A data-driven closed-loop dynamic real-time operation optimization and predictive control method

Abstract

The present invention discloses a data-driven closed-loop dynamic real-time operation optimization and predictive control method, which belongs to the field of industrial process optimization and control technology. It proposes a framework that combines data-driven closed-loop dynamic real-time operation optimization with predictive control for industrial processes with complex dynamic characteristics and economic optimization requirements. First, real industrial process data is collected, and operational constraints and economic performance evaluation indicators are sorted out; secondly, a data-driven closed-loop dynamic real-time optimization model is established as an upper-level optimization model, and the optimal setting trajectory of the lower-level control model is calculated by the upper-level optimization model; then, a robust data-driven predictive control model is established as a lower-level control model, and the lower-level control model is solved to calculate the optimal control strategy. Finally, the first calculated control action is implemented for rolling optimization, and the results are fed back to the upper-level optimization model. The present invention can maintain good dynamic control performance while improving operational economy.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial process optimization control, and relates to a data-driven closed-loop dynamic real-time operation optimization and predictive control method, which is a data-based industrial process operation optimization method. Background Art

[0002] With intensifying market competition and rising production costs, industrial processes must not only maintain stable operation but also urgently improve economic efficiency and be able to respond promptly and effectively to various internal and external disturbances that affect actual production. Therefore, integrating economic operation optimization and control tracking in industrial process operations is crucial. However, the increasing complexity and dynamic nature of modern industrial processes pose a significant challenge to this integration task.

[0003] In the field of industrial process optimization and control, traditional methods often employ a single-layer optimization framework. For example, the Economic Model Predictive Control (EMPC) approach proposed by Liu and Cui et al. (X. Liu and J. Cui, “Economic model predictive control of boiler-turbine system,” JProcess Control, vol. 66, pp. 59–67, Jun. 2018, doi: 10.1016 / j.jprocont.2018.02.010.) optimizes the economic objective function of the boiler-turbine system directly within the controller, rather than simply tracking a preset setpoint. This approach balances economic performance with tracking performance by adjusting weighting coefficients. However, the computational cost of this single-layer optimization framework increases significantly with the scale and complexity of the controlled industrial process, and the optimization calculations require frequent triggering, making it difficult to generalize in many practical industrial applications.

[0004] To overcome the limitations of the single-layer optimization framework, Choi, Kim et al. introduced a two-layer optimization framework (K. Choi, Y.Kim, KS Kim, and SK Kim, “Real-Time Optimal Torque Control of Interior Permanent Magnet Synchronous Motors Based on a Numerical Optimization Technique,” ​​IEEE Transactions on Control Systems Technology, vol. 29, no. 4,pp. 1815–1822, Jul. 2021, doi: 10.1109 / TCST.2020.3006900.), which structurally separates the economic optimization and control tracking tasks. The upper layer of the framework is typically the Real-Time Optimization (RTO) layer, responsible for optimizing economic indicators. It operates at a lower frequency and primarily addresses disturbances and changes on larger timescales. The lower layer of the framework employs advanced strategies such as Model Predictive Control (MPC), with the primary goal of tracking the set points provided by the upper layer. However, traditional RTO optimization is typically based on steady-state assumptions, which can lead to suboptimal operation when faced with the frequently changing operating conditions and numerous unknown disturbances in actual industrial processes. Furthermore, the models used in the two layers of the framework differ, and mismatches between the models can negatively impact the control effectiveness and economic benefits of actual production.

[0005] To address the shortcomings of traditional RTO, MacKinnon, Ramesh, and others extended the steady-state RTO to dynamic real-time optimization (DRTO) (L. MacKinnon, PS Ramesh, P.Mhaskar, and CLE Swartz, “Dynamic real-time optimization for nonlinearsystems with Lyapunov stabilizing MPC,” J Process Control, vol. 114, pp. 1–15, Jun. 2022, doi: 10.1016 / j.jprocont.2022.03.009.) and further proposed a closed-loop dynamic real-time optimization strategy (CL-DRTO) (L. MacKinnonand CLE Swartz, “Robust closed-loop dynamic real-time optimization,” JProcess Control, vol. 126, pp. 12–25, Jun. 2023, doi: 10.1016 / j.jprocont.2023.04.003.). Although these methods have made some progress, most existing DRTO methods still rely on mechanistic models or parameterized empirical models obtained by identifying historical plant data. Mechanistic models are often difficult to accurately establish, and the modeling process is complex and time-consuming. Parameterized empirical models may also suffer from problems such as low identification accuracy, poor adaptability to changing operating conditions, and model mismatch.

[0006] In recent years, data-driven system analysis and control methods have attracted considerable attention due to their lack of reliance on precise mathematical models. Related research includes adaptive model predictive control (AMPC), iterative feedback tuning (IFT), model-free adaptive control (MFAC), and learning-based control. While these methods avoid complex modeling to some extent, they also suffer from complex parameter estimation procedures, unstable identification accuracy, and time-consuming parameter training (often relying on offline simulators). These shortcomings limit their application in practical industrial processes. To address these issues, some research has begun replacing parametric models with nonparametric data-driven predictors (Verhoek C, Berberich J, Haesaert S, et al. Data-driven Dissipativity Analysis of Linear Parameter-Varying Systems[J].IEEE Transactions on Automatic Control, 2023.DOI:10.1109 / TAC.2024.3417855.). These methods directly utilize historical system input and output trajectory data, rather than explicit models, to predict future behavior. This approach has shown promise in addressing nonlinear system control problems involving noise and disturbances, but it has not yet fully considered the integration of economic optimization, and there is a concern that the performance of lower-level tracking control may adversely affect the effectiveness of upper-level economic optimization. Summary of the Invention

[0007] In order to overcome the shortcomings of existing industrial process optimization control methods, such as modeling difficulties, high computational complexity, and difficulty in coordinated optimization of economic performance and control performance, the present invention provides a data-driven closed-loop dynamic real-time operation optimization and predictive control method.

[0008] This paper proposes a framework combining data-driven closed-loop dynamic real-time operation optimization and predictive control (DD-RTO-PC), targeting industrial processes with complex dynamic characteristics and economic optimization requirements (e.g., production units or systems such as thermal power plants and chemical reaction processes). This framework, referred to as the DD-RTO-PC framework, employs a two-layer optimization architecture to separate economic optimization from dynamic tracking control tasks. The upper layer, the Data-Driven Closed-Loop Dynamic Real-Time Optimization (DD-DRTO) layer, considers the dynamic impact of lower-layer closed-loop feedback on future system responses and determines the optimal operating setpoint trajectory over a period of time, aiming to maximize process economic benefits. The lower layer, the Robust Data-Driven Predictive Control (RDDPC) layer, aims to accurately track the optimal setpoint trajectory issued by the upper layer, calculates and outputs the actual control action sequence, and simultaneously feeds the current system state and control results back to the upper layer. The method's upper and lower models are constructed and predicted directly using input and output data from industrial processes, eliminating the need for complex online parameter identification and precise prior knowledge of mechanistic models. Compared to existing technologies, the method has been validated through simulation and experimentation to improve the economic efficiency of industrial process operations while maintaining excellent dynamic control performance.

[0009] The technical solution adopted in the present invention is as follows:

[0010] A data-driven closed-loop dynamic real-time operation optimization and predictive control method includes: first, collecting real industrial process data, pre-processing the collected data as a modeling backup, and organizing the operating constraints and economic performance evaluation indicators. Secondly, considering the impact of closed-loop feedback on future responses in terms of equipment operation economy, a data-driven closed-loop dynamic real-time optimization model is established as an upper-level optimization model, with the goal of maximizing the economic benefits of the process, and the optimal set point trajectory in the future period is calculated. Then, based on the equipment control tracking performance, a robust data-driven predictive control model is established as a lower-level control model, with the goal of accurately tracking the optimal set point trajectory, and the optimal control sequence is calculated. Finally, the first control action in the optimal control sequence is implemented for rolling optimization, and the results are fed back to the upper-level optimization model. Specifically, the following steps are included:

[0011] S1: Data collection and preprocessing:

[0012] For the target industrial process control system (hereinafter referred to as the "target system"), historical and real-time operational data from its equipment is collected as raw data, including at least the key input and output variables that influence the system's economic and control performance. The data sampling interval is set based on the dynamic characteristics of the target system. The collected raw data is preprocessed, including operations such as removing outliers, filling missing data, filtering and noise reduction, and normalization to improve data quality. The preprocessed data is organized into a structured sequence of input and output data pairs and stored in an operational database. This dynamically updated dataset serves as the foundation for constructing subsequent data-driven models. Furthermore, based on the target system's design specifications, process requirements, and actual operating experience, the target system's operational constraints are organized and set as constraints for the subsequent optimization model, and its economic performance indicators are set to evaluate its operational performance.

[0013] S2: Build a data-driven closed-loop dynamic real-time optimization model as the upper-level optimization model:

[0014] Aiming at the operational economic objectives of the target system and taking into account the impact of the closed-loop feedback of the lower-level control model on the future dynamic response of the target system, a data-driven closed-loop dynamic real-time optimization model (DD-DRTO) is established as the upper-level optimization model. The upper-level optimization model is a two-level optimization problem. The outer layer is a dynamic real-time optimization (DRTO) problem, and the inner layer embeds a simplified data-driven predictive control (DDPC) sub-problem. While optimizing the economic objectives (the outer DRTO problem), the upper-level optimization model predicts the closed-loop response behavior of the target system under a given set point trajectory through the embedded DDPC sub-problem. By solving the upper-level optimization model, and under the premise of satisfying various constraints, the sequence of operating set point trajectories that optimizes the comprehensive economic benefits of the target system in the future period is calculated. The specific construction and solution process of the upper-level optimization model is as follows:

[0015] S2.1: Construct an outer DRTO model. This model usually selects the economic performance index of the target system in the future forecast time domain as the objective function. It is expressed as:

[0016] (1)

[0017] Where, is the economic performance objective function of the outer DRTO model, and The outer DRTO model is at the current moment Determined future Step prediction of the output and input reference trajectories in the time domain, and are the output and input set point trajectories provided to the DDPC sub-problem, and are also the current optimal set value finally output by the upper optimization model. and The outer DRTO model is at the current moment Determined future The prediction input and prediction output in the step prediction time domain, superscript Represents the variables of the outer DRTO model; is the prediction time domain length of the outer DRTO model; is a coefficient vector to be optimized, which implicitly expresses the dynamic characteristics of the target system and predicts future behavior through the linear combination of historical data; Regularization helps to choose simpler or more robust combinations, yes The regularization coefficient of . It is a slack variable used to deal with data noise or model mismatch to ensure the feasibility of the constraint. Regularization is done to avoid excessive slack and reduce the prediction accuracy. yes The regularization coefficient of .

[0018] The constraints of the outer DRTO model include:

[0019] 1) Data-driven prediction model constraints:

[0020] (2)

[0021] Formula (2) is an implicit prediction model in the form of Hankel matrix constructed based on the historical input and output data in the operation database. represents the Hankel matrix constructed based on historical input and output data, and They are the historical input and output data available in the running database, which are used to predict the future of the outer DRTO model. Step-by-step prediction of system inputs and outputs in the time domain. is the order of the target system, Represents the matrix transpose transformation; Formula (2) uses Willems's basic lemma and its extended form applicable to perturbation systems, through the linear combination of historical data (given by weighted) to predict the future behavior of the system without identifying an explicit state-space model or transfer function. Optionally, by Imposing constraints such as , which can constrain the predicted behavior to be within a convex combination of historical data when dealing with nonlinear systems.

[0022] 2) Initial state constraints:

[0023] (3)

[0024] Formula (3) is used to ensure that the predicted system internal state and The actual internal state of Indicates the step size of the prediction time domain of the outer DRTO model, where Take 0 to , represents the initial value of the predicted trajectory values, and Respectively represent the outer DRTO model The predicted input and predicted output of the step, formula (3) represents the initial prediction trajectory The input and output values ​​are respectively related to the current moment Previous (i.e. arrive The actual measured input and output Stay consistent to determine the moment The only initial state.

[0025] 3) Operation constraints:

[0026] (4)

[0027] Formula (4) represents the actual physical or process inequality constraint set that the prediction input and prediction output of the outer DRTO model need to satisfy; where, and Respectively represent the lower and upper limits of the outer DRTO model prediction input, and They represent the lower and upper limits of the prediction output of the outer DRTO model respectively.

[0028] 4) Reference point constraints (optional):

[0029] (5)

[0030] Formula (5) represents the actual physical or process inequality constraint set that the input reference trajectory and output reference trajectory determined by the outer DRTO model need to satisfy; where, and They represent the lower and upper limits of the input reference trajectory determined by the outer DRTO model; and They represent the lower and upper bounds of the output reference trajectory determined by the outer DRTO model, respectively.

[0031] 5) Set point transfer constraints:

[0032] (6)

[0033] Equation (6) is the reference trajectory and with the set point trajectory provided to the DDPC subproblem and Related equality constraints, where represents the reference trajectory determined by the outer DRTO model and Tracking of setpoint trajectories passed to its embedded DDPC subproblem and Conversion relationship between them.

[0034] 6) Relationship constraints between the outer DRTO model and the DDPC sub-problem variables:

[0035] The decision variables of the outer DRTO model (i.e., the predicted input variables ), is affected by the solution of its embedded DDPC subproblem. Specifically, when determining its trajectory, the DRTO takes into account the "closed-loop behavior" generated by the embedded DDPC subproblem to track that trajectory. This is usually achieved by applying the Karlos-Kuhn-Tucker (KKT) conditions of the embedded DDPC subproblem as constraints on the outer DRTO model (see S2.3). A simplified expression is as follows:

[0036] (7)

[0037] (8)

[0038] Formula (7) represents the first step, which determines the predicted input is the first control action of the optimal control sequence calculated by its embedded DDPC subproblem Provided. Equation (8) represents the first control variable of the optimal control sequence calculated using the DDPC subproblem, where represents the step size of the prediction time domain of the DDPC subproblem, is the prediction horizon of the DDPC subproblem; Indicates that the control sequence is obtained by solving the DDPC subproblem , represents the objective function of the DDPC subproblem. Equations (7) and (8) imply that when the outer DRTO model determines the set point, it has already estimated the “optimal” behavior that the lower control model will take to track the set point.

[0039] S2.2: Construct an embedded DDPC sub-problem model:

[0040] In the prediction step of the outer DRTO model , , we need to consider the embedded DDPC sub-problem. It should be noted that due to the previous variables ( ) has been determined by the initial state constraint of formula (2), so, from The goal of the embedded DDPC subproblem model is to simulate the lower control model under given set points ( and ), the objective function is to minimize the tracking error:

[0041] (9)

[0042] Formula (9) is the embedded DDPC sub-problem model along the outer DRTO model prediction time domain The objective function of the step is, and They represent the prediction time domain along the outer DRTO model. At the step, the prediction output and prediction input of the DDPC sub-problem model are embedded. Variables representing the embedded DDPC subproblem model. and They represent the prediction time domain along the outer DRTO model. The input set points and output set points of the embedded DDPC subproblem model are extracted from the reference trajectory of the outer DRTO model, and the matrix and The predicted outputs are and predicted input Its corresponding set point Penalty weight matrix for the distance between and its corresponding regularization coefficient The meaning of refers to formula (1) and , slack variables and its corresponding regularization coefficient Meaning refers to formula (1) and .

[0043] The constraints of the embedded DDPC subproblem model are as follows:

[0044] 1) Data-driven prediction model constraints:

[0045] (10)

[0046] Formula (10) has a similar meaning to Formula (2) and is the prediction model for the DDPC sub-problem. Here, The length of the historical data window of the Hankel matrix used by the embedded DDPC sub-problem model for prediction (same as the outer DRTO model prediction time domain) may be different), and They represent the historical input and output data used for prediction in the embedded DDPC sub-problem model.

[0047] 2) Initial state constraints:

[0048] When the iteration of the outer DRTO model begins (i.e. ), the initial value of the embedded DDPC sub-problem model (i.e. ) The input and output constraints are:

[0049] (11)

[0050] The meaning of this constraint is similar to that of formula (3), which is used to ensure that the predicted internal state is consistent with the target system at time The actual internal state of and represents the initial pre- condition for the output and input of the embedded DDPC subproblem model variables (i.e. ); and Indicates that the target system is at time Previous Actual measured inputs and outputs ( arrive ).

[0051] Since the subsequent embedded DDPC sub-problem models cannot access the actual measured inputs and outputs, the subsequent embedded DDPC sub-problem models (i.e. ), its initial state is obtained by rolling update of the prediction result of the previous embedded DDPC sub-problem model:

[0052] (12)

[0053] 3) Terminal equality constraints (optional):

[0054] (13)

[0055] Formula (13) represents the final prediction trajectory of the embedded DDPC sub-problem model The input and output values ​​should reach or be close to the target state and , used to ensure closed-loop stability or reach a specific terminal state; here, , Indicates the final prediction time domain of the embedded DDPC sub-problem model time domain.

[0056] 4) Control variable constraints:

[0057] (14)

[0058] Where, for The set of upper and lower bound constraints that need to be satisfied.

[0059] S2.3: Solve the upper optimization model:

[0060] The upper-level optimization model is a two-level optimization problem. A simultaneous solution strategy is adopted to replace each embedded DDPC subproblem model, i.e., Equations (9)-(14), with its equivalent first-order Karlsruhe-Kuhn-Tucker (KKT) optimality condition.

[0061] For each embedded DDPC subproblem model, its Lagrangian function can be written as:

[0062] (15)

[0063] In formula (15), Contains all optimization variables of the embedded DDPC subproblem model, that is, 、 ; Express the equality constraints in equations (10)-(13); Express the inequality constraint in equation (14); and They are and The Lagrange multiplier vector of .

[0064] The KKT optimality conditions include:

[0065] 1) Lagrangian gradient :

[0066] (16)

[0067] (17)

[0068] (18)

[0069] (19)

[0070] Where, and They represent the Lagrangian functions of the embedded DDPC sub-problem model respectively. and Derivative; and Respectively represent the embedded DDPC sub-problem model Respectively and Seek the derivative, and Respectively represent the embedded DDPC sub-problem model Respectively and Find the derivative.

[0071] 2) Original feasibility:

[0072] (20)

[0073] (twenty one)

[0074] Formula (20) represents the set of equality constraints in formulas (10)-(13), and formula (21) represents the set of inequality constraints in formula (14). The inequality constraints in formula (21) can be relaxed by introducing slack variables and Convert the inequality into an equality:

[0075] (twenty two)

[0076] (twenty three)

[0077] (twenty four)

[0078] Where, and are the lower and upper limits of the control variables in the embedded DDPC sub-problem model.

[0079] 3) Dual feasibility: The Lagrange multipliers associated with the inequality constraints must be non-negative:

[0080] (25)

[0081] 4) Complementary slackness condition: The product of the Lagrange multiplier of the inequality constraint and the inequality constraint is 0:

[0082] (26)

[0083] By replacing each embedded DDPC subproblem model, Equations (9)-(14), with its complete KKT condition, Equations (16)-(26), the upper-level DD-DRTO model, Equations (1)-(14), is reformulated as a single-level mathematical programming problem with complementarity constraints (MPCC). By solving it using the MPCC solver, the sequence of operating setpoint trajectories that optimizes the future economic performance of the target system is obtained as the target setpoint of the lower-level control model at the current moment.

[0084] S3: Build a robust data-driven predictive control model as the lower-level control model:

[0085] In response to the dynamic tracking performance requirements of the target system, and taking into account the data noise and unmodeled dynamics that may exist in actual industrial processes, a lower-level robust data-driven predictive control (RDDPC) model is established based on a real-time updated operation database as the lower-level control model. The goal of the lower-level control model is to accurately track the current optimal set value ( ), and calculate the future prediction time domain The optimal control sequence The lower-level control model is also based on data-driven thinking and uses historical input and output data to make predictions.

[0086] S3.1: The objective function of the lower control model is to minimize the set point tracking error:

[0087] (27)

[0088] In formula (27), Predicting the time domain for the target system, and are the future input and future output predicted by the lower control model, and is the target steady-state point that can be reached by online calculation, the coefficient vector and its corresponding regularization coefficient The meaning of refers to formula (1) and (9) and ; slack variables and its corresponding regularization coefficient The meaning refers to formula (1) and (9) and , where the slack variable The introduction of and regularization of it also enhances the robustness of the underlying control model to data noise and prediction accuracy. is the control input tracking error weight matrix, is the control output tracking error weight matrix, is the control input terminal constraint penalty weight matrix, is the penalty weight matrix controlling the output terminal constraints.

[0089] S3.2: The constraints of the lower control model are similar to those of Eqs. (10)-(14), but the prediction time domain is The length of historical input and output data used for prediction is different, including:

[0090] (28)

[0091] (29)

[0092] (30)

[0093] (31)

[0094] Equation (28) is a prediction model based on the Hankel matrix, which is similar to Equations (2) and (10), where and is the historical input and output data used by the lower control model to predict future trends. Equation (29) is the initial state constraint, similar to Equations (3) and (11). This constraint is used to ensure that the future input and future output trajectories predicted by the lower control model are input and output values and Compared with the current system ( The actual internal state of and express Before the moment Actual measurement inputs and outputs for determining time Equation (30) is similar to Equation (13) and is the final prediction of the future input and output trajectories of the lower control model. Terminal equality constraints on input and output values ​​are used to enhance the closed-loop stability of the system. and represent the final trajectory of the future input and future output predicted by the lower control model. variables. Formula (31) represents Constraints, and They represent the lower limit and upper limit of the control variables of the lower-level control model respectively.

[0095] The optimization problem of the lower control model, namely Equations (27)-(31), is a standard quadratic programming (QP) problem, which can be quickly solved by an optimization solver in each control cycle to obtain the optimal control sequence. .

[0096] S4: Control implementation and data update:

[0097] The optimal control sequence calculated by the lower control model The first control action Applied to the actuator of the actual industrial process. At the next sampling moment, the new actual output of the target system is measured . Based on the newly acquired input and Update the running database. The specific update method is as follows:

[0098] S4.1 Dataset update: Update the latest data to Add to the running database middle.

[0099] (32)

[0100] In order to keep the dimension of the data matrix fixed or avoid unlimited data growth, a sliding window mechanism is adopted, that is, the earliest data is removed while adding new data.

[0101] In order to ensure the continuous excitation of the data in the Hankel matrix, the trigger condition for data update can be set: when the actual output of the target system The target set point given by the upper optimization model The error is greater than the threshold , then execute data update.

[0102] The data update rule states that when the measured value Not yet at target set point The predetermined area, i.e. When the system is running, the operation database is continuously updated to obtain new data that can reflect the dynamic characteristics of the system; when Entering the predetermined neighborhood, i.e. and The error is less than or equal to the threshold and last for a period of time After that, the update is suspended to avoid introducing too much steady-state data. The time parameters are set in advance.

[0103] S4.2 Rolling Optimization: After completing the data update, repeat steps S2 to S4 to form a closed-loop dynamic real-time optimization and predictive control.

[0104] Ultimately, by continuously optimizing set points and implementing precise control, the target system can continue to move toward and maintain a more economically efficient operating state while meeting various constraints.

[0105] Beneficial effects of the present invention:

[0106] 1. Unlike traditional single-layer optimization frameworks (such as EMPC), which couple economic optimization and control tracking and use a weighted trade-off approach, this paper adopts a two-layer optimization architecture (upper-layer DD-DRTO and lower-layer RDDPC) to effectively separate and coordinate economic optimization objectives and dynamic control tracking tasks. The upper-layer DD-DRTO focuses on optimizing economic performance over a longer timescale, while the lower-layer RDDPC focuses on fast setpoint tracking. This provides a clear structure and facilitates design and tuning.

[0107] 2. Both the upper and lower layers of the present invention use a data-driven approach to construct the core "prediction model" (such as the Hankel matrix form in Equations (2), (10), and (28)). This approach directly utilizes historical and real-time industrial process input and output data to predict the future behavior of the system through linear combinations of these data. This approach avoids the need to establish precise, parameterized mechanism models or perform complex online system identification steps, reducing the reliance on prior knowledge of the model. Therefore, this method has better applicability for complex industrial processes that are difficult to accurately model.

[0108] 3. This invention explicitly considers the dynamic impact of lower-level closed-loop control behaviors on future system responses by embedding DDPC subproblems within the upper-level optimization model. This closed-loop strategy enables the upper-level system to more accurately predict the actual closed-loop dynamic response of the system at these setpoints when calculating the optimal economic setpoint trajectory. This optimizes the economic performance of the entire closed-loop system within the forecast horizon, improving both predictability and robustness of decision-making. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 This is a flow chart of the application of the present invention.

[0110] Figure 2 This figure shows the comparison of system output and control input under small-scale load variation conditions when the method of the present invention is applied to a simulation experiment of a 350MW supercritical coal-fired unit. (a) is the unit's power generation response curve, (b) is the unit's main steam pressure response curve, (c) is the coal feed rate control input curve, and (d) is the main steam valve opening control input curve.

[0111] Figure 3This figure shows a comparison of the system output and control input under a wide range of load variations when the method of the present invention is applied to a simulation experiment of a 350MW supercritical coal-fired unit. (a) is the unit's power generation response curve, (b) is the unit's main steam pressure response curve, (c) is the coal feed rate control input curve, and (d) is the main steam valve opening control input curve. DETAILED DESCRIPTION

[0112] In order to better understand the technical solutions and specific implementation methods of the present invention, the present invention is further described in detail below by taking the optimization control of a domestic 350MW supercritical coal-fired power generation unit (hereinafter referred to as the "coal-fired unit") as an example.

[0113] Example

[0114] This example uses the dynamic optimization and control of a 350MW supercritical coal-fired unit as a case study. The unit's primary controlled components include the boiler combustion system and the steam turbine regulation system. Its operating objectives are to minimize coal consumption and maintain stable main steam pressure while meeting grid load demand. Coal-fired units typically face two typical operating conditions: small load variations and large load variations.

[0115] A data-driven closed-loop dynamic real-time operation optimization and predictive control method, the application process is as follows Figure 1 As shown, the specific steps include:

[0116] S1: Data collection and preprocessing:

[0117] In this embodiment, the main input variables of the coal-fired unit system are: coal feeding rate (Unit: t / h), main steam valve opening (Unit: %), the main output variables are: unit power generation (Unit: MW) and main steam pressure (Unit: MPa), as the input and output variables for data acquisition.

[0118] S1.1 Data Collection: Collect the aforementioned historical input and output data for the coal-fired unit from November 1, 2024, to November 3, 2024, and combine it with data collected during real-time operation to form an operational database. The data sampling interval can be set based on the actual system dynamics. In this embodiment, the upper-level optimization model uses 5-second sampling data, while the lower-level control model uses 1-second sampling data.

[0119] S1.2 Data preprocessing: The following preprocessing operations are performed on the collected raw data: 1) Outlier detection and elimination: Use the 3-sigma rule to identify and remove obvious abnormal data points; 2) Missing value processing: For a small amount of missing data, linear interpolation or mean filling method can be used to fill it. In this embodiment, linear interpolation is used; 3) Filtering and noise reduction: Moving average filtering or low-pass filtering can be used to smooth high-frequency noise. In this embodiment, a low-pass filter is used; 4) Data normalization: All input and output data are normalized to the [0,1] interval to eliminate the influence of different variable dimensions and facilitate subsequent model calculations. The preprocessed data is organized into time series pairs. , stored in a dynamically updated running database, and used to construct the Hankel matrix required for subsequent data-driven models.

[0120] S1.3 Arrange equipment parameters and actual operating constraints: Based on the design parameters of the coal-fired unit and the on-site safe operation regulations, the input and output constraints are defined as follows:

[0121] (35)

[0122] (36)

[0123] These constraints will serve as boundary conditions in subsequent models.

[0124] S2: Build a data-driven closed-loop dynamic real-time optimization model as the upper-level optimization model:

[0125] The upper-level optimization model is a two-level optimization problem consisting of a DRTO problem and an embedded DDPC subproblem. While optimizing the economic objective using the DRTO problem, the upper-level optimization model also embeds a DDPC subproblem to predict the closed-loop response behavior of the target system under a given setpoint trajectory. In this embodiment, the upper-level optimization model aims to optimize the operating economics of the coal-fired unit, primarily considering load tracking capability (the deviation between actual generated power and grid demand), main steam pressure stability (critical for safe unit operation), and fuel cost (related to the coal feed rate).

[0126] S2.1: For coal-fired power plant systems, the objective function of the upper optimization model in Equation (1) is Specifically:

[0127] (37)

[0128] In formula (37), is the predicted generating power of the unit, is the grid demand load trajectory, Indicates the predicted main steam pressure of the unit, is the expected reference value of the main steam pressure, is the predicted coal feeding rate, and is the penalty coefficient, and its value is shown in Table 1. The goal of the upper optimization model is to minimize the load tracking deviation, main steam pressure deviation and fuel consumption. Including coal feeding rate and main steam valve opening, output variables Including unit power generation and main steam pressure.

[0129] The constraints are as shown in Equations (2)-(8), where the Hankel matrix in Equation (2) is constructed based on the coal-fired unit operation database after S1 preprocessing. The upper and lower limits in Equations (4) and (5) are set according to Equations (35) and (36). The specific expression of the setpoint transfer constraint in Equation (6) is as follows:

[0130] (38)

[0131] S2.2: Construct an embedded DDPC sub-problem model:

[0132] The objective function of the DDPC sub-problem is shown in formula (9). In this embodiment, its specific form is as follows:

[0133] (39)

[0134] Among them, the weight matrix And the regularization coefficient and See Table 1.

[0135] The constraints of the DDPC subproblem are as shown in Equations (10)-(14).

[0136] S2.3: Solve the upper optimization model:

[0137] Each embedded DDPC subproblem, Equation (39) and its corresponding constraints (Equations (10)-(14)), is transformed into a set of algebraic equations and complementary constraints through its KKT optimality conditions, Equations (15)-(26). Together with the objective function of the upper-level optimization model, Equation (37) and its corresponding constraints, it constitutes an MPCC problem. The MPCC problem is solved once in each DRTO optimization cycle (5 seconds) to obtain the future step The optimal operating set point trajectory .

[0138] S3: Build and solve the underlying robust data-driven predictive control model:

[0139] In view of the fast dynamic tracking performance requirements of coal-fired units, a lower-level robust data-driven predictive control model is established as the lower-level control model. The lower-level control model tracks the current set point transmitted by S2. As the goal, and calculate the optimal control sequence for a period of time in the future The relevant parameter settings of the DD-RTO-PC framework in this embodiment are shown in Table 1.

[0140] Table 1: Parameter configuration of the DD-RTO-PC framework

[0141]

[0142] S3.1: The objective function of the lower-level control model is shown in Equation (27), which is specifically expressed as:

[0143] (40)

[0144] Among them, the input variable Including coal feed rate and main steam valve opening , output variable Including unit power generation and main steam pressure System order as well as and See Table 1.

[0145] S3.2: The constraints of the lower-level control model are as shown in Equations (28)-(31), where the Hankel matrix of Equation (28) is constructed based on the coal-fired unit operation database preprocessed and updated in real time by S1, and the control variable constraints of Equation (31) are set according to Equations (35)-(36). The lower-level control model is solved once in each control cycle (1 second) to obtain the optimal control sequence .

[0146] S4: Control implementation and data update:

[0147] The first control action of the optimal control sequence calculated by the lower control model is Applied to the coal feed actuator and main steam valve actuator of coal-fired units.

[0148] S4.1: At the next sampling moment , measure the new unit power generation and main steam pressure , according to the current actual input and new measurement outputs Update the running database according to formula (32) , and uses a sliding window approach to maintain the running database at a fixed size.

[0149] Set data update criteria:

[0150] When the actual power generation With the target load given by the upper layer When the absolute value of the deviation is greater than the threshold value of 0.2MW, or the main steam pressure and its reference value When the deviation is greater than the threshold of 0.05MPa, it is considered that the coal-fired unit system has significant dynamics or deviates from the target, and the operation database is updated to capture these dynamic information. If both are within a small neighborhood of their respective target set points (power deviation is less than 0.2MW and main steam pressure deviation is less than 0.05MPa) and last for 30 seconds, it is considered that the coal-fired unit system has reached a good tracking state. At this time, the update of the operation database is suspended to ensure the continuous motivation of the data and avoid the introduction of too much redundant steady-state data.

[0151] S4.2 Rolling Optimization: After completing the data update, a new optimization control cycle begins, and steps S2 to S4 are repeated to form a closed-loop dynamic real-time optimization and predictive control.

[0152] Experimental comparison and analysis:

[0153] To validate the effectiveness of this embodiment's method (DD-RTO-DDPC), it was applied to a 350 MW supercritical coal-fired power plant simulation platform based on real data. The method was compared with a typical closed-loop model-based dynamic real-time operation optimization and model predictive control (DRTO-MPC) approach. The DRTO-MPC approach uses a simplified mechanistic model for the upper layer and a mechanistic model-based MPC for the lower layer. 100 Monte Carlo simulations were performed for each operating condition to evaluate the average performance under random disturbances and measurement noise.

[0154] Operating condition 1: Small range load change. The coal-fired unit initially operates at a certain stable load point. The desired target operating point is .

[0155] Operating condition 2: Large range load changes. The coal-fired unit initially operates at a lower load point. The desired target operating point is .

[0156] The simulation results are as follows Figure 2 and Figure 3 The statistical comparison results of relevant performance indicators are shown in Table 2.

[0157] from Figure 2 and Figure 3 The dynamic response curve shows that the method of this embodiment can effectively track the target load and keep the main steam pressure relatively stable under both small and large load change conditions. Compared with the traditional DRTO-MPC method, the method of this embodiment is more effective when the load changes over a large range (such as Figure 3 ), its power response has smaller overshoot and shorter adjustment time, showing better dynamic tracking performance.

[0158] Table 2: Comparison of statistical indicators between DD-RTO-DDPC and DRTO-MPC methods under different working conditions

[0159]

[0160] The statistical indicators in Table 2 show that in terms of control performance, the average tracking root mean square error (RMSE) of power and pressure for the method of this embodiment is generally less than or equal to that of the DRTO-MPC method under both operating conditions, demonstrating that the method of this embodiment has better control accuracy and robustness. In terms of economic performance, a comparison of the economic objective function (defined as the cumulative cost or deviation, with smaller values ​​being preferred) shows that the method of this embodiment can achieve comparable or even better economic benefits than the DRTO-MPC method under different operating conditions. This is due to the more accurate capture of actual process dynamics by its data-driven model and its closed-loop optimization strategy. In terms of computational efficiency, the average single-step computation time of the method of this embodiment is generally shorter than that of the DRTO-MPC method. This is because the data-driven model avoids the need for online solution or parameter identification of complex mechanistic models, and the underlying RDDPC is typically a QP problem, which results in a faster solution speed.

[0161] In summary, this embodiment combines data-driven closed-loop dynamic real-time operational optimization with predictive control, employing a two-layer architecture to separate economic optimization and tracking control. The upper-layer optimization model calculates the optimal economic target setpoint trajectory by embedding DDPC subproblems and employing a simultaneous solution strategy, fully accounting for the impact of lower-layer feedback on future responses. The lower-layer control model calculates specific control inputs based on a real-time updated data set to accurately track the setpoint. Case study results of coal-fired power plants demonstrate that this embodiment's approach can effectively improve the system's operational economy while ensuring excellent control performance (fast response, high-precision tracking, and strong robustness). It also boasts high computational efficiency and promising practical application prospects.

[0162] The above-mentioned embodiments only express several implementation methods of the present invention. The description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A data-driven closed-loop dynamic real-time operation optimization and predictive control method, characterized in that: include: First, real industrial process data is collected, pre-processed, and the operating constraints and economic performance evaluation indicators are sorted out; Secondly, focusing on the economic efficiency of equipment operation and considering the impact of closed-loop feedback on future responses, a data-driven closed-loop dynamic real-time optimization model is established as the upper-level optimization model. With the goal of maximizing process economic benefits, the optimal set point trajectory over a period of time is calculated. Then, focusing on the device control tracking performance, a robust data-driven predictive control model is established as the lower-level control model. With the goal of accurately tracking the optimal set-point trajectory, the optimal control sequence is calculated. Finally, the first control action in the optimal control sequence is implemented for rolling optimization, and the results are fed back to the upper-level optimization model. The specific steps include: S1: Data collection and preprocessing: For the target industrial process control system (hereinafter referred to as the "target system"), historical and real-time operating data of its equipment is collected as raw data and pre-processed. The pre-processed data is organized into a sequence of input and output data pairs and stored in the operation database. At the same time, the operating constraints and economic performance indicators of the target system are organized and set. S2: Build a data-driven closed-loop dynamic real-time optimization model as the upper-level optimization model: A data-driven closed-loop dynamic real-time optimization model is established as the upper-level optimization model. Its outer layer is a dynamic real-time optimization (DRTO) problem, and its inner layer embeds a data-driven predictive control (DDPC) sub-problem: S2.1: Construct an outer DRTO model; the objective function of the outer DRTO model is: （1） Where, is the economic performance objective function of the outer DRTO model, and The outer DRTO model is at the current moment Determined future Step prediction of the output and input reference trajectories in the time domain, and are the output and input set point trajectories provided to the DDPC subproblem, and are also the current optimal set value finally output by the upper optimization model; and The outer DRTO model is at the current moment Determined future Prediction input and prediction output within the step prediction time domain; is the prediction time domain length of the outer DRTO model; is the coefficient vector to be optimized, yes Regularization coefficient of ; is the slack variable, yes Regularization coefficient of ; The constraints of the outer DRTO model include: 1) Data-driven prediction model constraints: （2） Where, represents the Hankel matrix constructed based on historical input and output data, and These are the historical input and output data available in the operational database, respectively; is the order of the target system, Represents matrix transpose transformation; 2) Initial state constraints: （3） in, Indicates the step size of the prediction time domain of the outer DRTO model, where Take 0 to , represents the initial value of the predicted trajectory values, and Respectively represent the outer DRTO model The predicted input and predicted output of the step, formula (3) represents the initial prediction trajectory The input and output values ​​are respectively related to the current moment Previous Actual measured input and output Stay consistent; 3) Operation constraints: （4） in, and Respectively represent the lower and upper limits of the outer DRTO model prediction input, and They represent the lower and upper bounds of the prediction output of the outer DRTO model respectively; 4) Set point transfer constraints: （6） in, represents the reference trajectory determined by the outer DRTO model and Tracking of setpoint trajectories passed to its embedded DDPC subproblem and Conversion relationship between them; 5) Relationship constraints between the outer DRTO model and the DDPC sub-problem variables: （7） （8） Formula (7) represents the first step, which determines the predicted input is the first control action of the optimal control sequence calculated by its embedded DDPC subproblem Provided; Equation (8) represents the first control variable of the optimal control sequence calculated using the DDPC subproblem, where represents the step size of the prediction time domain of the DDPC subproblem, is the prediction horizon of the DDPC subproblem; Indicates that the control sequence is obtained by solving the DDPC subproblem , represents the objective function of the DDPC subproblem; S2.2: Construct an embedded DDPC sub-problem model: The objective function of the embedded DDPC sub-problem model is to minimize the tracking error: （9） in, and They represent the prediction time domain along the outer DRTO model. When step , the prediction output and prediction input of the DDPC sub-problem model are embedded; and They represent the prediction time domain along the outer DRTO model. The input set points and output set points of the embedded DDPC subproblem model are extracted from the reference trajectory of the outer DRTO model, and the matrix and The predicted outputs are and predicted input Its corresponding set point 、 The penalty weight matrix of the distance between them; and are the coefficient vector and its regularization term coefficient, respectively. and are the slack variables and their regularization term coefficients respectively; The constraints of the embedded DDPC subproblem model are as follows: 1) Data-driven prediction model constraints: （10） in, is the historical data window length of the Hankel matrix used for prediction by the embedded DDPC subproblem model, and Respectively represent the historical input and output data used for prediction in the embedded DDPC sub-problem model; 2) Initial state constraints: （11） Formula (11) is used to ensure that the predicted internal state and the target system are consistent at time The actual internal state of and represents the initial pre- condition for the output and input of the embedded DDPC subproblem model variables; and Indicates that the target system is at time Previous Actual measurement inputs and outputs; 3) Control variable constraints: （14） Where, for The set of upper and lower bound constraints that need to be satisfied; S2.3: Solve the upper optimization model: A simultaneous solution strategy is adopted to replace each embedded DDPC sub-problem model with its equivalent first-order Karl-Kuhn-Tucker (KKT) optimality condition. The upper-level optimization model is then reformulated as a single-level mathematical programming problem (MPCC) containing complementary constraints. The MPCC solver is used to solve the problem, and the sequence of operating set point trajectories that optimize the future economic performance of the target system is obtained as the target set point of the lower-level control model at the current moment. S3: Build a robust data-driven predictive control model as the lower-level control model: Based on the real-time updated operation database, a lower-level robust data-driven predictive control model is established as the lower-level control model; S3.1: The objective function of the lower control model is to minimize the set point tracking error: （27） In formula (27), Predicting the time domain for the target system, and are the future input and future output predicted by the lower control model, and is the target steady-state point that can be reached by online calculation, and are the coefficient vector and its regularization term coefficient, respectively. and are the slack variables and their regularization coefficients, is the control input tracking error weight matrix, is the control output tracking error weight matrix, is the control input terminal constraint penalty weight matrix, is the penalty weight matrix controlling the output terminal constraint; S3.2: The constraints of the lower-level control model include: （28） （29） （30） （31） Formula (28) is the prediction model of the Hankel matrix, where and is the historical input and output data used by the lower-level control model to predict future trends; Equation (29) is the initial state constraint, which is used to ensure that the future input and future output trajectories predicted by the lower-level control model are input and output values and and The actual internal state at the moment is consistent, and express Before the moment The actual measured input and output; Equation (30) is the final prediction of the future input and future output trajectory of the lower control model. terminal equality constraints for input and output values, and They represent the final trajectory of the future input and future output predicted by the lower control model. variables; Formula (31) represents Constraints, and They represent the lower and upper limits of the control variables of the lower-level control model respectively; Solve the lower-level control model in each control cycle and obtain the optimal control sequence after solving it ; S4: Control implementation and data update: Execute the optimal control sequence The first control action , at the next sampling moment, measure the new actual output of the target system ; Based on the newly acquired input and Update the running database; the specific update method is as follows: S4.1 Dataset update: Update the latest data to Add to the running database middle; （32） S4.2 Rolling Optimization: After completing the data update, repeat steps S2 to S4 to form a closed-loop dynamic real-time optimization and predictive control; Ultimately, by continuously optimizing the set points and implementing precise control, the target system can continue to move toward and maintain a more economically efficient operating state while meeting various constraints.

2. A data-driven closed-loop dynamic real-time operation optimization and predictive control method according to claim 1, characterized in that: In the aforementioned S1, the original data at least includes the main input variables and output variables that affect the system economy and control performance.

3. A data-driven closed-loop dynamic real-time operation optimization and predictive control method according to claim 1, characterized in that: In S2.1, when dealing with nonlinear systems, the coefficient vector Imposing constraints to constrain the predicted behavior to be within a convex combination of historical data.

4. A data-driven closed-loop dynamic real-time operation optimization and predictive control method according to claim 1, characterized in that: In S2.1, the constraints of the outer DRTO model also include reference point constraints: （5） in, and They represent the lower and upper limits of the input reference trajectory determined by the outer DRTO model; and They represent the lower and upper bounds of the output reference trajectory determined by the outer DRTO model, respectively.

5. The data-driven closed-loop dynamic real-time operation optimization and predictive control method according to claim 1, characterized in that: In S2.2, for the initial state constraint of the embedded DDPC sub-problem model, the subsequent embedded DDPC sub-problem model, that is, When , its initial state is obtained by rolling update of the prediction result of the previous embedded DDPC sub-problem model: （12）。 6. The data-driven closed-loop dynamic real-time operation optimization and predictive control method according to claim 1, characterized in that: In S2.2, the constraints of the embedded DDPC subproblem model also include terminal equality constraints: （13） Formula (13) represents the final prediction trajectory of the embedded DDPC sub-problem model The input and output values ​​should be at or close to and .

7. The data-driven closed-loop dynamic real-time operation optimization and predictive control method according to claim 1, characterized in that: In S2.3, each embedded DDPC subproblem model is replaced by its equivalent first-order Karlsruhe-Kuhn-Tucker (KKT) optimality condition as follows: For each embedded DDPC subproblem model, its Lagrangian function for: （15） in, Contains all optimization variables of the embedded DDPC subproblem model, that is, 、 、 、 ; Represents the equality constraints in the embedded DDPC subproblem model constraints; Represents the inequality constraints in the constraints of the embedded DDPC sub-problem model; and They are and The Lagrange multiplier vector of ; The KKT optimality conditions include: 1) Lagrangian gradient : （16） （17） （18） （19） Where, and They represent the Lagrangian functions of the embedded DDPC sub-problem model respectively. and Derivative; and Respectively represent the embedded DDPC sub-problem model Respectively and Seek derivation, and Respectively represent the embedded DDPC sub-problem model Respectively and Derivative; 2) Original feasibility: （20） （21） Formula (20) represents the set of equality constraints of the embedded DDPC subproblem model, and formula (21) represents the set of inequality constraints of the embedded DDPC subproblem model. For the inequality constraints in formula (21), the slack variables are introduced and Convert the inequality into an equality: （22） （23） （24） Where, and are the lower and upper bounds of the control variables in the embedded DDPC sub-problem model; 3) Dual feasibility: The Lagrange multipliers associated with the inequality constraints must be non-negative: （25） 4) Complementary slackness condition: The product of the Lagrange multiplier of the inequality constraint and the inequality constraint is 0: （26）。 8. The data-driven closed-loop dynamic real-time operation optimization and predictive control method according to claim 1, characterized in that: In S4.1, the data set is updated using a sliding window mechanism, which removes the oldest data while adding new data.

9. The data-driven closed-loop dynamic real-time operation optimization and predictive control method according to claim 1, characterized in that: In S4.1, in order to ensure the continuous excitation of the data in the Hankel matrix, the triggering conditions for data update are set: When the actual output of the target system The target set point given by the upper optimization model The error is greater than the threshold , then execute data update; when and The error is less than or equal to the threshold and last for a period of time After that, the update is suspended, among which, The time parameters are set in advance.

Images