in estimating the fixed gain of the extended state observer and the difficulty in tuning the parameters of the nonlinear feedback control law in existing active disturbance rejection control methods. The method includes: establishing a dynamic model of the isolated conductor charge management system; constructing a dual-error-constrained extended state observer; adaptively adjusting the observer gain using an RBF neural network to observe the potential and total disturbance; constructing a differential tracker to obtain the expected potential and its derivative; designing a nonlinear state error feedback control law; using the INFO algorithm for global optimization to obtain the optimal control parameters; and constructing a composite controller to output feedback control quantities. This invention achieves adaptive adjustment of the observer gain and automatic optimization of the controller parameters, making it suitable for space gravitational wave detection.

Description

Technical Field

[0001] This invention belongs to the field of charge control technology for space inertial sensors. Background Technology

[0002] Space-based gravitational wave detection missions rely on ultra-stable inertial references provided by high-precision space inertial sensors. An isolated conductor (Test Mass, TM) suspended inside the inertial sensor serves as the inertial reference, and its residual acceleration noise must be kept to an extremely low level. However, galactic cosmic rays and high-energy solar particles, after penetrating the spacecraft's outer shell, directly bombard the isolated conductor, causing a continuous accumulation of surface charge. When the accumulated charge exceeds a threshold, the Coulomb force between the isolated conductor and the surrounding electrode frame introduces non-negligible acceleration noise, severely interfering with the measurement of gravitational wave signals.

[0003] To maintain the net charge on the surface of an isolated conductor within acceptable limits, a charge management system is required for charge control. Currently, the mainstream method is non-contact ultraviolet discharge technology based on the photoelectric effect. This technology utilizes ultraviolet light to irradiate the surface of an electrode or isolated conductor to generate photoelectrons, and then controls the flow of these photoelectrons through an electric field, thereby neutralizing or regulating the charge on the surface of the isolated conductor.

[0004] However, existing charge control methods mainly face the following challenges: First, the charge rate in the space environment caused by high-energy solar particle events can experience transient surges, creating severe disturbances to the system; second, ultraviolet LED light sources suffer from power decay during long-term operation in orbit; and third, the quantum yield decreases due to contamination of the gold-plated surface inside the sensor by the space environment. These factors combined result in time-varying and uncertain parameters in the charge management system model.

[0005] Existing Active Disturbance Rejection Control (ADRC) techniques have achieved certain results by estimating and compensating for total disturbances using Extended State Observers (ESOs). However, this method still has limitations: First, traditional ESOs use fixed gains, which makes it difficult to simultaneously consider observation accuracy and response speed when the ambient charging rate changes drastically, resulting in lag or insufficient accuracy in disturbance estimation. Second, the Nonlinear State Error Feedback Control Law (NLSEF) contains multiple gain parameters that need to be tuned, and the parameters are strongly coupled. Currently, these parameters are mostly determined by trial and error based on human experience, making it difficult to obtain optimal control performance and limiting further improvements in control accuracy. Summary of the Invention

[0006] This invention addresses the problems in existing active disturbance rejection control methods, such as insufficient accuracy of fixed gain estimation by extended state observers under dynamic disturbances, difficulty in tuning nonlinear feedback control law parameters, and reliance on manual experience leading to suboptimal control accuracy. It provides an active disturbance rejection control method for the surface potential of an isolated conductor based on RBF neural networks and the INFO optimization algorithm.

[0007] The method for controlling the surface potential of an isolated conductor based on RBF neural network and INFO optimization algorithm described in this invention includes:

[0008] A dynamic model of the charge management system of an isolated conductor is established, and a double-error constrained extended state observer containing potential observation error and disturbance estimation error is constructed. The gain of the observer is adaptively adjusted using a radial basis function neural network, and the adjusted state observer is used to observe the surface potential and total charge rate disturbance of the isolated conductor to obtain the observation results.

[0009] Construct a differential tracker to generate the expected potential and its differential signal based on the reference potential, and obtain the expected potential and the differential of the expected potential.

[0010] A nonlinear state error feedback control law is designed, and a vector weighted average optimization algorithm (INFO) is introduced to globally optimize the gain parameters of the control law to obtain the optimal control parameters.

[0011] The observation results, expected potential and its derivative, and optimal control parameters of the dual-error-constrained extended state observer are substituted into the nonlinear state error feedback control law to obtain the feedback control quantity acting on the isolated conductor charge management system, thereby controlling the surface potential of the isolated conductor.

[0012] Furthermore, in this invention, the dynamic model of the isolated conductor charge management system is as follows:

[0013] ;

[0014] in, The surface potential of an isolated conductor; The environmental charging rate attenuation coefficient; The total attenuation coefficient of ultraviolet light power and quantum yield; This represents the total disturbance of the charging rate. For feedback control; It represents the rate of change of the surface potential of an isolated conductor.

[0015] Furthermore, in this invention, the dual-error constrained extended state observer, which includes potential observation error and disturbance estimation error, is as follows:

[0016] ;

[0017] in, Represents the total disturbance of the charging rate The observed values, Representative to The observed values, yes The observer gain coefficient, yes The observer gain coefficient, express rate of change, express rate of change, For the observation error of the surface potential of an isolated conductor, This represents the observation error due to charging rate perturbation.

[0018] Furthermore, in this invention, the observation error of the surface potential of an isolated conductor... and charging rate perturbation observation error for:

[0019] .

[0020] Furthermore, in this invention, the method for adaptively adjusting the observer gain using a radial basis function neural network is as follows:

[0021] by As the input to the RBF neural network, if a Gaussian function is chosen as the activation function of the hidden layer of the RBF neural network, then the output of the g-th node... and network gain compensation for:

[0022]

[0023] in, This is the derivative of the observation error of the surface potential of an isolated conductor. and These are the center vector and width of the basis functions, respectively. The weight matrix, A vector of basis functions;

[0024] The adaptive gain obtained by the observer adaptive adjustment is: ;

[0025] in, As the reference gain, Let i be the network gain compensation amount, where i = 1, 2; For the gain of the potential observer, For the perturbation observer gain;

[0026] Using a forgetting factor The adaptive law of the correction term updates the weight matrix;

[0027] ;

[0028] Wherein, error vector , The learning rate matrix, It is a forgetting factor.

[0029] Furthermore, in this invention, the nonlinear state error feedback control law is:

[0030]

[0031] Where u is the nonlinear state error feedback control law. For the expected potential Compared with observed values Feedback error, The differential signal of the expected potential, This is the DC bias voltage. This is the bias voltage conversion factor. It is a nonlinear function. , , These are the nonlinear function parameters of the potential error term, the nonlinear function parameters of the potential error integral term, and the nonlinear function parameters of the potential error differential term, respectively. For the threshold parameter of the linear segment, , , Let be the controller gain to be tuned, corresponding to the gains of the potential error term, the integral term of the error, and the derivative term of the error, respectively.

[0032] Furthermore, in this invention, the method of introducing a vector weighted average optimization algorithm to globally optimize the gain parameter of the control law is as follows:

[0033] The controller gain vector to be optimized As individuals within a population, the weighted average difference vector of random individuals in the population is calculated. A scaling factor that decays non-linearly with the number of iterations is used to dynamically balance global search capability and local exploitation capability. New candidate solutions are generated iteratively, and a greedy selection strategy is employed to retain the optimal individual, thus achieving a solution that satisfies the composite objective function. Minimize the globally optimal controller parameters .

[0034] The They are respectively The optimal value.

[0035] Furthermore, in this invention, the objective function for:

[0036]

[0037] in, For controller gain vector, Let be the objective function, and be the composite function of the time multiplication of the absolute error integral and the interference estimation error penalty term. For simulation time, These are the weighting coefficients. The expected potential at time t Compared with observed values Feedback error, Let t be the observation error of the charging rate perturbation at time t.

[0038] The method described in this invention first establishes a dual-error constraint mechanism and introduces an RBF neural network to achieve adaptive adjustment of the observer gain to dynamic disturbances. Compared with a fixed-gain ESO, this significantly improves the observation accuracy and response speed for time-varying charging rates. Secondly, addressing the challenge of tuning nonlinear feedback control law parameters, the INFO algorithm is used for global optimization. Using a composite function containing the error integral and disturbance estimation error as the objective, it automatically obtains the controller parameters that optimize system performance, avoiding the blindness and local optima problems of manual trial and error. Simulation results show that, under time-varying model parameters and strong external disturbances, the method of this invention significantly reduces the tracking error of the surface potential of isolated conductors and shortens the settling time compared to traditional ADRC, exhibiting stronger robustness and higher control accuracy. This provides an efficient and practical advanced control scheme for charge management systems in space gravitational wave detection. Attached Figure Description

[0039] Figure 1 This is a flowchart of the method for controlling the surface potential of an isolated conductor based on the RBF neural network and the INFO optimization algorithm according to the present invention.

[0040] Figure 2 This is a charge control block diagram of the isolated conductor surface potential self-disturbance control based on RBF neural network and INFO optimization algorithm of the present invention;

[0041] Figure 3 This is a graph showing the experimental results of tracking a step potential in an isolated conductor;

[0042] Figure 4 This is a comparison chart of tracking errors when an isolated conductor tracks a step potential.

[0043] Figure 5 This is a graph showing the experimental results of an isolated conductor tracking a stable potential;

[0044] Figure 6 This is a comparison chart of tracking errors when an isolated conductor tracks a stable potential. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0046] Specific implementation method one: Refer to Figure 1 and Figure 2 This embodiment specifically describes the isolated conductor surface potential active disturbance rejection control method based on RBF neural network and INFO optimization algorithm, which includes:

[0047] A dynamic model of the charge management system of an isolated conductor is established, and a double-error constrained extended state observer containing potential observation error and disturbance estimation error is constructed. The gain of the observer is adaptively adjusted using a radial basis function neural network, and the adjusted state observer is used to observe the surface potential and total charge rate disturbance of the isolated conductor to obtain the observation results.

[0048] Construct a differential tracker to generate the expected potential and its differential signal based on the reference potential, and obtain the expected potential and the differential of the expected potential.

[0049] A nonlinear state error feedback control law is designed, and a vector weighted average optimization algorithm (INFO) is introduced to globally optimize the gain parameters of the control law to obtain the optimal control parameters.

[0050] The observation results, expected potential and its derivative, and optimal control parameters of the dual-error-constrained extended state observer are substituted into the nonlinear state error feedback control law to obtain the feedback control quantity acting on the isolated conductor charge management system, thereby controlling the surface potential of the isolated conductor.

[0051] Furthermore, in this invention, the dynamic model of the isolated conductor charge management system is as follows:

[0052] ;

[0053] in, The surface potential of an isolated conductor; The environmental charging rate attenuation coefficient; The total attenuation coefficient of ultraviolet light power and quantum yield; This represents the total disturbance of the charging rate. For feedback control; It represents the rate of change of the surface potential of an isolated conductor.

[0054] Furthermore, in this invention, the dual-error constrained extended state observer, which includes potential observation error and disturbance estimation error, is as follows:

[0055] ;

[0056] in, Represents the total disturbance of the charging rate The observed values, Representative to The observed values, yes The observer gain coefficient, yes The observer gain coefficient, express rate of change, express rate of change, For the observation error of the surface potential of an isolated conductor, This represents the observation error due to charging rate perturbation.

[0057] Furthermore, in this invention, the observation error of the surface potential of an isolated conductor... and charging rate perturbation observation error for:

[0058] .

[0059] Furthermore, in this invention, the method for adaptively adjusting the observer gain using a radial basis function neural network is as follows:

[0060] by As the input to the RBF neural network, if a Gaussian function is chosen as the activation function of the hidden layer of the RBF neural network, then the output of the g-th node... and network gain compensation for:

[0061]

[0062] in, This is the derivative of the observation error of the surface potential of an isolated conductor. and These are the center vector and width of the basis functions, respectively. The weight matrix, A vector of basis functions;

[0063] The adaptive gain obtained by the observer adaptive adjustment is: ;

[0064] in, As the reference gain, Let i be the network gain compensation amount, where i = 1, 2; For the gain of the potential observer, For the perturbation observer gain;

[0065] Using a forgetting factor The adaptive law of the correction term updates the weight matrix;

[0066] ;

[0067] Wherein, error vector , The learning rate matrix, It is a forgetting factor.

[0068] Furthermore, in this invention, the nonlinear state error feedback control law is:

[0069]

[0070] Where u is the nonlinear state error feedback control law. For the expected potential Compared with observed values Feedback error, The differential signal of the expected potential, This is the DC bias voltage. This is the bias voltage conversion factor. It is a nonlinear function. , , These are the nonlinear function parameters of the potential error term, the nonlinear function parameters of the potential error integral term, and the nonlinear function parameters of the potential error differential term, respectively. For the threshold parameter of the linear segment, , , Let be the controller gain to be tuned, corresponding to the gains of the potential error term, the integral term of the error, and the derivative term of the error, respectively.

[0071] Furthermore, in this invention, the method of introducing a vector weighted average optimization algorithm to globally optimize the gain parameter of the control law is as follows:

[0072] The controller gain vector to be optimized As individuals within a population, the weighted average difference vector of random individuals in the population is calculated. A scaling factor that decays non-linearly with the number of iterations is used to dynamically balance global search capability and local exploitation capability. New candidate solutions are generated iteratively, and a greedy selection strategy is employed to retain the optimal individual, thus achieving a solution that satisfies the composite objective function. Minimize the globally optimal controller parameters .

[0073] The They are respectively The optimal value.

[0074] Furthermore, in this invention, the objective function for:

[0075]

[0076] in, For controller gain vector, The objective function is a composite function, which is a composite function of the time multiplication of the absolute error integral and the disturbance estimation error penalty term. For simulation time, These are the weighting coefficients. The expected potential at time t Compared with observed values Feedback error, Let t be the observation error of the charging rate perturbation at time t.

[0077] The control method of the present invention includes the following steps:

[0078] Step 1: Establish a dynamic model of the isolated conductor charge management system and construct a gain-adaptively adjustable double-error-constrained extended state observer (RBF-ESO).

[0079] For a charge management system consisting of an isolated conductor, an electrode frame, an electrode voltage, and a UV LED, its potential dynamic model is as follows:

[0080]

[0081] To improve the overall disturbance The estimation capability of conventional ESOs relies solely on potential observation errors. Correction is performed. This invention introduces a dual error constraint to additionally construct the perturbation estimation error. :in, For the surface potential of an isolated conductor, The environmental charge rate degradation coefficient. The total attenuation coefficient of ultraviolet light power and quantum yield is given. For the total disturbance of the charging rate, For feedback control, It represents the rate of change of the surface potential of an isolated conductor.

[0082]

[0083] Therefore, a dual-error-constraint ESO is constructed:

[0084]

[0085] and For observer gain, where, This is the error in observing the surface potential of an isolated conductor; This is the observation error due to charging rate perturbation. Representative to The observed values, among which, Representative to The observed values, yes The observer gain coefficient, yes The observer gain coefficient, express rate of change, express The rate of change.

[0086] To address the poor adaptability of fixed gain under dynamic perturbations, a three-layer RBF neural network is constructed. The network uses... and its derivative Input, output gain compensation amount The final adaptive gain is The weight matrix uses a forgetting factor. The modified learning law is updated to ensure that the weights are bounded and to prevent drift.

[0087] Step 2: Design the differential tracker.

[0088] Using the fastest synthesis function The differential tracker, based on the reference potential Obtain the expected potential and its differential signal The system is arranged with a fast, overshoot-free transition process as follows:

[0089] ;

[0090] Where l is the velocity factor and h is the filter factor.

[0091] Step 3: Design a nonlinear state error feedback control law and optimize its gain using the INFO algorithm.

[0092] The control law is in the form of:

[0093]

[0094] in, , , The three gain parameters are highly coupled, making manual tuning difficult. Representative to Observed values; yes The observer gain coefficient, yes The observer gain coefficient. express The rate of change; express The rate of change; define the optimization vector. The composite objective function of composite performance indicators:

[0095] ;

[0096] The INFO algorithm is used to solve this optimization problem. The algorithm calculates the mean vector. Guide the search and utilize dynamic scaling factors. Balancing exploration and development. Through iterative processes such as population initialization, fitness evaluation, position updating, and greedy selection, the globally optimal parameters are finally output.

[0097] The optimization process of the INFO algorithm includes: calculating the weighted average difference vector of random individuals in the population, dynamically balancing global search capability and local exploitation capability based on a scaling factor that decays non-linearly with the number of iterations, generating new candidate solutions through iteration, and using a greedy selection strategy to retain the optimal individual, ultimately obtaining the solution that satisfies the objective function. Minimize the globally optimal controller parameters .

[0098] Step 4: Construct a composite controller.

[0099] The perturbation observations obtained in step one The expected state obtained in step two , And the optimal controller gain after tuning in step three. , , Substitute into the control law to form the final control input. This drives the surface potential of an isolated conductor to accurately track a reference signal.

[0100] Stability analysis of the closed-loop system of the present invention, which includes adaptive gain adjustment of the RBF neural network:

[0101] Based on the charge management system model and the dual-error-constrained ESO structure, the error dynamic system can be obtained as follows:

[0102]

[0103] In the space environment, the rate of change of charging rate disturbance is bounded, i.e. ,in It is a positive real number.

[0104] Define the weight error of the RBF network as ,in For the ideal weights of the network, This is an estimate of the current weights.

[0105] To prove the convergence of the error and the boundedness of the network weights, the following Lyapunov function is defined:

[0106]

[0107] Differentiating the Lyapunov function and substituting it into the error dynamic equation and the weight adaptive law, we get:

[0108]

[0109] Scaling the cross terms in the above equation using Young's inequality:

[0110]

[0111]

[0112]

[0113] in, For the ideal weight matrix, substitute the above inequality into... From the expression, we can obtain:

[0114]

[0115] in, It is a bounded constant.

[0116] Therefore, it can be seen that as long as the adaptive gain of the RBF network output satisfies and Then there exists a constant. , so that:

[0117]

[0118] According to Lyapunov stability theory, solving this differential inequality yields:

[0119]

[0120] when At that time, the Lyapunov function Converging to a bounded region This proves that the system's state observation error... Interference estimation error and neural network weight error All are uniformly eventually bounded, and the closed-loop system satisfies the stability requirements. The above analysis provides a theoretical guarantee for the adaptive adjustment of the RBF neural network.

[0121] Example

[0122] To verify the effectiveness of this invention, simulation verification was performed based on an isolated conductor charge management system model. The core physical parameters of the system were set as follows: charging rate, actual decay rate. UV attenuation coefficient The single-sided spectral density of the particle charging rate shot noise is... Charge measurement noise is Total capacitance of an isolated conductor to ground The control parameters are set as follows: RBF neural network input node 2, hidden layer node 5, and learning rate matrix. Forgetting factor INFO algorithm population size Maximum number of iterations The optimal controller gain obtained through optimization is .

[0123] Simulation experiments were conducted on two types of potential tracking: step potential tracking and steady potential tracking. Performance was compared with PID control, Model Reference Adaptive Control (MRAC), Sliding Mode Control (SMC), and unoptimized Active Disturbance Rejection Control (ADRC). The standard deviation was used for the results. The mean absolute error (MAE) and root mean square error (RMSE) are used as evaluation indicators.

[0124] Figure 3 and Figure 4 The response and tracking error of the isolated conductor step potential tracking experimental system are described. The initial potential of the isolated conductor is set as follows: The target potential is based on , , The proposed method (improved ADRC) constructs a step-cycle sequence. Experimental results show that, under conditions of continuously increasing system decay, the RMSE of the proposed method (improved ADRC) decreases to 0.104 mV, and the MAE is 0.094 mV, both of which are superior to the comparative algorithms.

[0125] Figure 5 and Figure 6 The response and tracking error of the experimental system for tracking the steady-state potential of an isolated conductor are described. The initial potential of the isolated conductor is set as follows: The target potential is Under the condition of applying a step change in the ambient charging rate at 8000 s, the method of the present invention stabilizes the tracking error within 0.1 mV, with a standard deviation of 0.105 mV, a MAE of 0.093 mV, and an RMSE of 0.106 mV. All indicators are significantly better than ADRC, SMC, MRAC, and PID controllers, demonstrating excellent steady-state tracking performance and anti-interference ability.

[0126] The experimental results above demonstrate that the present invention, by adjusting the observer gain online through an RBF neural network and using the INFO algorithm to globally optimize the controller parameters, can achieve high-precision and robust control of the surface potential of an isolated conductor under conditions of internal parameter decay and strong external interference.

[0127] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for controlling the surface potential of an isolated conductor based on RBF neural network and INFO optimization algorithm, characterized in that, include: A dynamic model of the charge management system of an isolated conductor is established, and a double-error constrained extended state observer containing potential observation error and disturbance estimation error is constructed. The gain of the observer is adaptively adjusted using a radial basis function neural network, and the adjusted state observer is used to observe the surface potential and total charge rate disturbance of the isolated conductor to obtain the observation results. Construct a differential tracker to generate the expected potential and its differential signal based on the reference potential, and obtain the expected potential and the differential of the expected potential. A nonlinear state error feedback control law is designed, and a vector weighted average optimization algorithm (INFO) is introduced to globally optimize the gain parameters of the control law to obtain the optimal control parameters. The observation results, expected potential and its derivative, and optimal control parameters of the dual-error-constrained extended state observer are substituted into the nonlinear state error feedback control law to obtain the feedback control quantity acting on the isolated conductor charge management system, thereby controlling the surface potential of the isolated conductor.

2. The method for controlling the surface potential of an isolated conductor based on an RBF neural network and an INFO optimization algorithm according to claim 1, characterized in that, The dynamic model of an isolated conductor charge management system is as follows: ； in, The surface potential of an isolated conductor; The environmental charging rate attenuation coefficient; The total attenuation coefficient of ultraviolet light power and quantum yield; This represents the total disturbance of the charging rate. For feedback control; It represents the rate of change of the surface potential of an isolated conductor.

3. The method for controlling the surface potential of an isolated conductor based on an RBF neural network and an INFO optimization algorithm according to claim 2, characterized in that, The dual-error constrained extended state observer, which includes both potential observation error and disturbance estimation error, is as follows: ； in, Represents the total disturbance of the charging rate The observed values, Representative to The observed values, yes The observer gain coefficient, yes The observer gain coefficient, express rate of change, express rate of change, For the observation error of the surface potential of an isolated conductor, This represents the observation error due to charging rate perturbation.

4. The method for controlling the surface potential of an isolated conductor based on an RBF neural network and an INFO optimization algorithm according to claim 3, characterized in that, Error in observing surface potential of isolated conductor Total perturbation observation error of charging rate for: 。 5. The method for controlling the surface potential of an isolated conductor based on an RBF neural network and an INFO optimization algorithm according to claim 1, 2, 3, or 4, characterized in that, The method for adaptively adjusting the observer gain using a radial basis function neural network is as follows: by As the input to the RBF neural network, if a Gaussian function is chosen as the activation function of the hidden layer of the RBF neural network, then the output of the g-th node... and network gain compensation for: ； in, This is the derivative of the observation error of the surface potential of an isolated conductor. and These are the center vector and width of the basis functions, respectively. The weight matrix, A vector of basis functions; The adaptive gain obtained by the observer adaptive adjustment is: ; in, As the reference gain, Let i be the network gain compensation amount, where i = 1, 2; For the gain of the potential observer, For the perturbation observer gain; Using a forgetting factor The adaptive law of the correction term updates the weight matrix; ； Wherein, error vector , The learning rate matrix, It is a forgetting factor.

6. The method for controlling the surface potential of an isolated conductor based on an RBF neural network and an INFO optimization algorithm according to claim 4, characterized in that, The nonlinear state error feedback control law is as follows: ； Where u is the nonlinear state error feedback control law. For the expected potential Compared with observed values Feedback error, The differential signal of the expected potential, This is the DC bias voltage. This is the bias voltage conversion factor. It is a nonlinear function. , , These are the nonlinear function parameters of the potential error term, the nonlinear function parameters of the potential error integral term, and the nonlinear function parameters of the potential error differential term, respectively. For the threshold parameter of the linear segment, , , Let be the controller gain to be tuned, corresponding to the gains of the potential error term, the integral term of the error, and the derivative term of the error, respectively.

7. The method for controlling the surface potential of an isolated conductor based on an RBF neural network and an INFO optimization algorithm according to claim 6, characterized in that, The method of introducing a vector weighted average optimization algorithm to globally optimize the gain parameters of the control law is as follows: The controller gain vector to be optimized As individuals within a population, the weighted average difference vector of random individuals in the population is calculated. A scaling factor that decays non-linearly with the number of iterations is used to dynamically balance global search capability and local exploitation capability. New candidate solutions are generated iteratively, and a greedy selection strategy is employed to retain the optimal individual, thus achieving a solution that satisfies the composite objective function. Minimize the globally optimal controller parameters .

8. The method for controlling the surface potential of an isolated conductor based on an RBF neural network and an INFO optimization algorithm according to claim 4, characterized in that, objective function for: ； in, For controller gain vector, For a composite objective function, For simulation time, These are the weighting coefficients. The expected potential at time t Compared with observed values Feedback error, Let t be the observation error of the charging rate perturbation at time t.

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