A protocol-dependent event-triggered asynchronous control method for a heat exchanger

Abstract

The application relates to a protocol-dependent event-triggered asynchronous control method of a heat exchanger, which comprises the following steps: establishing a Roesser type two-dimensional system mathematical model to express the heat exchanger; developing a sliding window polling protocol for a multi-node transmission problem; introducing a two-dimensional event-triggered mechanism to reduce unnecessary signal transmission for a communication resource limited problem; designing a protocol-dependent event-triggered asynchronous controller for the non-synchronous switching behavior between a controlled object and the controller thereof, and constructing a two-dimensional closed-loop system; and based on Lyapunov analysis theory and decoupling skills, a corresponding controller design scheme easy for numerical solution is provided. The technical scheme provided by the application can not only solve the node scheduling problem in the multi-node transmission scene, reduce unnecessary data transmission under the communication resource limited condition, but also solve the non-synchronous switching problem between the controlled object and the controller thereof, and establish an asynchronous controller to stabilize the two-dimensional closed-loop system.

Description

Technical Field

[0001] This invention relates to the field of heat exchanger and networked control technology, and specifically to a protocol-dependent event-triggered asynchronous control method for heat exchangers. Background Technology

[0002] In practical engineering, the dynamic information of many signals and systems evolves along time and space. For example, during heat conduction in a heat exchanger, temperature changes with time and spatial location; image information and seismic data are also transmitted along time and space. These practical systems can all be categorized as two-dimensional systems.

[0003] The state-space theory of two-dimensional systems originated in the 1970s when scholars Givone and Roesser established the famous Roesser model during their research on iterative circuit problems. Thanks to the establishment of a simple mathematical expression for Roesser-type two-dimensional systems, a foundation was laid for the application of such systems in industrial scenarios. For example, in batch processing, a common process in industrial systems, the system updates information along both the batch processing direction and the time direction. Stability analysis has always been a core component of control theory. For two-dimensional systems, common analysis methods include frequency domain and time domain analysis. With the development and continuous improvement of Lyapunov theory, and the rise of convex optimization problems constrained by linear matrix inequalities, researchers have increasingly begun to approach the stability analysis of two-dimensional systems from a time domain perspective, based on state-space theory.

[0004] For complex two-dimensional systems in practical applications, it is difficult to accurately describe their dynamic characteristics using only a single differential or difference equation, leading to the development of switching systems. Switching systems typically consist of multiple subsystems and a switching law that determines the switching between subsystems. Switching laws can be broadly categorized into stochastic switching and deterministic switching. As a type of stochastic switching system, a jumping system consists of a series of interconnected subsystems corresponding to different modes, randomly switching between these modes under the control of a jumping rule. This type of system is well-suited for modeling systems where parameters undergo random mutations due to unexpected component failures. Furthermore, thanks to access to computer and communication networks, components distributed across different geographical locations can be connected via shared networks, offering advantages such as convenient network cabling, easy expansion, plug-and-play devices, low operating costs, and resource sharing. Therefore, research on networked two-dimensional systems is of great significance.

[0005] However, when considering networked control scenarios, the controlled object and its controller are usually located in different geographical locations. The channel inevitably faces network-induced problems, making it difficult for the controller to accurately capture system mode information, leading to asynchronous switching. Secondly, channel congestion due to limited communication resources is a crucial issue that networked control research must consider. To prevent this, a feasible approach is to allocate channel usage rights by developing reasonable communication scheduling protocols. Common protocols include random access protocols, one-attempt loss protocols, and polling protocols. Under these protocols, the channel allows a single node to access at a given time, which is clearly an extreme case of all nodes accessing a shared network. In reality, a shared network may allow more nodes to transmit data without exceeding the channel's maximum processing capacity. Furthermore, when considering signal transmission using a shared network, how to utilize limited bandwidth resources to complete control tasks is another important issue that networked control research must consider, especially for two-dimensional systems with larger signal transmission volumes.

[0006] Therefore, it is necessary to propose a protocol-dependent event-triggered asynchronous control method, which can not only solve the node scheduling problem in multi-node transmission scenarios and reduce unnecessary data transmission under the condition of limited communication resources, but also solve the asynchronous switching problem between the controlled object and its controller, and establish an asynchronous controller to make the two-dimensional closed-loop system stable.

[0007] Several patents concerning control and analysis methods for networked two-dimensional systems have emerged. For example, the invention patent titled "A Memory-Type Event-Triggering Control Method for a Two-Dimensional System Under Deception Attacks" (Application Publication Date: October 13, 2023; Application No.: 202310832715.2) discloses a memory-type event-triggered control method for a two-dimensional system under deception attacks. This method includes constructing a two-dimensional memory event triggering mechanism; introducing a mathematical model characterizing the probability of suffering a deception attack; and establishing a memory controller to ensure the stability of the closed-loop system. The drawback of this method is that it does not consider the node scheduling problem in multi-node transmission scenarios. In reality, a shared network may allow more nodes to transmit data without exceeding the channel's maximum processing capacity. Some studies indicate that increasing node access to the channel may help improve system performance.

[0008] For example, the invention patent titled "A Finite Region Control Method for Metal Rolling Process Based on Dissipative Properties" (Application Publication Date: July 3, 2020; Application No.: 201811378135.6) models the metal rolling process as a two-dimensional system and designs a dynamic output feedback controller for the two-dimensional system, enabling the metal rolling system to satisfy the properties of a bounded finite region and a two-dimensional finite region. Dissipation. This method addresses the problem of random data packet loss in network communication, resolving the issue of the controller and actuator not being able to update in real time in networked control. However, a drawback is that when using a shared network for signal transmission, it struggles with how to utilize limited bandwidth resources to complete the control task. In fact, for two-dimensional systems with even larger signal transmission volumes, this issue is even more crucial. Summary of the Invention

[0009] The purpose of this invention is to provide a protocol-dependent event-triggered asynchronous control method for heat exchangers, which can effectively solve the node scheduling problem in multi-node transmission scenarios and reduce unnecessary data transmission when communication resources are limited; it can also solve the asynchronous switching problem between the controlled object and its controller, and establish an asynchronous controller to stabilize the two-dimensional closed-loop system.

[0010] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0011] A protocol-dependent event-triggered asynchronous control method for a heat exchanger includes the following steps:

[0012] Consider a class of heat exchanger models described by partial differential equations, and model them as Roesser-type two-dimensional discrete systems;

[0013] In networked transmission scenarios, a sliding window polling protocol was developed to address the node scheduling problem in multi-node transmission scenarios.

[0014] Considering that in multi-node transmission scenarios, the number of nodes accessing channels can increase exponentially at a certain moment, a two-dimensional event-triggered transmission mechanism is introduced to avoid unnecessary data updates and reduce the data transmission rate.

[0015] Since the controlled object and its controller are often located in different geographical locations, using a shared network for signal transmission will result in asynchronous mode switching due to limited communication resources. To characterize this behavior, a protocol-dependent event-triggered asynchronous controller was designed, and a two-dimensional closed-loop system was constructed.

[0016] Based on Lyapunov analysis theory and decoupling techniques, an asymptotic mean square stability criterion for a two-dimensional closed-loop system with H∞ disturbance suppression level is proposed in the form of linear matrix inequalities, along with a corresponding protocol-dependent event-triggered asynchronous controller design scheme that is easy to solve numerically.

[0017] The heat exchanger model described by partial differential equations is as follows:

[0018]

[0019] In the formula, , and These represent pipe temperature, space, and time, respectively. Indicates the first Control input of each node ( );parameter and These are the real coefficients that depend on the system pattern; the subscripts of the real coefficients. These are jump parameters controlled by the Markov chain; for a given step size and The differential form of the pipe temperature, and the approximate forms of its spatial and temporal partial derivatives, are defined as follows:

[0020] ;

[0021] Next, by applying discretization to the heat exchanger model, the following equation can be obtained:

[0022] ;

[0023] definition and Consider four nodes performing a sliding window polling protocol, and assume that the state is perturbed. If the influence is considered, the above equation can be restated to describe a Roesser-type two-dimensional discrete system:

[0024]

[0025] in and Represents the horizontal and vertical states of the system; and These are control input, external disturbance, and measurement output, respectively. and It is a pre-known system matrix.

[0026]

[0027] Their changes depend on a finite set Markov chains that take values ​​from Two bidirectional transition probability matrices and The probability distributions are given by the following formulas.

[0028]

[0029] in and These represent the transition probabilities in the horizontal and vertical directions, respectively, for any mode. and , All meet the following conditions

[0030] .

[0031] A further approach involves developing a sliding window polling protocol. This protocol, used in the controller-actuator channel, aims to increase the number of nodes accessing the channel without exceeding its maximum processing capacity. A feasible multi-node scheduling scheme is presented, defining a sliding window size as follows: , , Given the total number of nodes, at any given time, only nodes within the sliding window are allowed to access the controller-actuator channel simultaneously; the rest... Each node will temporarily suspend its use of the channel. When a node is granted access to the channel, it also receives a channel token, indicating that it has the right to use the channel for signal transmission.

[0032] Here is a function. , representing a node At any moment The acquisition status of the token; when When, the node obtains the token, when At that time, the node cannot access the channel; then the node is defined. At any moment The available status signals are:

[0033]

[0034] in Therefore, the actual system signal is written as:

[0035]

[0036] here and .

[0037] A further approach is to allow multiple nodes to access the channel for signal transmission, provided that the channel's maximum processing capacity is not exceeded. However, as the number of nodes accessing the channel increases, redundant data packets will inevitably be generated. Therefore, a two-dimensional event-triggered mechanism dependent on the mode protocol is developed to alleviate the channel load pressure caused by redundant data packets in multi-node transmission scenarios.

[0038] Therefore, the next transmission time of the system status signal depends on the following two triggering conditions:

[0039]

[0040] in and These are the event trigger times in the horizontal and vertical directions, respectively; and It is in the interval in advance The event triggering parameter (or threshold) whose value is taken from the middle; and This is the event triggering matrix to be designed; and The transmission errors in the horizontal and vertical directions are given by the following formulas respectively:

[0041] ;

[0042] The event trigger will only select either the system's horizontal or vertical state for transmission when the triggering condition is met. Under this mechanism, for any... and ,have

[0043] ;

[0044] Established, among which .

[0045] A further proposed solution is that, considering the asynchronous switching behavior between the controller and the system in step S4, the following controller is constructed:

[0046]

[0047] In the formula, It is the controller gain, a random variable. The following conditional probability

[0048]

[0049] in The conditional transition probability matrix is ​​defined as follows: In addition, parameters Indicates the node at time [time]. Access to the channel. Therefore, a two-dimensional closed-loop system can be constructed as follows:

[0050]

[0051] in

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] .

[0058] A further proposed solution involves, in step S5, based on Lyapunov analysis theory and decoupling techniques, proposing a protocol-dependent event-triggered asynchronous controller design scheme that is easily solved numerically. The specific steps include:

[0059] First, consider the following pattern - protocol depends on Lyapunov functions, parameters For the mode dependency Lyapunov matrix:

[0060]

[0061] And define the positive difference operator:

[0062] ;

[0063] Substituting the aforementioned sliding window polling protocol and two-dimensional event triggering mechanism model into the Lyapunov function and performing expectation calculation yields:

[0064]

[0065] in:

[0066]

[0067] Here we introduce a relaxation matrix. Used to separate conditional probabilities product summation term That is:

[0068]

[0069] This means:

[0070]

[0071] Then there is in and It is any positive integer. yes The Euclidean norm; by... and Substitution and define ,in and They are and The largest eigenvalue can be obtained.

[0072]

[0073] Then, the following index function is introduced:

[0074]

[0075] because , can be obtained

[0076]

[0077] in ,

[0078] Using Schur supplement, there is

[0079]

[0080] when and At the time of establishment, the two-dimensional closed-loop system has a perturbation suppression level of H∞. asymptotically mean square stable;

[0081] Finally, considering There are coupling terms in it ,definition right Left multiplication and right multiplication and , noticed And on Using Schur's complement, we get:

[0082]

[0083] in:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] Therefore, the two-dimensional closed-loop system has an H∞ disturbance suppression level. The asymptotic mean square stability; in addition, control gain Depend on Sure.

[0090] All additional letters introduced in this invention are intermediate variables with no actual meaning; they are only used for clear mathematical representation.

[0091] The above-mentioned technical solution provides a protocol-dependent event-triggered asynchronous control method for a heat exchanger, comprising: establishing a mathematical model of a Roesser-type two-dimensional system to represent the heat exchanger; developing a sliding window polling protocol for multi-node transmission in a networked transmission scenario to solve the signal scheduling problem in multi-node transmission; considering a networked control framework, introducing a two-dimensional event-triggered mechanism to reduce unnecessary signal transmission and improve channel utilization to address the problem of limited communication resources; designing a protocol-dependent event-triggered asynchronous controller to address the asynchronous switching behavior between the controlled object and its controller, thus constructing a two-dimensional closed-loop system; and proposing an asymptotic mean-square stability criterion for the two-dimensional closed-loop system with H∞ disturbance suppression level and a corresponding controller design scheme that is easy to solve numerically, based on Lyapunov analysis theory and decoupling techniques, in the form of linear matrix inequalities. The technical solution provided by this invention not only solves the node scheduling problem in multi-node transmission scenarios and reduces unnecessary data transmission under limited communication resources, but also solves the asynchronous switching problem between the controlled object and its controller, establishing an asynchronous controller to stabilize the two-dimensional closed-loop system. Attached Figure Description

[0092] Figure 1 This is a flowchart illustrating a protocol-dependent event-triggered asynchronous control method for a heat exchanger.

[0093] Figure 2 This is a diagram of a heat exchanger architecture;

[0094] Figure 3 This is a schematic diagram of the sliding window polling protocol;

[0095] Figure 4 This is a diagram of a networked control architecture for heat exchangers;

[0096] Figure 5 It is the open-loop evolution trajectory of the horizontal state of a two-dimensional system;

[0097] Figure 6 It is the open-loop evolution trajectory of the vertical state of a two-dimensional system;

[0098] Figure 7 It is a two-dimensional system switching signal;

[0099] Figure 8 It is a controller switching signal;

[0100] Figure 9 It refers to the moment and interval when a horizontal event is triggered;

[0101] Figure 10 It refers to the instant and interval of the vertical event trigger;

[0102] Figure 11 It is the closed-loop evolution trajectory of the vertical state of a two-dimensional system;

[0103] Figure 12 It is the closed-loop evolution trajectory of the horizontal state of a two-dimensional system;

[0104] Figure 13 This refers to the token allocation status. Detailed Implementation

[0105] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0106] The technical solution adopted in this invention is as follows: Figures 1 to 13 As shown, a protocol-dependent event-triggered asynchronous control method for a heat exchanger includes the following steps:

[0107] Consider a class of heat exchanger models described by partial differential equations, and model them as Roesser-type two-dimensional discrete systems;

[0108] In networked transmission scenarios, a sliding window polling protocol was developed to address the node scheduling problem in multi-node transmission scenarios.

[0109] Considering that in multi-node transmission scenarios, the number of nodes accessing channels can increase exponentially at a certain moment, a two-dimensional event-triggered transmission mechanism is introduced to avoid unnecessary data updates and reduce the data transmission rate.

[0110] Since the controlled object and its controller are often located in different geographical locations, using a shared network for signal transmission will result in asynchronous mode switching due to limited communication resources. To characterize this behavior, a protocol-dependent event-triggered asynchronous controller was designed, and a two-dimensional closed-loop system was constructed.

[0111] Based on Lyapunov analysis theory and decoupling techniques, an asymptotic mean square stability criterion for a two-dimensional closed-loop system with H∞ disturbance suppression level is proposed in the form of linear matrix inequalities, along with a corresponding protocol-dependent event-triggered asynchronous controller design scheme that is easy to solve numerically.

[0112] like Figure 2 The heat exchanger model shown can be discretized to construct the following Roesser-type two-dimensional system model:

[0113]

[0114]

[0115] in

[0116]

[0117] Here is the discretization step size. and It was set to 0.1, and then given...

[0118]

[0119] The bidirectional transition probability matrix is

[0120]

[0121] The conditional transition probability matrix is

[0122]

[0123] Next, the initial values ​​of the two-dimensional system are given.

[0124]

[0125] In addition, external interference is set to ( Here we consider the case where the sliding window size is 2, then the matrix... It can be represented as:

[0126]

[0127] The following numerical solutions and simulations using MATLAB and the Mosek solver are used to verify the effectiveness of the protocol-dependent event-triggered asynchronous control method for heat exchangers proposed in this invention.

[0128] Based on the above system parameters, MATLAB and Mosek are used to solve the linear matrix inequalities. and The gain matrix of the protocol-dependent event-triggered asynchronous controller designed in this embodiment can be obtained as follows:

[0129]

[0130]

[0131] Corresponding optimal H∞ performance index . Figure 3 The protocol execution was simulated with 12 nodes and a sliding window size of 2. The nodes accessed the channel in the following order: The polling method is used.

[0132] Figure 5 and Figure 6 This is the open-loop state trajectory evolution diagram of the system, which shows that the system is unstable. Figure 7 and Figure 8 These are the switching signals between the system and its controller. Different colored blocks represent different modes of the system or controller. A careful comparison of the two figures reveals that at a certain moment, the colored blocks are not the same, which indicates that the mode switching between the system and the controller is asynchronous.

[0133] Figure 9 and Figure 10 These are the event trigger moments and release intervals in the horizontal and vertical directions, respectively. Careful observation reveals that the frequency of trigger events is high in the initial stage, but gradually decreases over time, and the release interval increases, indicating that the signal is no longer continuously updated. Figure 11 and Figure 12 It is a closed-loop state trajectory evolution diagram of the system, which shows that the system eventually tends to stabilize. Figure 13 This indicates the token allocation status. It shows that at any given time, exactly two nodes are granted access to the channel, and they access the channel in a predetermined order, taking turns. The order in which they access the channel is as follows: .

[0134] The embodiments of the present invention have been described in detail above with reference to the examples. However, the present invention is not limited to the above embodiments. For those skilled in the art, after learning the contents described in the present invention, several equivalent changes and substitutions can be made without departing from the principle of the present invention. These equivalent changes and substitutions should also be considered to fall within the protection scope of the present invention.

Claims

1. A protocol-dependent event-triggered asynchronous control method for a heat exchanger, characterized in that, Includes the following steps: S1: Consider a class of heat exchanger models described by partial differential equations, and model them as Roesser-type two-dimensional discrete systems; S2: To address the multi-node transmission problem, a sliding window polling protocol was developed. S3: Introducing a two-dimensional event-triggered transmission mechanism to reduce data transmission rate; S4: Design a protocol-dependent event-triggered asynchronous controller to build a two-dimensional closed-loop system; S5: Based on Lyapunov analysis theory and decoupling techniques, a corresponding protocol-dependent event-triggered asynchronous controller design scheme that is easy to solve numerically is proposed; Among them, the sliding window polling protocol in step S2 provides a multi-node scheduling scheme, namely: Define the size of a sliding window as , , Given the total number of nodes, at any given time, only nodes within the sliding window are allowed to access the controller-actuator channel simultaneously; the rest... Each node will suspend the use of the channel; when a node is allowed to access the channel, it also obtains a channel token, indicating that it has the right to use the channel for signal transmission; Here is a function. , representing a node At any moment The acquisition status of the token; when When, the node obtains the token, when At that time, the node cannot access the channel; then the node is defined. At any moment The available status signals are: ； in Therefore, the actual system signal is written as: ； here , ,and ; In step S5, based on Lyapunov analysis theory and decoupling techniques, a corresponding protocol-dependent event-triggered asynchronous controller design scheme that is easy to solve numerically is proposed. The specific steps include: First, consider the following pattern dependency on Lyapunov functions, with parameters... For the mode dependency Lyapunov matrix: ； And define the positive difference operator: ； Substituting the aforementioned sliding window polling protocol and two-dimensional event triggering mechanism model into the Lyapunov function and calculating the expected value, we obtain: ； in: ； Here we introduce a relaxation matrix. Used to separate conditional probabilities product summation term That is: ； This means: ； Then there is in and It is any positive integer. yes The Euclidean norm; by... and Substitution and define ,in and They are and The largest eigenvalue is obtained as follows: ； Then, the following index function is introduced. : ； because ,have to: ； in , Using Schur complement, we have: ； when and At the time of establishment, the two-dimensional closed-loop system has a perturbation suppression level of H∞. asymptotically mean-square stable; Finally, considering There are coupling terms in it ,definition right Left multiplication and right multiplication and , noticed And on Using Schur to obtain: ； in: ； Therefore, the two-dimensional closed-loop system has an H∞ disturbance suppression level. The asymptotic mean square stability; in addition, control gain Depend on Sure.

2. The protocol-dependent event-triggered asynchronous control method for heat exchangers according to claim 1, characterized in that: The mathematical model of the heat exchanger in step S1 is as follows: ； In the formula, , and These represent pipe temperature, space, and time, respectively. Indicates the first Control input of each node ( );parameter and These are the real coefficients that depend on the system pattern; the subscripts of the real coefficients. These are jump parameters controlled by the Markov chain; for a given step size and The differential form of the pipe temperature, and the approximate forms of its spatial and temporal partial derivatives, are defined as follows: ； Next, by applying discretization to the heat exchanger model, the following equation is obtained: ； definition and Consider four nodes performing a sliding window polling protocol, and assume that the state is perturbed. The effect is that the above equation can be restated to describe a Roesser-type two-dimensional discrete system: ； in and Represents the horizontal and vertical states of the system; and These are control input, external disturbance, and measurement output, respectively. and It is a pre-known system matrix. ； Their changes depend on a finite set Markov chains that take values ​​from Two bidirectional transition probability matrices and The probability distributions are given by the following formulas. ； in and These represent the transition probabilities in the horizontal and vertical directions, respectively, for any mode. and , All of them meet the following conditions: 。 3. The protocol-dependent event-triggered asynchronous control method for heat exchangers according to claim 1, characterized in that, Step S3 introduces a two-dimensional event-triggered transmission mechanism to relieve channel load pressure caused by redundant data packets in multi-node transmission scenarios: Therefore, the next transmission time of the system status signal depends on the following two triggering conditions: ； in and These are the event trigger times in the horizontal and vertical directions, respectively; and It is in the interval in advance The event trigger parameter whose value is taken from the middle; and This is the event triggering matrix to be designed; and The transmission errors in the horizontal and vertical directions are given by the following formulas respectively: ； The event trigger will only select either the system's horizontal or vertical state for transmission when the triggering condition is met. Under this mechanism, for any... and ,have: ， Established, among which .

4. The protocol-dependent event-triggered asynchronous control method for a heat exchanger according to claim 1, characterized in that, The design of the protocol-dependent event-triggered asynchronous controller in step S4 is as follows: ； In the formula, It is the controller gain, a random variable. The following conditional probabilities are satisfied: ； in The conditional transition probability matrix is ​​defined as In addition, parameters Indicates the node at time [time]. Access to the channel. Therefore, the two-dimensional closed-loop system is constructed as follows: ； in: 。

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