Air compressor cluster collaborative control and energy efficiency optimization method based on digital twinning

Abstract

The application discloses an air compressor cluster collaborative control and energy efficiency optimization method based on digital twinning, which comprises the following steps: collecting real-time operation data of an air compressor cluster and a gas supply system and performing time alignment to obtain time alignment data; establishing a digital twinning model of the air compressor cluster and the gas supply system; constructing a Zonotope observer to obtain an initialized coupled Zonotope; generating a candidate group control strategy set within a rolling optimization window; calling a reachable domain propagation operator to perform a prediction update to obtain a predicted coupled Zonotope; performing a consistency contraction to obtain an updated coupled Zonotope; loading each candidate group control strategy to the digital twinning model and performing simulation deduction; selecting an optimal control strategy from the candidate group control strategy set; and delivering the optimal control strategy to an air compressor cluster execution control system for execution. The application improves the feasibility of the air compressor cluster collaborative control strategy and the stable energy-saving effect.

Description

Technical Field

[0001] This invention relates to the field of industrial energy conservation and automation control technology, and in particular to a method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins. Background Technology

[0002] As a key power equipment in industrial air supply systems, the operation of air compressor clusters directly affects the stability of workshop air supply pressure and unit air production energy consumption. In actual engineering, air compressor clusters are usually composed of multiple fixed-frequency and variable-frequency units, forming a dynamic system coupled with the main pipeline network, air storage tanks, and air load. Existing control methods mostly adopt local PID pressure regulation, threshold start-stop, fixed reference unit rotation, or linkage control based on empirical rules. Basic air supply is guaranteed by setting the main pipeline pressure band and start-stop logic. Some systems introduce centralized monitoring platforms to collect data such as exhaust pressure, flow rate, power, and electricity price for statistical analysis, or provide operation suggestions and scheduling strategies on the host computer side.

[0003] However, existing technologies are generally based on point-value models or static calibration parameters, which makes it difficult to characterize the impact of uncertainties such as sensor errors, modeling errors, load fluctuations, and equipment performance drift on the system dynamics. This leads to deviations between simulation and field operation, and the strategy may encounter problems such as pressure overshooting, frequent start-stop, or unstable energy efficiency benefits when actually implemented. Especially in cluster collaborative control scenarios, start-stop, load distribution, and pressure setting are intercoupled, and relying solely on point-value prediction is insufficient to provide a strategy guarantee that is still feasible in the worst case. In addition, industrial field data sources are diverse, sampling periods are inconsistent, and clock drift and missing values ​​are common. Without systematic time alignment and validity screening, twin model errors can be further amplified, reducing the reliability and security of group control optimization.

[0004] Therefore, how to provide a method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] One objective of this invention is to propose a collaborative control and energy efficiency optimization method for air compressor clusters based on digital twins. This invention uses time alignment and high-fidelity digital twin modeling, combined with a Zonotope observer to characterize the coupled uncertainty of operating status and key parameters, and utilizes reachability domain propagation and observation consistency contraction to achieve online prediction updates and drift suppression. Within a rolling optimization window, candidate cluster control strategies are simulated and envelope evaluated, and the strategy that satisfies the constraints and has the lowest energy consumption is selected and executed, thereby improving the feasibility, robustness, and stable energy-saving effect of collaborative control of air compressor clusters.

[0006] The method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins according to embodiments of the present invention includes the following steps:

[0007] Collect real-time operating data of the air compressor cluster and air supply system and perform time alignment to obtain time-aligned data;

[0008] A digital twin model of an air compressor cluster air supply system was established based on time-aligned data;

[0009] In the digital twin model, a Zonotope observer is constructed, and an reachability propagation operator and an observation consistency contraction operator are set. The running state and key parameters of the digital twin model are jointly encoded into a coupled Zonotope and initialized to obtain the initialized coupled Zonotope.

[0010] Generate a set of candidate group control strategies within the scrolling optimization window based on the initialization coupling of Zonotope;

[0011] For each candidate group control strategy in the candidate group control strategy set, the reachability domain propagation operator is invoked to perform the prediction update of the Zonotope observer, resulting in a prediction-coupled Zonotope.

[0012] By using aligned data as observation input, a consistent shrinkage is performed on the prediction coupling Zonotope, and the coupling update of the running state and key parameters is completed simultaneously to obtain the updated coupling Zonotope.

[0013] With the updated coupling Zonotope as the initial condition, each candidate group control strategy is loaded into the digital twin model and simulation is performed. The envelope evaluation result and worst-case constraint satisfaction flag are generated. The optimal control strategy is selected from the candidate group control strategy set based on the minimum energy consumption index and then sent to the air compressor cluster execution control system for execution.

[0014] Optionally, obtaining the time-aligned data specifically includes:

[0015] Data acquisition interfaces and acquisition channels are configured on the air compressor cluster side and the air supply system side respectively to collect the operating data of the air compressor side and the operating data of the air supply system side. During the acquisition, a timestamp is written for each acquisition record to form the raw operating data.

[0016] The raw operating data is processed to normalize the data. The data collection records of the same air compressor are merged according to the equipment identifier, and the data collection records of the air supply system are merged according to the location identifier. The merged data collection records are processed to uniformly update the timestamps, and the normalized operating data is output.

[0017] Based on the regularized operating data, a unified alignment time axis is established and time alignment is performed. The records of each air compressor side and the air supply system side on the unified alignment time axis are matched and merged, and time alignment data is output.

[0018] Optionally, the establishment of the digital twin model specifically includes:

[0019] Based on time-aligned data, the digital twin modeling boundary and modeling objects of the air compressor cluster air supply system are determined, a twin object structure consistent with the physical system is established, and the correspondence between object identifiers and point identifiers is established. The mapping relationship between the twin object structure and the identifiers is output.

[0020] A model mapping relationship is established based on the twin object structure. Time-aligned data is written into the corresponding twin object structure according to the device identifier and the location identifier. The data mapping relationship and the mapped twin input data are output.

[0021] A high-fidelity mechanism model is constructed based on the twin object structure and the mapped twin input data, and the parameters of the high-fidelity mechanism model are calibrated and the consistency is verified.

[0022] The calibrated high-fidelity mechanism model and data mapping relationship are integrated, and a simulation deduction interface and a real-time data mapping interface are established to form a digital twin model of the air compressor cluster air supply system.

[0023] Optionally, obtaining the initial coupling Zonotope specifically includes:

[0024] In the digital twin model, the observer estimation object is determined, and a set of operating states to characterize the operating conditions of the air compressor cluster air supply system and a set of key parameters to characterize the performance drift of the air compressor cluster air supply system are established and jointly encoded as coupled variables according to a preset coding order.

[0025] Based on coupled variables, a Zonotope observer is constructed in the digital twin model. The data structure of the coupled Zonotope is set up and the central term and generator term are determined. The central term is used to store the central estimate of the coupled variables, and the generator term is used to store the uncertainty boundary of the coupled variables.

[0026] Configure the reachability propagation operator and the observation consistency contraction operator in the Zonotope observer, and output the calling interface of the reachability propagation operator and the observation consistency contraction operator;

[0027] The coupled Zonotope is initialized by writing the set of running states corresponding to the time-aligned data at the initial moment into the central term of the coupled Zonotope as the running state center, writing the preset parameter benchmark of the digital twin model into the central term of the coupled Zonotope as the key parameter center, and determining the magnitude of the generator term of the coupled Zonotope based on the upper bound of sensor accuracy, the upper bound of modeling error and the prior boundary of key parameters to form the initial uncertainty boundary, thus obtaining the initialized coupled Zonotope.

[0028] Optionally, obtaining the candidate group control strategy set specifically includes:

[0029] The initial set boundary of the rolling optimization window is set by the initial coupling Zonotope. The start time of the current control cycle is obtained as the starting point of the rolling optimization window. The length of the rolling optimization window is set and the end point of the rolling optimization window is determined. The rolling optimization window is discretized at equal intervals on the time axis according to the control cycle to form a continuous discrete time point. The discrete time sequence of the rolling optimization window is output.

[0030] Based on the discrete time sequence of the rolling optimization window, a joint control structure for candidate group control strategies is constructed. For each discrete time point, a set of joint control variables for the air compressor cluster is established, and the joint control variables of each discrete time point are arranged in time order to form a candidate control sequence as a candidate group control strategy.

[0031] For each candidate group control strategy, a cluster joint control sequence is generated sequentially, and cluster operation constraints are applied to the cluster joint control sequence to eliminate candidate group control strategies that do not meet the constraints, thus obtaining a set of candidate group control strategies within the rolling optimization window.

[0032] Optionally, obtaining the predicted coupling Zonotope specifically includes:

[0033] Perform time slicing on the candidate group control strategies in the candidate group control strategy set, extract the cluster joint control action corresponding to the current control cycle, and generate the propagation input packet;

[0034] The current coupled Zonotope is converted into a propagation expression and a generative vector library is established. The generative vector library is grouped and arranged to form a runtime generation sub-library and a key parameter generation sub-library. Order budgets and priorities are set for different generation sub-libraries. At the same time, a process perturbation injection vector library and a parameter drift injection vector library are constructed and spliced ​​and arranged with the generative vector library.

[0035] The reachable domain propagation operator is invoked to perform a set-state forward inference. The propagation input packet drives the digital twin model to complete one step of forward inference, obtaining the center propagation result. The generated vector level incremental inference is then performed on the generated vector library to obtain the boundary propagation result.

[0036] The center propagation results are combined with the boundary propagation results. Merging, pruning, and conservative envelope are performed according to the order budget and priority. The uncertainty contribution of each generated vector is calculated to form a priority ranking list and determine the retention set and candidate compression set. The generated vectors in the candidate compression set are grouped according to the consistency of direction and the overlap of the action variables. A group representative generated vector is created for each group. At the same time, the group representative generated vector replaces the other generated vectors in the current group to complete the merging. For the generated vectors that still exceed the order budget after merging, pruning is performed in order of priority from low to high. The boundary influence of the pruned generated vectors is recorded. Conservative envelope compensation is performed for each merging and each pruning. The maximum deviation of the replaced or pruned generated vector in each running state component and each key parameter component is transferred to the compensated generated vector. At the same time, it is incorporated into the initial prediction coupling Zonotope to ensure that the outer envelope relationship of the initial prediction coupling Zonotope does not shrink, thus obtaining the prediction coupling Zonotope.

[0037] Optionally, obtaining the updated coupling Zonotope specifically includes:

[0038] The time-aligned data is written into the observation channel that is consistent with the coupled Zonotope encoding order according to the data mapping relationship of the digital twin model. The validity screening of each observation channel is performed to remove missing values, out-of-bounds values ​​and inconsistent timestamp values, and the observation consistency constraint input is output.

[0039] Based on the upper limit of sensor accuracy and the allowable deviation range of time alignment, allowable deviation intervals are generated for each observation channel. Based on the data normalization processing rules, weights and update order are generated for each observation channel, and a set of observation consistency parameters is output.

[0040] An observation consistency constraint strip set is constructed based on the observation consistency parameter set. The observation consistency constraint strip set consists of different observation strips and each observation strip corresponds to an observation channel. The observation strips limit the output set of the prediction coupled Zonotope on the observation channel to fall within the allowable deviation range corresponding to the observation channel.

[0041] The observation consistency shrinkage operator is invoked to perform strip cross-cutting shrinkage on the predicted coupled Zonotope. Observation strips are selected sequentially according to the update order. Boundary judgment is performed on the set projection of the predicted coupled Zonotope on the observation channel corresponding to the observation strip, and the shrinkage coefficient is calculated. Based on the shrinkage coefficient, the central term of the predicted coupled Zonotope is corrected and the generated term is scaled. Set parts that are inconsistent with the observation strips are removed. After each shrinkage, the corresponding generated terms of the running status and key parameters are synchronously scaled according to the same shrinkage coefficient. At the same time, the generated terms are redistributed according to the preset coupling redistribution rules to maintain coupling consistency and obtain the updated coupled Zonotope.

[0042] Optionally, obtaining the optimal control strategy specifically includes:

[0043] Using the updated coupling Zonotope as the initial set boundary for simulation, each candidate group control strategy in the candidate group control strategy set is written into the control input interface of the digital twin model, and a candidate strategy simulation task queue is established.

[0044] For each candidate strategy simulation task in the candidate strategy simulation task queue, perform What-If analysis. Under the same initial conditions of the update coupling Zonotope, load different candidate group control strategies respectively, compare the differences in simulation output, load the update coupling Zonotope as the initial condition of the digital twin model and lock the cluster joint control sequence of the current candidate group control strategy. According to the discrete time sequence of the rolling optimization window, call the state update process of the digital twin model in a loop to generate the center trajectory. At the same time, call the reachable domain propagation operator to propagate the generation term to generate the set state envelope trajectory, and output the What-If inference results.

[0045] Based on the What-If deduction results, an envelope evaluation result is generated. At the same time, constraint verification is performed on the envelope evaluation results at each discrete time within the rolling optimization window. Candidate group control strategies that violate constraints are marked as constraint not satisfied, and the worst-case constraint satisfied flag is obtained.

[0046] Among the candidate group control strategies where the worst-case constraint is satisfied, the energy consumption index is calculated and the strategy with the lowest energy consumption index is selected to obtain the optimal control strategy.

[0047] The optimal control strategy is sent to the air compressor cluster execution control system, so that the air compressor cluster can implement start-stop linkage, load distribution linkage and pressure setting linkage according to the optimal control strategy within the same control cycle.

[0048] The beneficial effects of this invention are:

[0049] This invention regularizes and aligns the real-time operating data of air compressor clusters and air supply systems from multiple sources, establishes a unified aligned time axis, and maps the data to a twin object structure. This reduces the interference of inconsistent sampling periods, clock drift, and missing values ​​on modeling and decision-making, enabling the digital twin model to continuously obtain stable and usable inputs, thereby improving the reliability of simulation and control strategy generation from the source.

[0050] This invention constructs a Zonotope observer in a digital twin model, co-encoding the operating state and key parameters into a coupled Zonotope. It achieves prediction updates and online contraction through reachability domain propagation operators and observation consistency contraction operators, simultaneously completing the uncertain coupling update of state and parameters. This suppresses the twin's drift over time and provides a reliable boundary in set form, avoiding the problems of prediction distortion and unstable policy implementation in existing point-value twins under operating condition fluctuations and performance drift.

[0051] This invention uses the updated coupled Zonotope as the initial set boundary of the rolling optimization window, performs ensemble state simulation deduction on candidate group control strategies, generates envelope evaluation results such as pressure, air supply, and energy consumption, and outputs worst-case constraint satisfaction flags. This ensures that strategy selection not only considers minimum energy consumption but also guarantees constraint feasibility under uncertain operating conditions, thereby improving the feasibility and robustness of air compressor cluster start-stop linkage, load distribution linkage, and pressure setting linkage, achieving long-term stable energy-saving optimization effects. Attached Figure Description

[0052] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0053] Figure 1 The flowchart shows the air compressor cluster collaborative control and energy efficiency optimization method based on digital twin proposed in this invention.

[0054] Figure 2 This diagram illustrates the Zonotope observer prediction update and observation consistency shrinkage update in the digital twin-based air compressor cluster collaborative control and energy efficiency optimization method proposed in this invention. Detailed Implementation

[0055] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0056] refer to Figures 1-2 A method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins includes the following steps:

[0057] Collect real-time operating data of the air compressor cluster and air supply system and perform time alignment to obtain time-aligned data;

[0058] A digital twin model of an air compressor cluster air supply system was established based on time-aligned data;

[0059] In the digital twin model, a Zonotope observer is constructed, and an reachability propagation operator and an observation consistency contraction operator are set. The running state and key parameters of the digital twin model are jointly encoded into a coupled Zonotope and initialized to obtain the initialized coupled Zonotope.

[0060] Generate a set of candidate group control strategies within the scrolling optimization window based on the initialization coupling of Zonotope;

[0061] For each candidate group control strategy in the candidate group control strategy set, the reachability domain propagation operator is invoked to perform the prediction update of the Zonotope observer, resulting in a prediction-coupled Zonotope.

[0062] By using aligned data as observation input, a consistent shrinkage is performed on the prediction coupling Zonotope, and the coupling update of the running state and key parameters is completed simultaneously to obtain the updated coupling Zonotope.

[0063] With the updated coupling Zonotope as the initial condition, each candidate group control strategy is loaded into the digital twin model and simulation is performed to generate envelope evaluation results and worst-case constraint satisfaction flags. The optimal control strategy is selected from the candidate group control strategy set based on the minimum energy consumption index and sent to the air compressor cluster execution control system for joint control of the air compressor cluster, so that the air compressors can start and stop, load distribution and pressure setting are linked according to the predetermined coordination relationship within the same control cycle.

[0064] In this embodiment, obtaining the time alignment data specifically includes:

[0065] Data acquisition interfaces and acquisition channels are configured on both the air compressor cluster side and the air supply system side to collect operating data from both sides. During acquisition, a timestamp is written to each acquisition record to form raw operating data. The operating data on the air compressor side includes operating conditions, start / stop status, loading or unloading status, exhaust pressure, exhaust temperature, output flow, input power, and frequency converter frequency. The operating data on the air supply system side includes main pipeline pressure, air tank pressure, gas load data, and electricity price data.

[0066] The raw operating data is processed to normalize the data. The data collection records of the same air compressor are merged according to the equipment identifier, and the data collection records of the air supply system are merged according to the location identifier. The merged data collection records are processed to unify the timestamps. The unified timestamp processing includes converting timestamps from different sources to the same time zone and the same time precision, adding timestamps to data collection records with missing timestamps in the order of arrival, merging data collection records with duplicate timestamps into a single record according to a preset priority, and outputting normalized operating data.

[0067] Based on the regularized operating data, a unified alignment time axis is established and time alignment is performed. The records of each air compressor side and the air supply system side on the unified alignment time axis are matched and merged. The time alignment includes keeping and filling the most recent valid record that is earlier than the target time, matching the nearest record that is later than the target time but falls within the allowable deviation range, and marking or filling the points that have no valid records before and after the target time according to the preset missing processing rules, and outputting time alignment data.

[0068] In this embodiment, the establishment of the digital twin model specifically includes:

[0069] Based on time-aligned data, the digital twin modeling boundary and modeling objects of the air compressor cluster air supply system are determined. A twin object structure consistent with the physical system is established, and the correspondence between object identifiers and point identifiers is established. The mapping relationship between the twin object structure and the identifiers is output. The twin object structure includes air compressor units, pipeline units, air storage units, and air load units.

[0070] A model mapping relationship is established based on the twin object structure. Time-aligned data is written into the corresponding twin object structure according to the equipment identifier and the point identifier. The data mapping relationship and the mapped twin input data are output. The data mapping relationship includes mapping the air compressor side operation data to the air compressor unit, mapping the main pipeline measurement point data to the pipeline unit, mapping the gas storage tank measurement point data to the gas storage unit, and mapping the gas load data to the gas load unit.

[0071] A high-fidelity mechanism model is constructed based on the twin object structure and the mapped twin input data. The high-fidelity mechanism model is then calibrated and its consistency is verified. The high-fidelity mechanism model includes a single-unit performance model of the air compressor and a dynamic model of the air supply system. The dynamic model of the air supply system is used to describe the dynamic coupling relationship between the system pressure state and the supply and demand balance.

[0072] The calibrated high-fidelity mechanism model and data mapping relationship are integrated, and a simulation deduction interface and a real-time data mapping interface are established to form a digital twin model of the air compressor cluster air supply system.

[0073] This invention constructs a digital twin object structure consistent with the physical system and establishes a mapping relationship between object identifiers and location identifiers. This enables unified writing and traceable association of multi-source data from the air compressor side and the air supply system side. Based on this, the data mapping relationship is integrated with a high-fidelity mechanism model after calibration and consistency verification to form a digital twin model with real-time mapping and simulation capabilities. This improves the model's accuracy in depicting the dynamic coupling of pipeline pressure and supply and demand, as well as its online adaptability. It also reduces the impact of modeling and data access errors on strategy evaluation, and enhances the credibility of group control optimization decisions and the stability of engineering implementation.

[0074] In this embodiment, obtaining the initial coupling Zonotope specifically includes:

[0075] In the digital twin model, the observer estimation object is determined, and a set of operating states to characterize the operating conditions of the air compressor cluster air supply system and a set of key parameters to characterize the performance drift of the air compressor cluster air supply system are established and jointly encoded as coupled variables according to a preset coding order.

[0076] Based on coupled variables, a Zonotope observer is constructed in the digital twin model. The data structure of the coupled Zonotope is set up and the central term and generator term are determined. The central term is used to store the central estimate of the coupled variables, and the generator term is used to store the uncertainty boundary of the coupled variables.

[0077] In the Zonotope observer, the reachability propagation operator and the observation consistency contraction operator are set, and the calling interface of the reachability propagation operator and the observation consistency contraction operator is output. The reachability propagation operator is used to propagate the uncertainty of the running state and key parameters to the future along with the control input when the candidate group control strategy is loaded into the digital twin model for simulation, so that the simulation output is expanded from single point results to envelope evaluation results covering uncertain operating conditions, and supports the generation of worst case constraint satisfaction flags. The observation consistency contraction operator is used to suppress the drift of the digital twin over time.

[0078] The coupled Zonotope is initialized by writing the set of running states corresponding to the time-aligned data at the initial moment into the central term of the coupled Zonotope as the running state center, writing the preset parameter benchmark of the digital twin model into the central term of the coupled Zonotope as the key parameter center, and determining the magnitude of the generator term of the coupled Zonotope based on the upper bound of sensor accuracy, the upper bound of modeling error and the prior boundary of key parameters to form the initial uncertainty boundary, thus obtaining the initialized coupled Zonotope.

[0079] This invention establishes coupled variables by encoding the operating state and key parameters in a unified manner and establishing a coupled Zonotope with the central term and the generating term. It combines the reachability domain propagation operator and the observation consistency contraction operator to realize the computable propagation and online convergence suppression of uncertainty with control input. Furthermore, it initializes the uncertainty boundary based on the upper bound of sensor accuracy, the upper bound of modeling error, and the prior boundary of parameters. Thus, it simultaneously characterizes the fluctuation of operating conditions and performance drift in the digital twin and outputs an envelope evaluation basis covering uncertain operating conditions, thereby improving the credibility of worst-case constraint determination and the robustness of group control strategy selection.

[0080] In this embodiment, obtaining the candidate group control strategy set specifically includes:

[0081] The initial set boundary of the rolling optimization window is set by the initial coupling Zonotope. The start time of the current control cycle is obtained as the starting point of the rolling optimization window. The length of the rolling optimization window is set and the end point of the rolling optimization window is determined. The rolling optimization window is discretized at equal intervals on the time axis according to the control cycle to form a continuous discrete time point. The discrete time sequence of the rolling optimization window is output.

[0082] Based on the discrete time sequence of the rolling optimization window, a joint control structure for candidate group control strategies is constructed. For each discrete time point, a set of joint control variables for the air compressor cluster is established, and the joint control variables of each discrete time point are arranged in time order to form a candidate control sequence as a candidate group control strategy.

[0083] For each candidate group control strategy, a cluster joint control sequence is generated sequentially, and cluster operation constraints are applied to the cluster joint control sequence to eliminate candidate group control strategies that do not meet the constraints, thus obtaining a set of candidate group control strategies within the rolling optimization window. The cluster joint control sequence includes air compressor start / stop combination, air compressor load distribution combination, frequency converter setting combination, main pipeline pressure setting value, and reference machine selection result.

[0084] In this embodiment, obtaining the predicted coupling Zonotope specifically includes:

[0085] Time slices are performed on the candidate group control strategies in the candidate group control strategy set. The cluster joint control actions corresponding to the current control cycle are extracted and propagation input packets are generated. The cluster joint control actions include start and stop actions, load distribution actions, frequency conversion setting actions, pressure setting actions and reference machine selection actions.

[0086] The current coupled Zonotope is converted into a propagation expression and a generative vector library is established. The generative vector library is grouped and arranged to form a runtime generation sub-library and a key parameter generation sub-library. Order budgets and priorities are set for different generation sub-libraries. At the same time, a process perturbation injection vector library and a parameter drift injection vector library are constructed and spliced ​​and arranged with the generative vector library.

[0087] The reachable domain propagation operator is invoked to perform a forward inference of the set state. The propagation input packet drives the digital twin model to complete one step of forward inference, obtaining the central propagation result. The generated vector library is subjected to a generated vector-level incremental inference. The generated vector-level incremental inference includes performing forward perturbation inference and backward perturbation inference on each generated vector in the running state generation sub-library in sequence and recording the output difference to form the running state boundary contribution corresponding to the generated vector. The generated vector in the key parameter generation sub-library is subjected to forward bias inference and backward bias inference on each generated vector in sequence and recording the output difference to form the key parameter boundary contribution corresponding to the generated vector. Each injected vector in the process perturbation injection vector library is applied to the state update process of the digital twin model according to a preset perturbation amplitude and the output difference is recorded to form the process perturbation boundary contribution. Each injected vector in the parameter drift injection vector library is applied to the key parameter according to a preset drift amplitude and the output difference is recorded to form the parameter drift boundary contribution. The boundary propagation results are obtained by summing up the boundary contributions of each running state boundary, key parameter boundary, process perturbation boundary, and parameter drift boundary.

[0088] The center propagation results are combined with the boundary propagation results. Merging, pruning, and conservative envelope are performed according to the order budget and priority. The uncertainty contribution of each generated vector is calculated to form a priority ranking list and determine the retention set and candidate compression set. The generated vectors in the candidate compression set are grouped according to the consistency of direction and the overlap of the action variables. A group representative generated vector is created for each group. At the same time, the group representative generated vector replaces the other generated vectors in the current group to complete the merging. For the generated vectors that still exceed the order budget after merging, pruning is performed in order of priority from low to high. The boundary influence of the pruned generated vectors is recorded. Conservative envelope compensation is performed for each merging and each pruning. The maximum deviation of the replaced or pruned generated vector in each running state component and each key parameter component is transferred to the compensated generated vector. At the same time, it is incorporated into the initial prediction coupling Zonotope to ensure that the outer envelope relationship of the initial prediction coupling Zonotope does not shrink, thus obtaining the prediction coupling Zonotope.

[0089] This invention maps cluster joint control actions such as start-up and shutdown, load distribution, frequency conversion and pressure setting into propagation inputs, and incorporates the uncertainty of operating state, the uncertainty of key parameters, and process disturbances and parameter drift into the generation vector propagation framework coupled with Zonotope. It uses reachable domain propagation to obtain the set state prediction of the center propagation result and the boundary propagation result. At the same time, it performs grouping, merging and pruning of generation vectors according to order budget and contribution priority, and introduces conservative envelope compensation to maintain the outer envelope relationship without shrinking. Thus, while ensuring the credibility and conservatism of the prediction boundary, it suppresses generator explosion and improves the computational efficiency and robustness of rolling inference.

[0090] In this embodiment, obtaining the updated coupling Zonotope specifically includes:

[0091] The time-aligned data is written into the observation channel that is consistent with the coupled Zonotope encoding order according to the data mapping relationship of the digital twin model. The validity screening of each observation channel is performed to remove missing values, out-of-bounds values ​​and inconsistent timestamp values, and the observation consistency constraint input is output.

[0092] Based on the upper limit of sensor accuracy and the allowable deviation range of time alignment, allowable deviation intervals are generated for each observation channel. Based on the data normalization processing rules, weights and update order are generated for each observation channel, and a set of observation consistency parameters is output.

[0093] An observation consistency constraint strip set is constructed based on the observation consistency parameter set. The observation consistency constraint strip set consists of different observation strips and each observation strip corresponds to an observation channel. The observation strips limit the output set of the prediction coupled Zonotope on the observation channel to fall within the allowable deviation range corresponding to the observation channel.

[0094] The observation consistency shrinkage operator is invoked to perform strip cross-cutting shrinkage on the predicted coupled Zonotope. Observation strips are selected sequentially according to the update order. Boundary judgment is performed on the set projection of the predicted coupled Zonotope on the observation channel corresponding to the observation strip, and the shrinkage coefficient is calculated. Based on the shrinkage coefficient, the central term of the predicted coupled Zonotope is corrected and the generated term is scaled. Set parts that are inconsistent with the observation strips are removed. After each shrinkage, the corresponding generated terms of the running status and key parameters are synchronously scaled according to the same shrinkage coefficient. At the same time, the generated terms are redistributed according to the preset coupling redistribution rules to maintain coupling consistency and obtain the updated coupled Zonotope.

[0095] This invention writes time-aligned data into observation channels consistent with the coupled Zonotope according to the Siamese mapping relationship and performs validity screening. Based on the upper bound of sensor accuracy and the allowable alignment deviation, it constructs an observation consistency strip set and assigns weights and update order. It uses the observation consistency shrinkage operator to perform strip cross-conversion shrinkage on the predicted coupled Zonotope. By correcting the central term and scaling the generated term synchronously through the shrinkage coefficient, and combining it with coupling redistribution, it maintains consistent coupling updates of state and parameters. Thus, while ensuring the interpretability of observation constraints, it suppresses Siamese drift and significantly improves the fit of the set boundary and the robustness of online estimation.

[0096] In this embodiment, obtaining the optimal control strategy specifically includes:

[0097] Using the updated coupling Zonotope as the initial set boundary for simulation, each candidate group control strategy in the candidate group control strategy set is written into the control input interface of the digital twin model, and a candidate strategy simulation task queue is established. The candidate group control strategy corresponds to a set of cluster joint control sequences within the rolling optimization window. The cluster joint control sequence includes air compressor start / stop control sequence, air compressor load distribution control sequence, frequency converter setting control sequence, main pipeline pressure setting sequence, and reference machine selection sequence.

[0098] For each candidate strategy simulation task in the candidate strategy simulation task queue, perform What-If analysis. Under the same initial conditions of the update coupling Zonotope, load different candidate group control strategies respectively, compare the differences in simulation output, load the update coupling Zonotope as the initial condition of the digital twin model and lock the cluster joint control sequence of the current candidate group control strategy. According to the discrete time sequence of the rolling optimization window, call the state update process of the digital twin model in a loop to generate the center trajectory. At the same time, call the reachable domain propagation operator to propagate the generation term to generate the set state envelope trajectory, and output the What-If inference results.

[0099] Based on the What-If deduction results, envelope evaluation results are generated. At the same time, constraint checks are performed on the envelope evaluation results at each discrete time within the rolling optimization window. Candidate group control strategies that violate constraints are marked as constraint unsatisfied, and the worst-case constraint satisfaction flag is obtained. The envelope evaluation results include the main pipeline pressure envelope, gas storage unit pressure envelope, cluster gas supply envelope, and energy consumption envelope, and the envelope evaluation results corresponding to the candidate group control strategies are output.

[0100] Among the candidate group control strategies where the worst-case constraint is satisfied, the energy consumption index is calculated and the strategy with the lowest energy consumption index is selected. The energy consumption index is the sum of the products of the input power and the electricity price at each discrete moment within the rolling optimization window, and the optimal control strategy is obtained.

[0101] The optimal control strategy is sent to the air compressor cluster execution control system, so that the air compressor cluster can implement start-stop linkage, load distribution linkage and pressure setting linkage according to the optimal control strategy within the same control cycle.

[0102] This invention uses the updated coupled Zonotope as a unified initial boundary to perform What-If ensemble state simulation on candidate group control strategies. It utilizes reachability domain propagation to form the envelope evaluation results of pressure, gas supply, and energy consumption, and generates a worst-case constraint satisfaction flag. Among the candidate strategies that satisfy the worst-case constraints, the optimal control strategy is determined by minimizing the electricity price-weighted energy consumption index and then issued for execution. This enables coordinated linkage of start-up and shutdown, load distribution, and pressure setting under uncertain operating conditions, taking into account both the gas supply pressure safety boundary and stable energy-saving benefits.

[0103] Example 1: To verify the feasibility of this invention in practice, it was applied to the centralized air supply system of an air compressor in a discrete manufacturing enterprise. This system is a ring-shaped main pipeline shared by multiple workshops, with air storage tanks and multiple air-consuming branches at the end. The production load is characterized by frequent fluctuations and periodic surges. There are also problems such as asynchronous multi-source sampling, occasional missing measurement points, and pressure signal fluctuations due to interference. The enterprise has configured multiple air compressors to form a cluster, including both fixed-frequency and variable-frequency units. Normally, a start-stop linkage based on pressure bands and an experience-based load distribution strategy is used to maintain basic air supply. However, typical pain points easily occur when the load changes rapidly and the electricity price fluctuates. One type is that the main pipeline pressure drops briefly during high load surges or overshoots during start-stop switching, leading to insufficient air pressure alarms and frequent unloading at the end workstations. Another type is that after long-term operation of the cluster, the equipment efficiency and the equivalent resistance of the pipeline drift, and the original parameter calibration and point value prediction gradually become inaccurate. This makes the "seemingly optimal" strategy unstable in terms of energy consumption benefits when implemented, and even lead to increased electricity costs due to conservative settings.

[0104] After deploying this invention in this scenario, the system side uniformly collects and organizes the operating data of the air compressor side and the air supply system side. It writes information such as the operating conditions, start / stop and loading status, exhaust pressure and temperature, output flow, input power, frequency converter frequency, as well as main pipeline pressure, air tank pressure, gas load, and electricity price of each device into a unified aligned time axis. The data is then merged and marked according to arrival order, allowable deviation, and missing data rules to ensure that the input of the digital twin is traceable and consistent at the same time scale. The digital twin model consists of an object structure of air compressor unit, pipeline unit, air storage unit, and gas load unit. A mapping relationship is established through equipment identifiers and location identifiers, and aligned data is injected into the corresponding twin objects in real time. On the mechanism side, a single-unit performance model of the air compressor and a dynamic model of the air supply system are constructed to depict the coupling of supply and demand balance and pressure state. During the online phase, parameter calibration and consistency verification are completed, enabling the model to have an interpretable dynamic response within the engineering boundaries.

[0105] To address the critical issues of "model drift and policy distortion" in field implementation, this invention constructs a Zonotope observer within the digital twin model. This observer encodes the operating state (characterizing operational conditions) and key parameters (characterizing performance drift) as coupled variables. The central term represents the current central estimate, and the generated term represents the uncertainty envelope determined by the upper bound of sensor accuracy, the upper bound of modeling error, and the prior boundaries of key parameters. During operation, a set of candidate group control strategies is automatically generated within a rolling optimization window. These candidate strategies cover start-stop combinations, load distribution, frequency conversion settings, main network pressure settings, and benchmarks. The system selects and links control variables. Within each control cycle, the reachability domain propagation operator is first invoked to perform ensemble-state forward inference on the coupled Zonotope, allowing the uncertainties of the operating state and key parameters to propagate along with the candidate control inputs, resulting in the predictive coupled Zonotope corresponding to each candidate strategy. Subsequently, an observation consistency constraint strip set is constructed using aligned data as observation input, and strip cross-conversion shrinkage is applied to the predictive coupled Zonotope to complete center correction and synchronous scaling of generated terms. The system then maintains consistent coupling updates of the state and parameters according to the coupling redistribution rules, resulting in the updated coupled Zonotope. To avoid the expansion of the number of generators caused by ensemble propagation, the system sets order budgets and priorities for the generator vector library, performs merging and pruning based on contribution ranking, and introduces conservative envelope compensation to ensure that the outer envelope relationship does not shrink, thereby maintaining the reliability and conservatism of the prediction boundary under the premise of computational controllability.

[0106] During the strategy selection phase, the system uses the updated coupled Zonotope as a unified initial set boundary. For each candidate group control strategy, it performs What-If ensemble state simulation, outputting the main network pressure envelope, gas storage unit pressure envelope, cluster gas supply envelope, and energy consumption envelope. The envelope results are then constrained to generate a worst-case constraint satisfaction flag. Only within the candidate strategy set where the worst-case constraint satisfaction flag is true, the electricity price-weighted energy consumption index is further calculated, and the strategy with the lowest energy consumption is selected as the optimal control strategy and issued to the cluster execution control system. This ensures pressure safety boundaries and gas supply continuity even under uncertain operating conditions, and stably achieves energy-saving benefits. Simultaneously, an online contraction mechanism continuously suppresses twin drift, gradually converging the deviation between the strategy evaluation results and the field response, avoiding the situation of "simulation optimal, field unusable."

[0107] To quantify and verify the beneficial effects, statistical results of three operating modes were compared under the same production cycle and similar load fluctuation levels: traditional pressure band experience-based group control, point-value digital twin optimized group control (point-value simulation only, without ensemble propagation and consistency contraction), and the coupled Zonotope ensemble twin rolling optimized group control of this invention. Traditional pressure band experience-based group control uses the upper and lower limits of the main pipeline pressure and preset start / stop / load / unload rules to perform linked control of the air compressors, and achieves basic gas supply assurance by alternating between the experienced pressure band and the baseline machine. Point-value digital twin optimized group control performs point-value simulation and deduction of candidate group control strategies in the digital twin model and selects the optimal strategy based on energy consumption indicators for execution, but does not perform ensemble propagation for model state and parameter uncertainties, nor does it perform observation consistency contraction updates. The comparative data are presented as continuous sampling point statistics and cumulative gas production normalization. Pressure constraints are based on the allowable range of the main pipeline pressure, and energy efficiency is mainly reflected in unit gas production power consumption and electricity cost. Start / stop frequency and unloading ratio are also recorded to reflect control stability. The results are shown in Table 1.

[0108] Table 1. Comparison of Operational Stability Indicators for Air Compressor Cluster Control Method

[0109]

[0110] As shown in Table 1, compared with traditional pressure zone experience-based group control and point-value digital twin optimized group control, this invention performs better in both operational stability and energy efficiency: the pressure fluctuation of the main pipeline network is significantly reduced (standard deviation decreased from 0.020 / 0.017 to 0.012 MPa), and the alarms for pressure exceeding limits and insufficient terminal gas pressure are greatly reduced (from 8.6 / 4.1 to 0.9 times / 10,000 alarms and from 5.2 / 2.9 to 0.7 times / 10,000 alarms, respectively). Furthermore, the frequency of start-stop switching and the unloading ratio decrease simultaneously (from 6.8 / 6.1 ​​to 4.3 times / 10,000 alarms and from 21.5% / 17.8% to 12.6%). Based on this, the unit gas production power consumption and unit gas production power cost are further reduced (from 0.118 / 0.112 to 0.104 kWh / Nm³). 3 The price dropped from 0.096 / 0.090 to 0.083 yuan / Nm³. 3 Meanwhile, the worst-case constraint satisfaction rate has increased to 99.4%, demonstrating its feasibility and robust energy-saving advantages under uncertain operating conditions.

[0111] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins, characterized in that, Includes the following steps: Collect real-time operating data of the air compressor cluster and air supply system and perform time alignment to obtain time-aligned data; A digital twin model of an air compressor cluster air supply system was established based on time-aligned data; In the digital twin model, a Zonotope observer is constructed, and an reachability propagation operator and an observation consistency contraction operator are set. The running state and key parameters of the digital twin model are jointly encoded into a coupled Zonotope and initialized to obtain the initialized coupled Zonotope. Generate a set of candidate group control strategies within the scrolling optimization window based on the initialization coupling of Zonotope; For each candidate group control strategy in the candidate group control strategy set, the reachability domain propagation operator is invoked to perform the prediction update of the Zonotope observer, resulting in a prediction-coupled Zonotope. By using aligned data as observation input, a consistent shrinkage is performed on the prediction coupling Zonotope, and the coupling update of the running state and key parameters is completed simultaneously to obtain the updated coupling Zonotope. With the updated coupling Zonotope as the initial condition, each candidate group control strategy is loaded into the digital twin model and simulation is performed. The envelope evaluation result and worst-case constraint satisfaction flag are generated. The optimal control strategy is selected from the candidate group control strategy set based on the minimum energy consumption index and then sent to the air compressor cluster execution control system for execution.

2. The method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins according to claim 1, characterized in that, The acquisition of the time-aligned data specifically includes: Data acquisition interfaces and acquisition channels are configured on the air compressor cluster side and the air supply system side respectively to collect the operating data of the air compressor side and the operating data of the air supply system side. During the acquisition, a timestamp is written for each acquisition record to form the raw operating data. The raw operating data is processed to normalize the data. The data collection records of the same air compressor are merged according to the equipment identifier, and the data collection records of the air supply system are merged according to the location identifier. The merged data collection records are processed to uniformly update the timestamps, and the normalized operating data is output. Based on the regularized operating data, a unified alignment time axis is established and time alignment is performed. The records of each air compressor side and the air supply system side on the unified alignment time axis are matched and merged, and time alignment data is output.

3. The method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins according to claim 1, characterized in that, The establishment of the digital twin model specifically includes: Based on time-aligned data, the digital twin modeling boundary and modeling objects of the air compressor cluster air supply system are determined, a twin object structure consistent with the physical system is established, and the correspondence between object identifiers and point identifiers is established. The mapping relationship between the twin object structure and the identifiers is output. A model mapping relationship is established based on the twin object structure. Time-aligned data is written into the corresponding twin object structure according to the device identifier and the location identifier. The data mapping relationship and the mapped twin input data are output. A high-fidelity mechanism model is constructed based on the twin object structure and the mapped twin input data, and the parameters of the high-fidelity mechanism model are calibrated and the consistency is verified. The calibrated high-fidelity mechanism model and data mapping relationship are integrated, and a simulation deduction interface and a real-time data mapping interface are established to form a digital twin model of the air compressor cluster air supply system.

4. The method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins according to claim 1, characterized in that, The specific steps involved in obtaining the initial coupling Zonotope are as follows: In the digital twin model, the observer estimation object is determined, and a set of operating states to characterize the operating conditions of the air compressor cluster air supply system and a set of key parameters to characterize the performance drift of the air compressor cluster air supply system are established and jointly encoded as coupled variables according to a preset coding order. Based on coupled variables, a Zonotope observer is constructed in the digital twin model. The data structure of the coupled Zonotope is set up and the central term and generator term are determined. The central term is used to store the central estimate of the coupled variables, and the generator term is used to store the uncertainty boundary of the coupled variables. Configure the reachability propagation operator and the observation consistency contraction operator in the Zonotope observer, and output the calling interface of the reachability propagation operator and the observation consistency contraction operator; The coupled Zonotope is initialized by writing the set of running states corresponding to the time-aligned data at the initial moment into the central term of the coupled Zonotope as the running state center, writing the preset parameter benchmark of the digital twin model into the central term of the coupled Zonotope as the key parameter center, and determining the magnitude of the generator term of the coupled Zonotope based on the upper bound of sensor accuracy, the upper bound of modeling error and the prior boundary of key parameters to form the initial uncertainty boundary, thus obtaining the initialized coupled Zonotope.

5. The method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins according to claim 1, characterized in that, The specific steps to obtain the candidate group control strategy set include: The initial set boundary of the rolling optimization window is set by the initial coupling Zonotope. The start time of the current control cycle is obtained as the starting point of the rolling optimization window. The length of the rolling optimization window is set and the end point of the rolling optimization window is determined. The rolling optimization window is discretized at equal intervals on the time axis according to the control cycle to form a continuous discrete time point. The discrete time sequence of the rolling optimization window is output. Based on the discrete time sequence of the rolling optimization window, a joint control structure for candidate group control strategies is constructed. For each discrete time point, a set of joint control variables for the air compressor cluster is established, and the joint control variables of each discrete time point are arranged in time order to form a candidate control sequence as a candidate group control strategy. For each candidate group control strategy, a cluster joint control sequence is generated sequentially, and cluster operation constraints are applied to the cluster joint control sequence to eliminate candidate group control strategies that do not meet the constraints, thus obtaining a set of candidate group control strategies within the rolling optimization window.

6. The method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins according to claim 1, characterized in that, The specific steps involved in obtaining the predicted coupling Zonotope are as follows: Perform time slicing on the candidate group control strategies in the candidate group control strategy set, extract the cluster joint control action corresponding to the current control cycle, and generate the propagation input packet; The current coupled Zonotope is converted into a propagation expression and a generative vector library is established. The generative vector library is grouped and arranged to form a runtime generation sub-library and a key parameter generation sub-library. Order budgets and priorities are set for different generation sub-libraries. At the same time, a process perturbation injection vector library and a parameter drift injection vector library are constructed and spliced ​​and arranged with the generative vector library. The reachable domain propagation operator is invoked to perform a set-state forward inference. The propagation input packet drives the digital twin model to complete one step of forward inference, obtaining the center propagation result. The generated vector level incremental inference is then performed on the generated vector library to obtain the boundary propagation result. The center propagation results are combined with the boundary propagation results. Merging, pruning, and conservative envelope are performed according to the order budget and priority. The uncertainty contribution of each generated vector is calculated to form a priority ranking list and determine the retention set and candidate compression set. The generated vectors in the candidate compression set are grouped according to the consistency of direction and the overlap of the action variables. A group representative generated vector is created for each group. At the same time, the group representative generated vector replaces the other generated vectors in the current group to complete the merging. For the generated vectors that still exceed the order budget after merging, pruning is performed in order of priority from low to high. The boundary influence of the pruned generated vectors is recorded. Conservative envelope compensation is performed for each merging and each pruning. The maximum deviation of the replaced or pruned generated vector in each running state component and each key parameter component is transferred to the compensated generated vector. At the same time, it is incorporated into the initial prediction coupling Zonotope to ensure that the outer envelope relationship of the initial prediction coupling Zonotope does not shrink, thus obtaining the prediction coupling Zonotope.

7. The method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins according to claim 1, characterized in that, The specific steps involved in obtaining the updated coupling Zonotope are as follows: The time-aligned data is written into the observation channel that is consistent with the coupled Zonotope encoding order according to the data mapping relationship of the digital twin model. The validity screening of each observation channel is performed to remove missing values, out-of-bounds values ​​and inconsistent timestamp values, and the observation consistency constraint input is output. Based on the upper limit of sensor accuracy and the allowable deviation range of time alignment, allowable deviation intervals are generated for each observation channel. Based on the data normalization processing rules, weights and update order are generated for each observation channel, and a set of observation consistency parameters is output. An observation consistency constraint strip set is constructed based on the observation consistency parameter set. The observation consistency constraint strip set consists of different observation strips and each observation strip corresponds to an observation channel. The observation strips limit the output set of the prediction coupled Zonotope on the observation channel to fall within the allowable deviation range corresponding to the observation channel. The observation consistency shrinkage operator is invoked to perform strip cross-cutting shrinkage on the predicted coupled Zonotope. Observation strips are selected sequentially according to the update order. Boundary judgment is performed on the set projection of the predicted coupled Zonotope on the observation channel corresponding to the observation strip, and the shrinkage coefficient is calculated. Based on the shrinkage coefficient, the central term of the predicted coupled Zonotope is corrected and the generated term is scaled. Set parts that are inconsistent with the observation strips are removed. After each shrinkage, the corresponding generated terms of the running status and key parameters are synchronously scaled according to the same shrinkage coefficient. At the same time, the generated terms are redistributed according to the preset coupling redistribution rules to maintain coupling consistency and obtain the updated coupled Zonotope.

8. The method for collaborative control and energy efficiency optimization of air compressor clusters based on digital twins according to claim 1, characterized in that, The optimal control strategy is obtained specifically through: Using the updated coupling Zonotope as the initial set boundary for simulation, each candidate group control strategy in the candidate group control strategy set is written into the control input interface of the digital twin model, and a candidate strategy simulation task queue is established. For each candidate strategy simulation task in the candidate strategy simulation task queue, perform What-If analysis. Under the same initial conditions of the update coupling Zonotope, load different candidate group control strategies respectively, compare the differences in simulation output, load the update coupling Zonotope as the initial condition of the digital twin model and lock the cluster joint control sequence of the current candidate group control strategy. According to the discrete time sequence of the rolling optimization window, call the state update process of the digital twin model in a loop to generate the center trajectory. At the same time, call the reachable domain propagation operator to propagate the generation term to generate the set state envelope trajectory, and output the What-If inference results. Based on the What-If deduction results, an envelope evaluation result is generated. At the same time, constraint verification is performed on the envelope evaluation results at each discrete time within the rolling optimization window. Candidate group control strategies that violate constraints are marked as constraint not satisfied, and the worst-case constraint satisfied flag is obtained. Among the candidate group control strategies where the worst-case constraint is satisfied, the energy consumption index is calculated and the strategy with the lowest energy consumption index is selected to obtain the optimal control strategy. The optimal control strategy is sent to the air compressor cluster execution control system, so that the air compressor cluster can implement start-stop linkage, load distribution linkage and pressure setting linkage according to the optimal control strategy within the same control cycle.

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