Automatic replenishment control method for electroplating solution additives based on conductivity monitoring data

Abstract

The present application relates to the technical field of electrochemical processing, and in particular to an electroplating solution additive automatic replenishment control method based on conductivity monitoring data. The method comprises: obtaining the temperature and original conductivity of the electroplating solution and the concentration of carbonate ions, determining the activation energy coefficient based on the change trend of the original conductivity and the temperature, performing dynamic thermodynamic decoupling processing on the original conductivity to generate the net conductivity of the electroplating solution; calculating the transport inertia factor of the electroplating solution according to the cumulative change amount of the net conductivity in the historical time period and the total amount of additives in the historical time period, combined with the concentration of carbonate ions, determining the retardation risk index based on the evolution trend of the transport inertia factor, reconstructing the PID control algorithm to obtain the replenishment amount of the additives, and performing automatic replenishment control based on the replenishment amount. The method improves the accuracy of automatic replenishment control by evaluating the deterioration state of the bath solution components and adaptive integral saturation inhibition.

Description

Technical Field

[0001] This application relates to the field of electrochemical processing technology, specifically to an automatic replenishment control method for electroplating solution additives based on conductivity monitoring data. Background Technology

[0002] Gas-insulated metal-enclosed switchgear (GIS) is a core piece of equipment in ultra-high voltage power transmission and transformation systems. The surface treatment quality of its aluminum alloy casing directly affects the equipment's insulation performance and service life. In the electroplating process of the aluminum alloy casing, the concentration of brighteners, leveling agents, and other additives in the electroplating solution is a key factor determining the microcrystalline density and smoothness of the plating layer. Therefore, in actual production, an automatic dosing system is typically configured, using online conductivity sensors to monitor the state of the plating bath and replenish additives accordingly to maintain the dynamic balance of the electroplating solution components.

[0003] Currently, PID (Proportional-Integral-Derivative) control algorithms are widely used in industrial settings to adjust the amount of additives supplied based on conductivity deviations. The PID algorithm is a classic feedback control strategy, typically consisting of a signal acquisition unit, a deviation calculation unit, and a control execution unit. This algorithm calculates the control output based on a linear combination of the proportional, integral, and derivative of the error, and is widely used in automotive manufacturing, chemical production, and other scenarios, reducing manual intervention and improving production efficiency.

[0004] However, in large-scale continuous electroplating scenarios for GIS aluminum alloy shells, existing PID control methods face serious physical adaptability problems. As the electroplating cycle lengthens, aluminum ion impurities and carbonate byproducts inevitably accumulate in the plating bath, leading to a gradual increase in viscosity and ion migration resistance, resulting in component degradation. This change in physicochemical properties causes a mass transfer delay in the conductivity sensor readings after additive injection. Under these degraded conditions, because the change in conductivity lags behind the dosing action, the standard PID algorithm misjudges it as ineffective replenishment, leading to integral saturation through continuous accumulation of the integral term and issuing excessive dosing commands. By the time the additive finally diffuses uniformly and causes a sudden change in conductivity, the bath concentration has already exceeded the limit, resulting in pinholes or scorching defects on the aluminum alloy shell surface. The PID algorithm cannot identify this time-varying physical parameter of bath component degradation and executes fixed-gain control, which is the main cause of plating bath instability.

[0005] Therefore, there is an urgent need for a control method that can accurately identify the deterioration state of the bath solution components and adaptively suppress excessive replenishment under high hysteresis conditions, in order to solve the problems of integral saturation and unstable coating quality caused by response hysteresis in the existing technology. Summary of the Invention

[0006] To address the issues of integral saturation and over-replenishment caused by response lag in PID algorithms during plating bath aging scenarios, this invention proposes an automatic replenishment control method for electroplating bath additives based on conductivity monitoring data, comprising: The temperature, initial conductivity, and carbonate concentration of the electroplating solution are obtained. The activation energy coefficient of the electroplating solution is determined based on the changing trends of the initial conductivity and temperature to reflect the sensitivity of ion migration in the electroplating solution to temperature changes. The initial conductivity is subjected to dynamic thermodynamic decoupling to eliminate the influence of temperature fluctuations on conductivity, thereby generating the net conductivity of the electroplating solution. Based on the cumulative change in net conductivity over a preset historical period and the total amount of additives during that historical period, combined with the carbonate concentration, the transport inertia factor of the electroplating solution is calculated to reflect the degree of lag in the electroplating solution's response to additive replenishment. The electroplating solution is controlled by PID control algorithm to replenish additives. Based on the transport inertia factor, the resistance risk index of the electroplating solution is calculated by combining the evolution trend of the transport inertia factor over time. The integral term of the PID control algorithm is reconstructed in real time using the aforementioned resistance risk index, and the amount of additive replenishment is obtained based on the reconstructed PID control algorithm. The electroplating solution is then automatically replenished based on the replenishment amount.

[0007] This technical solution first eliminates temperature interference at the data source through dynamic thermodynamic decoupling, ensuring the purity of the control signal. By calculating the transmission inertia factor, it quantifies the degree of component degradation and response hysteresis characteristics of the bath solution from a physical perspective. Then, by utilizing integral confidence, it intelligently suppresses and attenuates the blind accumulation of integral terms in the PID algorithm when mass transfer in the bath solution is hindered. This mechanism avoids integral saturation and system overshoot caused by hysteresis, ensuring the accuracy of additive replenishment.

[0008] Preferably, the activation energy coefficient of the electroplating solution is determined based on the following method: At each chemical addition point in the electroplating process, the natural logarithm of the original conductivity and the reciprocal of the temperature at all historical chemical addition points within a preset historical time period are obtained. The natural logarithm and reciprocal of the temperature at all historical chemical addition points are then fitted using the least squares method to obtain the slope of the fitted line. Based on the slope, the activation energy coefficient at the chemical addition point is determined using the Arrhenius law.

[0009] This technical solution achieves thermodynamic decoupling by introducing a dynamic Arrhenius equation based on real-time multidimensional data regression of the electroplating solution. By calculating the activation energy coefficient in real time, the algorithm can adapt to the influence of component changes in the electroplating solution on the thermosensitive properties, thereby achieving high-precision temperature compensation for the electroplating solution throughout its entire life cycle.

[0010] Preferably, the net conductivity of the electroplating solution is determined based on the following method:

[0011] in, This is the time to wait for the medication to be added. The net conductivity of the electroplating solution at the moment before chemical addition is applied. The original conductivity of the electroplating solution at the moment before chemical addition. It is a natural exponential function. The activation energy coefficient of the electroplating solution at the moment of chemical addition is given. Let be the ideal gas constant. The temperature of the electroplating solution at the moment the chemical is to be added. This is the preset standard temperature.

[0012] This technical solution introduces a real-time calculated activation energy coefficient to construct a dynamic thermodynamic decoupling mechanism that conforms to the Arrhenius law of ion migration. During the electroplating process of GIS aluminum alloy shells, the temperature of the bath fluctuates due to the Joule heating effect, and the aging of the bath causes its thermosensitive properties (i.e., activation energy) to drift. Based on the current microscopic ion migration energy barrier, the physical interference of temperature change on the original conductivity is offset, so that the calculated net conductivity can maintain a linear response to the solute concentration even under drastic temperature fluctuations, thereby eliminating thermodynamic noise and providing an accurate chemical composition feedback signal for subsequent control.

[0013] Preferably, the transmission inertia factor satisfies the following relationship:

[0014] in, For electroplating solution in The inertia factor of time transmission It is the hyperbolic tangent function. This is a preset dimensional balance coefficient used to convert the calculation terms within parentheses into dimensionless values. The length of the historical period For integration variables, for The dosage at specific times, for The rate of change of net conductivity at time t. This is a preset measure to prevent positive numbers with a denominator of 0. For electroplating solution in The relative growth rate of carbonate concentration at time t. The weighting coefficient is the effect of carbonate concentration on the viscosity of the electroplating solution, which was determined in advance through experiments.

[0015] This technical solution quantifies the mass transfer hindrance state of the electroplating solution from a physical and dynamic perspective. It constructs a dynamic ratio of historical dosing excitation to net conductivity response and introduces the relative growth rate of carbonate concentration as a correction term. In actual operation, as carbonate accumulates, the viscosity of the plating solution increases, hindering the Brownian motion and convection diffusion of the additives, leading to sensor response lag. By calculating the dynamic gain ratio and combining it with viscosity correction, this macroscopic response delay is mapped to a normalized inertia factor. When the transmission inertia factor approaches 1, it accurately identifies the system as being in a high-viscosity, high-damping physical blockage zone, thus providing the control algorithm with a basis for determining whether ineffective dosing is due to sufficient concentration or impeded diffusion.

[0016] Preferably, the carbonate concentration at the time of drug addition is obtained by an online ion concentration analyzer or determined by receiving periodic test data input through a human-computer interaction interface.

[0017] Preferably, the relative growth rate of carbonate concentration in the electroplating solution at the time of chemical addition is obtained by first obtaining the carbonate concentration of the electroplating solution determined at the initial tank preparation, calculating the relative increment of carbonate concentration at the time of chemical addition and carbonate concentration determined at the initial tank preparation, and taking the ratio of the relative increment to carbonate concentration determined at the initial tank preparation as the relative growth rate of carbonate concentration in the electroplating solution at the time of chemical addition.

[0018] Preferably, the resistance risk index of the electroplating solution is determined as follows: the transport inertia factor is obtained for each historical dosing moment within a historical time period of the time to be added, and a linear regression is performed to obtain a fitting slope. To reflect the evolution gradient of the transmission inertia factor; calculate the stagnation risk index:

[0019] in, This represents the resistance risk index of the electroplating solution at the moment of chemical addition. To provide an inert factor for the electroplating solution at the moment of chemical addition. For symbolic functions, It is a nonlinear normalization function. It is the absolute value symbol.

[0020] This technical solution effectively distinguishes between steady-state high viscosity and transient stagnation deterioration by introducing a product model of static reference and dynamic modulation. It uses a sign function to accurately determine the direction of the evolution gradient, automatically degenerating to a static reference in steady state to ensure control continuity. In deterioration, it uses the product effect to amplify the risk signal, enabling keen detection of acute faults. In the recovery period, it uses the negative gradient to decay the risk, enabling advanced prediction of system improvement. This mechanism allows the PID control algorithm to no longer blindly rely on current values, but instead incorporates historical trend analysis, ensuring a high degree of consistency between risk assessment and the actual physical mass transfer process.

[0021] Preferably, the real-time reconstruction of the integral term of the PID control algorithm using the stall risk index includes: mapping the stall risk index to a value in the range of 0 to 1 using a nonlinear decay function as an integral confidence level; and using the integral confidence level to perform a weighted operation on the integral term of the PID control algorithm to obtain the reconstructed PID control algorithm.

[0022] Preferably, the amount of additive to be supplied is determined based on the following relationship using the real-time reconstructed PID control algorithm: ;in, This refers to the amount of additives to be replenished in the electroplating solution at the time of chemical addition. These are the proportional gain constant, integral gain constant, and derivative gain constant of the pre-set PID control algorithm. for The deviation between the net conductivity at a given time and the preset standard conductivity. for The integral confidence level at time step. This is the derivative of the deviation with respect to time. It involves integrating over time.

[0023] This technical solution reconstructs the integral kernel of the traditional PID control algorithm at the principle level by utilizing the calculated integral confidence level. Unlike the traditional algorithm that blindly accumulates errors, this solution embeds dynamic weights into the integral term, giving it the ability to sense the system state. When the plating solution is detected to be in the causal hysteresis zone of component deterioration, the algorithm automatically freezes the integral action to prevent integral saturation caused by sensor reading delays. This control strategy ensures that the final output replenishment control quantity can match the actual ion diffusion rate of the electroplating solution, avoiding pinholes and scorching defects in the plating layer caused by excessive chemical addition, and improving the robustness of the process.

[0024] Preferably, the automatic replenishment control of the electroplating solution based on the replenishment amount includes: at the time when the chemical is to be added, driving the additive replenishment device to release the additive into the electroplating solution according to the replenishment amount.

[0025] The present invention has the following effects: This invention overcomes the limitations of traditional PID algorithms in time-varying, lag-dependent systems. By dynamically calculating the ion migration activation energy, it achieves high-precision temperature decoupling. By introducing a transport inertia factor that includes the influence of carbonate ions, it endows the control system with the ability to identify the deterioration state of the plating solution components and their micro-dynamic mechanisms. By reconstructing the integral confidence degree based on the lag risk index, it achieves adaptive defense against integral saturation. This dual mechanism of dynamic physical identification and environmental adaptive suppression solves the problems of chemical dosing lag and over-feeding caused by the deterioration of the plating solution components. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a comparison chart showing the additive effects of the reconstructed PID control algorithm of this invention and the existing PID control algorithm. Detailed Implementation

[0027] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0028] The present invention provides an automatic replenishment control method for electroplating bath additives based on conductivity monitoring data, such as... Figure 1 As shown, it includes: S1: Obtain the temperature and original conductivity of the electroplating solution, calculate the activation energy coefficient, perform dynamic thermodynamic decoupling treatment on the original conductivity, and generate the net conductivity of the electroplating solution.

[0029] At the moment of chemical addition in the electroplating process, considering that the conductivity of the electroplating solution is extremely sensitive to temperature changes, and that this thermosensitivity is not constant, as the electroplating solution is used for a long time, the accumulation of impurity ions and the decomposition of organic additives will change the microstructure of the solution, thereby changing its ion migration activation energy, this step aims to perform adaptive thermodynamic decoupling pretreatment. Using the temperature fluctuation data that naturally occurs during the production process, the activation energy characteristics at the current moment are analyzed in real time by regression analysis. The dynamic Arrhenius equation is used to remove the influence of temperature and extract high-fidelity net conductivity, providing a pure concentration feedback signal for subsequent control.

[0030] First, the activation energy coefficient is obtained dynamically: The time when medication is to be administered is recorded as follows: At any given moment, the temperature, initial conductivity, and carbonate concentration of the electroplating solution are acquired. The temperature is obtained in real-time using a temperature sensor, such as a PT100 resistance temperature detector (RTD) or a type K thermocouple, within the electroplating bath's circulation pipeline or the bath itself. The carbonate concentration is obtained using an online ion concentration analyzer, and the initial conductivity is obtained in real-time using an immersion or flow-through online conductivity sensor, such as an electromagnetic induction conductivity probe.

[0031] A historical time period moving forward along the time axis is constructed as the historical time period for when the additive is to be added. To ensure the validity of the statistics and to adapt to the slow time-varying characteristics of the tank solution changes, this historical time period includes 10 historical addition times, meaning that the additive has been added 10 times within this historical time period. For each historical addition time, a data set is constructed. ,in, The original conductivity at that historical moment of drug administration. The temperature at that historical moment of administering the medication. The function is logarithmic, which will result in a series of data combinations. We then use the least squares method to perform linear regression on these data combinations to construct a linear equation: ,in, The slope The intercept term is obtained through regression calculation. and According to Arrhenius's law, the following relation is satisfied: ,in, The activation energy coefficient of the electroplating solution at the moment of chemical addition is given. The ideal gas constant Therefore, the activation energy coefficient at the time of drug administration The physical significance of this mechanism lies in its ability to capture the sensitivity of the electroplating solution's conductivity to temperature changes. When the electroplating solution is relatively new and contains few impurities, The temperature is relatively low, with moderate temperature compensation. However, when the bath solution ages or its viscosity increases, ion migration is hindered, typically resulting in greater sensitivity to temperature. Increase.

[0032] Next, an activation energy coefficient is introduced to perform dynamic thermodynamic decoupling on the original conductivity, so as to eliminate the influence of temperature fluctuations on conductivity and generate the net conductivity of the electroplating solution.

[0033] Specifically, the net conductivity of the electroplating solution at the moment of chemical addition satisfies the following relationship:

[0034] in, For the electroplating solution at the moment when the chemical is to be added ( Net conductivity at time (time) The original conductivity of the electroplating solution at the moment before chemical addition. It is a natural exponential function. The activation energy coefficient of the electroplating solution at the moment of chemical addition is given. Let be the ideal gas constant. The temperature of the electroplating solution at the moment the chemical is to be added. The preset standard temperature is usually set to 25 degrees Celsius.

[0035] In this relation, This represents the difference between the reciprocal of the real-time temperature and the reciprocal of the reference temperature, reflecting the degree of thermodynamic deviation of the current temperature relative to the standard temperature. This represents the ratio of the activation energy coefficient to the gas constant, and is used to reflect the sensitivity of the electroplating solution's conductivity to temperature changes. This represents a dimensionless temperature compensation index, used to reflect the magnitude of the theoretical deviation in conductivity caused by temperature deviation under the current activation energy characteristics. The overall structure constitutes a temperature compensation coefficient, used to reflect the factor by which the original conductivity needs to be corrected, regardless of... Regardless of how it changes, the temperature compensation coefficient always follows the laws of thermodynamics: when... hour, If the value is negative, the exponent is less than 0, the temperature compensation coefficient is less than 1, and the temperature compensation coefficient affects the original conductivity. This reduces the surface area, offsetting the increased ion mobility caused by high temperatures and eliminating any artificially high conductivity. hour, A positive number, an exponent greater than 0, a temperature compensation coefficient greater than 1, and a temperature compensation coefficient affecting the original conductivity. It has an amplifying effect, compensates for the decrease in ion mobility caused by low temperature, and eliminates the artificially low component in the original conductivity.

[0036] In the formula, Used to reflect the raw conductivity value directly measured by the sensor at the current temperature, and Multiplication means multiplying the original measured value by a dynamically calculated compensation coefficient. Through physical-level correction, interference from temperature fluctuations is eliminated, restoring the true conductivity determined solely by solute concentration. This dynamic closed-loop process ensures... It always accurately reflects the solute concentration and is not affected by the drift of thermal properties caused by the aging of the bath solution.

[0037] As the electroplating process proceeds, the Joule heating effect causes the temperature of the electroplating solution to gradually rise. At a physical level, the increased temperature imparts higher kinetic energy to the ions, causing the original conductivity read by the sensor to naturally increase even when the additive concentration remains unchanged. Without this dynamic decoupling step, the control system might mistakenly assume that the additive concentration is already high enough, resulting in an artificially high conductivity, and thus incorrectly stop replenishing the solution. The net conductivity calculated in real time reflects the thermosensitive characteristics of the electroplating solution at the moment of chemical addition. When the electroplating solution ages, leading to increased viscosity and enhanced thermosensitivity, and a larger net conductivity, this relationship automatically applies a larger correction coefficient to eliminate the false increment caused by temperature. The final net conductivity accurately reflects the conductivity fluctuations caused by changes in chemical composition under temperature fluctuations, providing an accurate basis for subsequent precise control.

[0038] S2: Calculate the transport inertia factor of the electroplating solution based on the cumulative change of the net conductivity over a preset historical period and the total amount of additives during the historical period, combined with the carbonate concentration.

[0039] After obtaining the net conductivity, in order to solve the problem that the PID algorithm cannot identify the response lag caused by the deterioration of the bath composition, it is necessary to quantify the current mass transfer resistance. This step aims to establish a dynamic state identification mechanism that integrates multi-dimensional physical characteristics. By comprehensively analyzing the dynamic ratio of the dosage and conductivity change, and introducing carbonate concentration as a correction factor, the transport inertia factor is accurately calculated. The transport inertia factor not only reflects the macroscopic response lag, but also reveals the microscopic electrochemical blockage, providing a reliable physical basis for the integral reconstruction of the PID control algorithm.

[0040] Specifically, at the time when the additive is to be added, the total amount of additives already replenished at all historical addition times within the historical time period is obtained, and the rate of change of net conductivity at each historical addition time is calculated. That is, the net conductivity at the current historical addition time and the net conductivity at the previous historical addition time are differentially calculated, and the difference between the net conductivity at the current historical addition time and the net conductivity at the previous historical addition time is calculated. The difference is then divided by the time interval between the two historical addition times to obtain the rate of change of net conductivity, which reflects the transient response speed of the electroplating solution to the additive.

[0041] Next, the transport inertia factor of the electroplating solution at the moment of chemical addition is calculated:

[0042] in, The transport inertia factor of the electroplating solution at the moment of chemical addition, with a value range of [value missing]. , This is the hyperbolic tangent function, used to map the calculation result to the interval between 0 and 1. This is a preset dimensional balance coefficient with a scalar value of 1. Its unit is the reciprocal of the unit of the fractional calculation term within the parentheses. Its physical meaning is to cancel out the dimensions of the fraction, thus balancing the dimensionality of the fraction. The input to the function becomes a dimensionless value. The length of the historical time period for when medication is to be administered, i.e., how many historical medication administration times are included. For integration variables, for The dosage at specific times, for The rate of change of net conductivity at any given time reflects the dynamic response sensitivity of the electroplating solution to the replenishment of additives. A high rate of change indicates that the additive has been rapidly diffused into the entire plating solution after being added, which usually means that the plating solution is in good condition with low viscosity, good fluidity, and sufficient agitation. A low rate of change indicates that the additive has been added but diffuses slowly, and the sensor cannot read the change in value for a long time. This reflects that the plating solution may have component deterioration, increased viscosity, more carbonate accumulation, and greater mass transfer resistance. To prevent positive numbers with a denominator of 0 by default, it is usually set to To prevent the denominator from being zero due to no change in conductivity, This represents the relative growth rate of carbonate concentration in the electroplating solution at the time of chemical addition. The weighting coefficient for the effect of carbonate concentration on the viscosity of the electroplating solution, which was determined in advance through experiments, is calibrated in advance through experiments to reflect the degree of influence of viscosity on diffusion. The value is 0.5. This term physically corrects the pure physical diffusion hysteresis caused by the increase in viscosity.

[0043] In this formula, the method for obtaining the relative growth rate of carbonate concentration in the electroplating solution at the moment of chemical addition is as follows: first, obtain the carbonate concentration of the electroplating solution determined at the initial tank preparation stage; then, calculate the relative increment of the carbonate concentration at the moment of chemical addition compared to the carbonate concentration determined at the initial tank preparation stage; finally, use the ratio of this relative increment to the carbonate concentration determined at the initial tank preparation stage as the relative growth rate of carbonate concentration in the electroplating solution at the moment of chemical addition. Specifically, ,in, It is the carbonate concentration in the electroplating solution at the moment the chemical is to be added. It is the carbonate concentration at the initial tank preparation stage.

[0044] In this relation, Historical time period for when medication is to be administered The total amount of additives in the container, for Historical time period The cumulative change in net conductivity within the system, and the ratio of the total amount of additives to the cumulative change in net conductivity, construct a dynamic gain ratio. The numerator is the recent input amount, reflecting the system's excitation, and the denominator is the resulting change in net conductivity, reflecting the system's response. The larger the ratio, the more it indicates that "a lot of drug was administered but the conductivity did not respond," characterizing the system's high damping or high hysteresis characteristics. Using the integral form is more noise-resistant than using the instantaneous value and can smooth out short-term fluctuations.

[0045] In this relation, Part of the equation is a correction term based on changes in carbonate concentration. Carbonate accumulation is a typical characteristic of aluminum alloy electroplating aging, leading to increased viscosity and hindering ion diffusion. Multiplying the correction term by the dynamic gain ratio constructs a composite hysteresis index that integrates macroscopic input-output efficiency and microscopic viscosity resistance. A larger dynamic gain ratio means more reagent is added but less reaction occurs, and a larger relative increase in carbonate concentration indicates a higher viscosity of the electroplating solution. This signifies that the electroplating solution is in a state of mass transfer blockage and response hysteresis. The larger the value, the more sensitive the electroplating solution is to its response; conversely, the smaller the values, the faster the additives can produce an effect. The smaller the value, the better. The tanh function is used to normalize and map physical calculation values, which may have a large range, to the interval [0,1). Considering the smooth saturation characteristics of the function, it can prevent extreme outliers from causing factor overflow, while preserving the trend of change.

[0046] When the electroplating solution is in good condition, the response is sensitive (large denominator), the carbonate concentration is low, and the calculated composite hysteresis index is small. After mapping, tanh approaches 0, and the system determines that the electroplating solution is in a low-inertia state, meaning "input equals output," and the electroplating solution is in a smooth mass transfer state. At this time, the diffusion channels of additives are unobstructed, the sensor can provide real-time feedback on concentration changes, and the control system can operate according to conventional logic. When the plating solution deteriorates, the conductivity does not change after adding chemicals, and the accumulation of impurities further amplifies this value. tanh quickly saturates and approaches 1, indicating that the electroplating solution is in a high-inertia state, meaning "high input but low output." The system is in a state of blocked mass transfer, additive diffusion is lagy, and the control system needs to be wary of the risk of integral saturation.

[0047] The transport inertia factor of the electroplating solution at the moment of chemical addition no longer depends on a preset static reference, but is based entirely on the current dynamic input-output relationship and electrochemical state of the system, thus realizing real-time and accurate quantification of hysteresis characteristics.

[0048] This step, in its physical essence, is a kinetic diagnosis of the electroplating bath solution. During bath aging, carbonate ions accumulate at high concentrations, significantly increasing the macroscopic viscosity of the solution and creating a paste-like fluid environment. This acts as a damper, hindering the microscopic Brownian motion and convective diffusion of additive molecules. When the control system executes the dosing operation... When the concentration increases, if the additive is encapsulated by the high-viscosity plating solution, the cumulative amount of net conductivity of the plating solution will increase. When the value is relatively small, the dynamic gain ratio will expand sharply. Combined with the further amplification of the correction term based on the change in carbonate concentration, the transport inertia factor... The increase, approaching 1, is equivalent to issuing a warning to the control system, informing it that the unchanged conductivity is not due to a lack of additives, but rather because the system is in a state of extremely high damping and physical blockage. Continuing to blindly add additives at this point will lead to severe supersaturation. When the plating bath is in good condition, the carbonate ion concentration is low, and the bath maintains a low-viscosity fluid environment similar to clear water. This allows additive molecules to undergo unimpeded Brownian motion and efficient convection diffusion. At this time, the additives are not encapsulated by the high-viscosity bath, and the sensor responds quickly. Under the same additive excitation, the cumulative net conductivity of the electroplating solution... When the value is relatively large, the dynamic gain ratio will decrease, and combined with the further attenuation of the carbonate correction term, this leads to a transport inertia factor. When the conductivity decreases and approaches 0, the system is informed that the current conductivity remains unchanged because no drug has been added or the dosage is insufficient, and the mass transfer of the system is normal. At this point, the drug addition operation can be performed normally, and the integral term can be allowed to accumulate to eliminate steady-state error.

[0049] S3: Based on the transport inertia factor, and combined with the evolution trend of the transport inertia factor over time, calculate the resistance risk index of the electroplating solution.

[0050] After determining the transport inertia factor, in order to accurately adjust the integral action of the PID algorithm, this step takes into account that the transport inertia factor of the electroplating solution is high when the solution is in a stable high viscosity state and a transient state of stagnation deterioration. Therefore, this step further analyzes the evolution gradient of the transport inertia factor over time and uses a static benchmark and dynamic modulation model to calculate the stagnation risk of the electroplating solution at the moment of chemical addition, so as to distinguish whether the electroplating solution is in a stable high viscosity state or a transient state of stagnation deterioration.

[0051] First, obtain the transport inertia factor for each historical dosing time within the historical time period of the time to be dosing, and perform linear regression fitting, specifically using the least squares method, to obtain a fitting slope. To reflect the evolution gradient of the transmission inertia factor, if This means that the electroplating solution is in a state of continuous stagnation and deterioration. This means that the electroplating solution is in a state of continuous improvement in diffusion recovery. This means that the electroplating solution is in a stable equilibrium state.

[0052] Then, calculate the obstruction risk index:

[0053] in, This represents the resistance risk index of the electroplating solution at the moment of chemical addition. To provide an inert factor for the electroplating solution at the moment of chemical addition. If it is a sign function, then , ,like , ,like , , It is a non-linear normalization function used to... Mapping to the range of 0 to 1 can be achieved using the hyperbolic tangent function. , It is the absolute value symbol.

[0054] In this relation, It reflects the magnitude of the evolution gradient of the transport inertia factor. It reflects the direction of the evolution gradient of the transmission inertia factor. It reflects the baseline state of the electroplating solution.

[0055] If the transmission inert factor The evolution gradient direction is relatively high, but there is almost no direction for evolution. This indicates that the electroplating solution had a high viscosity at the moment of chemical addition, but the viscosity remained stable over a historical period without any sudden abrupt changes or blockages. This suggests that the electroplating solution was likely in a stable high viscosity state at the moment of chemical addition. The increased viscosity due to long-term use is an inherent characteristic of the electroplating solution. At this point, Become , The stagnation risk index strictly degenerates into the transport inertia factor at the moment of dosing, dominated by the transport inertia factor. The larger the transport inertia factor, the larger the stagnation risk index. For the PID control algorithm, in this case, the strategy should be to maintain an appropriate integral confidence level. Since the electroplating solution is in a steady state, the conductivity deviation truly reflects the concentration gap. However, due to the high background viscosity and slow mass transfer, by making the stagnation risk index equal to the transport inertia factor, a moderately low integral confidence level is maintained, allowing the integral term to slowly accumulate the replenishment amount. This ensures that the target concentration is eventually reached while avoiding instantaneous over-dosing caused by viscosity.

[0056] If the transmission inert factor The value is relatively high, and the evolution gradient direction is positive. This indicates that not only is the viscosity of the electroplating solution high at the moment of chemical addition, but the trend has been continuously deteriorating over a historical period, with a sustained decline in its responsiveness to chemical addition. The electroplating solution's response to additives is deteriorating rapidly, and increased additive input has yielded no effect. This is usually due to the large-scale generation of colloidal byproducts in the plating solution or the failure of the filtration system, leading to a sharp increase in plating solution viscosity and blockage of ion migration channels. It has achieved the goal of The amplification effect occurs when the stagnation risk index is greater than the transmission inertia factor. For PID control algorithms, the appropriate strategy in this situation is to significantly reduce the integral confidence or even completely block the integral. At this point, the conductivity deviation is unreliable. If the integral is allowed, the algorithm will mistakenly believe that the additive is insufficient and will accumulate output excessively. By amplifying the stagnation risk index, the integral confidence is forced to approach 0, freezing the integral action at the physical level until the drug solution diffuses and the gradient falls back, thus avoiding integral saturation.

[0057] If the evolution gradient direction is negative This indicates that the transport inertia factor over the historical period is decreasing, and the responsiveness of the electroplating solution is recovering. Although the transport inertia factor at the moment of chemical addition may still be high, the evolutionary trend over the historical period is improving. If only the transport inertia factor at the moment of chemical addition is considered, it may lead to a sluggish replenishment response. Therefore, the improving trend is used to offset the high basic inertia and release the integral capability in advance. It has achieved the goal of The reduction effect makes it lower than the transport inertia factor at the time of chemical addition. For PID control algorithms, in this case, a strategy of increasing integral confidence should be adopted. This allows the PID control algorithm to predict the recovery of the electroplating solution, allowing the integral term to accelerate its intervention to compensate for the concentration deficit accumulated during the initial stagnation period, thereby shortening the system settling time.

[0058] S4: The integral term of the PID control algorithm is reconstructed in real time using the aforementioned resistance risk index, and the amount of additive to be supplied is obtained based on the reconstructed PID control algorithm.

[0059] Traditional PID algorithms are prone to integral saturation under lag conditions, essentially because the algorithm unconditionally trusts the conductivity deviation fed back by the sensor. This step uses a lag risk index to calculate a dynamic integral confidence level, which is used to adjust the participation of the integral term in real time.

[0060] First, the hindering risk index is mapped to a value between 0 and 1 using a nonlinear decay function, serving as an integral confidence level. Specifically, it satisfies the following relationship:

[0061] in, for The integral confidence level at time step (t) represents the effectiveness of the control level, and its value ranges from (0,1). It is a natural exponential function. For electroplating solution in The moment-to-moment delay risk index represents the degree of unreliability at the physical level.

[0062] use It can smoothly map any resistance risk index to a dimensionless interval of (0,1], compared to linear functions. exist When the value is small, the function curve is flat. Maintaining a high level close to 1 ensures the system's high sensitivity under normal operating conditions; however, once the stall risk index exceeds a critical value, the function curve drops sharply. The rapid drop to 0, this nonlinear mechanism ensures that the integral term is prevented from blindly accumulating under unreliable signals at the moment a severe blockage is detected.

[0063] Then, the integral term of the PID control algorithm is weighted using the integral confidence level to obtain the reconstructed PID control algorithm. The amount of additive to be added is then determined based on the real-time reconstructed PID control algorithm. A higher stagnation risk index indicates that the electroplating solution is more likely to be in a state of stagnation and deterioration at the time of addition. This is mapped to a smaller integral confidence level via a negatively correlated exponential function. This means the PID control algorithm no longer trusts the current deviation signal, considering it an illusion caused by lag. The cumulative error of the integral term is frozen, avoiding the integral saturation effect and preventing excessive addition of the additive. Conversely, a smaller stagnation risk index indicates that the electroplating solution is more likely to be in a stable or improving state at the time of addition. This is mapped to a larger integral confidence level via a negatively correlated exponential function. This means the PID control algorithm trusts the current deviation signal, considering it a true change in the state of the electroplating solution. The cumulative error of the integral term is restored, quickly eliminating steady-state errors and ensuring accurate addition of the additive to maintain net conductivity.

[0064] Through this confidence-weighted integration mechanism, the system can automatically pause integration in the blind zone of sensor response lag, and resume integration when the response recovers or reaches steady state, thus achieving adaptive control for complex electrochemical conditions.

[0065] In order to output the final control command for the dosing machine, this physical constraint must be incorporated into the execution of the control algorithm. This step aims to use integral confidence to reconstruct the integral part of the traditional PID control algorithm in real time, and output a final control quantity that can respond quickly and avoid component degradation lag overshoot.

[0066] Specifically, the amount of additive to be supplied, obtained from the real-time reconstructed PID control algorithm, is determined based on the following relationship:

[0067] in, This refers to the amount of additives to be replenished in the electroplating solution at the time of chemical addition. These are the proportional gain constant, integral gain constant, and derivative gain constant of the PID control algorithm, which are usually set based on empirical values. , for The deviation between the net conductivity at a given time and the preset standard conductivity is specifically the preset standard conductivity minus the net conductivity at that time. A positive deviation indicates a lack of additives, requiring pump replenishment. The PID control algorithm outputs a positive replenishment amount, and vice versa. yes The integral confidence level at time step. This is the derivative of the deviation with respect to time. This indicates that integration is performed over time.

[0068] in, For the proportional term, it provides basic corrective force. The differential term is used to predict trends and suppress oscillations. For the integral term, by introducing Dynamic start-stop is achieved through integral action, whereas the integral term of the traditional PID control algorithm is a function of the deviation. direct integral This invention integrates confidence levels. When injected into the integral term, and the electroplating solution is in a state of deteriorating resistance, the resistance risk index is very high, leading to... Extremely small, even close to zero, the accumulation rate of the integral term is slowed down or even stopped at a physical level, even if the error is at this point. It persists, and the integral terms will not accumulate indefinitely; this is the control quantity. It will not surge blindly, thus avoiding integral saturation; when the electroplating solution is in diffusion recovery or steady state, the resistance risk index is very small, leading to... With the integral term's accumulation function restored to normal, it can quickly respond and eliminate deviations, thereby ensuring that the conductivity accurately returns to the set target value.

[0069] In this relation, , Standard conductivity represents the theoretical conductivity of an electroplating solution at its optimal component concentration, i.e., the optimal additive and main salt concentration specified in the initial tank preparation or standard process formula, at a standard temperature. Specifically, it is obtained as follows: First, according to the standard electroplating process formula, prepare a fresh standard sample of the electroplating solution with precise component content. Place the standard sample in a constant temperature environment, controlling its temperature to stabilize at the standard temperature. Measure the conductivity value under this condition using a high-precision conductivity meter, and then solidify it as the set value. In actual control, It is a static reference. The goal of the PID control algorithm is to supplement the additive so that the net conductivity after temperature decoupling always approaches this static reference. yes Net conductivity at time t, This represents the magnitude of the control demand, while This represents the reliability of the deviation at the time of drug administration, in the integral term. middle, It is an error term responsible for providing direction and magnitude, informing the controller whether to add or subtract pesticide, and how large the gap is. It is a weighting term responsible for determining whether this error should be accumulated.

[0070] If the electroplating solution is in a state of poor mass transfer and has a large transport inertia factor, the resulting deviation will be significant. This is often due to false persistence errors caused by the fact that the error has not yet spread. A value approaching 0 effectively disqualifies the error from being included in the integral accumulation; the deviation will not be counted in the cumulative amount. This is equivalent to the integration process automatically pausing during physical blockage to prevent oversaturation. If the electroplating solution is in a state of good mass transfer and the transport inertia factor is small, the resulting deviation... The real, persistent error is often caused by the diffusion of the drug solution. When the value approaches 1, it is equivalent to approving the error to enter the integral accumulation, and the integral term resumes normal accumulation, executing regular control. This mechanism mathematically eliminates the integral saturation phenomenon caused by the continuous existence of error during the sensor response lag, ensuring that the amount of additive replenishment is driven only by the effective error.

[0071] It should be noted that since the dosing metering pump is usually a unidirectional actuator, it can only perform the dosing action. If the calculated replenishment amount is negative, it indicates that the current net conductivity is higher than the standard conductivity. In this case, dosing will be stopped until the replenishment amount returns to a positive value.

[0072] S5: Automatic replenishment control of electroplating solution based on replenishment amount.

[0073] After obtaining the replenishment amount at the time of chemical addition, the additive replenishment device is driven to release the additive into the electroplating solution according to the replenishment amount.

[0074] Specifically, additive replenishment equipment is typically a metering pump. The replenishment amount is mapped to a control signal for the metering pump, and the replenishment control amount is determined based on the type of pump. Mapped to one of the following two control signals: one is duty cycle control mode: suitable for electromagnetic diaphragm metering pumps, with a fixed control cycle of 30 seconds set. The linear mapping is the on-time within that cycle, for example, if If the value is 50%, the pump is controlled to start for 15 seconds and stop for 15 seconds within the cycle; another is frequency control mode: suitable for metering pumps driven by variable frequency motors, which... The linear mapping is to the pump's stroke frequency. For example, if the maximum frequency of the pump is set to 120 strokes per minute, then... If the value is 50%, the output control command adjusts the pump to run at a frequency of 60 times / minute. Based on the control signal, the flow rate of the dosing metering pump is controlled to be the same as the replenishment amount, so as to realize the replenishment operation of the additive.

[0075] In summary, this control logic based on physical state reshaping overcomes the specific defect of PID control algorithms in time-varying component deterioration baths, which leads to excessive replenishment due to response lag, thus ensuring the uniformity and accuracy of electroplating.

[0076] To more intuitively illustrate the effects of the present invention, such as Figure 2 As shown, this paper compares the dynamic control response of the reconstructed PID control algorithm of this invention with that of the existing PID control algorithm under the typical condition of component deterioration due to long-term use of electroplating solution. The horizontal axis represents the control time, and the vertical axis represents the normalized relative concentration of additive. The target value is set to 1. In the initial stage of control, due to the aging of the plating solution, the mass transfer lag is caused by the aging of the plating solution, and the change in conductivity fed back by the sensor is not obvious. For the existing technology, the traditional PID control algorithm cannot identify the physical lag and misjudges it as insufficient dosage, which leads to the continuous accumulation of false error signals in the integral term and integral saturation. When the reagent finally diffuses and takes effect, the accumulated excessive control command is released instantly, causing the concentration to rise sharply to above 1.4 and fall into the high-risk zone. However, the present invention, through the reconstruction algorithm, automatically reduces the integral confidence and actively suppresses the blind accumulation of the integral term during the physical lag period. When the lag ends (about 30 cycles later), the system smoothly transitions to steady-state control and maintains reasonable robustness in following high-frequency sensor noise and small environmental disturbances. The comparative results show that the present invention effectively solves the problem of integral saturation caused by the deterioration of electroplating solution components, eliminates overshoot phenomenon, and ensures that the additive concentration is always within the safe process window.

[0077] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An automatic replenishment control method for electroplating bath additives based on conductivity monitoring data, characterized in that, include: The temperature, initial conductivity, and carbonate concentration of the electroplating solution are obtained. The activation energy coefficient of the electroplating solution is determined based on the trends in the initial conductivity and temperature. At each chemical addition point in the electroplating process, the natural logarithm of the initial conductivity and the reciprocal of the temperature at all historical chemical addition points within a preset historical time period are obtained. A linear regression is performed on the natural logarithm and reciprocal values ​​using the least squares method to obtain the slope of the fitted line. Based on the slope, the activation energy coefficient at the chemical addition point is determined using Arrhenius law to reflect the sensitivity of ion migration in the electroplating solution to temperature changes. The initial conductivity is then subjected to dynamic thermodynamic decoupling to eliminate the influence of temperature fluctuations on conductivity, generating the net conductivity of the electroplating solution. , ;in, This is the time to wait for the medication to be added. The original conductivity of the electroplating solution at the moment before chemical addition. It is a natural exponential function. The activation energy coefficient of the electroplating solution at the moment of chemical addition is given. Let be the ideal gas constant. The temperature of the electroplating solution at the moment the chemical is to be added. The preset standard temperature; Based on the cumulative change in net conductivity over a preset historical period and the total amount of additives during that historical period, combined with the carbonate concentration, the transport inertia factor of the electroplating solution is calculated to reflect the degree of lag in the electroplating solution's response to additive replenishment. The electroplating solution is controlled by PID control algorithm to replenish additives. Based on the transport inertia factor, the resistance risk index of the electroplating solution is calculated by combining the evolution trend of the transport inertia factor over time. The integral term of the PID control algorithm is reconstructed in real time using the aforementioned hindrance risk index, and the additive supply amount is obtained based on the reconstructed PID control algorithm. , ;in, These are the proportional gain constant, integral gain constant, and derivative gain constant of the pre-set PID control algorithm. for The deviation between the net conductivity at a given time and the preset standard conductivity. for The integral confidence level at time step. This is the derivative of the deviation with respect to time. It involves integrating time and automatically controlling the replenishment of the electroplating solution based on the replenishment amount.

2. The automatic replenishment control method according to claim 1, characterized in that, The transport inertia factor of the electroplating solution is determined based on the following method: ； in, To provide an inert factor for the electroplating solution at the moment of chemical addition. It is the hyperbolic tangent function. This is a preset dimensional balance coefficient used to convert the calculation terms within parentheses into dimensionless values. The length of the historical time period during which medication is to be administered. For integration variables, and They are respectively The rate of change of drug dosage and net conductivity at any given time. This is a preset measure to prevent positive numbers with a denominator of 0. This represents the relative growth rate of carbonate concentration in the electroplating solution at the time of chemical addition. The weighting coefficient is the effect of carbonate concentration on the viscosity of the electroplating solution, which was determined in advance through experiments.

3. The automatic replenishment control method according to claim 2, characterized in that, The carbonate concentration at the time of drug addition is determined by obtaining it from an online ion concentration analyzer or by receiving periodic test data input through a human-computer interaction interface.

4. The automatic replenishment control method according to claim 2, characterized in that, The relative growth rate of carbonate concentration in the electroplating solution at the time of chemical addition is determined by first obtaining the carbonate concentration of the electroplating solution at the initial tank preparation, calculating the relative increment of carbonate concentration at the time of chemical addition and carbonate concentration at the initial tank preparation, and taking the ratio of the relative increment to carbonate concentration at the initial tank preparation as the relative growth rate of carbonate concentration in the electroplating solution at the time of chemical addition.

5. The automatic replenishment control method according to claim 1, characterized in that, The resistance risk index of electroplating solutions is determined based on the following method: The transport inertia factor for each historical dosing moment within the historical time period to be dosing is obtained, and a linear regression is performed to obtain a fitting slope. This reflects the evolution gradient of the transmission inertia factor; Calculate the resistance risk index: ;in, This represents the resistance risk index of the electroplating solution at the moment of chemical addition. To provide an inert factor for the electroplating solution at the moment of chemical addition. For symbolic functions, It is a nonlinear normalization function. It is the absolute value symbol.

6. The automatic replenishment control method according to claim 5, characterized in that, The integral term of the PID control algorithm is reconstructed in real time using the aforementioned sluggishness risk index, including: The stagnation risk index is mapped to a value between 0 and 1 using a nonlinear decay function, which serves as an integral confidence level. This integral confidence level is then used to weight the integral term of the PID control algorithm to obtain the reconstructed PID control algorithm.

7. The automatic replenishment control method according to claim 1, characterized in that, Automatic replenishment control of the electroplating solution based on the replenishment amount includes: when the chemical is to be added, driving the additive replenishment device to release the additive into the electroplating solution according to the replenishment amount.

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