Damping low-frequency double-event trigger control method for semi-submersible floating platform

Abstract

The invention discloses a damping low-frequency double-event trigger control method for a semi-submersible floating platform, and belongs to the technical field of offshore platforms. The method comprises the following steps: constructing a system kinetic equation through a Newton-Euler formula; based on the constructed system kinetic equation, establishing a multi-agent system through fuzzy logic; constructing a consistency error through a Laplacian matrix based on a multi-agent system; the method comprises the following steps: designing a group of error variables and constructing an obstacle Lyapunov function; in order to overturn the mode platform, the obstacle Lyapunov function is solved on the basis of limitation consideration on the size of the consistency error, so that the consistency error is converged to be infinitely small. According to the method, the initial condition dependency of the threshold is relaxed, the event triggering frequency can be remarkably reduced, so that communication resources are effectively saved, next triggering is allowed only when the threshold bandwidth requirement error is introduced to cross the bandwidth, the generation of a sesame phenomenon is avoided, the triggering frequency is reduced, and the communication resources are saved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of offshore platforms, and particularly relates to a damping low-frequency double-event triggered control method for a semi-submersible floating platform. BACKGROUND

[0002] In recent years, the semi-submersible floating platform has been widely used as a conversion carrier for clean energy such as wave energy. Wave energy, as a high-energy-density clean energy, has attracted widespread attention from academia and industry. The wind and wave integrated power generation floating platform plays an important role in clean power utilization. The stability of the semi-submersible floating platform is affected by waves and wind, so it is particularly important to ensure the stability of the platform.

[0003] Under the disturbance of wind and wave, the pitching and rolling motion of the platform is inevitable, which means that the overall stability of the platform is disturbed, so the anti-disturbance control of the platform is very important. However, wind and wave disturbance is not continuous, that is, it does not occur all the time, and the control of the stability of the platform requires a large amount of energy consumption. Therefore, when the wind and wave do not occur or are small, the influence on the stability of the platform is small, and the communication resource interaction is reduced to save the consumption, so the event triggered control is introduced.

[0004] Event triggered control has attracted great attention in networked control systems in recent years due to its potential advantages in resource utilization efficiency and enhanced feedback capability. This method determines when to perform information transmission or control update based on specific events triggered by system behavior, which means that the update timing is determined by the triggering mechanism. Compared with the periodic sampling strategy, this event-based scheduling ensures that control execution only occurs when necessary, effectively avoiding unnecessary resource consumption. At the same time, event triggered control relies on an event-driven monitoring mechanism, which can respond to system state changes in time while reducing the execution frequency, and shows strong adaptability when dealing with nonlinear and uncertain systems.

[0005] In order to avoid a large number of unnecessary sampling data into the network waste limited network resources. In order to solve this problem, researchers have proposed a traditional fixed threshold event triggered scheme, but note that the event triggered scheme is designed only one fixed threshold, can not adapt to the change of the system, leading to the lack of communication resources. In order to solve this problem, many scholars have established a dynamic event triggered mechanism, saving communication resources, dynamic threshold mechanism provides stronger flexibility and adaptability, while maintaining control performance significantly reduces unnecessary triggering, improve communication efficiency and system robustness, but ordinary dynamic threshold mechanism, although better than fixed threshold mechanism algorithm, but still exist preset dependence, limited adaptability, these limitations are the main motivation for researchers to further develop adaptive threshold mechanism. Because the traditional adaptive threshold event triggered mechanism in operation for a period of time often become fixed threshold, can not adapt to the system error throughout the control process, therefore, in order to reduce the dependence on the initial threshold value, further reduce the triggering frequency, while saving communication resources, it is necessary to design a kind of can realize low frequency event triggered mechanism. SUMMARY

[0006] In order to solve the above technical problems, the application provides a damping low frequency double event triggered control method for semi-submersible floating platform.

[0007] In order to realize the above technical scheme, the steps are as follows: S1, based on the physical model of semi-submersible floating foundation platform, the system dynamics equation is constructed by Newton-Euler formula; By controlling the up and down displacement of the three floating center of mass of the semi-submersible floating foundation platform, the center of mass can be kept on the same horizontal plane, that is, the platform as a whole is in a stable state; Assuming that the mass of the whole platform is uniformly distributed in three floating cylinders, according to Newton-Euler formula, the system dynamics equation can be established as follows: In the formula, represents the displacement state vector of the three floating cylinders; represents the first order derivative of displacement, i.e. velocity; represents the second order derivative of displacement, i.e. acceleration; represents the mass matrix of the three floating cylinders; represents the damping matrix of the three floating cylinders; represents the stiffness matrix of the three floating cylinders; represents the input coupling matrix of the three floating cylinders; represents the control input force of the three floating cylinders; represents the external dynamic disturbance received by the three floating cylinders, which is treated as disturbance; wherein, represents , Indicates floats 1 through 3; Represented as , This indicates the mass distribution of floats 1 through 3; Represented as , This indicates the damping characteristics of floats 1 through 3; Represented as , This indicates the stiffness characteristics of floats 1 through 3; Represented as , This indicates the control input force for floats 1 through 3; Represented as , This indicates external interference with floats 1 through 3; , Indicates the first The first float and the second Information on the coupling effect of individual floats ,but No. The control force of the float Transmitting information about the first through platform structure The coupling effect generated by the individual floats; S2. Based on the constructed system dynamics equations, establish a multi-agent system using fuzzy logic. The steps include: S2.1. Regarding the stability control problem of a semi-submersible floating foundation platform under wind and wave disturbances, the system dynamic equation of the float is transformed to obtain a second-order multi-input multi-output system, as shown in the following expression: make: ; ; in, Represents a lumped nonlinear function; Indicates the first The nonlinear function corresponding to each float ,in, Indicates the first The vertical displacement of the float Indicates the first The speed of the float; This represents the control input quantity after normalization by the quality matrix. This represents the equivalent control input for the three floats; The following second-order multiple-input multiple-output system can be obtained: In the formula, Indicates the first The speed of the float; Indicates the first The first derivative of the displacement of each float; Indicates the first The acceleration of the buoy; , and They represent the first The control gain function of the nth float is used to describe the nth float. Each float is controlled by input force. , and The impact; Indicates the first Let the output of the nth float be equal to the output of the nth float. The displacement of the float; S2.2 Introduce saturation constraints and low-pass filters in the fuzzy logic system; To address the issue of strong coupling between inputs in multi-input multi-output (MIMO) systems, directly designing a controller using the inverse method presents certain difficulties. This approach also has limitations in terms of scalability and interpretability. To resolve this problem, a saturation constraint is introduced at the input, establishing a clear upper bound, namely... In this invention, take =15N / m, and then a fuzzy logic system (FLS) is used to approximate and compensate for input coupling effects and external interference; Because a second-order multiple-input multiple-output system is subject to saturation... Coupled with unknown functions, controller design is difficult; therefore, it is necessary to separate the variables and let... A low-pass filter is introduced, as shown below: In the formula, Indicates the first The rate of change of the control input force of each float; Indicates filter parameters, ; This represents the actual control law, also known as the filter's command signal. It is worth noting that The input is designed based on the low-pass filtering characteristics of a second-order multiple-input multiple-output system, from which the following can be derived. The signal; Indicates the first The state variables of the floats are set to an upper bound. ; S2.3. Based on saturation constraints and low-pass filters, the second-order multiple-input multiple-output system is extended to obtain a multi-agent system, as expressed below: In the formula, Represents unknown nonlinear dynamics, where, , In subsequent designs, a fuzzy logic system will be used to approximate the unknown function. .

[0008] S3. Constructing consistency error based on the Laplace matrix in a multi-agent system; Directed graphs are used for information exchange between agents in multi-agent systems (MASs). It means that, among them, A set of nodes; Let be the set of edges, defined and These are the sets of followers and the sets of leaders, respectively. For directed graphs The adjacency matrix, The elements in the adjacency matrix represent the nodes from which nodes originate. To the node The connection weight, when hour ,otherwise ;remember Let be the in-degree matrix; let For the image The Laplace matrix; The expression for the consistency error is as follows: In the formula, Indicates the first The vertical displacement of the neighboring float ; Represents the elements in the adjacency matrix; Indicates the first Consistency error of individual floats; The control objective of this invention is to design a controller that ensures system stability and consistent error. The small neighborhood that converges to zero, i.e. In the formula, The control target is a positive constant that can be infinitesimally small by choosing appropriate parameters.

[0009] S4. By designing a set of error variables and constructing a barrier Lyapunov function; The expressions for a set of error variables are as follows: In the formula, Indicates the first The first error variable for each float; Indicates the first The second error variable for each float; , , and They represent the first The vertical velocity and acceleration of each pontoon, virtual control law 1 and virtual control law 2 (the purpose of designing virtual control laws is to assist in the analysis of stability and the design of the controller). The expression for the barrier Lyapunov function is as follows: In the formula, Represents the square of the error variable; Indicates the adaptive threshold of the design; and Let these represent the first and second positive constants of the design, respectively; and These represent the errors of the first fuzzy weight and the second fuzzy weight, respectively. This represents the transpose operation; the error calculation method for fuzzy weights is as follows: ,in, and These represent the estimation of fuzzy weights (constants) and fuzzy weights, respectively.

[0010] S5. To prevent platform overturning, and considering the limitations on the magnitude of consistency error, the obstacle Lyapunov function is solved. The steps include: S5.1, In order to address consistency errors To limit the error and prevent it from becoming too large and causing the platform to overturn, an obstacle function is designed to constrain it. First, the error variable is defined. The expression is as follows: In the formula, Indicates the error variable; Indicates the first Consistency error of individual floats; This represents the maximum permissible error, i.e., the maximum value of the relative displacement between pontoons converted from the maximum tilt angle, and is a positive number; passed through the obstacle function. Consistency error can be At ± Between, that is The idea behind designing the barrier function: because >0 requires | |<1, therefore ; S5.2 Design a low-frequency dual-event triggering mechanism for damping, the expression is as follows: In the formula, Indicates the current time; Indicates the first The first float The next trigger moment; Indicates the first The first float The next trigger moment; Indicates the first A float at any moment Consistency error; This indicates the trigger preparation ratio coefficient. The present invention takes ; Indicates time Adaptive threshold at time; Indicates the trigger bandwidth. ,in The larger the value of , the greater the tolerance for error; therefore, it should not be too large. This invention uses . Its triggering mechanism is designed so that it only triggers when the absolute value of the consistency error reaches a certain threshold. When, i.e., the absolute value of the consistency error Reduce to Only then is it allowed to enter the pre-triggering time. Continuing as the absolute value of the consistency error continues to increase beyond Sometimes Only then is it allowed to be triggered; S5.3. Differentiating the barrier Lyapunov function, we get: In the formula, Indicates the error variable; Represents the square of the error variable; Indicates the first The infeed of the buoy; Indicates the first The first error variable for each float; Indicates the first Virtual control law 1 for the vertical direction of each pontoon; Represents the elements in the adjacency matrix; Indicates the first The vertical velocity of the neighboring float; This indicates the maximum permissible error, which is the maximum value of the relative displacement between the pontoons converted from the maximum tilt angle; it is a positive number. Indicates the first The first error variable for each float; Represents unknown nonlinear dynamics; Indicates the first The second error variable for each float; Indicates the first Virtual control law 2 for the vertical direction of each pontoon; Indicates the first The derivative of the virtual control law 1 for each pontoon; and Let these represent the first and second positive constants of the design, respectively; This represents the error of the first fuzzy weight; The derivative of the error of the first fuzzy weights; Indicates the adaptive threshold of the design; This represents the adaptive threshold change rate of the design; Indicates the first The second error variable for each float; Indicates filter parameters; No. The vertical acceleration of each pontoon; Represents the actual control law; Indicates the first The derivative of the virtual control law 2 in the vertical direction of each pontoon; This represents the error of the second fuzzy weight; The derivative of the error of the second fuzzy weight; Indicates the transpose operation; S5.4 Design the backstepping control law to represent the parameters in the obstacle Lyapunov function, including: In the formula, ， ， ， and These represent the third, fourth, fifth, sixth, and seventh normal numbers, respectively. S5.5 Design an adaptive threshold, the expression of which is as follows: In the formula, Indicates the adjustment gain (positive number); Indicates the damping coefficient (a positive constant); S5.6 Substitute the backstepping control law and adaptive threshold into the differentiated obstacle Lyapunov function and scale it using Young's inequality; Yang's inequality is expressed as: In the formula, Indicates the first scaling constant; Indicates the second scaling constant; Indicates the third scaling constant; This represents the fourth scaling constant; The scaled representation is as follows: We can obtain: In the formula, Represents the convergence rate coefficient; This represents the convergence boundary.

[0011] S5.7 Solving for the scaled obstacle Lyapunov function yields the control objective, expressed as follows: at this time, When the vertical displacement of the three pontoons is consistent, it means that the centers of mass of the three pontoons are on the same horizontal plane, that is, the platform is in a stable state.

[0012] Beneficial effects of the present invention This invention designs a damped low-frequency dual-event triggering mechanism. This mechanism significantly reduces the event triggering frequency while relaxing the dependence on initial threshold conditions, thus effectively saving communication resources. Furthermore, it introduces a threshold bandwidth requirement that the error must cross the bandwidth before the next trigger is allowed, avoiding the Zeno phenomenon and further reducing the number of triggers, thus saving communication resources.

[0013] The damped low-frequency dual-event triggering algorithm proposed in this invention introduces a time-varying threshold function. This function can be dynamically adjusted according to changes in consistency error to reflect changes in the stability of the floating foundation under wind and wave disturbances. Specifically, when the error decreases, the threshold increases to reduce the number of triggers, thereby reducing communication overhead; when the error increases, the threshold decreases accordingly to increase the triggering frequency, thereby ensuring the stability control of the platform under wind and wave coupling. Attached Figure Description

[0014] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a consistency diagram of the simulation results of the embodiments of the present invention; Figure 3 This is a consistency error diagram of the simulation results of the embodiments of the present invention; Figure 4 This is an adaptive threshold graph of the simulation results of an embodiment of the present invention; Figure 5This is a filtered input diagram of the simulation results of an embodiment of the present invention; Figure 6 This is a trigger interval diagram showing the simulation results of an embodiment of the present invention. Detailed Implementation

[0015] The present invention will be further described in detail below with reference to specific embodiments.

[0016] like Figure 1 As shown, a damped low-frequency dual-event triggered control method for semi-submersible floating platforms includes the following steps: S1. Based on the physical model of the semi-submersible floating foundation platform, the system dynamic equations are constructed using the Newton-Euler formula; By controlling the vertical displacement of the centers of mass of the three pontoons in the physical model of the semi-submersible floating foundation platform, ensuring they remain on the same horizontal plane, the platform as a whole can be kept stable. Assuming the mass of the entire platform is uniformly distributed among the three pontoons, the dynamic equations of the system can be established according to the Newton-Euler formula as follows: In the formula, This represents the displacement state vector of the three floats; The first derivative of displacement, i.e., velocity; The second derivative of displacement, i.e., acceleration; This represents the mass matrix of the three floats; This represents the damping matrix of the three floats; This represents the stiffness matrix of the three floats; This represents the input coupling matrix of the three floats; This represents the control input force of the three floats; This indicates that the external dynamic disturbances experienced by the three floats are treated as disturbances; among them, Represented as , Indicates floats 1 through 3; Represented as , This indicates the mass distribution of floats 1 through 3; Represented as , This indicates the damping characteristics of floats 1 through 3; Represented as , This indicates the stiffness characteristics of floats 1 through 3; Represented as , This indicates the control input force for floats 1 through 3; Represented as , This indicates external interference with floats 1 through 3; , Indicates the first The first float and the second Information on the coupling effect of individual floats ,but No. The control force of the float Transmitting information about the first through platform structure The coupling effect generated by the individual floats; S2. Based on the constructed system dynamics equations, establish a multi-agent system using fuzzy logic. The steps include: S2.1. Regarding the stability control problem of a semi-submersible floating foundation platform under wind and wave disturbances, the system dynamic equation of the float is transformed to obtain a second-order multi-input multi-output system, as shown in the following expression: make: ; ; in, Represents a lumped nonlinear function; Indicates the first The nonlinear function corresponding to each float ,in, Indicates the first The vertical displacement of the float Indicates the first The speed of the float; This represents the control input quantity after normalization by the quality matrix. This represents the equivalent control input for the three floats; The following second-order multiple-input multiple-output system can be obtained: In the formula, Indicates the first The speed of the float; Indicates the first The first derivative of the displacement of each float; Indicates the first The acceleration of the buoy; , and They represent the first The control gain function of the nth float is used to describe the nth float. Each float is controlled by input force. , and The impact; Indicates the first Let the output of the nth float be equal to the output of the nth float. The displacement of the float; S2.2 Introduce saturation constraints and low-pass filters in the fuzzy logic system; To address the issue of strong coupling between inputs in multi-input multi-output (MIMO) systems, directly designing a controller using the inverse method presents certain difficulties. This approach also has limitations in terms of scalability and interpretability. To resolve this problem, a saturation constraint is introduced at the input, establishing a clear upper bound, namely... In this invention, take =15N / m, and then a fuzzy logic system (FLS) is used to approximate and compensate for input coupling effects and external interference; Introduction to Fuzzy Logic Systems (FLS): For any continuous nonlinear function There exists a fuzzy logic Satisfy the following expression: In the formula, Indicates in set Seeking the higher realms; Indicates compactness; This represents the real-time output of the fuzzy system. Indicates the transpose operation; This represents the upper bound of the approximation error; The ideal parameter vector is as follows: In the formula, Indicates a compact set of parameters; function satisfy , Indicates the approximation error; Because a second-order multiple-input multiple-output system is subject to saturation... Coupled with unknown functions, controller design is difficult; therefore, it is necessary to separate the variables and let... A low-pass filter is introduced, as shown below: In the formula, Indicates the first The rate of change of the control input force of each float; Indicates filter parameters, ; This represents the actual control law, also known as the filter's command signal. It is worth noting that The input is designed based on the low-pass filtering characteristics of a second-order multiple-input multiple-output system, from which the following can be derived. The signal; Indicates the first The state variables of the floats are set to an upper bound. ; S2.3. Based on saturation constraints and low-pass filters, the second-order multiple-input multiple-output system is extended to obtain a multi-agent system, as expressed below: In the formula, Represents unknown nonlinear dynamics, where, , In subsequent designs, a fuzzy logic system will be used to approximate the unknown function. .

[0017] S3. Constructing consistency error based on the Laplace matrix in a multi-agent system; Multi-agent systems (MASs) are composed of One leader and The MAS consists of a group of followers, and the information exchange between agents in the MAS is represented by a directed graph. It means that, among them, A set of nodes; Let be the set of edges, where and To represent two distinct nodes, define and These are the sets of followers and the sets of leaders, respectively. For directed graphs The adjacency matrix, The elements in the adjacency matrix represent the nodes from which nodes originate. To the node The connection weight, when hour ,otherwise ;remember Let be the in-degree matrix, where , indicating the first The in-degree of each agent; let For the image The Laplace matrix; In this invention, the adjacency matrix in-degree matrix Let the Laplace matrix be... ; The expression for the consistency error is as follows: In the formula, Indicates the first The vertical displacement of the neighboring float ; Represents the elements in the adjacency matrix; Indicates the first Consistency error of individual floats; The control objective of this invention is to design a controller that ensures system stability and consistent error. The small neighborhood that converges to zero, i.e. In the formula, The control target is a positive constant that can be infinitesimally small by choosing appropriate parameters.

[0018] S4. By designing a set of error variables and constructing a barrier Lyapunov function; The expressions for a set of error variables are as follows: In the formula, Indicates the first The first error variable for each float; Indicates the first The second error variable for each float; , , and They represent the first The vertical velocity and acceleration of each pontoon, virtual control law 1 and virtual control law 2 (the purpose of designing virtual control laws is to assist in the analysis of stability and the design of the controller). The expression for the barrier Lyapunov function is as follows: In the formula, Represents the square of the error variable; Indicates the adaptive threshold of the design; and Let these represent the first and second positive constants of the design, respectively; and These represent the errors of the first fuzzy weight and the second fuzzy weight, respectively. This represents the transpose operation; the error calculation method for fuzzy weights is as follows: ,in, and These represent the estimation of fuzzy weights (constants) and fuzzy weights, respectively.

[0019] S5. To prevent platform overturning, and considering the limitations on the magnitude of consistency error, the obstacle Lyapunov function is solved. The steps include: S5.1, In order to address consistency errors To limit the error and prevent it from becoming too large and causing the platform to overturn, an obstacle function is designed to constrain it. First, the error variable is defined. The expression is as follows: In the formula, Indicates the error variable; Indicates the first Consistency error of individual floats; This represents the maximum permissible error, i.e., the maximum value of the relative displacement between pontoons converted from the maximum tilt angle, and is a positive number; passed through the obstacle function. Consistency error can be At ± Between, that is The idea behind designing the barrier function: because >0 requires | |<1, therefore ; S5.2 Design a low-frequency dual-event triggering mechanism for damping, the expression is as follows: In the formula, Indicates the current time; Indicates the first The first float The next trigger moment; Indicates the first The first float The next trigger moment; Indicates the first A float at any moment Consistency error; This indicates the trigger preparation ratio coefficient. The present invention takes ; Indicates time Adaptive threshold at time; Indicates the trigger bandwidth. ,in The larger the value of , the greater the tolerance for error; therefore, it should not be too large. This invention uses . Its triggering mechanism is designed so that it only triggers when the absolute value of the consistency error reaches a certain threshold. When, i.e., the absolute value of the consistency error Reduce to Only then is it allowed to enter the pre-triggering time. Continuing as the absolute value of the consistency error continues to increase beyond Sometimes Only then is it allowed to be triggered; S5.3. Differentiating the barrier Lyapunov function, we get: In the formula, Indicates the error variable; Represents the square of the error variable; Indicates the first The infeed of the buoy; Indicates the first The first error variable for each float; Indicates the first Virtual control law 1 for the vertical direction of each pontoon; Represents the elements in the adjacency matrix; Indicates the first The vertical velocity of the neighboring float; This indicates the maximum permissible error, which is the maximum value of the relative displacement between the pontoons converted from the maximum tilt angle; it is a positive number. Indicates the first The first error variable for each float; Represents unknown nonlinear dynamics; Indicates the first The second error variable for each float; Indicates the first Virtual control law 2 for the vertical direction of each pontoon; Indicates the first The derivative of the virtual control law 1 for each pontoon; and Let these represent the first and second positive constants of the design, respectively; This represents the error of the first fuzzy weight; The derivative of the error of the first fuzzy weights; Indicates the adaptive threshold of the design; This represents the adaptive threshold change rate of the design; Indicates the first The second error variable for each float; Indicates filter parameters; No. The vertical acceleration of each pontoon; Represents the actual control law; Indicates the first The derivative of the virtual control law 2 in the vertical direction of each pontoon; This represents the error of the second fuzzy weight; The derivative of the error of the second fuzzy weight; Indicates the transpose operation; S5.4 Design the backstepping control law to represent the parameters in the obstacle Lyapunov function, including: In the formula, , , , and These represent the third, fourth, fifth, sixth, and seventh normal numbers, respectively. S5.5 Design an adaptive threshold, the expression of which is as follows: In the formula, Indicates the adjustment gain (positive number); Indicates the damping coefficient (a positive constant); S5.6 Substitute the backstepping control law and adaptive threshold into the differentiated obstacle Lyapunov function and scale it using Young's inequality; Yang's inequality is expressed as: In the formula, Indicates the first scaling constant; Indicates the second scaling constant; Indicates the third scaling constant; This represents the fourth scaling constant; The scaled representation is as follows: We can obtain: In the formula, Represents the convergence rate coefficient; Indicates the convergence boundary; ; .

[0020] S5.7 Solving for the scaled obstacle Lyapunov function yields the control objective, expressed as follows: at this time, When the vertical displacement of the three pontoons is consistent, it means that the centers of mass of the three pontoons are on the same horizontal plane, that is, the platform is in a stable state.

[0021] To verify the invention, a simulation experiment was conducted, and the results are as follows: Figures 2-6 As shown, Figure 2 and Figure 3 As shown in the figure, the visualization analysis of the simulation results reveals that under the control of the controller proposed in this invention, the displacement of the pontoon can maintain good consistency, and the consistency error is within the allowable range, meaning that the platform's tilt angle is always limited to within the maximum safe tilt angle.Figure 4 As shown, the method proposed in this invention relaxes the selection conditions for the initial value of the threshold, thereby avoiding the singularity problem that may occur in traditional methods. Figure 5 The system input is displayed, with the filtered input exhibiting a stepped pattern, reflecting the control update characteristics under the damped low-frequency dual-event triggering mechanism. Finally, as... Figure 6 As shown, the triggering interval of the three pontoons further demonstrates that the damped low-frequency dual-event triggering mechanism proposed in this invention can significantly reduce the number of triggers, thereby effectively saving communication resources. In summary, this invention can achieve efficient utilization of communication and control resources while ensuring the stability of the semi-submersible floating foundation platform.

Claims

1. A semi-submersible floating platform oriented damping low frequency double event triggered control method, characterized in that, The method comprises the following steps: S1, based on the physical model of the semi-submersible floating foundation platform, the system dynamics equation is constructed by Newton-Euler formula; S2, based on the constructed system dynamics equation, a multi-agent system is established by fuzzy logic; S3, based on the multi-agent system, the consistency error is constructed by Laplace matrix; S4, a set of error variables is designed and the barrier Lyapunov function is constructed; S5, for the overturning of the platform, based on the limitation of the size of the consistency error, the barrier Lyapunov function is solved, so that the consistency error converges to infinitesimal, and the construction of the control method is completed.

2. The semi-submersible platform-oriented damping low-frequency double event-triggered control method according to claim 1, characterized in that, In the S1, the expression of the system dynamics equation is as follows: In the formula, represents the displacement state vector of three floats; represents the first derivative of displacement, i.e. velocity; represents the second derivative of displacement, i.e. acceleration; represents the mass matrix of three floats; represents the damping matrix of three floats; represents the stiffness matrix of three floats; represents the input coupling matrix of three floats; represents the control input force of three floats; represents the external dynamic disturbance suffered by three floats, which is treated as disturbance; wherein, represents , represents the first float; represents , represents the mass distribution of the first float; represents , represents the damping characteristics of the first float; represents , represents the stiffness characteristics of the first float; represents , represents the control input force of the first float; represents , represents the external disturbance of the first float; , represents the coupling effect information between the th float and the th float, then the control force of the th float is transmitted to the th float through the platform structure to generate the coupling effect.

3. The semi-submersible platform-oriented damping low-frequency double event-triggered control method according to claim 1, characterized in that, The step of S2 comprises: S2.1, the system dynamics equation of the floater is transformed to obtain a second-order multi-input multi-output system, and the expression is as follows: Let: ； ； wherein, represents a lumped non-linear function; represents the own non-linear function of the th buoy, wherein, represents the vertical displacement of the th buoy, represents the velocity of the th buoy; represents the control input quantity normalized by the mass matrix, represents the equivalent control input of the three buoys; The second-order multi-input multi-output system can be obtained as follows: wherein represents the velocity of the th buoy; represents the first derivative of the displacement of the th buoy; represents the acceleration of the th buoy; represents the output of the th buoy, such that the output is equal to the displacement of the th buoy;​​​​​​​​ S2.2, saturation constraint and low-pass filter are introduced in the fuzzy logic system; Let and introduce a low-pass filter, denoted as follows: wherein represents the control input force rate of change of the th float; represents a filter parameter, ; represents the actual control law; represents the state variable of the th float; S2.3, based on the saturation constraint and low-pass filter, the second-order multi-input multi-output system is extended to obtain a multi-agent system, and the expression is as follows: wherein represents an unknown non-linear dynamics, wherein , .

4. The semi-submersible platform-oriented damping low-frequency double event-triggered control method according to claim 1, characterized in that, In the S3, the information interaction between each agent in the multi-agent system is represented by a directed graph , wherein, is a node set; is an edge set; is an adjacency matrix of the directed graph ; it is denoted that is an in-degree matrix; let be a Laplacian matrix of the graph ; Setting an adjacency matrix , an incidence matrix , a Laplacian matrix as ; The expression of the consistency error is as follows: wherein represents the vertical displacement of the th neighboring float, ; represents an element in the adjacency matrix; represents the consistency error of the th float. converge to zero converge to zero, expressed as: In the formulae, represents a control target.

5. The semi-submersible platform-oriented damping low-frequency double event-triggered control method according to claim 1, characterized in that, In the S4, the expression of the set of error variables is as follows: wherein represents a first error variable of the th buoy; represents a second error variable of the th buoy; ， ， and respectively represent a vertical direction velocity, an acceleration, a virtual control law 1 and a virtual control law 2 of the th buoy; The expression of the barrier Lyapunov function is as follows: wherein denotes the square of the error variable; denotes the designed adaptive threshold; and denote the designed first and second normal numbers, respectively; and denote the error of the first and second fuzzy weight, respectively; denotes the transpose operation; the error of the fuzzy weight is calculated as: wherein and denote the fuzzy weight and the estimate of the fuzzy weight, respectively.

6. The semi-submersible platform-oriented damping low-frequency double event-triggered control method according to claim 1, characterized in that, In the S5, the solving step comprises: S5.1, design the barrier function to constraint, first define the error variable The expression is as follows: wherein represents an error variable; represents the conformity error of the th float; represents the maximum allowed error; S5.2, a damping low-frequency double event trigger mechanism is designed, and the expression is as follows: In the formula, represents the current time; represents the time of the first trigger of the th float; th trigger of the th float; th trigger of the th float; represents the consistency error of the th float at time ; represents the trigger preparation proportion coefficient, , ; represents the adaptive threshold at time ; represents the trigger bandwidth, , taken ; S5.3, the derivative of the barrier Lyapunov function is obtained as follows: wherein denotes an error variable; denotes the square of an error variable; denotes the degree of entry of the th buoy; denotes the first error variable of the th buoy; denotes the second error variable of the th buoy; denotes an element in the adjacency matrix; denotes the vertical velocity of the th neighboring buoy; denotes the maximum allowed error, i.e. the maximum value of the relative displacement between two buoys converted from the maximum inclination angle, which is positive; denotes the first error variable of the th buoy; denotes an unknown nonlinear dynamics; denotes the second error variable of the th buoy; denotes the virtual control law 2 in the vertical direction of the th buoy; denotes the derivative of the virtual control law 1 of the th buoy; and denote the first and second design constants, respectively; denotes the error of the first fuzzy weight; denotes the derivative of the error of the first fuzzy weight; denotes the adaptive threshold value designed; denotes the adaptive threshold value change rate designed; denotes the second error variable of the th buoy; denotes a filter parameter; the vertical acceleration of the th buoy; denotes the actual control law; denotes the derivative of the virtual control law 2 in the vertical direction of the th buoy; denotes the error of the second fuzzy weight; the derivative of the error of the second fuzzy weight; denotes a transpose operation; S5.4, a backstepping control law is designed to represent the parameters in the barrier Lyapunov function, including: wherein ， ， ， and respectively represent a third normal number, a fourth normal number, a fifth normal number, a sixth normal number, and a seventh normal number; S5.5, an adaptive threshold is designed, and the expression is as follows: In the formula, represents a regulation gain (a normal number); represents a damping coefficient (a normal number); S5.6, the backstepping control law and the adaptive threshold are substituted into the derivative barrier Lyapunov function, and scaling is performed by Young inequality; Young inequality is expressed as: wherein represents a first scaling constant; represents a second scaling constant; represents a third scaling constant; represents a fourth scaling constant; After scaling, it is expressed as: It can be obtained as follows: In the formula, denotes a convergence rate coefficient; denotes a convergence bound; ； 。 S5.7, the scaled barrier Lyapunov function is solved to obtain the control target, and the expression is as follows: At this time, The three pontoons reach consistency in vertical displacement, meaning that the center of mass of the three pontoons is at the same level, and the platform is in a stable state.

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