A distributed cooperative control method for array rectification multi-agent system

Abstract

This invention provides a distributed cooperative control method for an array-type distillation multi-agent system, comprising: constructing an array-type distillation multi-agent system; constructing a mathematical model using a closed-loop subspace identification method to determine the baseline cluster and cooperative cluster; establishing a dynamic event triggering mechanism and an observer network architecture; constructing a distributed cooperative control model; and establishing state-space equations and conducting consistency performance tests. By introducing a dynamic event triggering mechanism and an observer network, this invention achieves leader-follower consistency control under state constraints, reduces frequent switching of control commands, suppresses the Zeno phenomenon, and improves the robustness and stability of the system under disturbances.

Description

Technical Field

[0001] This invention relates to the field of chemical process control technology, specifically but not limited to a distributed collaborative control method for an array-type distillation multi-agent system. Background Technology

[0002] Distillation, as a core unit operation in chemical separation, directly impacts product quality, energy consumption, and overall economic efficiency through its control performance. Array distillation systems, through specific combinations of multiple distillation columns, can achieve efficient separation of complex mixtures; however, their control systems face significant challenges due to their complex structure. This system involves the coordinated control of multiple key process variables (controlled variables), such as column top pressure, column bottom temperature, reflux ratio, and feed flow rate, as well as operational variables like reboiler heat load, condenser refrigerant flow rate, and reflux tank level control valve position. These variables exhibit significant strong coupling relationships; fluctuations in any one variable can trigger a chain reaction throughout the system via the coupling path, leading to operational instability, product defects, or increased energy consumption.

[0003] Currently, the control of array distillation systems in practice mostly adopts traditional multivariate control strategies, focusing on enabling the controlled variables (such as top pressure and bottom temperature) to track quickly and accurately, ensuring process stability and product quality. However, the smooth control and optimization of the dynamic behavior of the operating variables themselves are generally neglected. In the distillation process, operating variables (such as reboiler steam consumption and reflux pump power) directly reflect production costs. Ignoring effective tracking and smooth adjustment of operating variables means that the control system fails to directly incorporate economic performance indicators into the design of the control law. This can easily lead to frequent or large fluctuations in operating variables in actual operation, resulting in energy and material waste, thereby directly increasing production costs and weakening the company's market competitiveness. In addition, the production processes in the chemical industry are highly nonlinear, time-varying, and uncertain. Traditional control strategies often lack robustness and reliability when facing such complex dynamics, leading to decreased control performance and even system instability.

[0004] In recent years, distributed control methods based on Multi-Agent Systems (MAS) have shown great potential in the field of complex system control. This method decomposes a large system into multiple interconnected subsystems, each controlled by an agent with autonomous decision-making, communication, and collaboration capabilities. The multiple agents work together to achieve the global control objective through local perception, information exchange, and collaborative decision-making. This architecture endows the system with stronger robustness, reliability, and flexibility. When a local unit fails or operating conditions change drastically, the system can adaptively adjust through collaboration among the agents. Multi-agent consistent control technology, as a key technology, ensures that the states or outputs of all agents tend to be consistent during dynamic processes, which is crucial for achieving coordinated and stable operation between columns and variables in an array distillation system.

[0005] In view of this, a new control method is needed to solve at least some of the above problems. Summary of the Invention

[0006] To address one or more problems in the prior art, this invention proposes a distributed cooperative control method for an array-type distillation multi-agent system. It integrates a state observer for estimating unit dynamics and a dynamic event triggering mechanism to optimize communication resources. Through Lyapunov analysis, a stability criterion is derived, and the control problem is expressed as a set of linear matrix inequalities (LMIs), achieving system consistency under hard state constraints in finite states.

[0007] The technical solution to achieve the purpose of this invention is as follows:

[0008] A distributed cooperative control method for an array-type distillation multi-agent system includes:

[0009] S1: Based on the leader-follower consistency of array-type distillation system and multi-agent system, construct array-type distillation multi-agent system, wherein multiple parallel and coupled cluster-type distillation units constitute the agents in the array-type distillation multi-agent system;

[0010] S2: Construct the mathematical model of the array-type distillation multi-agent system by means of the closed-loop subspace identification method, determine the reference cluster and the cooperative cluster, perform local control on the reference cluster and initially configure its poles, wherein the reference cluster is a cluster-type distillation unit that provides a reference frame, and the cooperative cluster is other cluster-type distillation units that keep synchronized with the reference cluster.

[0011] S3: Based on the benchmark cluster and the cooperative cluster, a dynamic event triggering mechanism and an observer network architecture are established. Under the dynamic event triggering mechanism, if the triggering condition is met, the distributed cooperative controller is updated to ensure the strict consistency and stability of the array-type distillation multi-agent system. The observer is used to monitor the state of the cooperative cluster in real time, and the state serves as the input to the distributed cooperative control model.

[0012] S4: Based on the dynamic event triggering mechanism and observer network architecture, a distributed cooperative control model is constructed using Lyapunov functions and consistency objectives to achieve consistency of output product quality and output consistency between the leader cluster and the follower cluster.

[0013] S5: Based on the mathematical model, establish the state space equation of the array-type distillation multi-agent system, use the PID parameter tuning method to determine the constraint range of the state variables, conduct distributed cooperative control consistency performance tests on the array-type distillation multi-agent system under the initial state and different disturbances, and analyze the input and output status of the array-type distillation multi-agent system.

[0014] Optionally, in step S2, the state equation of the reference cluster is:

[0015] ,

[0016] The state equation of the i-th cooperative cluster is:

[0017] ,

[0018] in, , Let these represent the states of the i-th cooperative cluster and the reference cluster at time t, respectively. and Let A represent the outputs of the i-th cooperative cluster and the reference cluster at time t, respectively. Let A be the cooperative cluster state matrix, B be the control matrix, and C be the output matrix. L The baseline cluster state matrix, , Let these represent the operational variable states of the i-th cooperative cluster and the reference cluster at time t, respectively. This represents the distributed control input of the i-th cooperative cluster at time t.

[0019] Optionally, in step S2, the local control of the reference cluster includes:

[0020] Introducing state feedback control law ;

[0021] Based on the state feedback control law and the open-loop state equation of the cooperative cluster, the closed-loop state equation of the reference cluster is obtained as follows:

[0022] ,

[0023] The state matrix of the reference cluster then satisfies: ;

[0024] A Routh array is constructed based on the Routh-Hurwitz criterion, and the first column is checked to see if all elements are positive. If all elements are positive, then the state matrix is... The Hurwitz matrix is ​​used, and the benchmark cluster output satisfies the dynamic requirements.

[0025] Optionally, in step S3, the dynamic event triggering mechanism is as follows:

[0026] ,

[0027] in, , They represent the first The first agent of the intelligent agent sequence The timing of this event trigger; Represents the infimum; Indicates the current moment; This is a function that triggers dynamic events. As an auxiliary dynamic variable, and , , The system matrix is ​​positive definite, and α and β are positive constants. This is the current cooperative error signal; This is the sample-and-hold error signal; For dynamic threshold variables;

[0028] The observer network architecture is as follows:

[0029] ,

[0030] in, This represents the estimated state of the i-th cooperative cluster observer. ; For the system matrix, G is the control matrix, and G is the monitoring error coefficient matrix. Estimate the state of the operational variables for the i-th cooperative cluster at time t. This is the distributed control input for the i-th cooperative cluster.

[0031] Optionally, in step S4, constructing the distributed cooperative control model includes:

[0032] S4-1: When there are no state variable constraints, under the combined action of the distributed collaborative controller, dynamic event triggering mechanism, and observer, if the following conditions are met:

[0033] Q1>0, Q2>0, G, T1>0, T2>0,

[0034] ,

[0035] ,

[0036] This achieves consistency in product quality output between the leader cluster and the follower cluster; where Q1, Q2, T1, and T2 are the system positive definite matrices, and G is the monitoring error coefficient matrix. The matrix inequalities derived from the Lyapunov derivative, , , , , , for The submatrix, where BK is the feedback term. C is the coupling term, and C is the output matrix;

[0037] S4-2: When state variable constraints exist, under the combined effect of the dynamic event triggering mechanism and the observer, if the following conditions are met:

[0038] ,

[0039] Where Ω′ and Q represent the block matrix structure of the closed-loop stability condition, and satisfy:

[0040] ;

[0041] The submatrix Ω′1 corresponds to the dynamic characteristics of the baseline cluster and includes the feedback term BK and the coupling term. Submatrix Indicates gain and output matrix The observer-related subsystem; submatrix Consistency gain (LG) describes the coupling between the baseline cluster and the coordination cluster. Since these two clusters have symmetrical coupling, there is... Submatrix The relationship between the event triggering parameters and the observer matrix is ​​defined as follows:

[0042] ,

[0043] Under the above conditions, for any given , If the outputs of the baseline cluster and the cooperative cluster are consistent, then it is considered that the outputs of the baseline cluster and the cooperative cluster are consistent.

[0044] Optionally, in step S4, the distributed collaborative control protocol is:

[0045] ,

[0046] in, This represents the input to the i-th cooperative cluster controller. Indicates the controller gain. Represents the adjacency matrix weights. This represents the communication weight between the baseline cluster and the i-th cooperative cluster;

[0047] Considering state limitations The corresponding expression:

[0048] ,

[0049] in, The cost of state consistency deviation, To control energy consumption costs, the outer layer is summed. This represents the cumulative cost over the time period triggered by each event, expressed as the inner integral. Indicates the interval The sum of internal state deviation and energy consumption.

[0050] Optionally, the expressions for the state consistency deviation cost and the control energy consumption cost are:

[0051] ,

[0052] ,

[0053] in, The cost of state consistency deviation, Represents a positive definite weight matrix. The difference in state between adjacent clusters The expression means at any time The degree to which the states of each cluster in the entire system deviate from consistency; To control the cost of energy consumption, To control the weighting matrix (positive definite). It is the first Control inputs for each cluster The expression means the impact of the control input size on the system's energy consumption / actuator utilization.

[0054] Optionally, in step S5, the distributed collaborative control consistency performance test includes:

[0055] S5-1: Establish the state-space equations of the array-type distillation multi-agent system based on the system state variables;

[0056] S5-2: Under unconstrained state conditions, the system convex optimization inequalities are solved using the MATLAB toolbox to calculate the controller gain and observer gain.

[0057] S5-3: Set the limit range for system state variables;

[0058] S5-4: Obtain the input and output states of the system under normal conditions to verify the effectiveness of the distributed cooperative control protocol; obtain the input and output states of the system under initial state changes to verify that the state variables can meet the expected consistency control objective under the premise of satisfying the constraints.

[0059] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0060] 1. The distributed cooperative control method of the array-type distillation multi-agent system of the present invention realizes leader-follower consistency control in a multi-cluster cooperative system, which can minimize the problem of frequent switching of control commands. The effectiveness of cooperative control has been proven within the constraints. At the same time, the triggering mechanism introduces dynamic thresholds and auxiliary variables to suppress the Zeno phenomenon, thereby realizing adaptive updates and real-time energy-saving control.

[0061] 2. The distributed cooperative control method of the array-type distillation multi-agent system of the present invention provides a sufficiency proof of the stability of the system under two states, which can adapt to the strong coupling and nonlinear dynamic characteristics of the array-type distillation system, and can simultaneously take into account the tracking performance of the controlled variable and the economic performance of the manipulated variable.

[0062] 3. The distributed cooperative control method of the array-type distillation multi-agent system of the present invention is designed for array-type distillation multi-agent systems with limited communication and state constraints. It constructs a distributed control protocol that integrates the observer network and dynamic event triggering strategy. It constructs a local consistency signal by using the neighborhood state difference and the information of the guiding node. It uses the control gain matrix (K) and the observation gain matrix (L) for collaborative design, so that the overall state of the system is asymptotically consistent under limited communication and energy budget. Attached Figure Description

[0063] The accompanying drawings are provided to further illustrate the invention and, together with the description, serve to explain embodiments of the invention, but do not constitute a limitation thereof. In the drawings:

[0064] Figure 1 A schematic diagram of the array-type distillation system of the present invention is shown;

[0065] Figure 2 A schematic diagram of the information topology of the multi-agent system of the present invention is shown;

[0066] Figure 3A schematic diagram of the distributed cooperative control of the array-type distillation multi-agent system of the present invention is shown;

[0067] Figure 4 A schematic diagram of the information transmission of the distributed collaborative control protocol of the present invention is shown;

[0068] Figure 5 A schematic diagram of the performance evaluation simulation results under normal conditions of the present invention is shown;

[0069] Figure 6 A schematic diagram illustrating the changes in system state variables under a change in the initial state of the present invention is shown. Detailed Implementation

[0070] To further understand the present invention, preferred embodiments of the present invention are described below in conjunction with examples. However, it should be understood that these descriptions are only for further illustrating the features and advantages of the present invention, and not for limiting the scope of the claims of the present invention.

[0071] The description in this section pertains only to typical embodiments, and the present invention is not limited to the scope of the embodiments described. Combinations of different embodiments, substitution of some technical features in different embodiments, and substitution of similar or identical prior art with some technical features in the embodiments are also within the scope of the description and protection of the present invention.

[0072] This invention proposes a distributed cooperative control method for an array-type distillation multi-agent system. This embodiment provides a detailed description of achieving system consistency control objectives in the distillation processes of p-chlorotoluene and o-chlorotoluene under state variable constraints. Figure 3 As shown, the distributed cooperative control method specifically includes:

[0073] S1: Using Aspen Plus, we simulated the array-type distillation device and constructed a mathematical model of the array-type distillation multi-agent system by combining the concept of multi-agent system.

[0074] The relevant symbols are explained in Table 1 below.

[0075] Table 1

[0076] symbol Symbol Explanation set of real numbers 3D real vector space set of positive real numbers Real matrix space vector transpose matrix The reverse 3D identity matrix Zero-dimensional matrix A column vector with all elements equal to 0. A column vector with all elements equal to 1. Positive definite matrix phalanx Maximum eigenvalue phalanx set of eigenvalues by A matrix with diagonal elements Element is of 1-th order matrix

[0077] The structure of an array-type distillation system is as follows: Figure 1 As shown, this model integrates several clustered distillation units, each physically independent and uniformly distributed, with no mass transfer or radial material flow. Although the unit structures are identical, fluctuations in feed or inconsistent initial parameters among the units during production result in inconsistent product concentrations, failing to meet product quality requirements. To improve product quality, a distributed control strategy is needed to collaboratively regulate each distillation unit, ensuring consistent product concentration.

[0078] The construction of multi-agent systems is based on directed graph theory. , Represents the set of all non-empty nodes in the network. This represents the set of edges between nodes. In a directed graph, Node pointing to A node indicates that information flows from one node to another. . It is a matrix that describes the relationships between nodes and edges in a cooperative cluster, and is called the adjacency matrix. And there are >0. The in-degree matrix is ​​defined as... Furthermore, from the vertex To the top The path is an ordered sequence of vertices such that every direct pair of vertices is an edge. The Laplace operator for a directed graph is: Information topology such as Figure 2 As shown, the arrow from RC0 to SC1 indicates that RC0 transmits information to SC1, and the bidirectional arrow between SC2 and SC5 indicates mutual communication.

[0079] S2: Determine the expressions for the cooperative cluster and the reference cluster.

[0080] The expression for a cooperative cluster is as follows:

[0081]

[0082] The expression for the baseline cluster is as follows:

[0083]

[0084] Among them, A, B, C, A L Represents the state matrix expression with appropriate dimensions. , Let these represent the operational variable states of the i-th cooperative cluster and the reference cluster at time t, respectively. and To correspond to the output quantities of the cooperative cluster and the reference cluster, , This represents distributed control input.

[0085] S3: To address the limitations of traditional control protocols, this paper clarifies the error and information topology of the leader and follower clusters and constructs a consistency control protocol based on the cooperative cluster and the benchmark cluster.

[0086] S3-1: The steps for proposing a traditional multi-agent distributed control protocol are as follows:

[0087] A1. Construct a dynamic model for a conventional system. Consider a multi-agent system consisting of N followers and 1 leader. The dynamic model for each follower i is as follows:

[0088]

[0089] in For state vectors, To control the input, For nonlinear terms that satisfy the Lipschitz condition.

[0090] A2. Construct a directed topological network of agents based on graph theory and the Laplace matrix, expressed as follows:

[0091]

[0092] A3. Define the state error between follower i and leader i as... The consensus goal is

[0093] A4. Design a distributed control protocol based on neighbor node information and leader information.

[0094]

[0095] S3-2: Traditional distributed control technology assumes that all intelligent agents can freely adjust all operational variables without considering their constrained states. If the system's operational capacity has reached its safety limits, it may still issue instructions exceeding the equipment's capacity, leading to system instability or dangerous safety accidents. To solve this problem, state constraints need to be introduced into the distributed consensus protocol. The feasibility of control commands was verified by adjusting dynamic thresholds.

[0096] A1. Kronecker Matrix Theory: Suppose that matrix A is represented by... A dimensional matrix, B is a single matrix. For a given matrix, the Kronecker product of the matrix is... It can be represented as:

[0097]

[0098] Each element Multiply by the entire matrix B to obtain the corresponding submatrix. Kronecker satisfies the following property.

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] A2. Schur's Complementary Lemma: If any symmetric matrix

[0105] ,

[0106] in , Then the matrix Equivalent to any of the following conditions:

[0107] 1) ,

[0108] 2) .

[0109] A3, Jensen's Inequality: For scalars ,matrix and integral variables Then the following inequalities hold:

[0110] .

[0111] Jensen's inequality in Lemma 2.2 is applied to find The upper boundary.

[0112] A4. Gronwall's Inequality: If the function y(t) is absolutely continuous on the interval [a, b], and ,in If it is integrable on [a,b], then .

[0113] When studying the properties of solutions to ordinary differential equations, the differential form of the Gronwall inequality is used to estimate the growth rate of the solution and determine whether the solution will grow unbounded in a finite time.

[0114] A5. The relevant symbols for the Linear Matrix Inequality (LMI) are explained in Table 2 below:

[0115] Table 2

[0116] symbol meaning illustrate Lyapunov matrix structure Auxiliary weight matrix Weighting for two types of error subsystems (in blocks of Ω) DETM weighted matrix Weighted separately and Error energy Trigger stability item Ensure event triggering error is controllable Jacobian matrix of joint system It is obtained by rearranging from Lyapunov derivatives, and requires... These correspond to state error, observation error, and their cross term, respectively. <![CDATA[Its specific expression is composed of the combination of A, B, K, L, T1, and T2]]>

[0117] S3-3: Determine the dynamic event triggering mechanism and system observer network architecture. Influenced by control signals, the controller will be updated once the triggering condition is met, when the system auxiliary dynamic variables... After the update, if the dynamic parameter value is smaller, the system performance will be better.

[0118] S4: Construct a distributed control protocol based on the above-mentioned cooperative cluster and benchmark cluster using Lyapunov functions and consistency objectives to achieve output product quality consistency between the leader cluster and follower cluster and output consistency under the DETC-observer network architecture.

[0119] S4-1: An array-based integrated distillation system achieves consistent product quality between the leader and follower clusters through the combined action of a controller, a dynamic event triggering mechanism, and an observer. The core idea is to treat the system (including observation and triggering errors) as a joint closed-loop dynamical system, construct a joint Lyapunov function, and organize its derivatives into a block matrix quadratic form. As long as this block matrix (via LMI) is negative definite, the energy will monotonically decrease, thus causing the tracking error to converge to zero, thereby achieving consistency. The derivation steps are as follows:

[0120] A1, the i-th cooperative cluster controller is ,in:

[0121]

[0122] A2. Under unconstrained conditions, define the consistency error between the leader cluster and the follower cluster in the system as: The error between the actual state of the following cluster and the observation estimator is defined as... Let the error between the event trigger state and the system observer be... Easy to obtain .

[0123] Here, we assume variables

[0124]

[0125]

[0126] The total system error is Then its derivative state is:

[0127]

[0128] A3. Design Lyapunov functions as follows: In the formula, Q>0, ,in >0.

[0129] A4. Taking the derivative of the Lyapunov function, we get:

[0130]

[0131] Since α, β > 0, therefore We can then obtain:

[0132]

[0133] A5. If Theorem 1 holds, then it satisfies The LMI above ensures that the principal convergence matrix is ​​sufficiently negative, and that perturbations from the observer and event triggering terms are strictly controlled and absorbed, thus ensuring global consistency.

[0134] S4-2: The condition for the system to achieve follower consistency under finite state constraints is the existence of a gain matrix that enables the system to achieve consistent quality output between the reference cluster and the cooperative cluster under the control protocol, satisfying... The derivation steps are as follows:

[0135] A1. The system state variables are represented as follows: The vector-matrix expression for the dynamic changes of the closed-loop system is obtained from the cooperative cluster state equation:

[0136]

[0137] in , , . This represents the Laplace matrix corresponding to all cooperative clusters.

[0138] A2. Decompose the entire dynamics of a multi-agent system into consistent and inconsistent dynamics. Given the non-singular transformation, convert the Laplace matrix... Convert to a diagonal block matrix. A non-singular matrix can be defined as... Its inverse matrix expression is: .

[0139] A3. The error between the cooperative cluster and the reference cluster can be expressed as: Then it makes the following equation hold:

[0140]

[0141] according to We can obtain:

[0142]

[0143] A4. Through the following non-singular transformations... Blocks in Diagonalization is performed. Because there are communication channels from the base cluster to each cooperative cluster, therefore... It is positive definite and symmetric. Introduce an orthogonal matrix. ,exist

[0144]

[0145] in Represents the system's Laplace matrix Left eigenvalue.

[0146] A5, Order The system can be written as:

[0147]

[0148] S4-3: Design a consensus criterion for the baseline cluster and cooperative cluster states of a multi-agent system under finite conditions. The relevant derivation is as follows:

[0149] A1. When system constraints exist, the Lyapunov function design remains unchanged. , The expression can be adjusted to:

[0150]

[0151] A2. From the above expression, we know that the Lyapunov function is monotonically decreasing. Regarding time... Using Gronwall's inequality, we can obtain:

[0152]

[0153] To promote, for It can be deduced that .

[0154] A3. For any There exists an integer k, i.e. , so that:

[0155]

[0156] At this point, we can deduce... This also means that multi-agent systems can achieve consistent control.

[0157] S4-4: Based on the above derivation, the improved distributed control protocol is as follows:

[0158]

[0159] in , and Satisfy the following expression:

[0160]

[0161] S5: Evaluate and simulate the operational performance of the control algorithm, and analyze the system input and output conditions. Define the system state-space equations, set the range of system control variables with reference to traditional PID parameter tuning methods, and prove the effectiveness of the control method when the system operating variables do not exceed the state constraints.

[0162] S5-1: The main system state variables are reboiler heat load, condenser heat load, top reflux ratio, and bottom liquid output. The state-space equation can be expressed as:

[0163]

[0164]

[0165] S5-2: Under unconstrained conditions, derive and solve for the controller gain K according to the derivation in S4-1 above. Using the MATLAB toolbox, solve the system convex optimization inequalities and calculate the system matrix to obtain the consistent controller gain and observer gain.

[0166]

[0167] S5-3: The upper and lower limits for state variables are set as shown in Table 3:

[0168] Table 3

[0169] Operands unit upper limit of range Lower limit of range Condenser heat load GJ / Hr -13.5 -14.5 Reboiler heat load GJ / Hr 14.5 13.5 reflux ratio - 23 40 Unit bottom liquid phase recovery rate Kmol / Hr 0.9 1.5

[0170] S5-4: Among the above indicators, the top heat load is appropriately increased to stabilize the top temperature and product quality; the increase in the bottom heat load enhances the evaporation capacity of the bottom liquid, thereby increasing the amount of rising steam in the column and the yield of the top product. A moderate increase in the reflux ratio helps improve the purity of the top product, but a balance must be struck between product quality and energy consumption. Furthermore, the increase in the reboiler steam flow rate further increases the evaporation rate of the bottom liquid, thus optimizing the amount of rising steam in the column and the yield of the top product. Combined with the o-chlorotoluene distillation process, these adjustment strategies stabilize the system within a finite time. When system inputs fluctuate, they have a significant impact on the operating variables (top heat load, bottom heat load, reflux ratio, and reboiler steam flow rate).

[0171] S5-5: First, consider the system operation under normal conditions (no disturbance), such as... Figure 5 The changes in system operating variables are illustrated in the first five hours. The system output state finally achieved synchronization at 3.8 hours, demonstrating the effectiveness of the designed cooperative control protocol, which enables the system to achieve synchronization within a specified time frame.

[0172] S5-6: To verify the changes in system performance under constrained state variables, the multi-agent system assumes that the target state or desired output of the baseline cluster is the ideal setpoint of the system. The goal of the cooperative cluster is to track the leader's state as closely as possible to achieve consistency. Under the initial conditions, the manipulated variables are: condenser load -13.9362 GJ / Hr, reboiler load 13.9480 GJ / Hr, reflux ratio 25.4458, bottom product 1.3567 kmol / Hr, system top pressure 0.76 bar, and distillation column concentration 99%.

[0173] System output and changes in manipulated variables, such as Figure 6 As shown in the figure, after a small fluctuation, the system error norm eventually approaches 0 within 2.56 hours after changing the initial state of the system, indicating that the system cooperative cluster eventually achieves state consistency with the reference cluster. According to the range of changes in the system operating variables given in Table 3, it is easy to see that the system operating variables never exceed the upper and lower limits of the state constraints, and the state constraint J satisfies the constraint conditions, verifying the effectiveness of the control method.

[0174] This invention proposes a distributed cooperative control method for an array-type distillation multi-agent system. It introduces a distributed consensus algorithm under state constraints, employs a base cluster and reference cluster model distributed controller, and combines a dynamic event triggering mechanism to minimize the problem of frequent control command switching. The method simulates the changes in system state variables of the array-type distillation system under different disturbance states, and provides controller solution methods under both unconstrained and state-constrained conditions. Furthermore, it proves the sufficiency conditions for system stability under both states. Finally, it presents the system stability fluctuation under different initial state changes, and based on system sensitivity analysis, provides detailed fluctuation ranges of system operating variables, ensuring that the system operating variables remain within safe operating ranges under different disturbance states and initial states, thereby improving the system's robustness and stability under disturbances.

[0175] The description and application of the present invention herein are illustrative and not intended to limit the scope of the invention to the embodiments described above. The effects or advantages described in the specification may not be apparent in actual experimental cases due to uncertainties in specific conditions or other factors, and such descriptions are not intended to limit the scope of the invention. Variations and modifications to the embodiments disclosed herein are possible, and various substitutions and equivalents of the components in the embodiments are well known to those skilled in the art. It should be understood by those skilled in the art that the invention can be implemented in other forms, structures, arrangements, proportions, and with other components, materials, and parts without departing from the spirit or essential characteristics of the invention. Other variations and modifications can be made to the embodiments disclosed herein without departing from the scope and spirit of the invention.

Claims

1. A method for distributed collaborative control of an array distillation multi-agent system, characterized in that, include: S1: Based on the leader-follower consistency of array-type distillation system and multi-agent system, construct array-type distillation multi-agent system, wherein multiple parallel and coupled cluster-type distillation units constitute the agents in the array-type distillation multi-agent system; S2: Construct the mathematical model of the array-type distillation multi-agent system by means of the closed-loop subspace identification method, determine the reference cluster and the cooperative cluster, perform local control on the reference cluster and initially configure its poles, wherein the reference cluster is a cluster-type distillation unit that provides a reference frame, and the cooperative cluster is other cluster-type distillation units that keep synchronized with the reference cluster. S3: Based on the benchmark cluster and the cooperative cluster, a dynamic event triggering mechanism and an observer network architecture are established. Under the dynamic event triggering mechanism, if the triggering condition is met, the distributed cooperative controller is updated to ensure the strict consistency and stability of the array-type distillation multi-agent system. The observer is used to monitor the state of the cooperative cluster in real time, and the state serves as the input to the distributed cooperative control model. S4: Based on the dynamic event triggering mechanism and observer network architecture, a distributed cooperative control model is constructed using Lyapunov functions and consistency objectives to achieve consistency of output product quality and output consistency between the leader cluster and the follower cluster. S5: Based on the mathematical model, establish the state space equation of the array-type distillation multi-agent system, use the PID parameter tuning method to determine the constraint range of the state variables, conduct distributed cooperative control consistency performance tests on the array-type distillation multi-agent system under the initial state and different disturbances, and analyze the input and output status of the array-type distillation multi-agent system.

2. The method of claim 1, wherein, In step S2, the state equation of the reference cluster is: ， The state equation of the i-th cooperative cluster is: ， wherein, , respectively represent the state of the i-th cooperative cluster and the reference cluster at time t, and respectively represent the output of the i-th cooperative cluster and the reference cluster at time t, A is a cooperative cluster state matrix, B is a control matrix, C is an output matrix, A L is a reference cluster state matrix, , respectively represent the operating variable state of the i-th cooperative cluster and the reference cluster at time t, represents a distributed control input of the i-th cooperative cluster at time t.

3. The distributed collaborative control method of the array distillation multi-agent system according to claim 1 or 2, characterized in that, In step S2, the local control of the reference cluster includes: Introducing a state feedback control law ; Based on the state feedback control law and the open-loop state equation of the cooperative cluster, the closed-loop state equation of the reference cluster is obtained as follows: ， The state matrix of the reference cluster satisfies: ; Based on Routh-Hurwitz criterion, Routh array is constructed, and it is checked whether the first column elements are all positive, if all positive, the state matrix is Hurwitz matrix, and the reference cluster output satisfies dynamic demand.

4. The method of claim 1, wherein, In step S3, the dynamic event triggering mechanism is as follows: ， wherein, , denote the first , second , third event-triggering time of the i-th agent, respectively; represents the lower bound; denotes the current time; is a dynamic event-triggering function, is an auxiliary dynamic variable, and , , is a positive definite matrix of the system, and a, b are normal numbers; is the current cooperative error signal; is the sample-and-hold error signal; is a dynamic threshold variable; The observer network architecture is as follows: ， in, This represents the estimated state of the i-th cooperative cluster observer. ; For the system matrix, G is the control matrix, and G is the monitoring error coefficient matrix. Estimate the state of the operational variables for the i-th cooperative cluster at time t. This is the distributed control input for the i-th cooperative cluster.

5. The distributed cooperative control method for an array-type distillation multi-agent system according to claim 1, characterized in that, In step S4, constructing the distributed cooperative control model includes: S4-1: When there are no state variable constraints, under the combined action of the distributed collaborative controller, dynamic event triggering mechanism, and observer, if the following conditions are met: Q1>0, Q2>0, G, T1>0, T2>0, ， ， This achieves consistency in product quality output between the leader cluster and the follower cluster; where Q1, Q2, T1, and T2 are the system positive definite matrices, and G is the monitoring error coefficient matrix. The matrix inequalities derived from the Lyapunov derivative, , , , , , for The submatrix, where BK is the feedback term. C is the coupling term, and C is the output matrix; S4-2: When state variable constraints exist, under the combined effect of the dynamic event triggering mechanism and the observer, if the following conditions are met: ， Where Ω′ and Q represent the block matrix structure of the closed-loop stability condition, and satisfy: ； The submatrix Ω′1 corresponds to the dynamic characteristics of the baseline cluster and includes the feedback term BK and the coupling term. Submatrix Indicates gain and output matrix The observer-related subsystem; submatrix Consistency gain (LG) describes the coupling between the baseline cluster and the coordination cluster. Since these two clusters have symmetrical coupling, there is... Submatrix The relationship between the event triggering parameters and the observer matrix is ​​defined as follows: ， Under the above conditions, for any given , If the outputs of the baseline cluster and the cooperative cluster are consistent, then it is considered that the outputs of the baseline cluster and the cooperative cluster are consistent.

6. The distributed cooperative control method for an array-type distillation multi-agent system according to claim 1 or 5, characterized in that, In step S4, the distributed collaborative control protocol is as follows: ， in, This represents the input to the i-th cooperative cluster controller. Indicates the controller gain. Represents the adjacency matrix weights. This represents the communication weight between the baseline cluster and the i-th cooperative cluster; Considering state limitations The corresponding expression: ， in, The cost of state consistency deviation, To control energy consumption costs, the outer layer is summed. This represents the cumulative cost over the time period triggered by each event, expressed as the inner integral. Indicates the interval The sum of internal state deviation and energy consumption.

7. The distributed cooperative control method for an array-type distillation multi-agent system according to claim 6, characterized in that, The expressions for the state consistency deviation cost and the control energy consumption cost are: ， ， in, The cost of state consistency deviation, Represents a positive definite weight matrix. The difference in state between adjacent clusters The expression means at any time The degree to which the states of each cluster in the entire system deviate from consistency; To control the cost of energy consumption, To control the weighting matrix (positive definite). It is the first Control input for each cluster The expression means the impact of the control input size on the system's energy consumption / actuator utilization.

8. The distributed cooperative control method for an array-type distillation multi-agent system according to claim 1, characterized in that, In step S5, the distributed collaborative control consistency performance test includes: S5-1: Establish the state-space equations of the array-type distillation multi-agent system based on the system state variables; S5-2: Under unconstrained state conditions, the system convex optimization inequalities are solved using the MATLAB toolbox to calculate the controller gain and observer gain. S5-3: Set the limit range for system state variables; S5-4: Obtain the input and output states of the system under normal conditions to verify the effectiveness of the distributed cooperative control protocol; obtain the input and output states of the system under initial state changes to verify that the state variables can meet the expected consistency control objective under the premise of satisfying the constraints.

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