A method and system for dynamic pH control in a plant calcium extraction process

Abstract

The application relates to the technical field of process control, in particular to a pH dynamic regulation method and system in a plant calcium extraction process, which comprises the following steps: constructing a pH-temperature and calcium dissolution rate lookup table model; based on the model, a multi-stage optimal control problem with the minimum total time as the target is established, and a dynamic programming algorithm is used for solving, so that continuous optimal pH and temperature control trajectories are generated; a compound controller combining feedforward and feedback is designed to accurately track the trajectories; an online trajectory correction mechanism is established, when it is monitored in real time that the process state seriously deviates from the expectation, the re-planning can be automatically triggered, the control strategy is dynamically adjusted and updated. The application deeply integrates process modeling, optimal control and adaptive adjustment, realizes dynamic optimization and closed-loop control of the whole cycle of the plant calcium extraction process, significantly shortens the extraction time, and improves the extraction rate of calcium and the stability of the quality of the final product.

Description

Technical Field

[0001] This application relates to the field of process control technology, specifically to a method and system for dynamic pH regulation during plant calcium extraction. Background Technology

[0002] In the industrial extraction of calcium from plants, the efficiency of the extraction process and the quality of the final product are key performance indicators. pH and temperature are the core process parameters affecting the rate of calcium dissolution from plants.

[0003] Existing plant calcium extraction processes typically employ static or segmented fixed parameter settings for control. For example, pH and temperature are maintained at constant values ​​throughout the extraction cycle or within several preset stages. However, the dissolution of plant calcium is a complex, nonlinear, and dynamic process, with rates varying significantly under different pH and temperature conditions. This fixed control strategy makes it difficult to match the optimal dissolution conditions for each stage in real time, and it also fails to effectively address the impacts of raw material batch fluctuations or operational disturbances.

[0004] Existing technologies generally suffer from long extraction cycles, unstable total extraction rates, and difficulty in ensuring consistent final product quality.

[0005] In view of this, this application proposes a method and system for dynamic pH control during plant calcium extraction. Summary of the Invention

[0006] To achieve the above objectives, this application provides a method and system for dynamic pH control during plant calcium extraction, the specific technical solution of which is as follows:

[0007] A method for dynamic pH control during plant calcium extraction includes:

[0008] Data on calcium dissolution rates at different pH and temperature were obtained, and a mapping relationship between pH-temperature and calcium dissolution rate was established by fitting. A lookup table model of pH-temperature and calcium dissolution rate was constructed.

[0009] Based on the constructed lookup table model, a multi-stage optimal control problem is established. The extraction process is divided into multiple extraction periods. The objective function is to minimize the total extraction time. Constraints are set on calcium extraction rate, pH and temperature change rate, and pH and temperature operating range. The duration of each stage and the set values ​​of pH and temperature are used as optimization variables to participate in the solution.

[0010] The optimal control problem is solved by dynamic programming. The time is discretized into adaptive step size. At each time step, the reaction rate corresponding to pH and temperature is looked up using a lookup table model. The cost function is calculated for different pH and temperature values. The optimal pH and temperature values ​​at each time are obtained by reverse recursion, generating a step-like control sequence. The continuous control trajectory of pH and temperature values ​​is obtained by smoothing.

[0011] Design a composite controller with feedforward and feedback. The feedforward part outputs a reference control quantity according to the preset optimal pH and temperature control trajectory. The feedback part adjusts according to the deviation between the measured pH and temperature values ​​and the set values. Based on the calcium concentration deviation detection mechanism, it is determined that when the calcium concentration detection value deviates significantly from the expectation, the control trajectory replanning is triggered.

[0012] A control trajectory correction mechanism is established, with calcium concentration deviation threshold and extraction time over-limit threshold set as trigger conditions. After triggering, the optimal pH and temperature control trajectory for the remaining process are recalculated based on the current state, and the new control trajectory is updated to the composite controller in real time.

[0013] Preferably, a quadratic polynomial regression model of pH-temperature and calcium dissolution rate is established using response surface methodology, and the coefficients of the quadratic polynomial regression model are determined by least squares fitting.

[0014] A lookup table model of pH-temperature and calcium dissolution rate was constructed. The fitted continuous function was discretized into a lookup table. The change step size of pH and temperature was set, and a lookup grid was established. For lookup requests at non-grid points, the rate value was obtained by bilinear interpolation.

[0015] Preferably, the extraction process of plant calcium is divided into different extraction stages: acidic dissolution period, neutral transition period, and alkaline extraction period, and different pH constraint ranges are set for each extraction stage.

[0016] The objective function is to minimize the total extraction time. A calcium extraction rate constraint is set, and the calcium accumulation is obtained by integrating the dissolution rate in the lookup table model. Constraints are also set for the rate of pH change and the rate of temperature change.

[0017] Preferably, an optimized set of variables is set for each extraction stage, including stage duration, starting and ending pH values, and starting and ending temperatures; inter-stage transition constraints are added to maintain the continuity of pH and temperature when switching between adjacent stages;

[0018] Simultaneously, pH and temperature operating range constraints were set for the entire extraction process of plant calcium.

[0019] Preferably, the time axis of the entire extraction process of plant calcium is divided into equally spaced discrete time steps, and a three-dimensional state space is defined that includes the current time step, the current amount of calcium extracted, and the current extraction stage.

[0020] Construct a cost function that comprehensively considers time cost and extraction efficiency, including a time step term and a quadratic penalty term for changes in control variables;

[0021] The Bellman equation is used to recursively calculate the value function. Starting from the termination time, the recursion proceeds backward. At each time step, the combinations of pH and temperature within the constraints are enumerated, and the control value that minimizes the total cost is selected as the optimal decision.

[0022] Preferably, a ladder-like control sequence is generated by forward backtracking, and the optimal pH and temperature values ​​for each time step are determined sequentially from the initial state according to the optimal strategy table obtained by reverse recursion.

[0023] A combination of moving average filtering and spline interpolation is used to smooth the stepped control sequence. First, moving average filtering is applied to the stepped sequence to eliminate high-frequency jitter, and then cubic spline interpolation is used to generate a continuous control trajectory.

[0024] The feasibility of the generated control trajectory is verified. Numerical integration along the control trajectory is performed to verify whether the final calcium extraction amount meets the target requirements. The derivative of the control trajectory is calculated to check whether the pH and temperature change rates meet the constraints.

[0025] Preferably, a feedforward and feedback composite controller is designed to regulate the pH and temperature during the plant calcium extraction process. The feedforward and feedback composite controller includes a feedforward control part and a feedback control part.

[0026] The feedforward control section generates a reference control signal based on the preset optimal pH and temperature control trajectory. According to the time progress, it looks up the set value at the corresponding time in the lookup table model of pH-temperature and calcium dissolution rate and outputs the corresponding control quantity.

[0027] The feedback control section uses a proportional-integral control algorithm. It calculates the correction amount based on the deviation between the real-time measured values ​​of pH and temperature sensors and the set values. The feedforward control amount and the feedback correction amount are superimposed as the output of the feedback control section.

[0028] An adaptive adjustment mechanism for controller parameters is set up to dynamically adjust the proportional and integral parameters of the feedforward and feedback composite controller according to different extraction stages.

[0029] Preferably, the deviation of calcium concentration is monitored, the deviation rate between the actual calcium concentration and the expected value is calculated, and a replanning trigger signal is generated when the deviation rate exceeds a set threshold.

[0030] Establish control quantity limiting and change rate limiting mechanisms to ensure that the output pH and temperature control signals are within the actuator's capability range.

[0031] Preferably, a dual triggering criterion mechanism is set up, including calcium concentration deviation triggering and extraction time exceeding the limit triggering. A sliding window strategy is used to determine the triggering conditions, and trajectory replanning is only started when multiple consecutive sampling points meet the triggering conditions.

[0032] A fast solution strategy that reduces the search space is adopted, the remaining time range is estimated based on the remaining extraction amount, and the discrete granularity of pH and temperature is adaptively adjusted.

[0033] The trajectory is updated through a gradual switching strategy, and the old and new control trajectories are weighted and fused using a time-varying weight function during the transition time.

[0034] A dynamic pH control system for plant calcium extraction, used in the aforementioned dynamic pH control method for plant calcium extraction, includes: a lookup table model construction module, an optimal control problem construction module, a dynamic programming solution module, a composite controller module, and a control trajectory correction module;

[0035] The lookup table model construction module is used to obtain calcium dissolution rate data at different pH and temperature, fit and create a mapping relationship between pH-temperature and calcium dissolution rate, and construct a lookup table model between pH-temperature and calcium dissolution rate.

[0036] The optimal control problem construction module establishes a multi-stage optimal control problem based on the constructed lookup table model. The extraction process is divided into multiple extraction periods. The objective function is to minimize the total extraction time. Constraints are set on calcium extraction rate, pH and temperature change rate, and pH and temperature operating range. The duration of each stage and the pH and temperature setpoints are used as optimization variables to participate in the solution.

[0037] The dynamic programming solution module uses dynamic programming to solve the optimal control problem. It discretizes time into adaptive step size, uses a lookup table model to look up the reaction rate corresponding to pH and temperature at each time step, calculates the cost function under different pH and temperature values, obtains the optimal pH and temperature values ​​at each time by reverse recursion, generates a step-like control sequence, and obtains the continuous control trajectory of pH and temperature values ​​through smoothing.

[0038] The composite controller module is designed as a feedforward and feedback composite controller. The feedforward part outputs a reference control quantity according to the preset optimal pH and temperature control trajectory. The feedback part adjusts according to the deviation between the measured pH and temperature values ​​and the set values. Based on the calcium concentration deviation detection mechanism, it is determined that when the calcium concentration detection value deviates significantly from the expectation, the control trajectory replanning is triggered.

[0039] The control trajectory correction module creates a control trajectory correction mechanism, sets a calcium concentration deviation threshold and an extraction time exceedance threshold as trigger conditions, and after triggering, recalculates the optimal pH and temperature control trajectory for the remaining process based on the current state, and updates the new control trajectory to the composite controller in real time.

[0040] The beneficial effects of this application are as follows: This application establishes an accurate process characteristic model through experiments and data fitting; the created lookup table model transforms complex function calculations into efficient queries, providing a fast and accurate data foundation for subsequent dynamic optimization, and ensuring the scientific nature and reliability of the control strategy.

[0041] This application transforms complex engineering objectives into well-structured mathematical optimization problems, with the goal of minimizing total time. It also comprehensively considers constraints such as product quality, equipment capacity, and operational safety, ensuring the economy, feasibility, and safety of the final optimized solution.

[0042] This application employs a dynamic programming method, which can find the globally optimal control strategy, fundamentally improving efficiency. Subsequent smoothing processes generate continuous control trajectories, making them easy for physical devices to execute precisely, thus achieving a balance between theoretical optimality and engineering feasibility.

[0043] The feedforward and feedback composite controller designed in this application achieves high-precision tracking of the optimal trajectory. The feedforward control provides fast trajectory following capability, while the feedback control compensates for model errors and external disturbances. The two work together to ensure the accurate implementation of the optimization strategy.

[0044] The trajectory correction mechanism created in this application endows the plant calcium extraction process with adaptive capabilities in the face of significant uncertainties. When the process deviates significantly, it can automatically replan the optimal path for the remaining processes, greatly enhancing the robustness of the method and ensuring a high degree of consistency in the quality of the final product. Attached Figure Description

[0045] Figure 1 This application provides a flowchart of a method for dynamic pH control during plant calcium extraction.

[0046] Figure 2 The flowchart for dynamic programming solution and control trajectory generation provided in this application;

[0047] Figure 3 A flowchart of the composite controller with feedforward and feedback provided for this application;

[0048] Figure 4 A flowchart illustrating the control trajectory correction mechanism provided in this application;

[0049] Figure 5This is a structural diagram of a dynamic pH control system for the extraction of calcium from plants, provided in this application. Detailed Implementation

[0050] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the specific embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0051] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0052] Secondly, the term "an embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of this application. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single embodiment or an embodiment selectively excluded from other embodiments.

[0053] Example 1

[0054] Reference Figures 1 to 4 This is the first embodiment of the present application, such as Figure 1 As shown, a method for dynamic pH control during plant calcium extraction is provided.

[0055] Step 1: Obtain calcium dissolution rate data at different pH and temperature, fit and create a mapping relationship between pH-temperature and calcium dissolution rate, and construct a lookup table model of pH-temperature and calcium dissolution rate.

[0056] In the extraction of calcium from plants, pH and temperature are key factors affecting the calcium dissolution rate. To achieve precise dynamic control, it is first necessary to establish a quantitative relationship model between pH, temperature, and calcium dissolution rate. This step involves obtaining basic data through experiments and constructing a lookup table model to provide data support for subsequent optimization control.

[0057] An orthogonal experiment was designed to obtain data on pH, temperature, and calcium dissolution rate. For example, the pH range was divided into 2.0 to 12.0, with 21 pH test points at 0.5 intervals; the temperature range was 20℃ to 80℃, with 13 temperature test points at 5℃ intervals. Under each pH-temperature combination, the same mass of plant material was used for calcium extraction experiments, with each experiment repeated three times to ensure data reliability. During the experiment, the pretreated plant material was placed in a constant-temperature reactor, and an extraction solution with a specific pH value was added. Extraction was carried out with stirring at the set temperature, maintaining a stirring speed of 300 rpm. Samples were taken every 10 minutes for 2 consecutive hours, and the calcium ion concentration in the extract was determined using atomic absorption spectrometry. This systematic experimental design comprehensively covers the operating conditions that may occur in actual production, ensuring the applicability and accuracy of subsequent models.

[0058] The calcium dissolution rate was calculated using the finite difference method. Calcium dissolution rate at each sampling time point The calculation formula is: ;in, Indicates the first Calcium ion concentration (mg / L) at each sampling time point. Indicates the first Calcium ion concentration at each sampling time point This indicates the sampling time interval. The average calcium dissolution rate at each time point is taken as the representative dissolution rate value under that pH-temperature condition. This calculation method can effectively eliminate the influence of instantaneous fluctuations and obtain stable and reliable rate data.

[0059] In the data fitting phase, response surface methodology was used to establish the mapping relationship between pH-temperature and calcium dissolution rate. A quadratic polynomial regression model was constructed: ;in, This indicates that at a pH value of Temperature is Calcium dissolution rate under the given conditions (mg / (L·min)) The coefficient of the constant term, and These are the coefficients of the first-order terms for pH and temperature, respectively. and These are the coefficients of the quadratic terms for pH and temperature, respectively. The coefficients represent the interaction term between pH and temperature. The least squares method was used to fit the experimental data to determine the values ​​of each coefficient.

[0060] A gridded storage strategy is employed to construct a lookup table model, discretizing the fitted continuous function into a lookup table. A refined lookup grid is established with a step size of 0.1 in the pH dimension and 1℃ in the temperature dimension. For each grid node... , This represents the j-th pH value. This represents the k-th temperature, and the corresponding calcium dissolution rate is calculated using a fitted model. j and k are index parameters and are stored in a two-dimensional array.

[0061] For query requests that do not involve grid points, the rate value is obtained using bilinear interpolation.

[0062] ;in, Indicates the interpolation weights in the pH direction. Interpolation weights representing the temperature direction, , , , These represent the calcium dissolution rate values ​​of four adjacent grid points. The method of combining table lookup with interpolation ensures both lookup efficiency and high accuracy, and significantly improves the response speed of real-time control compared to directly calculating the fitting function.

[0063] To further improve the robustness of the lookup table model, boundary processing and outlier correction are performed on the lookup data. When the pH or temperature queried exceeds the experimental range, a boundary value truncation strategy is adopted to avoid extrapolation errors. Simultaneously, outliers in the lookup table are identified and smoothed, and median filtering is used to eliminate local abrupt changes. These measures ensure that the lookup table model provides reasonable and reliable rate predictions across the entire operating range.

[0064] The pH-temperature and calcium dissolution rate lookup table model established in this step enables a rapid mapping between key parameters and target responses in the plant calcium extraction process, providing an efficient rate lookup interface for subsequent multi-stage optimization control. Simultaneously, the model construction method based on experimental data ensures the accuracy of the predictions; the relative error between the predicted values ​​from the lookup model and the validation experiments is quite small, laying a solid data foundation for achieving precise dynamic pH control.

[0065] Step 2: Based on the constructed lookup table model, establish a multi-stage optimal control problem, divide the extraction process into multiple extraction periods, take minimizing the total extraction time as the objective function, set constraints on calcium extraction rate, pH and temperature change rate, and pH and temperature operating range, and use the duration of each stage, pH and temperature setpoints as optimization variables to participate in the solution.

[0066] Based on the lookup table model constructed in step 1, this step establishes a framework for the multi-stage optimal control problem of plant calcium extraction. Considering the differences in the dissolution mechanism of plant calcium under different pH conditions, the entire extraction process is scientifically divided into three characteristic stages: acidic dissolution period, neutral transition period, and alkaline extraction period. By constructing an optimization problem with the goal of minimizing the total extraction time, the extraction efficiency of plant calcium is maximized.

[0067] In terms of stage division, the acidic dissolution stage corresponds to a pH range of 2.0-5.0. This stage primarily relies on acidolysis to disrupt the plant cell wall structure and release bound calcium. The neutral transition stage corresponds to a pH range of 5.0-8.0. This stage achieves a smooth transition from acidic to alkaline conditions, avoiding calcium precipitation loss caused by drastic pH changes. The alkaline extraction stage corresponds to a pH range of 8.0-12.0. This stage promotes the conversion and dissolution of insoluble calcium salts under alkaline conditions. The duration of each stage is dynamically determined based on actual extraction needs, without setting a fixed ratio. This flexible stage division strategy fully utilizes the extraction advantages under different pH conditions, improving overall extraction efficiency.

[0068] The objective function is constructed with minimizing the total extraction time as its core objective, and its mathematical expression is: ;in, Indicates the total extraction time. Indicates the first The duration of each phase These correspond to the acidic dissolution period, the neutral transition period, and the alkaline extraction period, respectively.

[0069] Create a calcium extraction rate constraint to ensure the final product quality meets requirements. The constraint condition is expressed as follows: ;in, Indicates the total calcium extraction rate. This indicates the quality of the extracted calcium. This indicates the total calcium mass in the raw materials. This represents the target extraction rate. For example, for high-quality plant-based calcium products, the target extraction rate can be set to 0.85, meaning that at least 85% of the calcium in the raw material must be extracted. The cumulative calcium content during the extraction process is calculated using the dissolution rate in an integral lookup table model, ensuring the real-time verifiability of the constraints.

[0070] A pH change rate constraint is constructed to prevent excessively rapid pH adjustments from impacting the reaction system during plant calcium extraction. The constraint expression is as follows: ;in, Indicates the first pH values ​​at each sampling time point, where t is time. This indicates the maximum rate of pH change (pH / min). For example, based on the mixing capacity of an industrial stirred reactor, It can be set to 0.5 pH / min. The pH change rate constraint ensures the stability of pH adjustment and avoids calcium precipitation or equipment corrosion caused by local pH unevenness.

[0071] To construct a temperature change rate constraint, considering the actual capacity of the heating and cooling equipment, the temperature change rate constraint condition is as follows: ;in, Indicates the first Temperature at each sampling time point, This indicates the maximum rate of temperature change. For example, based on the heat transfer capacity of an industrial-grade heat exchanger... The set temperature change rate is 2℃ / min. This reasonable constraint on the rate of temperature change ensures the feasibility of temperature control while avoiding damage to the equipment from thermal stress.

[0072] Set pH operating range constraints to ensure the extraction process is conducted within a safe and effective range: ;in, Indicates the first pH values ​​at each sampling time point Indicates the lower limit of pH. This indicates the upper limit of pH. For example, depending on the corrosion resistance of the equipment material and the requirements of the extraction process, the pH operating range can be set to 2.0-12.0; the pH operating range constraint prevents extreme pH conditions from damaging the equipment, while ensuring the safety of the extraction process.

[0073] Set temperature operating range constraints to maintain the plant calcium extraction process within a reasonable temperature range. :in, Indicates the lower limit of temperature. This indicates the upper limit of the temperature. Considering energy consumption control and extract stability, the operating temperature range is set at 20-80℃. An appropriate temperature range can ensure extraction efficiency while preventing degradation of active ingredients caused by high temperatures.

[0074] Optimize variable settings, including key control parameters for each stage. For each stage... Set up the set of optimization variables ,in Indicates the first Phase duration, and They represent the first The starting and ending pH values ​​of the phase, and They represent the first The start and end temperatures of each stage. By optimizing these variables, the optimal operating conditions and switching timing for each stage can be determined.

[0075] To ensure continuity between stages, add transition constraints: ;in, Indicates the sequence number of adjacent stages. and This indicates two adjacent stages.

[0076] This step establishes a multi-stage optimal control problem framework, transforming the complex plant calcium extraction process into a mathematical optimization problem. It clarifies the optimization objective and constraints, providing a standardized problem description for subsequent solution algorithms. The multi-stage partitioning strategy fully considers the differences in extraction mechanisms under different pH conditions, and the constraints balance extraction efficiency, product quality, and equipment safety. The constructed optimization problem exhibits good solvability and engineering practicality, laying a theoretical foundation for the intelligent control of the plant calcium extraction process.

[0077] Step 3: Solve the optimal control problem using dynamic programming. Discretize the time step into adaptive steps. At each time step, use a lookup table model to find the reaction rate corresponding to pH and temperature, calculate the cost function for different pH and temperature values, and obtain the optimal pH and temperature values ​​at each time step through reverse recursion. Generate a step-like control sequence, and obtain the continuous control trajectory for pH and temperature values ​​through smoothing. See also Figure 2 This is a flowchart for the dynamic programming solution and control trajectory generation in this step.

[0078] For the multi-stage optimal control problem established in step 2, this step uses dynamic programming to solve it. Through time discretization and state space search, the optimal pH and temperature control values ​​at each time point in the process of extracting calcium from plants are determined, and an executable continuous control trajectory is generated.

[0079] The extraction process is discretized, dividing the entire extraction time of plant calcium into equally spaced discrete time steps. The discrete time step size is then set. The total extraction time was divided into Each time step, i.e. ,in This indicates the estimated maximum extraction time. This indicates a rounding up operation. For example, when the estimated maximum extraction time is 180 minutes, the time step can be set to 1 minute, resulting in a total of 180 discrete time points.

[0080] The definition of state space includes three dimensions: the current time step. Current calcium extraction volume and the current extraction stage At each time step, the feasible range of pH and temperature values ​​is determined based on the current stage and rate of change constraints. pH discretization employs an adaptive step-size strategy, using smaller step sizes during the acidic dissolution and alkaline extraction phases to improve control accuracy, and larger step sizes during the neutral transition phase to accelerate computation. Temperature discretization uses a uniform step size to ensure smooth temperature control.

[0081] The construction of the cost function comprehensively considers time cost and extraction efficiency, for time steps arrive The state transition, the cost function is defined as: ;in, Indicates the first The switching cost of the step and They represent the first pH and temperature of the step, This indicates the change in pH value. , representing the amount of temperature change. Indicates the penalty coefficient. This represents a penalty function for changes in the control variable. The penalty function is in quadratic form. It is used to suppress drastic changes in control variables and improve the stability of control. It is the independent variable of the penalty function. , .

[0082] The value function is recursively calculated using the Bellman equation. The value function represents the minimum cumulative cost from a given state to the endpoint under the optimal policy, and is obtained recursively from the end state to the beginning using the Bellman equation after setting the terminal conditions. The value function is defined as follows: To start from time step To begin, with the current extraction volume being... In the stage Under the given conditions, the minimum cost required to achieve the target extraction rate can be expressed recursively as follows:

[0083]

[0084] in, This indicates taking the minimum value. This indicates the updated calcium extraction amount. This represents the calcium dissolution rate under current conditions obtained through a lookup table model. Indicates according to The new phase identifier is determined. Boundary conditions are set as follows: when hour, ;otherwise ,in Indicates the target calcium extraction amount. This represents the amount of calcium extracted at the Nth time step. It is the value function at the terminal moment, that is, the minimum cumulative cost at time step N.

[0085] The reverse recursive solution process starts from the termination time and gradually progresses towards the initial time. At each time step... For all feasible The combination is enumerated, the sum of the corresponding transfer costs and future costs is calculated, and the control value that minimizes the total cost is selected as the optimal decision at that moment.

[0086] In the search for pH and temperature values ​​at each time step, the fast lookup characteristic of the table lookup model is fully utilized. For a given... The combination allows for direct retrieval of calcium dissolution rates from a lookup table model. This avoids complex function calculations. When the query point is not on a grid node, bilinear interpolation is used to obtain the rate value, ensuring the continuity and accuracy of rate prediction.

[0087] A stepped control sequence is generated by forward backtracking. Starting from the initial state, the optimal pH and temperature values ​​for each time step are determined sequentially based on the optimal strategy table obtained by backward recursion, forming a discrete control sequence. ,in, The first one obtained by dynamic programming Step to the optimal pH setting value, The first one obtained by dynamic programming The optimal temperature setpoint is determined step by step. Although the step sequence meets the pH optimization requirements, it may cause frequent adjustments to the controller in actual production applications, increasing the difficulty of execution.

[0088] To smooth the discrete control sequence, a combination of moving average filtering and spline interpolation is used. First, a moving average filter is applied to the step-like sequence, with the window width set to... At each time step, the filtered pH value is calculated as follows:

[0089]

[0090] in, Indicates the filtered first... pH value of the step, The number of time steps is the window width. For index parameters, This indicates the floor function. It is the th element in the optimal discrete control sequence obtained by reverse recursion. The optimal pH setpoint for each time step is used for subsequent moving average filtering and spline interpolation. For example, when the window width is set to 5, the filtered value for each point is determined by the average of the two points before and after it. The temperature series undergoes the same filtering process. The filtered control series eliminates high-frequency jitter while still maintaining the main trend.

[0091] Furthermore, cubic spline interpolation is used to generate a continuous control trajectory. This is applied to the filtered discrete point sequence. Perform spline fitting. Indicates the first The timestamps of discrete time points are used to obtain the continuous pH control trajectory function. Spline functions in each interval The inner expression is a cubic polynomial, satisfying the second derivative continuity condition at the nodes, ensuring the smoothness of the control trajectory. Temperature control trajectory. The same method was used to generate the continuous control trajectory. The generated trajectory retains the optimality characteristics of the optimization solution while also meeting the smoothness requirements of actual control.

[0092] A feasibility check is performed on the generated continuous control trajectory. Numerical integration is performed along the control trajectory to verify whether the final calcium extraction amount meets the target requirements. The derivative of the control trajectory is calculated to check whether the pH and temperature change rates meet the constraints. It is confirmed that the pH and temperature values ​​throughout the control trajectory are within the operating range. If the verification fails, the smoothing parameters are adjusted and the control trajectory is regenerated until all constraints are met.

[0093] The dynamic programming solution and control trajectory generation in this step transform the complex optimal control problem into an executable control strategy. The generated continuous control trajectory balances optimality and feasibility. The dynamic programming method guarantees the acquisition of the global optimal solution and avoids the trap of local optima; the smoothing technique makes the control trajectory more suitable for actual execution and reduces the adjustment burden on the controller; thus, a reliable control trajectory planning scheme is provided for the precise control of the plant calcium extraction process.

[0094] Step 4: Design a composite controller with feedforward and feedback. The feedforward part outputs a reference control quantity according to the preset optimal pH and temperature control trajectory. The feedback part adjusts based on the deviation between the measured pH and temperature values ​​and the set values. When the detected calcium concentration value deviates significantly from the expected value, it triggers control trajectory replanning. See [link / reference] Figure 3 This is a flowchart of the design of a feedforward and feedback composite controller for this step.

[0095] Based on the optimal control trajectory generated in step 3, this step designs a feedforward and feedback composite controller structure to achieve precise tracking and control of pH and temperature during the extraction of calcium from plants, and establishes a calcium concentration deviation detection mechanism to ensure the stability and robustness of the extraction process.

[0096] The composite controller employs a dual-channel parallel architecture, independently controlling pH and temperature. Each channel comprises a feedforward controller and a feedback controller. The feedforward controller generates a reference control signal based on a preset optimal control trajectory, providing the primary driving force for control. The feedback controller compensates for deviations between measured and setpoint values, eliminating the effects of disturbances and model errors. This composite structure fully leverages the foresight of control trajectory planning and the adaptability of feedback control, enabling high-precision control trajectory tracking.

[0097] The feedforward controller for the pH channel is based on the optimal pH control trajectory. Calculate the required acid-base addition rate; the formula for calculating the feedforward control quantity is: ;in, This represents the feedforward control factor for pH, i.e., the rate at which acid or alkaline solutions are added. This represents the pH feedforward gain coefficient (mL·min / pH unit). This represents the rate of change of the optimal pH control trajectory (pH units / min). This represents the baseline addition rate (mL / min) required to maintain the current pH. The feedforward gain coefficient is determined based on the reactor volume and the acid / base solution concentration; for example, for a 1000L reactor using a 2mol / L acid / base solution, The value was taken as 50 mL·min / pH unit. The baseline addition rate was obtained through steady-state experiments to compensate for natural pH drift during plant calcium extraction.

[0098] The feedforward controller for the temperature channel is based on the optimal temperature control trajectory. Calculate heating or cooling power; the expression for the feedforward control quantity is: ;in, This represents the temperature feedforward control quantity (kW), i.e., the heating / cooling power. This represents the temperature feedforward gain coefficient (kW·min / ℃). This represents the rate of change of the optimal temperature control trajectory. This represents the heat loss compensation amount (kW) at the current temperature. The temperature feedforward gain is calculated based on the reactor's heat capacity, and the heat loss compensation amount is estimated through a heat transfer model, taking into account the effects of ambient temperature and insulation conditions.

[0099] The pH feedback controller employs a proportional-integral (PI) control strategy to correct pH deviations in real time; the formula for calculating the feedback control quantity is: ;in, This indicates the pH feedback control level (mL / min). This indicates pH tracking error. This indicates the measured pH value. This indicates the pH proportional gain (mL·min / pH unit). This indicates the pH integral gain (mL / pH unit). Represents the integral variable. This represents the instantaneous tracking error of pH. The proportional term provides a fast response, while the integral term eliminates steady-state error.

[0100] The temperature feedback controller also uses a PI control structure: ;

[0101] in, This represents the temperature feedback control quantity (kW). Indicates temperature tracking error. This represents the measured temperature value. This indicates the temperature proportional gain (kW / ℃). This represents the temperature integral gain (kW·min / ℃). Represents the integral variable. This represents the instantaneous tracking error of the temperature. Control parameters are tuned through step response tests to ensure the speed and stability of temperature control.

[0102] The total output of the composite controller is the superposition of the feedforward and feedback control quantities: ; ;in, and These represent the total control outputs for pH and temperature, respectively. To prevent control saturation, an output limiting mechanism is implemented to confine the control quantity within the actuator's capability range. Simultaneously, an anti-integral saturation strategy is introduced, stopping the accumulation of the integral term when the control quantity reaches the limit value, thus avoiding overshoot problems caused by integral saturation.

[0103] A calcium concentration deviation detection mechanism monitors the progress of the extraction process in real time. A target control trajectory for calcium concentration is set. The dissolution rate is obtained through an integral lookup table model: ;in, Indicates time The expected calcium concentration (mg / L). This represents the dissolution rate function of the lookup table model. Represents the integral variable. Indicates at time The optimal pH setting value, Indicates at time The optimal temperature setting value.

[0104] Real-time detection of calcium concentration Calculate the relative deviation by comparing it with the expected value: ;in, This indicates the relative deviation of calcium concentration. A deviation threshold is set. Exemplary The value is set to 0.15, which allows for a 15% deviation. When the deviation exceeds the threshold for multiple consecutive sampling periods, it is considered a serious deviation, triggering a control trajectory replanning signal.

[0105] Offset detection uses a sliding window strategy, with a set window length. Each sampling period, when the window exceeds [number] sampling periods, A deviation event is confirmed when the deviation of a sampling point exceeds a threshold. This deviation detection method filters out the influence of instantaneous disturbances, avoiding frequent false triggers. For example, setting the window length to 5 sampling periods triggers replanning when the deviation of more than 3 sampling points exceeds the threshold, ensuring both timely detection and improved reliability of the judgment.

[0106] The composite controller integrates data logging and status monitoring functions to record setpoints and measured values ​​of pH and temperature in real time, calculate and store tracking errors and control outputs, and monitor the trend of calcium concentration changes. This data provides crucial information for process analysis and control optimization, as well as data support for anomaly diagnosis.

[0107] For example, pH adjustment is achieved by precisely adding acid and alkali solutions using metering pumps. When a decrease in pH is needed, the metering pump injects a specific concentration of acid (e.g., 2 mol / L hydrochloric acid solution) into the reactor at a set flow rate; when a increase in pH is needed, a specific concentration of alkali (e.g., 2 mol / L sodium hydroxide solution) is injected. Temperature control is achieved through a jacketed heat exchange system. When heating is required, hot water or low-pressure steam at 95°C is introduced into the jacket; when cooling is required, the system switches to a cooling water circulation system at 15°C. The injection rate of the acid and alkali solutions is dynamically calculated based on the pH deviation and reactor volume, with a typical injection rate range of 50-500 mL / min. The flow rate of the heat exchange medium is controlled by an electrically operated regulating valve, with a flow rate range of 10-100 L / min, ensuring that the rate of temperature change meets process requirements.

[0108] The feedforward and feedback composite controller designed in this step achieves precise tracking of the optimal pH and temperature control trajectories. The feedforward control provides rapid control trajectory following capability, while the feedback control compensates for model errors and external disturbances. The synergistic effect of the two can achieve accurate pH and temperature control precision. The constructed calcium concentration deviation detection mechanism promptly detects process anomalies and provides trigger signals for control trajectory adjustment, ensuring that the extraction process always operates in an optimal or near-optimal state, significantly improving the efficiency and stability of plant calcium extraction.

[0109] Step 5: Create a control trajectory correction mechanism, setting calcium concentration deviation thresholds and extraction time exceedance thresholds as trigger conditions. Upon triggering, the optimal pH and temperature control trajectories for the remaining process are recalculated based on the current state, and the new control trajectory is updated to the composite controller in real time. See also... Figure 4 This is a flowchart for creating the control trajectory correction mechanism in this step.

[0110] This step creates a control trajectory correction mechanism. By setting multiple trigger conditions, the extraction process status is monitored in real time. When an abnormal deviation is detected, the control trajectory replanning program is automatically started to ensure that the extraction process can adapt to changes in raw material characteristics and external disturbances, and maintain optimal control performance.

[0111] The control trajectory correction triggering condition design employs a dual-criteria mechanism, including a first criterion and a second criterion. The first criterion is triggered by calcium concentration deviation, determined by real-time comparison of the actual calcium concentration with the expected calcium concentration. The calcium concentration deviation rate is defined as: ;in, Indicates the calcium concentration deviation rate. This indicates the actual measured calcium concentration at the current moment. This represents the expected calcium concentration planned based on the initial control trajectory. When Time-triggered control trajectory replanning, among which This represents the calcium concentration deviation rate threshold. For example, in a high-precision extraction process... It can be set to 0.15, meaning that correction will be initiated when the actual concentration deviates from the expected value by more than 15%. The relative deviation criterion can adapt to the control accuracy requirements at different concentration levels, avoiding the problem that the absolute deviation criterion is too sensitive at low concentrations and too insensitive at high concentrations.

[0112] The second criterion is triggering the extraction time limit, used to prevent the extraction process from being excessively prolonged. The time limit exceeding the limit indicator is defined as follows: ;in, Indicates the time progress ratio. Indicates the extraction time that has already occurred. This indicates the planned cumulative time corresponding to that moment. When Time-triggered control trajectory replanning, among which This indicates a time limit exceeding the threshold. For example, The time limit is set to 1.2, meaning that a correction is initiated when the actual time exceeds the planned time by 20%. This time limit exceedance criterion ensures the controllability of the production schedule and prevents the overall production plan from spiraling out of control due to a decrease in local efficiency.

[0113] The trigger condition determination adopts a sliding window strategy to improve robustness, and the determination window width is set to [value missing]. Each sampling period, only when continuous Control trajectory replanning only begins when all sampling points meet the triggering conditions. The sliding window strategy effectively filters out the effects of instantaneous measurement noise and brief disturbances, avoiding the disruption of control system stability caused by frequent control trajectory adjustments. For example, when the sampling period is 30 seconds and the window width is set to 3, a continuous 1.5-minute abnormal state is required to trigger correction, ensuring both timely response and maintaining the stability of the extraction process.

[0114] The control trajectory replanning algorithm reconstructs the optimization problem based on the current state, defining a new objective function as follows:

[0115]

[0116] in, This represents the objective function value for reprogramming. Indicates the index of the current time step. This represents the total number of time steps to be re-estimated. Indicates the first The duration of each time step. This represents the penalty weight for deviations in extraction volume. This represents the final expected extraction amount of the replanned control trajectory. This represents the target calcium extraction amount. Compared to the initial planning, the replanning objective function incorporates consideration of extraction accuracy by adjusting the weights. Balancing the requirements of time efficiency and extraction accuracy.

[0117] During the reprogramming process, constraints are inherited and updated from the original constraint system. The initial values ​​of pH and temperature are updated to the current actual measured values ​​to ensure the continuity of the control trajectory. ;in, and These represent the currently measured pH value and temperature, respectively. , These represent the pH and temperature at the current time step, respectively. The remaining extraction capacity constraint is adjusted to... ,in, This represents the remaining amount of calcium to be extracted. The time constraint is appropriately relaxed based on the flexibility of the production plan, representing the difference between the target and the current cumulative extraction amount. The rate of change constraint remains unchanged to ensure the executability of the replanned control trajectory.

[0118] A search space reduction method is employed as a fast solution strategy to improve reprogramming efficiency. The remaining time range is estimated based on the remaining extraction amount and the current extraction rate, limiting the search space to a reasonable interval. The discrete granularity of pH and temperature is adaptively adjusted, using fine granularity during critical transition periods and coarse granularity during stable periods to achieve a balance between accuracy and efficiency. The initial control trajectory is used as heuristic information, prioritizing the search of the solution space near the initial control trajectory to accelerate the convergence process.

[0119] A gradual switching strategy is adopted for control trajectory updates to ensure control smoothness, and a transition time is defined. During this period, the old and new control trajectories are merged using a weighted average: ;in, This represents the pH control trajectory after fusion. and These represent the pH values ​​of the original control trajectory and the new control trajectory, respectively. The time-varying weighting function decreases linearly from 1 to 0. The temperature control trajectory uses the same fusion method. For example, the transition time is set to 2 minutes to ensure that changes in the control quantity do not impact the current state of plant calcium extraction.

[0120] The newly generated control trajectory undergoes feasibility and safety checks. Forward simulation is used to predict the calcium extraction process under the new control trajectory, verifying whether the final extraction rate meets requirements. The pH and temperature change rates throughout the control trajectory are checked to ensure they do not exceed equipment capacity limits. The impact of control trajectory switching on downstream processes is assessed, and adjustment notifications are sent to relevant systems if necessary. Only control trajectories that pass all verifications are officially applied to the control system.

[0121] The control trajectory correction mechanism established in this step achieves closed-loop optimized control of the extraction process, enabling timely response to process deviations and external disturbances, and dynamic adjustment of the control strategy. Dual triggering criteria ensure the necessity and timeliness of corrections, a fast reprogramming algorithm guarantees the feasibility of online application, and incremental control trajectory updates maintain control smoothness. The constructed correction mechanism improves the robustness and adaptability of the plant calcium extraction process, maintaining near-optimal control performance even under uncertainties such as fluctuations in raw material characteristics and changes in equipment performance. This significantly enhances the stability and reliability of the extraction process, ensuring the consistency of the final product quality.

[0122] Example 2

[0123] Reference Figure 5 This is the second embodiment of the present application, which provides a dynamic pH control system for the extraction of calcium from plants.

[0124] The system includes: a lookup table model construction module, an optimal control problem construction module, a dynamic programming solution module, a composite controller module, and a control trajectory correction module.

[0125] The lookup table model construction module is used to obtain calcium dissolution rate data at different pH and temperature, fit and create a mapping relationship between pH-temperature and calcium dissolution rate, and construct a lookup table model of pH-temperature and calcium dissolution rate.

[0126] The optimal control problem construction module establishes a multi-stage optimal control problem based on the constructed lookup table model. The extraction process is divided into multiple extraction periods. The objective function is to minimize the total extraction time. Constraints are set on calcium extraction rate, pH and temperature change rate, and pH and temperature operating range. The duration of each stage and the set values ​​of pH and temperature are used as optimization variables to participate in the solution.

[0127] The dynamic programming solution module uses dynamic programming to solve the optimal control problem. It discretizes time into adaptive step sizes, uses a lookup table model to look up the reaction rate corresponding to pH and temperature at each time step, calculates the cost function for different pH and temperature values, obtains the optimal pH and temperature values ​​at each time step through reverse recursion, generates a step-like control sequence, and obtains the continuous control trajectory of pH and temperature values ​​through smoothing.

[0128] The composite controller module is designed as a feedforward and feedback composite controller. The feedforward part outputs a reference control quantity according to the preset optimal pH and temperature control trajectory. The feedback part adjusts according to the deviation between the pH and temperature measurement values ​​and the set values. When the calcium concentration detection value deviates significantly from the expectation, the control trajectory is replanned.

[0129] The control trajectory correction module creates a control trajectory correction mechanism, sets a calcium concentration deviation threshold and an extraction time exceedance threshold as trigger conditions, and after triggering, recalculates the optimal pH and temperature control trajectory for the remaining process based on the current state, and updates the new control trajectory to the composite controller in real time.

[0130] In the embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the displayed or discussed mutual couplings or direct couplings or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0131] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments under the guidance of this application without departing from the spirit and scope of protection of the claims. All of these variations are within the protection scope of this application.

Claims

1. A method for dynamic pH control during plant calcium extraction, characterized in that, include: Data on calcium dissolution rates at different pH and temperature were obtained, and a mapping relationship between pH-temperature and calcium dissolution rate was established by fitting. A lookup table model of pH-temperature and calcium dissolution rate was constructed. Based on the constructed lookup table model, a multi-stage optimal control problem is established. The extraction process is divided into multiple extraction periods. The objective function is to minimize the total extraction time. Constraints are set on calcium extraction rate, pH and temperature change rate, and pH and temperature operating range. The duration of each stage and the set values ​​of pH and temperature are used as optimization variables to participate in the solution. The optimal control problem is solved by dynamic programming. The time is discretized into adaptive step size. At each time step, the reaction rate corresponding to pH and temperature is looked up using a lookup table model. The cost function is calculated for different pH and temperature values. The optimal pH and temperature values ​​at each time are obtained by reverse recursion, generating a step-like control sequence. The continuous control trajectory of pH and temperature values ​​is obtained by smoothing. Construct a cost function for each time step. arrive The state transition, the cost function is defined as: ; Indicates the first The switching cost of the step and They represent the first pH and temperature of the step, This indicates the change in pH value. , Indicates the amount of temperature change. Indicates the penalty coefficient. This represents a penalty function for changes in the control variable; The Bellman equation is used to perform recursive calculation of the value function. The calculation is performed in reverse from the termination time. At each time step, the pH and temperature combinations within the constraints are enumerated, and the control value that minimizes the total cost is selected as the optimal decision. A stepped control sequence is generated by forward backtracking. Starting from the initial state, the optimal pH and temperature values ​​for each time step are determined sequentially based on the optimal strategy table obtained by backward recursion, forming a discrete control sequence. , The first one obtained by dynamic programming Step to the optimal pH setting value, The first one obtained by dynamic programming Step to the optimal temperature setpoint; Continuous control trajectories are generated using cubic spline interpolation, and the filtered discrete point sequences are then analyzed. Perform spline fitting. Indicates the first The timestamps of discrete time points are used to obtain the continuous pH control trajectory function. ; Design a composite controller with feedforward and feedback. The feedforward part outputs a reference control quantity according to the preset optimal pH and temperature control trajectory. The feedback part adjusts according to the deviation between the measured pH and temperature values ​​and the set values. Based on the calcium concentration deviation detection mechanism, it is determined that when the calcium concentration detection value deviates significantly from the expectation, the control trajectory replanning is triggered. A control trajectory correction mechanism is established, with calcium concentration deviation threshold and extraction time over-limit threshold set as trigger conditions. After triggering, the optimal pH and temperature control trajectory for the remaining process are recalculated based on the current state, and the new control trajectory is updated to the composite controller in real time.

2. The method for dynamic pH control during plant calcium extraction according to claim 1, characterized in that, A quadratic polynomial regression model of pH-temperature and calcium dissolution rate was established using response surface methodology, and the coefficients of the quadratic polynomial regression model were determined by least squares fitting. A lookup table model of pH-temperature and calcium dissolution rate was constructed. The fitted continuous function was discretized into a lookup table. The change step size of pH and temperature was set, and a lookup grid was established. For lookup requests at non-grid points, the rate value was obtained by bilinear interpolation.

3. The method for dynamic pH control during plant calcium extraction according to claim 2, characterized in that, The extraction process of plant calcium is divided into different extraction stages: acidic dissolution period, neutral transition period, and alkaline extraction period. Different pH constraint ranges are set for each extraction stage. The objective function is to minimize the total extraction time. A calcium extraction rate constraint is set, and the calcium accumulation is obtained by integrating the dissolution rate in the lookup table model. Constraints are also set for the rate of pH change and the rate of temperature change.

4. The method for dynamic pH control during plant calcium extraction according to claim 3, characterized in that, For each extraction stage, set up an optimized set of variables, including stage duration, start and end pH values, and start and end temperatures; add inter-stage transition constraints. Simultaneously, pH and temperature operating range constraints were set for the entire extraction process of plant calcium.

5. The method for dynamic pH control during plant calcium extraction according to claim 4, characterized in that, A combination of moving average filtering and spline interpolation is used to smooth the stepped control sequence. First, the stepped sequence is subjected to moving average filtering, and then cubic spline interpolation is used to generate a continuous control trajectory. The feasibility of the generated control trajectory is verified. Numerical integration along the control trajectory is performed to verify whether the final calcium extraction amount meets the target requirements. The derivative of the control trajectory is calculated to check whether the pH and temperature change rates meet the constraints.

6. The method for dynamic pH control during plant calcium extraction according to claim 5, characterized in that, Design a feedforward and feedback composite controller to regulate pH and temperature during the plant calcium extraction process. The feedforward and feedback composite controller includes a feedforward control part and a feedback control part. The feedforward control section generates a reference control signal based on the preset optimal pH and temperature control trajectory. According to the time progress, it looks up the set value at the corresponding time in the lookup table model of pH-temperature and calcium dissolution rate and outputs the corresponding control quantity. The feedback control section uses a proportional-integral control algorithm. It calculates the correction amount based on the deviation between the real-time measured values ​​of pH and temperature sensors and the set values. The feedforward control amount and the feedback correction amount are superimposed as the output of the feedback control section. An adaptive adjustment mechanism for controller parameters is set up to dynamically adjust the proportional and integral parameters of the feedforward and feedback composite controller according to different extraction stages.

7. The method for dynamic pH control during plant calcium extraction according to claim 6, characterized in that, The deviation of calcium concentration is monitored, the deviation rate between the actual calcium concentration and the expected value is calculated, and a replanning trigger signal is generated when the deviation rate exceeds a set threshold. Establish control quantity limiting and change rate limiting mechanisms to ensure that the output pH and temperature control signals are within the actuator's capability range.

8. The method for dynamic pH control during plant calcium extraction according to claim 7, characterized in that, A dual triggering criterion mechanism is set up, including calcium concentration deviation triggering and extraction time exceeding the limit triggering. A sliding window strategy is used to determine the triggering conditions, and trajectory replanning is only initiated when multiple consecutive sampling points meet the triggering conditions. A fast solution strategy that reduces the search space is adopted, the remaining time range is estimated based on the remaining extraction amount, and the discrete granularity of pH and temperature is adaptively adjusted. The trajectory is updated through a gradual switching strategy, and the old and new control trajectories are weighted and fused using a time-varying weight function during the transition time.

9. A pH dynamic control system for plant calcium extraction, used to implement the pH dynamic control method for plant calcium extraction as described in any one of claims 1 to 8, characterized in that, include: The system includes a lookup table model building module, an optimal control problem building module, a dynamic programming solution module, a composite controller module, and a control trajectory correction module. The lookup table model construction module is used to obtain calcium dissolution rate data at different pH and temperature, fit and create a mapping relationship between pH-temperature and calcium dissolution rate, and construct a lookup table model between pH-temperature and calcium dissolution rate. The optimal control problem construction module establishes a multi-stage optimal control problem based on the constructed lookup table model. The extraction process is divided into multiple extraction periods. The objective function is to minimize the total extraction time. Constraints are set on calcium extraction rate, pH and temperature change rate, and pH and temperature operating range. The duration of each stage and the pH and temperature setpoints are used as optimization variables to participate in the solution. The dynamic programming solution module uses dynamic programming to solve the optimal control problem. It discretizes time into adaptive step size, uses a lookup table model to look up the reaction rate corresponding to pH and temperature at each time step, calculates the cost function under different pH and temperature values, obtains the optimal pH and temperature values ​​at each time by reverse recursion, generates a step-like control sequence, and obtains the continuous control trajectory of pH and temperature values ​​through smoothing. The composite controller module is designed as a feedforward and feedback composite controller. The feedforward part outputs a reference control quantity according to the preset optimal pH and temperature control trajectory. The feedback part adjusts according to the deviation between the measured pH and temperature values ​​and the set values. Based on the calcium concentration deviation detection mechanism, it is determined that when the calcium concentration detection value deviates significantly from the expectation, the control trajectory replanning is triggered. The control trajectory correction module establishes a control trajectory correction mechanism, sets a calcium concentration deviation threshold and an extraction time exceedance threshold as trigger conditions, and after triggering, recalculates the optimal pH and temperature control trajectory for the remaining process based on the current state, and updates the new control trajectory to the composite controller in real time.

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