A method for dynamic parameter optimization and calibration for an electroadsorption pilot-scale platform

Abstract

This invention discloses a dynamic parameter optimization and calibration method for an electroadsorption pilot-scale platform. The method injects a composite excitation voltage into the main power supply circuit, superimposed with a DC component, a high-frequency probe carrier, and a mid-frequency polarization sensing carrier with controlled frequency drift. Utilizing the hardware-level orthogonal demodulation separation response current characteristics, the equivalent fluid series resistance is calculated and the apparent double-layer capacitance is extracted. A microsecond-level transient depolarization action is triggered without interrupting the water production process, and the physical factor of the internal polarization saturation of the electrode is calculated based on the reverse discharge current at the moment of physical short circuit. The probe carrier frequency is synchronously updated through an exponential decay mapping relationship, and dynamic compensation is used to reduce the frequency dispersion error caused by the micropore time constant shift, reconstructing the corrected polarization capacitance. This invention achieves a balance between online high-precision in-situ calibration and optimal energy efficiency optimization, effectively eliminating dispersion measurement errors and ensuring system operational safety.

Description

Technical Field

[0001] This invention relates to the field of electrochemical water treatment technology, specifically to a method for dynamic parameter optimization and calibration for an electroadsorption pilot-scale platform. Background Technology

[0002] Electroadsorption technology is a desalination technique that utilizes the double-layer capacitance of porous electrode surfaces to adsorb ions in water. Under the drive of an electric field, cations and anions in the solution migrate towards the electrode with opposite charges and accumulate in the electrode pores, thereby reducing the ion concentration of the main solution. During operation, the ion adsorption capacity, polarization degree, and energy consumption of the electroadsorption system are directly affected by the DC operating voltage and the internal physical state of the electrode. In order to improve the desalination efficiency of the system and reduce energy consumption, it is necessary to dynamically optimize the system operating parameters and obtain the polarization state of the electrode in real time to adjust the control strategy.

[0003] In the existing electroadsorption pilot platform control and parameter calibration process, it is usually necessary to rely on external sensors to obtain macroscopic data. For example, the polarization adsorption state of the electrode can be indirectly estimated by measuring the fluid ion concentration through the effluent conductivity sensor, or the energy consumption can be evaluated by measuring the overall steady-state voltage and current of the system. When calibrating the system status or adjusting the parameters, it is often necessary to interrupt the normal adsorption water production process and perform a complete desorption or rinsing process to obtain the baseline parameters.

[0004] However, during prolonged adsorption, the transport line resistance-capacitance time constant within the porous electrode exhibits significant dynamic drift with increasing ion saturation. This core physical characteristic leads to significant errors in conventional fixed-frequency impedance probing during such nonlinear polarization processes. Consequently, the apparent capacitance deviates from its actual physical value due to frequency dispersion. Furthermore, in the absence of real-time feedback on the internal polarization state of the electrode, extreme value optimization control easily drives the operating voltage to approach or exceed the water electrolysis potential, triggering irreversible Faraday side reactions, resulting in electrode corrosion and a sharp drop in energy efficiency. Existing parameter calibration methods based on external macroscopic measurements suffer from significant physical hysteresis and state bias, making it difficult to accurately reflect the absolute polarization state within the electrode. Water conductivity sensors can only measure the concentration of the mixed solution flowing out of the component; the fluid transport within the pipeline... The process generates time delays of tens of seconds or even longer, and fluid diffusion and mixing smooth out transient changes in ion concentration inside the electrode. At the same time, conductivity measurements are highly susceptible to interference from fluctuations in influent water quality, ambient temperature, and air bubbles. Furthermore, the frequent interruption of the influent fluid process and the execution of complete desorption in order to obtain an accurate adsorption baseline not only severely disrupts the DC adsorption flow field already established by the electroadsorption system, but also forces the continuous water production process to stop, significantly reducing the effective operating time of the pilot platform and the overall water production efficiency. This reliance on delayed and easily interfered external measurement data makes it impossible for the control system to obtain the absolute polarization state of the space charge inside the electrode in real time and accurately without interrupting the physical process. Consequently, subsequent optimization control is unable to approach the true energy efficiency extreme value due to the lack of accurate underlying state feedback. Summary of the Invention

[0005] The technical problem to be solved by this invention is to address the defects of electroadsorption pilot-scale platforms during long-term operation, such as capacitive decoupling distortion caused by frequency dispersion effect and easy over-limit triggering of Faraday side reactions by the optimization voltage. This invention provides a method for dynamic parameter optimization and calibration of electroadsorption pilot-scale platforms.

[0006] The first aspect of this invention provides a method for dynamic parameter optimization and calibration for an electroadsorption pilot-scale platform, which is executed by a dynamic parameter optimization and calibration system, including an execution component and a control component. The dynamic parameter optimization and calibration method includes the following steps:

[0007] S100, the main control unit controls the signal generation unit to inject a composite excitation voltage into the main power supply circuit of the electroadsorption module. The composite excitation voltage superimposed a DC voltage component for driving ion adsorption, a high-frequency detection carrier component for penetrating the electrode interface, and a mid-frequency polarization sensing carrier component for sensing the interface polarization state with controlled frequency drift. The composite excitation voltage realizes the synchronous physical injection of electrostatic field establishment and microscopic impedance detection.

[0008] In the S200, the main control unit performs hardware-level quadrature demodulation of the total response current of the main circuit acquired by the current sensor through a dual-channel quadrature lock-in amplifier circuit. By separating and extracting the response current characteristics corresponding to the high-frequency detection carrier component and the intermediate-frequency polarization sensing carrier component, the main control unit calculates the equivalent fluid series resistance and further removes fluid conductivity interference to calculate the apparent double-layer capacitance at the intermediate-frequency detection frequency and obtain the polarization characteristics of the electrode interface.

[0009] In the S300, without interrupting the influent flow process, the main control unit periodically triggers microsecond-level transient depolarization actions according to a set time window. Since the microsecond-level short-circuit time is much smaller than the macroscopic desorption time constant, this operation does not significantly damage the macroscopic flow field and water production process of the system. The main control unit controls the fast-response solid-state switch to force short-circuit the two plates of the electroadsorption module, collects the reverse discharge current at the moment of microsecond-level short circuit and extracts the slope of the discharge current change. Based on this slope, the physical factor of the polarization saturation inside the electrode in the current calibration period is calculated, and the micro-disturbance online reference calibration independent of the effluent conductivity is completed.

[0010] S400, the main control unit extracts the physical factor of the polarization saturation inside the electrode, updates the center frequency of the intermediate frequency polarization sensing carrier component in the next cycle through the exponential decay mapping relationship, and substitutes the updated frequency parameters back into the impedance calculation model for dynamic compensation to reduce frequency dispersion error, obtains the corrected polarization capacitance, and maintains the numerical linearity of the measurement system in the nonlinear polarization process.

[0011] S500, the main control unit constructs the objective function of the system energy adsorption efficiency based on the change rate of the modified polarization capacitance and the DC power characteristics. It applies a low-frequency optimization disturbance detection signal to the DC operating voltage and iteratively updates the DC operating voltage command. During the optimization process, the main control unit synchronously monitors the step characteristics of the intermediate frequency phase angle difference. When the polarization potential approaches the side reaction boundary, it forcibly intervenes in the voltage optimization direction to maintain the safe operation of nonlinear extreme value optimization.

[0012] A second aspect of the present invention provides a dynamic parameter optimization and calibration system for an electroadsorption pilot-scale platform, comprising an execution component and a control component.

[0013] The actuation components include an electro-adsorption module, current and voltage sensors mounted on the main circuit, and a fast-response solid-state switch connected in series in the main circuit. The fast-response solid-state switch uses an insulated-gate bipolar transistor module or a silicon carbide metal-oxide-semiconductor field-effect transistor module to perform microsecond-level physical short-circuit state switching.

[0014] The control components include a main control unit, a signal generation unit, a dual-channel quadrature lock-in amplifier circuit, and a high-speed analog-to-digital converter circuit. The control output port of the main control unit is connected to the gate drive circuit of the signal generation unit and the fast-response solid-state switch, respectively. It processes the data characteristics fed back from the dual-channel quadrature lock-in amplifier circuit and the high-speed analog-to-digital converter circuit, and performs demodulation calculations and optimization algorithms on the underlying signals.

[0015] The present invention, by adopting the above technical solution, can bring the following beneficial effects:

[0016] 1. This invention achieves the effect of directly obtaining the absolute polarization state of the space charge inside the electrode online without disrupting the DC adsorption flow field and the continuity of water production by periodically triggering microsecond-level transient depolarization action and collecting reverse discharge current to calculate the physical factor of polarization saturation inside the electrode without interrupting the influent flow process. This solves the problems of response lag and susceptibility to environmental interference in traditional effluent conductivity measurement, and ensures the real-time performance and accuracy of the bottom-level data extraction under long-term continuous operation of the pilot platform.

[0017] 2. This invention achieves dynamic compensation for the offset of the RC time constant caused by the increase of polarization depth in porous electrodes by constructing a closed-loop tracking mechanism between the physical factor of polarization saturation inside the electrode and the center frequency of the intermediate frequency carrier and synchronously updating the detection frequency using the exponential decay mapping relationship. It also eliminates the interference of frequency dispersion caused by the mismatch between the injected signal period and the actual charge and discharge time constant on the impedance calculation, overcomes the calculation defects of apparent capacitance deviating from the actual physical capacitance value at a fixed frequency, and thus obtains the corrected polarization capacitance.

[0018] 3. This invention constructs an objective function reflecting energy adsorption efficiency using the modified polarization capacitance change rate and DC power characteristics, and simultaneously introduces a Faraday side reaction safety boundary constraint judgment mechanism in voltage optimization. This achieves the effect of maximizing the evolution of the driving DC working voltage towards the unit energy consumption ion adsorption increment while accurately avoiding hydrolysis side reactions. When the phase angle partial derivative touches the boundary threshold, the working voltage is forcibly intervened and retreated away from the gas evolution potential, cutting off the divergence path of the extreme value optimization algorithm in the boundary region and ensuring the lossless operation of the electrochemical system. Attached Figure Description

[0019] Figure 1 This is a diagram of the dynamic parameter optimization and calibration system of the present invention;

[0020] Figure 2 This is the overall main flowchart of the dynamic parameter optimization and calibration method of the present invention;

[0021] Figure 3 This is a schematic diagram of the transient depolarization timing control and characteristic sampling waveform of the present invention;

[0022] Figure 4 This is a control logic block diagram for the extremum optimization and Faraday side reaction safety boundary constraints of this invention. Detailed Implementation

[0023] 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 some embodiments of the present invention, and not all embodiments. 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.

[0024] Dynamic parameter optimization and calibration method for electroadsorption pilot-scale platforms

[0025] See attached document Figure 1-4 The present invention provides a dynamic parameter optimization and calibration system for an electroadsorption pilot platform, including an execution component and a control component. The execution component is configured in the water treatment pipeline and the power supply trunk line, and the control component is responsible for the acquisition and demodulation of the underlying signal and the calculation and output of the optimization algorithm.

[0026] The execution components include an electroadsorption module, a current sensor and a voltage sensor set on the main circuit of the electroadsorption module, and a fast-response solid-state switch connected in series in the main circuit. The electroadsorption module is a pilot-scale desalination component with fluid channels and porous carbon electrodes. The current sensor and voltage sensor are used to collect the total response current and the terminal voltage between the plates in the main circuit. The fast-response solid-state switch is used to perform microsecond-level physical short-circuit state switching. The fast-response solid-state switch adopts an insulated gate bipolar transistor module or a silicon carbide metal oxide semiconductor field-effect transistor module.

[0027] The control components include a main control unit, a signal generation unit, a dual-channel quadrature lock-in amplifier circuit, and a high-speed analog-to-digital converter circuit. The main control unit adopts a programmable logic controller, a digital signal processor, or a field-programmable gate array. The main control unit is communicatively connected to the signal generation unit. The output of the signal generation unit is electrically connected to the electro-adsorption module to inject a composite voltage excitation containing DC components and multi-frequency AC components.

[0028] The output of the current sensor is connected to the analog signal input of the dual-channel quadrature lock-in amplifier circuit and the high-speed analog-to-digital converter circuit, respectively. The output of the dual-channel quadrature lock-in amplifier circuit and the output of the high-speed analog-to-digital converter circuit are connected to the data interface of the main control unit to transmit the demodulated amplitude, phase angle characteristics and high-frequency sampling data to the internal register of the main control unit. The control output port of the main control unit is connected to the gate drive circuit of the signal generation unit and the fast response solid-state switch, respectively.

[0029] Furthermore, this invention provides a method for dynamic parameter optimization and calibration of an electroadsorption pilot-scale platform, which is executed based on the aforementioned system and specifically includes the following steps:

[0030] S100, the main control unit controls the signal generation unit to inject a composite excitation voltage into the main power supply circuit of the electro-adsorption module. The composite excitation voltage is superimposed with a DC voltage component for driving ion adsorption, a high-frequency detection carrier component for penetrating the electrode interface, and a mid-frequency polarization sensing carrier component for sensing the interface polarization state with controlled frequency drift.

[0031] S200: The main control unit performs hardware-level quadrature demodulation on the total response current of the main circuit acquired by the current sensor through a dual-channel quadrature lock-in amplifier circuit. It separates and extracts the response current characteristics corresponding to the high-frequency detection carrier component and the intermediate frequency polarization sensing carrier component. Based on the extracted current characteristics, the main control unit calculates the equivalent fluid series resistance and further removes fluid conductivity interference to calculate the apparent double-layer capacitance at the intermediate frequency detection frequency.

[0032] S300, without interrupting the influent flow process, the main control unit periodically triggers microsecond-level transient depolarization action according to the set time window. By controlling the fast-response solid-state switch to force short-circuit the two plates of the electro-adsorption module, the main control unit collects the reverse discharge current at the moment of microsecond-level short circuit and extracts the slope of the discharge current change. Based on the slope, it calculates the physical factor of the polarization saturation inside the electrode in the current calibration period.

[0033] S400: The main control unit extracts the physical factor of polarization saturation inside the electrode, updates the center frequency of the intermediate frequency polarization sensing carrier component in the next cycle through the exponential decay mapping relationship, and substitutes the updated frequency parameters back into the impedance calculation model to dynamically compensate for the frequency dispersion error caused by the micro-hole time constant shift and obtain the corrected polarization capacitance.

[0034] In the S500, the main control unit constructs the objective function of the system's energy adsorption efficiency based on the modified rate of change of polarization capacitance and DC power characteristics. The main control unit applies a low-frequency optimization perturbation detection signal to the DC operating voltage, analyzes the gradient vector of the objective function with respect to the detection signal, and performs discrete integration. The main control unit iteratively updates the DC operating voltage command in real time. During the optimization process, the main control unit synchronously monitors the step characteristics of the intermediate frequency phase angle difference. When the polarization potential approaches the side reaction boundary, it forcibly intervenes in the voltage optimization direction to maintain safe operation of nonlinear extreme value optimization.

[0035] Furthermore, based on the fluid mass transfer and electrochemical polarization mechanism inside the electroadsorption module, the main control unit constructs a composite excitation model that synchronously drives ion migration and detection interface. The composite excitation model is specifically manifested at the physical and electrical level as a composite excitation voltage superimposed on the main power supply circuit.

[0036] The composite excitation voltage is formed by the linear superposition of the DC working voltage component, the high-frequency detection carrier component, and the medium-frequency polarization sensing carrier component in the analog front end through an adder circuit. At the electrode power supply end, the three voltage components are applied synchronously to the fluid channel and the porous carbon electrode interface of the electroadsorption module. The DC working voltage component is dynamically output by the extreme value optimization control law of the main control unit and is used to establish a macroscopic electrostatic field between the two plates to drive the anions and cations in the water to undergo directional electrophoretic migration into the pores of the opposite electrode.

[0037] The high-frequency probe carrier component is a sinusoidal alternating current signal with a fixed amplitude and frequency. The porous electrodes of the electroadsorption module are microscopically equivalent to an impedance network composed of solution resistance and double-layer capacitance. When the high-frequency probe carrier component is injected, the capacitive reactance of the double-layer capacitance decreases sharply with increasing frequency. The electrode interface is equivalent to a low-impedance state for the high-frequency alternating signal. The high-frequency probe carrier component directly penetrates the double layer on the electrode surface. The current response excited by the high-frequency probe carrier component in the main circuit is entirely dominated by the equivalent fluid series resistance composed of the solution resistance and the hardware contact resistance. The frequency range of the high-frequency probe carrier component is configured as follows: to ;

[0038] The intermediate frequency (IF) polarization sensing carrier component is a sinusoidal AC level signal with a fixed amplitude and a controlled center frequency drift. The frequency band of the IF polarization sensing carrier component corresponds to the RC time constant response distribution region of the porous carbon electrode's internal interface. Within this frequency band, the applied alternating electric field induces periodic charging and discharging of ions within the double layer, resulting in a significant capacitive phase shift and impedance amplitude attenuation. The IF polarization sensing carrier component is used to extract the polarization charging and discharging characteristics of the electrode interface. The initial frequency range of the IF polarization sensing carrier component is configured as follows: to As ions occupy the micropore space during the adsorption process, causing the time constant to shift, the main control unit calculates and updates the center frequency of the intermediate frequency polarization sensing carrier component in real time.

[0039] To satisfy the linear time-invariant assumption of the electrochemical system and avoid additional illegal Radaic polarization disturbances or disruption of the original DC adsorption flow field caused by large-signal AC injection, the excitation amplitudes of the high-frequency probe carrier component and the mid-frequency polarization sensing carrier component are limited to small-amplitude AC levels. The amplitude constants of both the high-frequency probe carrier component and the mid-frequency polarization sensing carrier component are configured as follows: to Within the specified range, the voltage level set within the aforementioned range can extract the internal micro impedance parameters without changing the macroscopic operating state of the system.

[0040] In terms of underlying hardware implementation, the high-frequency detection carrier component and the intermediate-frequency polarization sensing carrier component are independently generated by a dual-channel direct digital frequency synthesizer chip configured inside the signal generation unit. The main control unit writes frequency control words to the direct digital frequency synthesizer through a serial peripheral interface bus to lock the carrier frequency point. The main control unit calculates the frequency control words. The calculation formula is:

[0041]

[0042] In the formula, When the target output frequency issued by the main control unit generates the high-frequency probe carrier component... Set as When generating intermediate frequency polarization sensing carrier components Set as ; The system reference clock frequency for the direct digital frequency synthesizer chip; This is the hardware bit width constant of the phase accumulator inside the direct digital frequency synthesizer;

[0043] The stepped wave output from the direct digital frequency synthesizer is smoothed by a passive low-pass reconstruction filter and then input together with the DC working voltage component output from the digital-to-analog converter into the in-phase adder topology constructed by the multiple operational amplifier to complete the physical synthesis of the composite excitation voltage.

[0044] Furthermore, based on the quadrature demodulation principle, the main control unit and the dual-channel quadrature lock-in amplifier circuit separate the amplitude and phase angle corresponding to a specific carrier frequency from the total response current containing broadband noise and DC baseline;

[0045] The current sensor collects the total response current in the main circuit, which is then converted into a proportional voltage signal by a transimpedance amplifier circuit. proportional voltage signal It contains DC response components, high-frequency response components, intermediate-frequency response components, and environmental electromagnetic interference noise. The output terminal of the transimpedance amplifier circuit is physically connected to the input terminal of the dual-channel quadrature lock-in amplifier circuit. The dual-channel quadrature lock-in amplifier circuit has demodulation channels arranged in parallel for independent operation at high-frequency and intermediate-frequency points.

[0046] A dual-channel quadrature lock-in amplifier circuit synchronously generates and injects a quadrature reference signal that is in phase and at the same frequency as the intermediate frequency polarization sensing carrier. The quadrature reference signal includes the in-phase reference signal. and quadrature reference signals The mathematical expressions are as follows:

[0047]

[0048]

[0049] In the formula, The current intermediate frequency carrier center frequency; It is a time variable;

[0050] The dual-channel quadrature lock-in amplifier circuit is equipped with a multiplier module, which multiplies the proportional voltage signal. With in-phase reference signal respectively and orthogonal reference signal Time-domain multiplication is performed. The proportional voltage signal is multiplied by the in-phase reference signal to generate an in-phase mixed signal, and the proportional voltage signal is multiplied by the quadrature reference signal to generate a quadrature mixed signal. The multiplication operation shifts the intermediate frequency response component carrying amplitude and phase angle information to the zero-frequency DC position, and shifts the non-in-phase interference signal and the fundamental frequency component to the high frequency band.

[0051] The dual-channel quadrature lock-in amplifier circuit cascades a low-pass filter module after the multiplier module. The cutoff frequency of the low-pass filter module is set to be much lower than the center frequency of the intermediate frequency carrier. The in-phase and quadrature mixing signals are respectively input to the low-pass filter module. After filtering out the high-frequency AC components, the low-pass filter module outputs a stable in-phase DC level component. With orthogonal DC level components In-phase DC level component and orthogonal DC level components The mathematical relationship satisfies:

[0052]

[0053]

[0054] In the formula, This is the combined transimpedance gain constant from the current sensor to the transimpedance amplifier circuit; For the extracted corresponding The amplitude of the second response current at the frequency point; To extract the phase angle difference between the second response current and the injected drive voltage, the internal arithmetic unit of the main control unit reads the in-phase DC level component. and orthogonal DC level components The amplitude of the second response current is calculated by coordinate transformation. With phase angle difference The mathematical expression for solving is:

[0055]

[0056]

[0057] For high-frequency points in a dual-channel quadrature lock-in amplifier circuit The demodulation channels use the same hardware topology and operational logic. The main control unit performs mixing and filtering calculations using the orthogonal reference signal corresponding to the high-frequency point to obtain the corresponding... First response current amplitude at frequency point Since the electrode exhibits a purely resistive response characteristic under extremely high frequency signal injection, the corresponding high-frequency phase angle difference approaches zero. Therefore, the main control unit only extracts and stores the amplitude of the first response current. This is to enable the system to perform division calculations of the equivalent fluid series resistance;

[0058] The aforementioned phase-locked demodulation model is based on continuous-time variables. The principle explanation, at the physical implementation level of the control components, is that the dual-channel quadrature lock-in amplifier circuit uses a field-programmable gate array to realize the quadrature demodulation and lock-in amplification functions in the digital domain, proportional voltage signal. After being discretely sampled by a system-level high-speed analog-to-digital converter, the signal is converted into a digital encoded stream and input to the input pins of a field-programmable gate array (FPGA). The FPGA is internally instantiated with a digital multiplier logic core and a finite-length unit impulse response digital low-pass filter logic core. According to the aforementioned principle, the equivalent discrete difference equation is calculated to complete the digital mixing and digital filtering operations of the discrete signal sequence.

[0059] Furthermore, the main control unit constructs the underlying computational logic based on a simplified electrochemical Randle equivalent circuit model. Under AC perturbation excitation, the electroadsorption module is equivalent to a passive network containing fluid mass transfer impedance and porous interface polarization impedance. The equivalent passive network is topologically abstracted as a series combination of equivalent fluid series resistance and apparent double-layer capacitance. The equivalent impedance calculation logic executed by the main control unit specifically includes the following sub-steps:

[0060] S201, the main control unit performs the calculation of the equivalent fluid series resistance. Under the frequency of the high-frequency probe carrier, the capacitive reactance of the apparent double-layer capacitance is approximately zero, and the electroadsorption system is equivalent to a purely resistive characteristic. The main control unit reads the amplitude of the first response current extracted by the phase-locked loop. And combined with the fixed high-frequency detection carrier amplitude within the system Calculate the equivalent fluid series resistance based on Ohm's law. The formula for calculating the equivalent fluid series resistance is:

[0061]

[0062] In the formula, Characterizes the total physical impedance contribution of influent fluid conductivity, electrode substrate resistance, and hardware contact resistance; It is a continuous-time variable;

[0063] S202, the main control unit performs the extraction of the system's comprehensive impedance modulus at a specific frequency point, and senses the current operating frequency of the carrier at the intermediate frequency polarization. Below, the system's terminal impedance is expressed as the complex vector sum of the equivalent fluid series resistance and the apparent double-layer capacitance reactance. The main control unit reads the amplitude of the second response current extracted by the phase-locked loop. And combined with intermediate frequency polarization sensing carrier amplitude Calculate the comprehensive impedance modulus of the system under the corresponding operating conditions. The formula for calculating the composite impedance modulus is:

[0064]

[0065] S203, the main control unit performs the separation calculation of the apparent double-layer capacitance. The main control unit uses the Pythagorean theorem geometric mapping relationship on the impedance complex plane to calculate the composite impedance modulus. Eliminating equivalent fluid series resistance Find the real interference component and obtain the pure capacitive reactance. The formula for calculating pure capacitive reactance is:

[0066]

[0067] The main control unit, based on the inverse proportional relationship between capacitive reactance and capacitance in AC circuits, converts pure capacitive reactance... Converted to the corresponding apparent double-layer capacitance The conversion calculation formula is as follows:

[0068]

[0069] In the formula, The transient polarization energy storage characteristics of the electrode interface under specific operating polarization states are characterized. The calculated apparent double-layer capacitance eliminates the measurement bias introduced by fluid conductivity fluctuations. When performing nonlinear algebraic operations such as square root and division, the main control unit calls the internally integrated hardware floating-point unit to perform discretization numerical processing. The main control unit has a pre-deployed moving average filtering algorithm program. Before substituting mathematical formulas into the calculation, the main control unit performs smoothing filtering calculations with a fixed data window length on the continuously read first response current amplitude sequence and second response current amplitude sequence. The discrete filtering calculation formula for the first response current amplitude is:

[0070]

[0071] In the formula, For discrete sampling time index variables, For the first Output of the first response current amplitude after smoothing and filtering of discrete sampling points; The fixed data window length is a constant. The filtering process for the discrete first response current amplitude extracted from history is the same as that for the second response current amplitude. The smoothing filter calculation removes the low-frequency mechanical pulsation noise generated by fluid pumping and the quantization truncation error accompanying the analog-to-digital conversion process. The main control unit substitutes the smoothed and filtered values ​​into the model in steps S201 to S203 to solve for the impedance parameters.

[0072] Furthermore, the main control unit constrains the turn-on and turn-off timing of the fast-response solid-state switch through an internal hardware timer and a pulse width modulation peripheral module. The system is equipped with two sets of fast-response solid-state switches, including a main circuit series switch connected in series in the main power supply circuit and a bypass discharge switch connected in parallel between the two plates of the electro-adsorption module.

[0073] Conventional electroadsorption state calibration requires a complete desorption process. The ions released during desorption disrupt the original desalination permeate flow field. The main control unit performs microsecond-level transient depolarization timing control, limiting the depolarization time to the microsecond level. It utilizes the instantaneous discharge physical characteristics of space charge within the micropores to acquire calibration data, maintaining the continuity of the feed water flow and the DC adsorption flow field. The specific steps of the main control unit performing transient depolarization timing control include:

[0074] S301, the main control unit is equipped with a calibration period timer, which operates within a set time window. For counting upwards from the period boundary, within the adsorption interval before the calibrated period timer overflows, the gate drive port of the main control unit outputs a high level to keep the main circuit series switch in the on state, and outputs a low level to keep the bypass discharge switch in the off state. Within this interval, the signal generation unit continuously injects a composite excitation voltage into the electro-adsorption module.

[0075] S302: When the calibration period timer count overflows and triggers a hardware interrupt, the main control unit enters the transient depolarization operation sequence. The main control unit outputs a low level to the gate drive circuit, turns off the main circuit series switch, and cuts off the physical path of the composite excitation voltage input. After turning off the main circuit series switch, the main control unit calls the internal dead-time generator to insert the system's preset dead-time. Dead time is used to wait for the minority carriers inside the series switch in the main circuit to fully recombine, preventing subsequent switch actions from causing a direct short circuit fault in the power supply trunk.

[0076] S303, at the end of the dead time, the main control unit outputs a high level to the gate drive circuit, turning on the bypass discharge switch connected between the two plates of the electro-adsorption module. The conduction of the bypass discharge switch establishes a physical short-circuit discharge loop for the space charge inside the electrode. The main control unit maintains the bypass discharge switch on for a microsecond-level short-circuit window. microsecond-level short-circuit window The specific value range is configured as follows to In the microsecond-level short-circuit window Inside the electrode micropores, localized high-density charges are released outward under the action of electrostatic repulsion, generating a reverse discharge current in the physical short-circuit discharge circuit. The main control unit synchronously triggers the high-speed analog-to-digital converter circuit to perform equally spaced discrete sampling of the reverse discharge current at a set sampling period. The main control unit stores the discrete sampling data blocks output by the analog-to-digital converter circuit into the buffer pool of the direct memory access controller. The main control unit extracts the first and last data points of the discrete sampling data blocks and calculates the slope of the discharge current change. Slope of discharge current change The calculation formula is:

[0077]

[0078] In the formula, For calibration period index; For microsecond-level short-circuit windows The total number of discrete sampling points obtained within the time limit is a constant. This is the first reverse discharge current value collected at the moment the short circuit begins; This is the last reverse discharge current value collected at the moment the short circuit ends; The discrete sampling period constant of the high-speed analog-to-digital converter circuit;

[0079] S304, microsecond-level short-circuit window At the end of the cycle, the main control unit shuts off the bypass discharge switch, cutting off the physical short-circuit discharge circuit, and then inserts an equal amount of dead time again. After the dead time ends, the main control unit outputs a high level again to turn on the main circuit series switch, restoring the physical path of the composite excitation voltage input. The system hardware returns to the adsorption and quadrature phase-locked demodulation process, within the microsecond-level short-circuit window on the timing constraint boundary. Subject to the macroscopic desorption time constant of the electrode Due to physical limitations, the microsecond-level short-circuit window set by the main control unit must satisfy the following boundary condition formula:

[0080]

[0081] In the formula, The macroscopic timescale constant required for ions to completely migrate from the inside of the micropores to the fluid channel satisfies the aforementioned time boundary constraints. This ensures that the charge transfer at the electrode interface is limited to the innermost Helmholtz layer of the double layer and the shallow region of the micropores. The ion bulk does not leave the electrostatic adsorption range and enter the fluid channel. The main control unit obtains the internal absolute polarization state data without affecting the quality of the produced water.

[0082] Furthermore, after acquiring the discrete sampling sequence of the reverse discharge current within the microsecond-level short-circuit window, the main control unit converts the time-domain current response into a numerical quantity characterizing the space charge state of the micropores, completing the online benchmark calibration of micro-perturbations independent of the effluent conductivity sensor. The specific steps of data extraction and calculation performed by the main control unit include:

[0083] In S310, the main control unit configures the hardware trigger source of the analog-to-digital converter circuit to be synchronized with the conduction level of the bypass discharge switch. At the instant the bypass discharge switch is turned on, the analog-to-digital converter circuit continuously acquires the analog amplitude of the reverse discharge current at a set discrete sampling period, and converts the analog amplitude into a discrete digital quantity. The main control unit uses a direct memory access controller to sequentially transport the converted discrete digital quantity to a pre-allocated linear buffer array in the internal static random access memory to form a discrete sampling data block.

[0084] S320: The main control unit reads the first and last data points of the discrete sampling data block in the linear buffer array, calls the arithmetic logic unit to perform first-order discrete difference operation, and calculates the slope of the discharge current change. The formula for calculating the slope of the discharge current change is:

[0085]

[0086] In the formula, For system calibration cycle index; This is a constant representing the total number of discrete sampling points acquired within a microsecond-level short-circuit window; This is the first reverse discharge current value collected at the moment the short circuit begins; This is the last reverse discharge current value collected at the moment the short circuit ends; The discrete sampling period constant of the analog-to-digital converter circuit;

[0087] S330, the main control unit is based on the discharge current change slope. The physical factors contributing to the polarization saturation within the electrode are calculated. Given a fixed micropore volume and double-layer capacity, the ion concentration within the micropores increases during adsorption, leading to increased space charge repulsion. This high-density charge distribution physically limits the slope of the reverse discharge current change during short-circuit events. Ion saturation reduces the effective capacitance or increases the mass transfer resistance within the micropores, increasing the discharge time constant and slowing the current decline rate. Therefore, the decrease in the discharge current slope is positively correlated with the ion saturation within the electrode. The main control unit reads the baseline clean state discharge slope constant stored in non-volatile memory. The reference clean state discharge slope constant is the maximum initial discharge slope reference value measured by injecting the same composite excitation voltage into the clean electrode and performing a microsecond-level short-circuit operation under the initial non-polarized desalination state of the system. The main control unit tunes in the discharge current change slope. Discharge slope constant compared to the baseline clean state Perform normalized subtraction to calculate the physical factor of the electrode's internal polarization saturation during the current calibration cycle. The calculation formula is:

[0088]

[0089] In the formula, As a dimensionless physical state quantity, to prevent hardware measurement noise from causing the physical state quantity to overflow beyond its limit, the main control unit calculates the physical factor of the internal polarization saturation of the electrode. Additional upper and lower limit constraints are applied when sensor noise causes the calculated amplitude to be affected. Greater than At that time, the main control unit forcibly assigns a value. When detected When the value is less than or equal to zero, the main control unit forces a value to be assigned. ;

[0090] When the electrode is in a completely clean state, the slope of the discharge current change tends to the reference value, and the physical factor of the polarization saturation inside the electrode... As the discharge current approaches zero and gradually becomes polarized to saturation, the slope of the discharge current change increases. Gradually decrease, physical factor of polarization saturation inside the electrode Gradually increasing and approaching a constant, the main control unit will limit the physical factor of the internal polarization saturation of the electrode. Stored in a global variable register, which is then used by the intermediate frequency carrier center frequency adaptive drift calculation model.

[0091] Furthermore, the apparent double-layer capacitance calculated by the main control unit based on a single intermediate frequency point exhibits nonlinear deviations after long-term system operation. The microstructure of the porous carbon electrode exhibits a distributed pore network characteristic. In AC impedance theory, the equivalent impedance of the porous electrode interface cannot be equivalent to an ideal capacitor, but rather manifests as a transmission line model with distributed parameters along the pore depth. The transient charge-discharge response speed of the system to this transmission line model is dominated by the time constant determined by the internal physical parameters of the pores, and the transient polarization time constant within the micropores... The following relationship must be satisfied:

[0092]

[0093] In the formula, The local mass transfer resistance inside the micropore is limited by the ion concentration gradient; The local double-layer capacitance inside the micropore varies with the space charge repulsion force; The adsorption run time is a variable;

[0094] The adsorption process encourages the continuous entry of cations and anions into the electrode micropores, altering the ion concentration gradient within the micropores and leading to increased local mass transfer resistance within the channels. As the double-layer structure increases, it gradually becomes saturated by space charge, leading to increased local double-layer capacitance. Exhibiting nonlinear decay, the nonlinear evolution of local physical parameters causes the overall transient polarization time constant of the electrode to change. Baseline shift occurred;

[0095] The shift in transient polarization time constant causes the phase response characteristics of the electrode's overall impedance to shift to the lower frequency band as the polarization depth increases. Under the condition of maintaining a fixed intermediate frequency detection frequency, the injected signal period and the actual charge and discharge time constant of the electrode are mismatched. The ratio of the capacitive reactance characteristic component to the impedance characteristic component presented by the electrode interface changes accordingly. The aforementioned change in ratio is manifested as the frequency dispersion of the microporous electrode.

[0096] If the intermediate frequency polarization sensing carrier component is maintained at a fixed initial center frequency, the detection frequency of the intermediate frequency polarization sensing carrier component will gradually deviate from the phase angle jump range where the double layer impedance is most sensitive to the frequency response due to the frequency dispersion phenomenon. The amplitude of the second response current and the phase angle difference demodulated by the main control unit using the fixed center frequency cannot truly reflect the transient polarization energy storage characteristics in the deep channel of the electrode.

[0097] The main control unit substitutes the current parameter containing dispersion deviation into the equivalent impedance calculation logic. The output apparent double-layer capacitance deviates from the actual physical capacitance value of the electrode. In the closed-loop control system without frequency intervention, an algebraic calculation error accumulates with adsorption time between the apparent double-layer capacitance and the actual polarization capacitance, resulting in decoupling distortion. The decoupling distortion causes the main control unit to obtain the distorted capacitance growth rate, which in turn causes the extreme value optimization controller to output a DC operating voltage command that deviates from the optimal optimization gradient.

[0098] To eliminate decoupling distortion errors caused by frequency dispersion, the system establishes a dynamic tracking closed loop between the intermediate frequency carrier center frequency and the electrode polarization depth. The main control unit uses the previously extracted physical factor of electrode internal polarization saturation as a feedback variable to perform frequency updates of the intermediate frequency polarization sensing carrier component, so as to dynamically track the baseline offset of the electrode transient polarization time constant. The main control unit uses the physical factor of electrode internal polarization saturation as the basis for... Real-time updates of the center frequency of the intermediate frequency polarization sensing carrier component The formula for calculating the frequency update is:

[0099]

[0100] In the formula, This is the initial intermediate frequency constant. For the set frequency drift sensitivity coefficient, the main control unit maintains the measurement linearity of the impedance calculation model in the nonlinear polarization process by dynamically updating the physical location of the frequency point, and outputs absolute polarization capacitance data that eliminates dispersion error for the extreme value optimization controller to call.

[0101] Furthermore, based on the acquired physical factors of the internal polarization saturation of the electrodes, the main control unit executes a carrier frequency drift control law. This law, through an exponential decay mapping relationship, ensures that the center frequency of the intermediate frequency polarization sensing carrier component is updated synchronously following the offset direction of the internal polarization time constant of the electrodes. The specific steps of the main control unit executing the carrier frequency drift control law include:

[0102] S410, the main control unit reads the physical factors of the electrode's internal polarization saturation stored in the internal global variable register. The main control unit executes the boundary determination command, when the physical factor of the polarization saturation inside the electrode... When the value is within the range of zero to one, a frequency update operation is triggered;

[0103] The S420 main control unit uses its internal floating-point arithmetic unit to perform exponential drift mapping calculations. The main control unit is based on the physical factors of the internal polarization saturation of the electrodes. Calculate the target intermediate frequency carrier center frequency in the next calibration period. The formula for calculating the center frequency of the target intermediate frequency carrier is:

[0104]

[0105] In the formula, For the first The target intermediate frequency carrier center frequency calculated from each calibration period; The initial intermediate frequency constant set for the system; The dimensionless frequency drift sensitivity coefficient set for the system;

[0106] S421, Main control unit executes frequency drift sensitivity coefficient Selected operation, frequency drift sensitivity coefficient The decay rate of the center frequency with polarization saturation is characterized. A lookup table mapping the initial equivalent fluid series resistance range to the frequency drift sensitivity coefficient is pre-configured in the non-volatile memory within the main control unit. The main control unit extracts the initial equivalent fluid series resistance calculated during the system initialization phase. The main control unit will convert the initial equivalent fluid series resistance The frequency drift sensitivity coefficient of the corresponding range is retrieved by comparing it with the preset resistance range in the mapping lookup table. Initial equivalent fluid series resistance The smaller the value, the higher the influent ion concentration, the faster the system polarization time constant shift rate, and the more sensitive the frequency drift coefficient retrieved by the main control unit from the mapping lookup table. The larger the value;

[0107] S430, the main control unit will calculate the target intermediate frequency carrier center frequency. Substituting into the aforementioned frequency control word calculation formula, a frequency control word that can be recognized by the underlying hardware is generated. The main control unit sends the frequency control word to the direct digital frequency synthesizer control register inside the signal generation unit through the serial peripheral interface bus. The main control unit sends an enable command to the direct digital frequency synthesizer to drive the hardware to output the intermediate frequency polarization sensing carrier component of the specified frequency.

[0108] S431, the main control unit is configured to operate the direct digital frequency synthesizer in phase continuous update mode. When the output carrier frequency is changed, the phase accumulator inside the direct digital frequency synthesizer keeps the current count value from returning to zero, and only changes the phase accumulation step size of a single clock cycle. The phase continuous update mode maintains the phase continuity of the composite excitation voltage at the frequency switching time, avoids high-frequency transient voltage change, and maintains the stability of the DC adsorption flow field. After the main control unit completes the physical offset update of the intermediate frequency carrier center frequency, it returns to perform synchronous orthogonal decoupling of the impedance parameters.

[0109] Furthermore, after completing the physical update of the carrier frequency, the main control unit performs capacitance reconstruction calculation based on the new signal injection state. The main control unit eliminates the measurement distortion caused by the micro-orifice time constant shift by synchronously replacing the drifted frequency parameters and current response parameters. The specific steps of the main control unit performing absolute polarization capacitance reconstruction include:

[0110] S440: The main control unit sets a delay wait instruction to wait for the underlying hardware circuitry to stabilize. After the signal generation unit outputs the updated intermediate frequency polarization sensing carrier component, both the system's physical impedance response network and the hardware low-pass filter of the dual-channel quadrature lock-in amplifier circuit have transient settling times. The main control unit uses an internal timer peripheral to set a hardware stabilization delay window. Hardware stable latency window The duration setting needs to be three to five times greater than the physical time constant of the low-pass filter in the dual-channel quadrature lock-in amplifier circuit to ensure complete attenuation of the step transient response. After the delay window ends, the main control unit reads the steady-state DC level component output by the dual-channel quadrature lock-in amplifier circuit at the new frequency point, calculates and extracts the updated second response current amplitude. ;

[0111] S450, the main control unit performs mathematical reconstruction operations on the absolute polarization capacitor, and the main control unit sets the target intermediate frequency carrier center frequency. and the updated second response current amplitude The main control unit reads the equivalent fluid series resistance acquired by the system in the corresponding time period from the temporary register of the internal arithmetic logic unit. The main control unit calls floating-point division and square root instructions to perform reconstruction calculations and obtain the absolute polarization capacitance after removing frequency dispersion errors. The formula for reconstructing the absolute polarization capacitance is:

[0112]

[0113] In the formula, Absolute polarization capacitors are used to eliminate dispersion distortion errors; The updated target intermediate frequency carrier center frequency; It is a fixed amplitude constant for the intermediate frequency polarization sensing carrier component; The amplitude of the second response current extracted at the new frequency point; This is the equivalent fluid series resistance;

[0114] In S460, the main control unit performs infinite impulse response digital low-pass filtering calculations on the absolutely polarized capacitors. The absolutely polarized capacitor sequence will serve as the reference input state variable for the subsequent extreme value optimization controller to extract the derivative of the objective function. Broadband random measurement noise mixed into the absolutely polarized capacitor sequence will be amplified in the numerical differentiation stage, causing the optimization control law to diverge. The main control unit converts the absolutely polarized capacitor sequence into discrete variables according to the discrete sampling period. And based on the first-order infinite impulse response discrete difference equation, smoothing and noise reduction are performed. The calculation formula of the filtering equation is as follows:

[0115]

[0116] In the formula, For the first The output value of the absolute polarization capacitor filter for each discrete sampling period; For the first The transient value of the absolute polarization capacitance obtained by reconstruction calculation of discrete sampling periods; This is the output balance of the absolute polarization capacitor filter from the previous discrete sampling period. The filter coefficient constants are fixed in the system, and The range of values ​​is strictly limited to Within the range;

[0117] The main control unit outputs the filtered absolute polarization capacitor value. The control law update service routine of the extreme value optimization controller directly reads the numerical variable from the specified static physical address through the pointer, which is written to the specified static physical address in the global shared memory area, and is used to construct the optimization objective function.

[0118] Furthermore, after obtaining the absolute polarization capacitance to eliminate frequency dispersion errors, the main control unit constructs an objective function to evaluate the transient energy adsorption efficiency of the system. The specific steps for the main control unit to construct the objective function include:

[0119] The S510 main control unit calculates the discrete rate of change of the absolute polarization capacitor. The internal extremum optimization controller of the main control unit is configured with an independent time base. It reads the filtered output value of the absolute polarization capacitor from the global shared memory area at a fixed control cycle. The main control unit calls the floating-point arithmetic unit to execute a first-order backward difference algorithm to calculate the derivative of the absolute polarization capacitor with respect to time. The formula for calculating the difference in the rate of change of the absolute polarization capacitor is:

[0120]

[0121] In the formula, For the first The rate of change of absolute polarization capacitance per control cycle; The absolute polarization capacitor filter output value is read for the current control cycle; This is the output value of the absolute polarization capacitor filter from the previous control cycle; The extreme value optimization control cycle constant set by the main control unit;

[0122] S520: The main control unit extracts the DC power characteristics of the main power supply circuit and reads the DC operating voltage command value output at the current moment. The main control unit smooths the total response current collected by the current sensor using a moving average filtering algorithm, filtering out the high-frequency probe carrier component, the intermediate frequency polarization sensing carrier component, and the high-frequency switching pulsation noise from the total response current, and extracting the pure DC response current component. The formula for discrete extraction and calculation of the pure DC response current component is as follows:

[0123]

[0124] In the formula, The moving average data window length constant is set for the system, and The value is configured to be an integer multiple of the current operating cycle of the intermediate frequency polarization sensing carrier component; The main control unit will use the discrete sampling sequence of the total response current of the main circuit acquired by the current sensor to input the DC operating voltage command value. With pure DC response current component Multiply to calculate the real-time DC power consumption of the system;

[0125] S530, the main control unit calculates the objective function value of the system's energy adsorption efficiency. The main control unit constructs a monotonic objective function value that reflects the adsorption energy efficiency to determine the gradient direction for extreme value optimization. The main control unit uses the product of the absolute polarization capacitance change rate and the square of the DC operating voltage as a characterization of the effective charge adsorption work power. The main control unit divides the characterization of the effective charge adsorption work power by the real-time DC power consumption to calculate the objective function value. The formula for calculating the objective function is:

[0126]

[0127] In the formula, For the first The objective function value for each control cycle; This is the DC operating voltage command value output in the current control cycle; The objective function is the pure DC response current component extracted during the current control cycle. It characterizes the product of the capacitance change rate and voltage per unit current, reflecting the ratio of effective adsorption power to consumed power. By eliminating static impedance interference caused by electrode aging and water quality fluctuations, the physical objective of extreme value optimization is guided to maximize the ion adsorption increment per unit energy consumption. The main control unit then calculates the objective function value. The data is stored in the observation state register of the optimization algorithm and provided to the subsequent gradient integration module for iterative updating of the working voltage.

[0128] Furthermore, based on the calculated objective function value, the main control unit executes the working voltage iteration command. The main control unit injects a low-frequency sinusoidal disturbance signal into the DC working voltage and extracts the response characteristics of the objective function to the disturbance signal. It then calculates the integral of the objective gradient to update the DC working voltage. The specific steps of the main control unit in performing the optimization disturbance injection and gradient integration include:

[0129] The S540's main control unit is equipped with a digital oscillator logic core. The main control unit writes an angular frequency configuration word to the digital oscillator logic core. Based on the microcontroller's system clock and extreme value optimization control cycle, the digital oscillator logic core generates a digital sinusoidal perturbation sequence. The calculation formula for the digital sinusoidal perturbation sequence is as follows:

[0130]

[0131] In the formula, For the first Digital sinusoidal disturbance sequence values ​​for each control cycle; The set optimization perturbation angular frequency constant; For controlling the periodic index; The extreme value optimization control period constant is set by the main control unit. To satisfy the time scale separation principle of extreme value optimization control, the disturbance angular frequency constant is optimized. The value is set to be strictly less than one-third of the physical response cutoff frequency of the electroadsorption module to ensure that the objective function can respond to dynamic changes in the operating voltage. The main control unit will use a digital sinusoidal perturbation sequence. Stored in a separate register of the internal optimization algorithm;

[0132] S550, the main control unit performs synchronous demodulation of the target gradient, and retrieves the target function value stored in the observation status register of the optimization algorithm. The main control unit calls the arithmetic logic unit to calculate the objective function value. With digital sinusoidal perturbation sequence Perform multiplication to obtain the eigenvalues ​​representing the transient gradient. The formula for calculating the transient gradient eigenvalue is:

[0133]

[0134] The main control unit demodulates the response component with the same frequency as the disturbance in the objective function into a DC characteristic quantity through multiplication. The algebraic sign of the DC characteristic quantity represents the gradient direction of the current working voltage command deviating from the extreme point.

[0135] In the S560, the main control unit performs discrete integration on the transient gradient eigenvalues. The main control unit acquires the transient gradient eigenvalues... Then, a time-accumulation calculation based on integral gain is performed. The integral operation smooths the high-frequency ripple components in the transient gradient eigenvalues ​​and extracts the stable operating voltage iteration. The calculation formula for discrete integration is:

[0136]

[0137] In the formula, For the first The working voltage iteration amount updated in each control cycle; This is the working voltage iteration amount of the previous control cycle; This refers to the optimization integral gain constant, which is subject to real-time control by the system's Faraday side reaction safety boundary constraint model. The absolute value of the voltage controls the approximation rate of the operating voltage along the gradient direction of the maximum value. The sign of the voltage determines the iterative physical direction of the working voltage;

[0138] S570, the main control unit generates and outputs the updated DC operating voltage command, and the main control unit updates the obtained operating voltage iteration. The system's fixed DC bias voltage reference value The main control unit outputs the first... and the second... and the third... DC operating voltage command for each control cycle The calculation formula is:

[0139]

[0140] In the formula, The amplitude constant of the disturbance signal set for the system;

[0141] The main control unit will send the DC operating voltage command. The signal is output to the signal generation unit through the digital-to-analog conversion circuit to update the physical DC driving force of the main circuit. The main control unit executes the optimization disturbance injection and gradient integration commands in a cycle with the extreme value optimization control cycle as the beat, driving the electro-adsorption system to spontaneously evolve towards the extreme point of maximum energy adsorption efficiency in a continuous operation state.

[0142] Furthermore, during the process of performing gradient integration for extreme value optimization, the main control unit simultaneously performs boundary constraint determination for Faraday side reactions. Since the extreme value optimization process may cause the DC voltage to exceed the electrode hydrolysis potential, triggering hydrogen evolution or oxygen evolution Faraday side reactions, the main control unit constructs physical safety constraint logic. The specific steps for the main control unit to execute safety boundary constraints include:

[0143] S580, the main control unit performs discrete difference calculation of the phase angle partial derivative, and reads the intermediate frequency phase angle difference discrete sequence output by the quadrature phase-locked demodulation module in the current control cycle. And retrieve the intermediate frequency phase angle difference of the previous control cycle temporarily stored in the internal register. The main control unit synchronously retrieves the DC operating voltage command for the current control cycle. DC operating voltage command from the previous control cycle The main control unit first calculates the absolute value of the voltage change between two adjacent control cycles. When the absolute value of the voltage change is less than the system's set voltage dead zone constant At that time, the main control unit forcibly assigns the phase angle partial derivative of the current control cycle. The value is set to zero to avoid division-by-zero anomalies in the microcontroller; when the absolute value of the voltage change is greater than or equal to the voltage dead zone constant. At this time, the main control unit calls the floating-point arithmetic unit to perform discrete differential calculations to obtain the partial derivative of the intermediate frequency phase angle difference with respect to the operating voltage. The formula for calculating partial derivatives is:

[0144]

[0145] In the formula, For the first Phase angle partial derivatives for each control cycle; The intermediate frequency phase angle difference extracted for the current control cycle; This represents the intermediate frequency phase angle difference from the previous control cycle; This is the DC operating voltage command output during the current control cycle; The DC operating voltage command for the previous control cycle;

[0146] S590, the main control unit performs a comparison and judgment between the phase angle partial derivative and the safety threshold. Within the safety potential window, the electroadsorption system is dominated by double-layer capacitive adsorption. The mid-frequency phase angle difference changes smoothly with fluctuations in the operating voltage. When the DC operating voltage approaches the Faraday side reaction potential, an electron transfer reaction occurs at the electrode interface, causing a sudden change in the system impedance characteristics from capacitive to resistive. This abrupt change in impedance characteristics leads to a drop in the mid-frequency phase angle difference, and the phase angle partial derivative... Numerically, it exhibits step pulse characteristics;

[0147] The main control unit extracts the preset side reaction phase angle step threshold constant from the internal non-volatile memory. Side reaction phase angle step threshold constant The empirical boundary value of the phase angle partial derivative when a weak gas evolution side reaction occurs in the system is characterized. The main control unit obtains the partial derivative using absolute value calculation instructions. The modulus value, and the modulus value is compared with the side reaction phase angle step threshold constant. Perform numerical comparison;

[0148] S600, the main control unit performs over-limit intervention on the DC operating voltage based on the judgment result, when the partial derivative The modulus is less than the side reaction phase angle step threshold constant. When the main control unit determines that the electrode interface is within the Faraday safety window, the main control unit maintains the gradient integral calculation result output of the extreme value optimization control law, and the DC working voltage continues to iterate along the maximum gradient direction of the energy adsorption efficiency objective function.

[0149] When the partial derivative The modulus is greater than or equal to the side reaction phase angle step threshold constant. When the main control unit determines that the electrode polarization potential has reached the boundary of the hydrolysis side reaction, the main control unit forcibly shields the integral update path of the extreme value optimization gradient and injects the system's preset negative voltage backoff step size constant into the arithmetic logic unit. The DC operating voltage command output by the main control unit decreases by a negative voltage backoff step constant, forcing the main power supply circuit voltage to retreat away from the oxygen or hydrogen evolution potential. Through real-time monitoring and forced backoff action, the main control unit cuts off the unidirectional divergence path of the extreme value optimization algorithm in the boundary region, maintaining the system operation in the lossless adsorption range.

Claims

1. A method for dynamic parameter optimization and calibration for an electroadsorption pilot-scale platform, characterized in that, The method, which relies on a dynamic parameter optimization and calibration system, including an execution component and a control component, comprises the following steps: S100, the main control unit controls the signal generation unit to inject a composite excitation voltage into the main power supply circuit of the electro-adsorption module. The composite excitation voltage is superimposed with a DC voltage component for driving ion adsorption, a high-frequency detection carrier component for penetrating the electrode interface, and a mid-frequency polarization sensing carrier component for sensing the interface polarization state with controlled frequency drift. S200, the main control unit performs hardware-level quadrature demodulation on the total response current of the main circuit collected by the current sensor through a dual-channel quadrature lock-in amplifier circuit, separates and extracts the response current characteristics corresponding to the high-frequency detection carrier component and the intermediate frequency polarization sensing carrier component, and calculates the equivalent fluid series resistance based on the extracted current characteristics, and further removes the fluid conductivity interference to calculate the apparent double-layer capacitance at the intermediate frequency detection frequency; S300, without interrupting the influent flow process, the main control unit periodically triggers microsecond-level transient depolarization action according to the set time window, and forcibly short-circuits the two plates of the electroadsorption module by controlling the fast-response solid-state switch, collects the reverse discharge current at the moment of microsecond-level short circuit and extracts the slope of the discharge current change, and calculates the physical factor of the electrode internal polarization saturation in the current calibration period based on the slope of the discharge current change. S400, the main control unit extracts the physical factor of polarization saturation inside the electrode, updates the center frequency of the intermediate frequency polarization sensing carrier component in the next cycle through the exponential decay mapping relationship, and substitutes the updated frequency parameters back into the impedance calculation model for dynamic compensation to reduce frequency dispersion error and obtain the corrected polarization capacitance. S500, the main control unit constructs the objective function of system energy adsorption efficiency based on the change rate of the modified polarization capacitance and the DC power characteristics; the main control unit applies a low-frequency optimization disturbance detection signal to the DC operating voltage and iteratively updates the DC operating voltage command; during the optimization process, the main control unit synchronously monitors the step characteristics of the intermediate frequency phase angle difference and synchronously executes the Faraday side reaction safety boundary constraint judgment; when the polarization potential approaches the side reaction boundary, it forcibly intervenes in the voltage optimization direction to maintain the safe operation of nonlinear extreme value optimization.

2. The method for dynamic parameter optimization and calibration of an electroadsorption pilot-scale platform according to claim 1, characterized in that, In step S100, the frequency range of the high-frequency detection carrier component is configured to be from 10 kHz to 100 kHz; The initial frequency range of the intermediate frequency polarization sensing carrier component is configured to be from 10 kHz to 1 kHz; The excitation amplitudes of both the high-frequency detection carrier component and the mid-frequency polarization sensing carrier component are configured to be small-amplitude AC levels ranging from 5mV to 50mV.

3. The method for dynamic parameter optimization and calibration of an electroadsorption pilot-scale platform according to claim 1, characterized in that, In step S200, the specific process by which the main control unit executes the solution logic is as follows: Based on the amplitude of the first response current extracted by the phase-locked loop With a fixed high-frequency detection carrier amplitude According to the formula Calculate the equivalent fluid series resistance. ; Based on the amplitude of the second response current extracted by the phase-locked loop With intermediate frequency polarization sensing carrier amplitude According to the formula: ， Calculate the apparent double-layer capacitance. ;in, The current intermediate frequency carrier center frequency.

4. The method for dynamic parameter optimization and calibration of an electroadsorption pilot-scale platform according to claim 3, characterized in that, Before substituting the values ​​into the formula for calculation, the main control unit performs a smoothing filter calculation with a fixed data window length on the continuously read first response current amplitude sequence and second response current amplitude sequence to filter out low-frequency mechanical pulsation noise generated by fluid pumping and quantization truncation error accompanying the analog-to-digital conversion process.

5. The method for dynamic parameter optimization and calibration of an electroadsorption pilot-scale platform according to claim 1, characterized in that, In step S300, the specific steps for the main control unit to perform transient depolarization timing control include: Turn off the main circuit series switch and insert dead time. Then, the bypass discharge switch is turned on and a short-circuit window of microseconds is maintained. ; Among them, the microsecond-level short-circuit window Boundary conditions must be met , The time constant for macroscopic desorption of the electrode; In the microsecond-level short-circuit window Inside, the main control unit synchronously triggers the high-speed analog-to-digital conversion circuit to perform equally spaced discrete sampling of the reverse discharge current.

6. The method for dynamic parameter optimization and calibration of an electroadsorption pilot-scale platform according to claim 5, characterized in that, The specific logic for the main control unit to calculate the physical factor of the internal polarization saturation of the electrode is as follows: Calculate the slope of discharge current change by extracting the first and last data points of the discrete sampled data block. ; Call the slope of the discharge current change Discharge slope constant of the cured baseline clean state According to the formula Calculate the physical factor of internal polarization saturation of the electrode during the current calibration period. ; Furthermore, the calculated physical factors of the internal polarization saturation of the electrode Additional upper and lower limit constraints are determined when Greater than Forced assignment ; when Force assignment when less than or equal to zero. .

7. The method for dynamic parameter optimization and calibration of an electroadsorption pilot-scale platform according to claim 1, characterized in that, In step S400, the main control unit executes the carrier frequency drift control law in the following manner: the initial equivalent fluid series resistance obtained during the system initialization phase is compared with the preset resistance range in the mapping lookup table, the corresponding frequency drift sensitivity coefficient is selected, and based on the frequency drift sensitivity coefficient and the physical factor of polarization saturation inside the electrode, the target intermediate frequency carrier center frequency in the next calibration period is obtained using the exponential drift mapping calculation model, so as to drive the underlying hardware to output the intermediate frequency polarization sensing carrier component of the specified frequency.

8. The method for dynamic parameter optimization and calibration of an electroadsorption pilot-scale platform according to claim 1, characterized in that, In step S500, the objective function for the energy adsorption efficiency of the constructed system specifically includes: S510, the discrete rate of change is obtained by calculating the derivative of the corrected polarization capacitance with respect to time using a first-order backward difference algorithm; The S520 extracts the pure DC response current component through a moving average filtering algorithm and multiplies it by the DC operating voltage command value to calculate the real-time DC power consumption of the system. S530, the product of the discrete rate of change and the square of the DC operating voltage command value is used as a characterization of the effective charge adsorption power, and the characterization is divided by the real-time DC power consumption to calculate and obtain the objective function value.

9. The method for dynamic parameter optimization and calibration of an electroadsorption pilot-scale platform according to claim 8, characterized in that, The iterative update of the DC operating voltage command specifically includes: The objective function value is multiplied by the digital sinusoidal perturbation sequence generated by the digital oscillator to obtain the eigenvalues ​​characterizing the transient gradient. Perform discrete integration operation based on the optimization integral gain constant on the feature value to obtain the working voltage iteration, and then perform algebraic superposition of the working voltage iteration, DC bias voltage reference value and the digital sinusoidal perturbation sequence to output the updated DC working voltage command; The determination of the safety boundary constraints for the simultaneous execution of the Faraday side reaction specifically includes: The main control unit calculates the phase angle partial derivative of the intermediate frequency phase angle difference with respect to the working voltage, and compares its magnitude with the preset side reaction phase angle step threshold constant. When the magnitude of the partial derivative of the phase angle is greater than or equal to the step threshold constant of the phase angle of the side reaction, it is determined that the boundary of the hydrolysis side reaction has been reached. The main control unit forcibly shields the integral update path of the extreme value optimization gradient and injects a preset negative voltage backoff step constant, forcing the main power supply circuit voltage to back off in a direction away from the oxygen evolution or hydrogen evolution potential.

10. A dynamic parameter optimization and calibration system for an electroadsorption pilot-scale platform, comprising: Execution components and control components; The actuation components include an electro-adsorption module, a current sensor and a voltage sensor mounted on the main circuit, and a fast-response solid-state switch connected in series in the main circuit; The control components include a main control unit, a signal generation unit, a dual-channel quadrature lock-in amplifier circuit, and a high-speed analog-to-digital converter circuit; The control output port of the main control unit is connected to the gate drive circuit of the signal generation unit and the fast response solid-state switch, respectively. The main control unit is configured to inject a composite excitation voltage into the main power supply circuit of the electroadsorption module by the control signal generation unit. The composite excitation voltage is superimposed with a DC voltage component for driving ion adsorption, a high-frequency detection carrier component for penetrating the electrode interface, and a mid-frequency polarization sensing carrier component for sensing the interface polarization state with controlled frequency drift. The main control unit is configured to perform hardware-level quadrature demodulation of the total response current of the main circuit acquired by the current sensor through a dual-channel quadrature lock-in amplifier circuit, separate and extract the response current characteristics corresponding to the high-frequency detection carrier component and the intermediate frequency polarization sensing carrier component, calculate the equivalent fluid series resistance, and remove fluid conductivity interference to calculate the apparent double-layer capacitance at the intermediate frequency detection frequency. The main control unit is configured to periodically trigger microsecond-level transient depolarization actions according to a set time window without interrupting the influent fluid process. It controls the fast-response solid-state switch to force short-circuit the two plates of the electroadsorption module, collects the reverse discharge current at the moment of microsecond-level short circuit and extracts the slope of the discharge current change, and calculates the physical factor of the polarization saturation inside the electrode in the current calibration period based on the slope of the discharge current change. The main control unit is configured to extract the physical factor of polarization saturation inside the electrode, update the center frequency of the intermediate frequency polarization sensing carrier component in the next cycle through the exponential decay mapping relationship, and substitute the updated frequency parameters back into the impedance calculation model for dynamic compensation to reduce frequency dispersion error and obtain the corrected polarization capacitance. The main control unit is configured to construct the objective function of the system energy adsorption efficiency based on the rate of change of the modified polarization capacitance and the DC power characteristics; apply a low-frequency optimization disturbance detection signal to the DC operating voltage and iteratively update the DC operating voltage command; during the optimization process, the main control unit is configured to synchronously monitor the step characteristics of the intermediate frequency phase angle difference, synchronously execute the Faraday side reaction safety boundary constraint judgment, and forcibly intervene in the voltage optimization direction when the polarization potential approaches the side reaction boundary to maintain the safe operation of nonlinear extreme value optimization.

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