High-precision stable control method for temperature of industrial metal gallium electrolytic deposition process

Abstract

The application discloses a kind of high-precision stable control methods for industrial metal gallium electrolytic deposition process temperature, comprising: the dynamic mechanism model of metal gallium electrolytic process temperature is established, and the steady-state temperature of electrolytic process is solved;Collect metal gallium electrolytic process temperature control input and temperature output data, and construct input-output data set;According to the preset mechanism enhancement proportion, replace several data points of original output data set with steady-state temperature value, and obtain mechanism-enhanced output data set;Using mechanism-enhanced output data set and original input data set, a subspace identification method is used to obtain a temperature prediction model;According to Lyapunov theorem, the stable solution of control quantity is solved, and the objective function of asymptotically stable model predictive control is constructed using the temperature prediction model;And under the premise of meeting the system constraint condition, the optimal control quantity sequence of temperature is solved by rolling optimization.The application can efficiently and stably control the temperature of metal gallium electrolytic deposition process.

Description

Technical Field

[0001] This invention belongs to the field of industrial control technology, specifically relating to a high-precision and stable temperature control method for industrial gallium electrolytic deposition processes. Background Technology

[0002] A typical industrial gallium electrolytic deposition process is as follows: Figure 1 As shown, this process is a continuous electrochemical reduction process carried out in an alkaline gallium-containing electrolyte system. The electrolysis temperature is a key process control parameter throughout the pretreatment of the raw solution, electrolytic deposition, and product discharge. Therefore, maintaining the electrolysis temperature within a reasonable and stable process window is a crucial prerequisite for achieving high current efficiency, high purity deposition, and low energy consumption operation.

[0003] However, temperature stability control in the gallium electrolytic deposition process faces significant technical challenges. On the one hand, the electrolytic system has a complex reaction mechanism, with strong nonlinearity, strong coupling, and time-varying characteristics among multiple variables such as temperature, current density, electrolyte alkali concentration, and impurity composition. Temperature changes not only directly affect electrode reaction kinetic parameters but also indirectly amplify current efficiency fluctuations by altering the competition between hydrogen evolution and gallium deposition, making it difficult for empirical models based on simplified assumptions to accurately describe the dynamics of the real process. On the other hand, the long-term operation of industrial electrolysis processes is inevitably affected by disturbances such as fluctuations in the raw solution composition, impurity accumulation, and changes in electrode state. Temperature is highly sensitive to these disturbances; even small deviations can trigger deposition instability or even system instability. This makes traditional temperature control strategies based on fixed models or empirical rules difficult to achieve long-term stable operation under the complex conditions of gallium electrolytic deposition, necessitating an advanced control method that can accurately characterize temperature dynamics and ensure stability.

[0004] Extensive research has been conducted by scholars both domestically and internationally on the temperature effect in gallium electrolytic deposition, revealing the significant influence of electrolysis temperature on gallium deposition behavior. However, existing work mainly focuses on mechanism analysis and optimization of single process parameters under ideal or quasi-steady-state conditions, failing to systematically address the stability issues caused by dynamic temperature changes and multi-disturbance coupling in industrial environments from a process control perspective. To address this control requirement, Model Predictive Control (MPC), with its ability to explicitly handle multivariate constraints and its rolling optimization mechanism's adaptability to dynamic disturbances, has become the preferred choice for controlling such complex industrial processes. However, the closed-loop stability of traditional MPC typically relies on empirical tuning of parameters such as the prediction time domain and weight matrix, lacking rigorous mathematical proof. In the temperature-sensitive and variable complex gallium electrolysis system, it is difficult to guarantee long-term control stability, posing a potential risk to its reliable application in key process stages. Summary of the Invention

[0005] This invention provides a high-precision and stable temperature control method for industrial gallium electrolytic deposition processes, which can efficiently and stably control the temperature of the gallium electrolytic deposition process.

[0006] To achieve the above technical objectives, the present invention adopts the following technical solution:

[0007] A high-precision and stable temperature control method for industrial gallium electrolytic deposition processes includes:

[0008] A dynamic mechanism model of temperature in the gallium electrolysis process was established, and the steady-state temperature was solved.

[0009] Collect the input control variables and temperature measurement data of the gallium electrolysis process over a period of time, and construct the control variable input dataset and the original temperature output dataset.

[0010] According to the preset mechanism enhancement ratio, several data points are uniformly selected in the original temperature output dataset and replaced with steady-state temperature values ​​obtained by solving the dynamic mechanism model to obtain the mechanism-enhanced temperature output dataset.

[0011] Using a mechanism-enhanced temperature output dataset and a collected control input dataset, a state-space equation-based prediction model for the temperature of the gallium electrolysis process is obtained by employing a subspace identification method.

[0012] Based on Lyapunov's theorem, solve for the stable solution of the control quantities in the gallium electrolytic deposition process.

[0013] Using a temperature prediction model and based on the stable solution of the control quantity, an objective function for asymptotically stable model predictive control is constructed; and under the premise of satisfying the system constraints, the optimal temperature control quantity sequence is solved through rolling optimization.

[0014] Furthermore, a dynamic mechanism model for the temperature during the gallium electrolysis process is established as follows:

[0015] ;

[0016] In the formula, The electrolyte temperature For time, , , These are the density, specific heat capacity, and volume of the electrolyte, respectively. and These represent the voltage and current of the electrolytic cell, respectively. This is the equivalent coefficient for converting electrical energy into heat energy. Characterizes the overall heat transfer capacity between the electrolytic cell and the environment. For ambient temperature, This refers to the electrolyte circulation mass flow rate. This refers to the reflux electrolyte temperature.

[0017] When the system reaches thermal steady state, that is At that time, the steady-state temperature of the electrolysis process is obtained. :

[0018] .

[0019] Furthermore, the number of data points replacing the steady-state temperature values. The proportion is enhanced by a pre-set mechanism. The calculation yielded: , This represents the number of data points in the original temperature output dataset.

[0020] Furthermore, the N4SID subspace identification method is used to obtain a prediction model of the gallium electrolysis process temperature based on the state-space equation, specifically:

[0021] Step A1, the prediction model of the gallium electrolysis process temperature based on the state-space equation is expressed as:

[0022] ;

[0023] in, , , These represent the input control quantity, output measured value, and process state quantity for temperature control in the electrolysis process, respectively. , and These are the dimensions of control variables, output variables, and state variables, respectively. , , , It is the coefficient matrix of the prediction model;

[0024] Step A2: Using the mechanism-enhanced temperature output dataset and the collected input control dataset, construct the Hankel matrix of the past and future input control datasets. And the Hankel matrix of past and future output temperature datasets. ,use and The prediction model is represented as follows:

[0025] ;

[0026] in, It is an observable matrix. For a block-based Teplitz matrix, These are datasets representing past and future states, respectively.

[0027] Step A3, define past system states and future system state They are respectively:

[0028] ;

[0029] Perform QR decomposition on the past and future system states, and then rearrange the data to obtain the relationship expression between the future output and the known past inputs / outputs and future inputs:

[0030] ;

[0031] in, The first element in the R matrix obtained from QR decomposition is... Line number The block matrix corresponding to the column;

[0032] Step A4: Compare the prediction models from steps A2 and A4 to obtain... , ; through the Perform SVD decomposition:

[0033] ;

[0034] In the formula, express The observable matrix is ​​composed of the first n left singular vectors in the left singular vector matrix obtained by SVD decomposition. It is a matrix composed of the remaining left singular vectors; express The state sequence consisting of the first n right singular vectors in the right singular vector matrix obtained by SVD decomposition; Represents a diagonal matrix with non-zero singular values;

[0035] Step A5, write the decomposition results as , T is used to... Split into and The invertible state coordinate transformation matrix; take the diagonal matrix. Center front 1 element, and the The percentage threshold where the sum of a few elements is greater than the sum of all elements. and will The dimension of the state variables is determined, and the coefficients of the state-space equations are solved based on this. The matrix formed:

[0036] ;

[0037] in, , , , ; and In the state sequence The state quantum sequence obtained in and The control quantum sequence and output temperature subsequence obtained from the enhanced dataset; Based on dataset size and hyperparameters The intermediate variables obtained from the calculation ;

[0038] Step A6 will use the least squares method to solve for the coefficient matrix of the prediction model;

[0039] ;

[0040] In the formula, This represents the F-norm.

[0041] Furthermore, based on Lyapunov's theorem, the steady-state solution of the control quantity of temperature in the gallium electrolytic deposition process based on the state-space equation is obtained, specifically:

[0042] Step B1, assuming the gallium electrolytic deposition process The actual temperature measurement value at that time is and the desired temperature value Then the temperature error is Derivation based on state-space equations Temperature error at time for:

[0043] ;

[0044] in, , , , It is the coefficient matrix of the prediction model based on the state-space equation;

[0045] Step B2, construct the quadratic Lyapunov function Based on the temperature stability requirements of the gallium electrolytic deposition process, it is necessary to ensure Select linear input ,in For the feedback gain matrix, Given the feedforward matrix, we get:

[0046] ;

[0047] in It is the identity matrix;

[0048] Step B3, during the gallium electrolytic deposition process, the temperature reference output It is a constant value, determined by selecting the feedforward matrix. This allows the steady-state error terms to cancel each other out, resulting in a simplified error evolution form. ,in satisfy Substitute Simplifying, we get:

[0049] ;

[0050] Step B4, Solve for the feedback gain matrix , making ; and then according to Solving for the feedforward matrix yields the solution. ;

[0051] Step B5, based on the current state variable and desired temperature output ,according to Calculate the input control quantity at this time. That is, the Lyapunov stable solution of the control quantity. .

[0052] Furthermore, the objective function for predictive control of the asymptotically stable model is constructed and expressed as:

[0053] ;

[0054] In the formula, Let be the objective function. For temperature prediction models The predicted temperature value at that moment. This is the optimal set temperature value. , and They are weights, and These are the control and prediction step sizes, for Control increment at any time, for The stable solution of the control quantity at time.

[0055] This invention addresses the critical issues of difficult modeling and susceptibility to instability in the temperature control process of gallium electrolytic deposition, proposing an effective method integrating high-precision modeling and stability control. First, a mechanism-enhanced subspace modeling method is studied to establish a high-precision, highly interpretable temperature model of the electrolytic process, laying a reliable foundation for control system design. Simultaneously, an asymptotically stable model predictive control method is proposed. This method inherits the multivariable constraint handling and rolling optimization capabilities of traditional MPC (Multivariable Predictive Control) while ensuring the stability of the closed-loop system through rigorous theoretical proof. This invention effectively addresses the problems of unclear mechanisms, difficulty in establishing temperature models, and susceptibility to instability during long-term operation in the electrolytic process, providing a reliable solution for achieving stable and efficient temperature control in the gallium electrolytic deposition process. Attached Figure Description

[0056] Figure 1 This is a process flow diagram of gallium electrolytic deposition.

[0057] Figure 2 This is a comparison chart of model prediction and actual data results of the method described in the embodiments of this application. (a) is the result of the model training stage, and (b) is the result of the model testing stage.

[0058] Figure 3 This is a control result diagram of the method described in the embodiments of this application. Detailed Implementation

[0059] The embodiments of the present invention will be described in detail below. These embodiments are based on the technical solutions of the present invention, and provide detailed implementation methods and specific operation processes to further explain the technical solutions of the present invention.

[0060] This embodiment provides a high-precision and stable temperature control method for industrial gallium electrolytic deposition processes, including the following steps:

[0061] Step 1: Establish a dynamic mechanism model of temperature in the gallium electrolysis process and solve for the steady-state temperature of the electrolysis process.

[0062] In the process of gallium electrolytic deposition, to describe the dynamic changes in electrolysis temperature, this invention takes the electrolyte in the electrolytic cell as the research object and constructs a temperature mechanism model of the electrolysis process based on the principle of energy conservation. By analyzing the main heat terms such as exothermic reaction, Joule heating, and heat flow during heat exchange, the basic mechanism of temperature change is established. To simplify the model structure and highlight the main influencing factors, the following reasonable assumptions are made during the modeling process:

[0063] a1. The electrolyte in the electrolytic cell is thoroughly mixed and the temperature field is uniform. A lumped parameter model can be used, employing a single temperature... Describe the thermal state of the system;

[0064] a2. Density of the electrolyte within the normal operating temperature range Specific heat capacity and volume Treat it as a constant;

[0065] a3. The heat generated during electrolysis mainly comes from electrical energy conversion, including ohmic heat and electrode reaction heat, while other chemical heat effects can be incorporated into the equivalent electrolysis heat generation item.

[0066] a4. Heat exchange between the electrolytic cell and the environment mainly occurs through convection and conduction, while radiation heat transfer is negligible.

[0067] a5. During the electrolyte circulation process, the electrolyte entering and leaving the tank only affects the energy balance within the tank through sensible heat exchange.

[0068] During electrolysis, the system's heat input mainly comes from the electrolytic heat generated by electrical energy conversion, while the heat output includes heat transfer losses between the electrolytic cell and the environment, as well as the sensible heat carried away by electrolyte circulation. Taking the electrolytic cell as the control volume, its transient energy balance can be expressed as:

[0069] (4);

[0070] In the formula, The electrolyte temperature and These represent the voltage and current of the electrolytic cell, respectively. This is the equivalent coefficient for converting electrical energy into heat energy. Characterizes the overall heat transfer capacity between the electrolytic cell and the environment. For ambient temperature, This refers to the electrolyte circulation mass flow rate. Let be the temperature of the reflux electrolyte. Rearranging the above equations yields a dynamic mechanism model of the electrolysis process temperature:

[0071] (5);

[0072] This model uses electrolysis temperature as the output variable to quantitatively reflect the combined influence of electrolysis electrical parameters, cycle conditions, and environmental conditions on temperature evolution. When the system reaches thermal steady state, i.e. Then, the steady-state temperature expression for the electrolysis process can be obtained:

[0073] (6);

[0074] The steady-state temperature obtained above refers to the instantaneous steady-state temperature, which means that at a certain moment, the system described by the differential equation satisfies... The instantaneous steady-state temperature at that time.

[0075] This expression reveals the quantitative relationship between electrolysis parameters and process temperature, providing a theoretical basis for optimizing electrolysis conditions and designing temperature control strategies. However, due to the complex reaction mechanism, numerous perturbation factors, and parameter variations inherent in the gallium electrolytic deposition process, relying solely on mechanistic models is insufficient to fully characterize the dynamic temperature behavior during actual industrial operation, and the models still have certain limitations in terms of accuracy and adaptability.

[0076] Step 2: Collect the input control quantities and temperature measurement data of the gallium electrolysis process over a period of time, and construct the control quantity input dataset and the original temperature output dataset.

[0077] Step 3: According to the preset mechanism enhancement ratio, select several data points evenly in the original temperature output dataset and replace them with the steady-state temperature values ​​obtained by solving the dynamic mechanism model to obtain the mechanism-enhanced temperature output dataset.

[0078] To enhance the physical interpretability of the model, after generating high-confidence prediction data based on the temperature dynamic mechanism model established in step 1, the corresponding past and future mechanism output data matrices are constructed. and A matrix of actual temperature measurements from the past and future. and Mechanism-enhanced replacements are performed on certain columns within the matrix. Specifically, from the matrix... and Medium spacing in column dimensions Each column index constitutes a set of replacement indexes. This is to ensure the uniform distribution of the replacement columns throughout the overall structure. Subsequently, the mechanism-enhanced data matrix replacement is performed as follows:

[0079] (7);

[0080] Among them, the proportion of mechanism enhancement It can be dynamically selected based on the data quality level.

[0081] Step 4: Using the mechanism-enhanced temperature output dataset and the collected input control dataset, a subspace identification method is employed to obtain a state-space equation-based prediction model for the temperature of the gallium electrolysis process.

[0082] Compared to mechanistic modeling methods, system identification methods based on operational data typically offer higher modeling accuracy in depicting the dynamic characteristics of complex industrial processes. Subspace identification methods, such as N4SID, can directly utilize input and output data to establish a state-space model, offering advantages such as high computational efficiency and strong noise resistance, and can accurately describe the dynamic changes in temperature during electrolysis. However, purely data-driven models lack clear physical meaning, and their parameters struggle to reflect the heat transfer and reaction mechanisms in actual electrolysis processes. Furthermore, their reliability and generalization ability are limited when operating conditions change significantly. Therefore, this embodiment combines mechanistic models with subspace identification methods, proposing a mechanistic-enhanced subspace modeling method. This method, while using the N4SID subspace identification method to construct the Hankel matrix to describe the system's dynamic characteristics, utilizes data generated from the mechanistic model to physically constrain the system model structure, thereby enhancing the model's mechanistic consistency. This allows the modeling method to balance model interpretability and modeling accuracy, achieving a high-precision description of the temperature dynamics of the gallium electrolysis deposition process. The system model equations are as follows:

[0083] (8);

[0084] in For the system's input control quantity, The system output measurement value, For the process state variables of the system, , and These are the dimensions of control variables, output variables, and state variables, respectively. , , , This is the coefficient matrix of the model. The iterative system (8) can be obtained...

[0085] (9);

[0086] in It is a custom hyperparameter, and it must be strictly greater than the state variable. The dimension of . To simplify the notation, equation (9) is written in an equivalent form. ,in It is an observable matrix. For a block-based Teplitz matrix, For the output vector, The input vector is the input vector. Based on the output and input vectors, the past and future are considered. At each time step, the Hankel matrix of the dataset can be written in the following form:

[0087] ;

[0088] (10);

[0089] in It depends on the dataset size. and hyperparameters Seeking, .

[0090] Based on formulas (8-9) and the updated output Hankel matrix (7), the input-output equation can be obtained:

[0091] (11);

[0092] in Each column vector of the past and future matrices forms a relation pair, and formula (11) covers such relation pairs across the entire dataset. The past and future system states are defined from the input and output matrices:

[0093] (12);

[0094] QR decomposition can transform the input-output matrix into the following form:

[0095] (13);

[0096] The one on the left The matrix is ​​a lower triangular matrix, and the right side... The matrix is ​​an orthogonal matrix. Observe. The third column of the matrix reveals that past inputs and outputs were zero, and future inputs are also zero. Therefore, we can conclude that future outputs will also be zero. =0. From the result of QR decomposition (13), we can obtain the expression for the relationship between the future output and the known past input output and future input:

[0097] (14);

[0098] By comparing this relational expression with formula (11), we can obtain... , Examining the latter equation, since the state vector is a variable that acts as a memory in the exchange of information between the past and the future, and The intersection of the states is empty, and the dimension of the state vector is... It cannot be obtained directly; its dimensions need to be determined through SVD decomposition.

[0099] (15);

[0100] The result of the decomposition can be written as , Theoretically, the dimension of the state vector diagonal matrix The rank of the matrix is ​​determined by the sum of its elements, but in reality, matrix elements are not perfectly zero or non-zero. Therefore, a certain percentage threshold is taken where the sum of the elements exceeds the sum of all elements. The former With the state variables defined, the form of the system's state-space equations is also clear. Based on this, the coefficients of the state-space equations can be solved. The matrix formed:

[0101] (16);

[0102] Except for the coefficient matrix of the state-space equation, all other matrix variables are known. , , , .in and Future state sequence Obtain from, and The data was obtained after mechanism enhancement. For the linear equation (16), the least squares method can be used to solve it, yielding...

[0103] (17);

[0104] Thus, a high-precision model capable of accurately depicting the dynamic temperature changes during the gallium electrolytic deposition process was successfully established. This model, while maintaining physical interpretability, possesses good prediction accuracy and engineering applicability, providing a reliable model foundation for the design and implementation of subsequent temperature stability control strategies.

[0105] Step 5: According to Lyapunov's theorem, solve for the stable solution of the control quantity of the gallium electrolytic deposition process temperature based on the state-space equation.

[0106] In process industries, Multi-Process Control (MPC) has become a mainstream advanced control method, especially suitable for complex processes with strong coupling and multiple constraints, such as gallium electrolytic deposition. However, while traditional MPC performs excellently in handling process constraints and optimization objectives, its closed-loop stability analysis is usually based on assumptions of local linearization or nominal models, and its stability is highly dependent on manual tuning of parameters such as the prediction time domain and weight matrix. Inappropriate parameter selection can easily lead to a decline in control performance or even closed-loop instability. When facing highly nonlinear process systems, the guarantee of stability often relies more on the engineering tuning experience of operators and lacks rigorous theoretical support. To address this, this invention proposes an asymptotically stable MPC method for the complex nonlinear temperature characteristics of the gallium electrolytic deposition process. This method rigorously proves the asymptotic stability of the closed-loop system through theoretical derivation, thus providing a solid stability guarantee for the control system while maintaining excellent dynamic performance.

[0107] Specifically, the system's stable solution to the temperature state-space equation for the gallium electrolytic deposition process is first obtained using Lyapunov's theorem. The actual system output is... Assume the system expects the output to be The error is Then there is

[0108] (18);

[0109] Constructing quadratic Lyapunov functions To ensure system stability, it is necessary to guarantee Select linear input ,in For the feedback gain matrix, If we consider the feedforward matrix, then we can obtain...

[0110] (19);

[0111] in This is the identity matrix. The reference output for temperature during gallium electrolytic deposition. It is a constant value, which can be achieved by selecting an appropriate feedforward matrix. This causes the steady-state error terms to cancel each other out, thus yielding a simplified form of the error evolution. ,in satisfy Substitute Simplifying, we get:

[0112] (20);

[0113] Solve for a feedback gain matrix , making The input obtained at this time This is a Lyapunov stable solution, denoted as the control quantity stable solution. .

[0114] Step 6: Using the temperature prediction model and based on the stable solution of the control quantity, construct the objective function of the asymptotically stable model predictive control; and under the premise of satisfying the system constraints, solve the optimal temperature control quantity sequence through rolling optimization.

[0115] The stable solution of the system control quantity obtained in step 5 can only guarantee the stability of the control system, but cannot satisfy the dynamic optimization of control performance. Therefore, this invention proposes an asymptotically stable MPC method to construct the Lyapunov stability term of the objective function. The specific objective function is as follows:

[0116] (twenty one);

[0117] in, It is the optimal setting value. , and They are weights, and These refer to the control and prediction step sizes, respectively. Based on the objective function described above, the model predictive control problem, under the premise of satisfying system constraints, solves for the optimal control sequence through rolling optimization and applies it to the controlled object.

[0118] The asymptotically stable model predictive control method of this invention can guarantee the stability of the closed-loop control system, and its stability conclusion can be given by the following theorem.

[0119] Theorem 1: For the system described by equation (7), the closed-loop system is asymptotically stable under the action of the objective function given by equation (21).

[0120] Proof: The proof of Theorem 1 consists of two steps.

[0121] First, prove the control input sequence Converging to a definite limit ,Right now .

[0122] From the objective function It is possible to obtain, in the first Always:

[0123] (twenty two);

[0124] Based on the rolling optimization characteristics of MPC:

[0125] (twenty three);

[0126] in Then it can be proved that .

[0127] Secondly, prove the limit. The corresponding stable equilibrium point of the system indicates that the proposed control law can guarantee the asymptotic stability of the closed-loop system.

[0128] From equation (19-21), we can obtain the input... Lyapunov sub-items of the system (8) under action It is always less than 0, which is known from Lyapunov's theorem. This corresponds to a stable equilibrium point in the system, ensuring the stability of the closed-loop system. Therefore, the temperature control sequence of the asymptotically stable MPC method can be proved. It can ensure the stability of the closed-loop system.

[0129] To verify the effectiveness of the temperature modeling method for gallium electrolytic deposition proposed in this invention, 6000 sets of valid data samples were selected for modeling experiments, of which 3000 sets were used for model training and 3000 sets were used for model testing. The root mean square error (RMSE) was used as a quantitative evaluation index for model accuracy.

[0130] (twenty four);

[0131] in For the size of the dataset to be evaluated, and For each of the output variables, the i-th value on the test set is... The actual and model prediction results are combined, and the indicators are used to test the model's ability to describe the dynamic temperature changes in the electrolysis process.

[0132] Experimental results are as follows Figure 2 As shown, the red dashed line represents the measured temperature during the electrolysis process, and the blue solid line represents the model prediction. (a) shows the results of the model training phase, and (b) shows the results of the model testing phase. Qualitative results indicate that under different operating conditions, the model-predicted temperature can track the measured temperature change trend well without significant lag or deviation. Quantitative analysis results show that the RMSE during the model training phase is 0.0121, and the RMSE during the testing phase is 0.0175, indicating that the established temperature dynamic model has high prediction accuracy and good generalization ability, and can accurately characterize the dynamic temperature characteristics during gallium electrolytic deposition, providing a reliable model basis for the design of subsequent temperature control strategies.

[0133] To verify the effectiveness and stability of the temperature stability control method proposed in this invention under long-term industrial operating conditions, a long-term temperature control experiment for the electrolysis process was conducted. Based on actual production experience, maintaining the electrolysis temperature within the range of 54–57℃ yields higher current efficiency and a stable deposition state. Therefore, this temperature range was selected as the target control range in the control experiment, and three different temperature setpoints were set to simulate temperature setpoint changes caused by variations in raw material conditions, production cycle adjustments, or process strategy switching during actual production. By introducing multiple setpoint switching operations within the same operating cycle, the tracking capability of the control method under different target temperature conditions and its ability to maintain system stability during continuous operation can be comprehensively examined.

[0134] Controlled experimental results as follows Figure 3 As shown, the red dashed line represents the electrolysis temperature setpoint, and the blue solid line represents the actual controlled electrolysis temperature. Qualitative analysis shows that when the temperature setpoint changes, the method of this invention can quickly and accurately adjust the electrolysis temperature to the new setpoint, indicating that the method has good stability and tracking performance under operating condition switching conditions during long-term control. Quantitative analysis results show that the RMSE of the temperature control error during the entire control process is 0.057, indicating that the control method can achieve high-precision and stable control of the electrolysis temperature under long-term operating conditions.

[0135] Therefore, this invention, through high-precision process modeling and asymptotically stable model predictive control, achieves online prediction and closed-loop regulation of electrolysis temperature, which can improve the operational stability, current efficiency, and product quality of the gallium electrolytic deposition process. This invention can be directly applied to industrial gallium electrolytic deposition and electrolytic refining production lines to stably control the temperature of the electrolytic cell and electrolyte circulation system, thereby suppressing hydrogen evolution side reactions, reducing gallium back-dissolution, and impurity co-deposition. It is applicable to various alkaline gallium-containing electrolytic systems and can be implemented as an upgrade solution for the control system of existing electrolytic devices. Furthermore, the method of this invention has good versatility and can be extended to other temperature-sensitive electrolytic deposition or electrolytic refining processes, as well as intelligent and digital electrolytic production systems for strategic metal preparation.

[0136] The above embodiments are preferred embodiments of this application. Those skilled in the art can make various changes or improvements based on them. Without departing from the overall concept of this application, these changes or improvements should fall within the scope of protection claimed in this application.

Claims

1. A high-precision and stable temperature control method for industrial gallium electrolytic deposition processes, characterized in that, include: A dynamic mechanism model of temperature in the gallium electrolysis process was established, and the steady-state temperature was solved. Collect the input control variables and temperature measurement data of the gallium electrolysis process over a period of time, and construct the control variable input dataset and the original temperature output dataset. According to the preset mechanism enhancement ratio, several data points are uniformly selected in the original temperature output dataset and replaced with steady-state temperature values ​​obtained by solving the dynamic mechanism model to obtain the mechanism-enhanced temperature output dataset. Among them, the number of data points that replace steady-state temperature values The proportion is enhanced by a pre-set mechanism. The calculation yielded: , The number of data points in the original temperature output dataset; mechanism enhancement weight. Dynamically selected based on data quality level; Using a mechanism-enhanced temperature output dataset and a collected control input dataset, a state-space equation-based prediction model for the temperature of the gallium electrolysis process is obtained by employing a subspace identification method. Based on Lyapunov's theorem, solve for the stable solution of the control quantities in the gallium electrolytic deposition process. Using a temperature prediction model and based on the stable solution of the control quantity, an objective function for asymptotically stable model predictive control is constructed; and under the premise of satisfying the system constraints, the optimal temperature control quantity sequence is solved through rolling optimization.

2. The high-precision stable temperature control method for industrial gallium electrolytic deposition process according to claim 1, characterized in that, The dynamic mechanism model of temperature in the gallium electrolysis process is established as follows: ； In the formula, The electrolyte temperature For time, , , These are the density, specific heat capacity, and volume of the electrolyte, respectively. and These represent the voltage and current of the electrolytic cell, respectively. This is the equivalent coefficient for converting electrical energy into heat energy. Characterizes the overall heat transfer capacity between the electrolytic cell and the environment. For ambient temperature, This refers to the electrolyte circulation mass flow rate. This refers to the reflux electrolyte temperature. When the system reaches thermal steady state, that is At that time, the steady-state temperature of the electrolysis process is obtained. : 。 3. The high-precision stable temperature control method for industrial gallium electrolytic deposition process according to claim 1, characterized in that, A state-space equation-based prediction model for the temperature of the gallium electrolysis process is obtained using the N4SID subspace identification method. Specifically: Step A1, the prediction model of the gallium electrolysis process temperature based on the state-space equation is expressed as: ； in, , , These represent the input control quantity, output measured value, and process state quantity for temperature control in the electrolysis process, respectively. , and These are the dimensions of control variables, output variables, and state variables, respectively. , , , It is the coefficient matrix of the prediction model; Step A2: Using the mechanism-enhanced temperature output dataset and the collected input control dataset, construct the Hankel matrix of the past and future input control datasets. And the Hankel matrix of past and future output temperature datasets. ,use and The prediction model is represented as follows: ； in, It is an observable matrix. For a block-based Teplitz matrix, These are datasets representing past and future states, respectively. Step A3, define past system states and future system state They are respectively: ； Perform QR decomposition on the past and future system states, and then rearrange the data to obtain the relationship expression between the future output and the known past inputs / outputs and future inputs: ； in, The first element in the R matrix obtained from QR decomposition is... Line number The block matrix corresponding to the column; Step A4: Compare the prediction models from steps A2 and A3 to obtain... , ; through the Perform SVD decomposition: ； In the formula, express The observable matrix is ​​composed of the first n left singular vectors in the left singular vector matrix obtained by SVD decomposition. It is a matrix composed of the remaining left singular vectors; express The state sequence consisting of the first n right singular vectors in the right singular vector matrix obtained by SVD decomposition; Represents a diagonal matrix with non-zero singular values; Step A5, write the decomposition results as , T is used to... Split into and The invertible state coordinate transformation matrix; take the diagonal matrix. Center front 1 element, and the The percentage threshold where the sum of a few elements is greater than the sum of all elements. and will The dimension of the state variables is determined, and the coefficients of the state-space equations are solved based on this. The matrix formed: ； in, , , , ; and In the state sequence The state quantum sequence obtained in and The control quantum sequence and output temperature subsequence obtained from the mechanism-enhanced dataset Based on dataset size and hyperparameters The intermediate variables obtained from the calculation ; Step A6 will use the least squares method to solve for the coefficient matrix of the prediction model; ； In the formula, This represents the F-norm.

4. The high-precision stable temperature control method for industrial gallium electrolytic deposition process according to claim 1, characterized in that, According to Lyapunov's theorem, the steady-state solution of the control quantity of temperature in the gallium electrolytic deposition process based on the state-space equation is obtained, specifically: Step B1, assuming the gallium electrolytic deposition process The actual temperature measurement value at that time is and the desired temperature value Then the temperature error is Derivation based on state-space equations Temperature error at time for: ； in, , , , It is the coefficient matrix of the prediction model based on the state-space equation; Step B2, construct the quadratic Lyapunov function Based on the temperature stability requirements of the gallium electrolytic deposition process, it is necessary to ensure Select linear input ,in For the feedback gain matrix, Given the feedforward matrix, we get: ； in It is the identity matrix; Step B3, during the gallium electrolytic deposition process, the temperature reference output It is a constant value, determined by selecting the feedforward matrix. This allows the steady-state error terms to cancel each other out, resulting in a simplified error evolution form. ,in satisfy Substitute Simplifying, we get: ； Step B4, Solve for the feedback gain matrix , making ; and then according to Solving for the feedforward matrix yields the solution. ; Step B5, based on the current state variable and desired temperature output ,according to Calculate the input control quantity at this time. That is, the Lyapunov stable solution of the control quantity. .

5. The high-precision stable temperature control method for industrial gallium electrolytic deposition process according to claim 1, characterized in that, The objective function for constructing the asymptotically stable model predictive control is expressed as: ； In the formula, Let be the objective function. For temperature prediction models The predicted temperature value at that moment. This is the optimal set temperature value. , and They are weights, and These are the control and prediction step sizes, for Control increment at any time, for The amount of control at any given moment for The stable solution of the control quantity at time.

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