A time delay compensation control method for wave energy converter

Abstract

This invention discloses a time-delay compensation control method for wave energy converters, belonging to the field of wave energy converter control technology. Based on the physical model of the wave energy converter, this method establishes the dynamic equations of the wave energy converter system. After defining the maximum power control problem of the wave energy converter, the dynamic equations of the wave energy converter system are transformed into a second-order linear system form, obtaining the system state variables, system parameters, and input time delay. After constructing an auxiliary system, an error variable is defined. Based on the error variable, a virtual control law is designed, and then an actual control law is constructed. By constructing the characteristic equation, the critical time delay threshold of the wave energy converter system is calculated. Lyapunov stability analysis proves that the system tracking error converges to a preset small neighborhood, thus completing the time-delay compensation control method for the wave energy converter. This invention can ensure that the critical time delay threshold of the system is always greater than the actual input time delay by adjusting the control parameters, guaranteeing system controllability.

Description

Technical Field

[0001] This invention relates to the field of control technology for wave energy converters, specifically to a time-delay compensation control method for wave energy converters. Background Technology

[0002] With the increasing exploration of sustainable and renewable energy concepts, wave energy shows great potential to meet the world's growing energy demands compared to other renewable resources. While wave energy meets the needs of commercialization and practical deployment, the technologies involved are still immature, resulting in a higher levelized cost of energy compared to other marine renewable energy sources, such as wind power. Therefore, maximizing energy output through wave energy converter devices attempts to harvest energy from ocean waves and use control systems to convert the absorbed mechanical energy into electrical energy.

[0003] The maximum power control of wave energy converters has received considerable attention from both academia and engineering. This involves constructing an energy-optimal reference angle trajectory to ensure the reference angle and excitation torque are as in phase as possible, pushing the system towards near resonance to enhance energy capture. In practical engineering implementation, this power maximization link is highly sensitive to time alignment. This is because the input torque command issued by the controller experiences input time delays during sampling and calculation, communication transmission and time synchronization, and the limited response of the driver or actuator. This causes the actual torque to arrive later than the expected time. If the input time delay exceeds the critical time delay value of the wave energy converter system, it introduces phase lag at the main frequency and disrupts the in-phase and near-resonance conditions, leading to poorer tracking performance, decreased average power, and a higher likelihood of torque saturation and inducing compensatory oscillations. Simultaneously, the negative power range and bidirectional energy flow increase, ultimately weakening the energy maximization effect and closed-loop stability margin. Therefore, obtaining the critical input time delay value is of great guiding significance for the maximum power capture of wave energy converters.

[0004] In wave energy converter systems, there is often an input time lag between the control input (target torque command) and the actual applied torque. This lag primarily originates from inherent delays in the sampling and calculation output process of the digital control link, fixed or time-varying delays and jitter caused by communication transmission and clock synchronization errors between the controller and the driver or valve controller, and the limited response speed of the actuator and power chain itself. This time lag introduces phase lag at the dominant frequency, causing a mismatch between the input torque and the desired in-phase and near-resonant energy capture conditions. This leads to poorer reference speed tracking, a decrease in average extractable power, and a greater likelihood of triggering torque saturation and compensatory oscillations. Simultaneously, phase mismatch increases the negative power range and bidirectional energy flow, further amplifying efficiency losses and weakening closed-loop robustness and stability margin. Numerous studies have attempted compensation designs based on time-lag systems to address the impact of these time lags, which can indeed improve closed-loop performance to a certain extent. However, most traditional compensations only guarantee robust stability within a given upper bound and cannot directly provide the critical threshold for instability triggered by increasing time lag. Once the actual time lag exceeds the compensator design assumptions, the control effect will rapidly decay or even completely fail. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a time-delay compensation control method for wave energy converters. The method first calculates a critical threshold for the system time delay. Then, by comparing the system time delay value with the critical threshold and adjusting parameters, the critical value is always controlled to the right of the actual time delay, thereby ensuring the controllability and stability of the wave energy converter. This strategy significantly improves the robustness and verifiability to uncertain time delays under complex sea conditions and execution constraints, providing a quantitative and feasible engineering guarantee for the maximum power control of wave energy converters during large wave disturbances.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a time-delay compensation control method for wave energy converters, specifically including the following steps: S1. Based on the physical model of the wave energy converter, establish the dynamic equation of the wave energy converter system. After defining the maximum power control problem of the wave energy converter, transform the dynamic equation of the wave energy converter system into a second-order linear system form. Based on the physical model of the wave energy converter, the dynamic equations of the wave energy converter system are expressed as follows: ; in, , and These represent the float's rotation angle, angular velocity, and angular acceleration, respectively. This represents the sum of the rigid body moment of inertia and the additional moment of inertia of the float (including rigid body parts such as connecting rods) relative to the pitch axis. This represents the coefficient of the restoring moment in still water. Indicates the viscous damping moment coefficient. and These represent the equivalent radiation torque and equivalent wave excitation torque at the hinge point, respectively, and can be obtained through system identification. Related expressions, This represents the control torque exerted by the damper on the system. It is a time variable.

[0007] First, regarding the maximum power control problem of the wave energy converter, this invention first transforms its dynamic equation (1) to obtain: ; in, .

[0008] The form of a second-order linear system is as follows: ; in, The state variable is the rotation angle. Let angular velocity be the state variable, since If it is a linear function related to the system state, then it can be written as ,in, and The linear coefficients obtained for system identification. The first linear coefficient, The second linear coefficient, It is the input signal. The input time delay is a known non-negative constant. It is the output of a second-order linear system. It is the set of real numbers.

[0009] S2. Define the tracking error based on the second-order linear system, construct the auxiliary system, define the error variable, design the virtual control law based on the error variable, and set the first control parameter. Second control parameter ; The tracking error of the system can be defined as follows: ; in, For system output, It is a reference trajectory. For tracking error; The control objective of this invention is to design a controller. This stabilizes the system and reduces tracking errors. The small neighborhood that converges to zero, i.e.: ; In the formula, As a preset positive constant, it can be arbitrarily small by selecting appropriate parameters. It is a time variable.

[0010] To eliminate the impact of input time delay on controller design, this invention constructs the following auxiliary system, expressed as follows: ; in, For the state variables of the first auxiliary controller, Let be the state variable of the second auxiliary controller, and and , and These are the control parameters of the design. The first control parameter, This is the second control parameter.

[0011] To aid in the analysis, a set of error variables is defined as follows: ; in, As the first error variable, As the second error variable, This is a virtual control law.

[0012] The purpose of designing a virtual control law is to assist in stability analysis and controller design. The expression is as follows: ; in, This is the adjustment coefficient for the first error variable. It is the first derivative of the reference trajectory.

[0013] S3. Design the actual control law based on the virtual control law; Designing actual control laws based on virtual control laws. The expression is as follows: ; in, The feedback gain coefficient for the first error variable. The feedback gain coefficient for the second error variable. The feedback gain coefficient of the first auxiliary variable. This is the feedback gain coefficient of the second auxiliary variable.

[0014] S4. Based on the actual control law, the critical time delay threshold of the wave energy converter system is calculated by constructing the characteristic equation. make As a combined state vector, it can be represented in the following vector form: ; in, For the instantaneous state matrix, Let be the time-delay state matrix; Then it can be expressed as: ; in Then its determinant is as follows: ; because Not included That is, when When, its root always lies in the left half-plane. Therefore, when Any imaginary axis crossings that occur during a change can only originate from... The characteristic equation is as follows: ; in, and , These are the coefficients of the characteristic equation. For the constant term of the characteristic equation, These are characteristic roots. For the time delay term coefficient, The constant coefficient of the time delay term; Due to input time delay This makes the equation have a purely imaginary root. According to Euler's formula It is possible ,in, The imaginary unit, Since is the imaginary frequency, the critical time delay threshold of the wave energy converter system is calculated as follows: ; S5, Based on input time delay and critical time delay threshold By comparing time delay values, the effective combination of control parameters is output; Only when the system's critical time delay threshold is reached... Greater than the system's input time delay Only when the designed adaptive tracking controller with time delay compensation is in place can it achieve tracking of the optimal angle; otherwise, the system will become unstable. As can be seen from the formula for calculating the critical time delay threshold, this can be achieved by adjusting... and Make the critical time delay Increase this, and consequently, the system input time delay Compared with the traditional direct design time-delay compensation tracking controller, the control strategy proposed in this invention can make the system always controllable, avoiding the situation where the traditional controller cannot compensate.

[0015] 1) When Then the current control parameters and Effective; the wave energy converter system is controllable and outputs effective power. and Control parameters; 2) When Then the current control parameters and The stability of the wave energy converter system cannot be guaranteed. It is necessary to return to S2 and readjust the control parameters. S6. Based on the actual control law of effective control parameters, time-delay compensation control is performed on the wave energy converter, and the tracking error of the system converges to the preset small neighborhood through Lyapunov stability analysis, thus completing the time-delay compensation control method of the wave energy converter.

[0016] Compared with the prior art, the present invention provides a time-delay compensation control method for wave energy converters, which has the following advantages: This invention presents a time-delay compensation control method for wave energy converters. After calculating a time-delay threshold, it compares this threshold with the actual time-delay value of the system. By adjusting control parameters, the time-delay threshold is always kept to the right of the system's time-delay, thus preventing excessive time delays that would render compensation impossible. Compared to traditional methods that directly design compensation strategies for time-delayed systems, this method ensures the time-delay threshold remains to the right of the system's time delay, avoiding situations where compensation is impossible. This invention addresses the issue of input time delays in wave energy converters. Existing time-delay compensation methods often experience a sharp drop in compensation effectiveness or even fail to compensate when the time delay is too large. This invention addresses this issue and proposes a solution that avoids such situations. Attached Figure Description

[0017] Figure 1 This is a flowchart of a time-delay compensation control method for wave energy converters according to the present invention. Figure 2 This is a diagram of the wave energy converter of the present invention; Figure 3 For the present invention, y and under different input time delays The trajectory diagram; Figure 4 The tracking error of this invention under different input time delays The trajectory diagram; Figure 5 The auxiliary variables of this invention under different input time delays The trajectory diagram; Figure 6 The auxiliary variables of this invention under different input time delays The trajectory diagram. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Due to the periodic delay of discrete sampling calculation and the limited response speed of the actuator, the wave energy converter introduces the influence of input time delay. When the input time delay is too large, some time delay compensation-based strategies will fail. Therefore, it is necessary to overcome the influence of input time delay, and thus a time delay compensation control method for wave energy converter is proposed. Therefore, the research objective of this invention is to calculate the time delay threshold, compare it with the actual input time delay value of the system, and adjust the control parameters to ensure that the time delay threshold is always on the right side of the system time delay, thus avoiding the phenomenon that the time delay is too large and cannot be compensated.

[0020] Please see Figures 1-6 A time-delay compensation control method for wave energy converters includes the following steps: S1. Based on the physical model of the wave energy converter, establish the dynamic equation of the wave energy converter system. After defining the maximum power control problem of the wave energy converter, transform the dynamic equation of the wave energy converter system into a second-order linear system form. In this invention, the physical model of the wave energy converter is as follows: Figure 2 As shown; Based on the physical model of the wave energy converter, the dynamic equations of the wave energy converter system are expressed as follows: (1); in, , and These represent the float's rotation angle, angular velocity, and angular acceleration, respectively. This represents the sum of the rigid body moment of inertia and the additional moment of inertia of the float (including rigid body parts such as connecting rods) relative to the pitch axis. This represents the coefficient of the restoring moment in still water. Indicates the viscous damping moment coefficient. and These represent the equivalent radiation torque and equivalent wave excitation torque at the hinge point, respectively, and can be obtained through system identification. Related expressions, This represents the control torque exerted by the damper on the system. It is a time variable.

[0021] First, regarding the maximum power control problem of the wave energy converter, this invention first transforms its dynamic equation (1) to obtain: (2); in, .

[0022] make = and The original system (2) can be transformed into the following second-order linear system, with the following expression: (3); in, The state variable is the rotation angle. Let angular velocity be the state variable, since If it is a linear function related to the system state, then it can be written as ,in, and The linear coefficients obtained for system identification. The first linear coefficient, The second linear coefficient, It is the input signal. The input time delay is a known non-negative constant. It is the output of a second-order linear system. It is the set of real numbers.

[0023] S2. Define the tracking error based on the second-order linear system, construct the auxiliary system, define the error variable, design the virtual control law based on the error variable, and set the first control parameter. Second control parameter ; The tracking error of the system can be defined as follows: (4); in, For system output, It is a reference trajectory. For tracking error; The control objective of this invention is to design a controller. This stabilizes the system and reduces tracking errors. The small neighborhood that converges to zero, i.e.: (5); In the formula, As a preset positive constant, it can be arbitrarily small by selecting appropriate parameters. It is a time variable.

[0024] To eliminate the impact of input time delay on controller design, this invention constructs the following auxiliary system, expressed as follows: (6); in, For the state variables of the first auxiliary controller, Let be the state variable of the second auxiliary controller, and and , and These are the control parameters of the design. The first control parameter, This is the second control parameter.

[0025] To aid in the analysis, a set of error variables is defined as follows: (7); in, As the first error variable, As the second error variable, This is a virtual control law.

[0026] The purpose of designing a virtual control law is to assist in stability analysis and controller design. The expression is as follows: (8); in, This is the adjustment coefficient for the first error variable. It is the first derivative of the reference trajectory.

[0027] S3. Design the actual control law based on the virtual control law; Designing actual control laws based on virtual control laws. The expression is as follows: (9); in, This is the adjustment coefficient for the second error variable. The first derivative of the virtual control law. Given a linear function, and to calculate the critical time delay threshold, the control law in (9) is used. Rewritten as follows: (10); in, The feedback gain coefficient for the first error variable. The feedback gain coefficient for the second error variable. The feedback gain coefficient of the first auxiliary variable. This is the feedback gain coefficient of the second auxiliary variable.

[0028] S4. Based on the actual control law, the critical time delay threshold of the wave energy converter system is calculated by constructing the characteristic equation. make Substituting equations (8) and (10) into equations (6) and (7) respectively, the sum can be expressed in the following vector form: (11); in, set up Then (11) can be expressed as: (12); in Then its determinant is as follows: (13); because Not included That is, when When, its root always lies in the left half-plane. Therefore, when Any imaginary axis crossings that occur during a change can only originate from... The characteristic equation is as follows: (14); in, and , These are the coefficients of the characteristic equation. For the constant term of the characteristic equation, These are characteristic roots. For the time delay term coefficient, The constant coefficient of the time delay term; Due to input time delay This makes the equation have a purely imaginary root. According to Euler's formula It is possible ,in, The imaginary unit, Since is the imaginary frequency, the critical time delay threshold of the wave energy converter system is calculated as follows: (15); S5, Based on input time delay and critical time delay threshold By comparing time delay values, the effective combination of control parameters is output; Only when the system's critical time delay threshold is reached... Greater than the system's input time delay Only when the designed adaptive tracking controller with time delay compensation is in place can it achieve tracking of the optimal angle; otherwise, the system will become unstable. As can be seen from equations (14) and (15), the system can be stabilized by adjusting... and Make the critical time delay Increase this, and consequently, the system input time delay Compared with the traditional direct design time-delay compensation tracking controller, the control strategy proposed in this invention can make the system always controllable, avoiding the situation where the traditional controller cannot compensate.

[0029] 1) When Then the current control parameters and Effective, system controllable, output valid. and Control parameters; 2) When Then the current control parameters and System stability cannot be guaranteed; it is necessary to return to S2 and readjust the control parameters. S6. Based on the actual control law of effective control parameters, the wave energy converter is subjected to time delay compensation control, and the tracking error of the system is proved to converge to the preset small neighborhood through Lyapunov stability analysis, thus completing the time delay compensation control method of the wave energy converter. The following are the stability analyses of the system under the action of the controller: Consider the following Lyapunov candidate function: (16); For equation (16) Differentiation yields (17); Substituting equations (8) and (9) into equation (17) yields... (18); in From (16) and (18) By defining the error variable, we can derive its characteristics. and It is bounded, in order to ensure tracking error The boundedness of the auxiliary system (6) will then be discussed. and The boundedness of the function. First, select the following function as a Lyapunov candidate function.

[0030] (19); for Differentiation is possible (20); in It is a positive constant, and has and .

[0031] By using the Cauchy-Schwarz inequality, we can obtain (twenty one); Substituting (21) into (20), we get (twenty two); From equations (8) and (9), we can obtain information about and The following results were obtained.

[0032] (twenty three); in and yes Function. According to and The boundedness of the present invention has (twenty four); (25); in and If it is a positive constant, then we have (26); Among them are and Therefore, the following formula can be obtained: (27); Then, the following results can be obtained: (28); Among them are , and .

[0033] Substituting (28) into (22), we get (29); Now, choose the following Lyapunov function for the entire auxiliary system. (30); The derivative is: (31); In addition, the following results were clearly established: (32); (33); Substituting (32) and (33) into (30), we get the following: (34); in, From (34), we can conclude that It is bounded, that is, the auxiliary system (6) is uniformly eventually bounded, that is, when From time to time This means that by selecting appropriate control parameters, auxiliary variables It can be very small, because It can be proven It is bounded, thus concluding that all signals in the closed-loop system are bounded, thereby achieving the control objective (5). It can be seen that the swing angle of this wave energy conversion device can track the optimal angle.

[0034] Figures 3 to 6 The states, errors, and input trajectories of the wave energy converter system under different input time delays (input time delay greater than the critical time delay, input time delay equal to the critical time delay, and input time delay less than the critical time delay) are shown. Figure 3 and Figure 4 As shown, traditional methods directly design compensation strategies to compensate for the impact of input time delay in a system. However, when the time delay is too large and exceeds the time delay threshold, it becomes impossible to compensate, leading to system instability and error divergence. Under the same system input time delay, based on the adjustment strategy proposed in this paper, the critical time delay value for system instability is calculated and then compared with the system time delay. By adjusting the control parameters, the critical time delay is always kept to the right of the system time delay, ensuring system stability and allowing the wave energy conversion device's angle tracking error to converge to a small neighborhood near zero. In other words, the tracking performance of the entire wave energy conversion device system is guaranteed. Figure 5 and Figure 6 Auxiliary variables under different critical time delays are shown. , The trajectory change curve.

[0035] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A time delay compensation control method for a wave energy converter, characterized by, Includes the following steps: S1. Based on the physical model of the wave energy converter, establish the dynamic equations of the wave energy converter system. After defining the maximum power control problem of the wave energy converter, transform the dynamic equations of the wave energy converter system into a second-order linear system form, and obtain the system state variables, system parameters, and input time delay. ; The system state variables include: rotation angle state variables and angular velocity state variables; S2. Define the tracking error based on the second-order linear system, construct the auxiliary system, define the error variable, design the virtual control law based on the error variable, and set the first control parameter. Second control parameter ; S3. Design the actual control law based on the virtual control law; S4. Based on the actual control law, the critical time delay threshold of the wave energy converter system is calculated by constructing the characteristic equation. S5, Based on input time delay and critical time delay threshold By comparing time delay values, an effective combination of control parameters is output; S6. Based on the actual control law of effective control parameters, time-delay compensation control is performed on the wave energy converter, and the tracking error of the system converges to the preset small neighborhood through Lyapunov stability analysis, thus completing the time-delay compensation control method of the wave energy converter.

2. The time-delay compensation control method for wave energy converters according to claim 1, characterized in that, In S1, the dynamic equations of the wave energy converter system are expressed as follows: ； in, , and These represent the float's rotation angle, angular velocity, and angular acceleration, respectively. This represents the sum of the rigid body moment of inertia and the additional moment of inertia of the float relative to the pitch axis. Indicates the still water restoring moment coefficient. Indicates the viscous damping moment coefficient. and These represent the equivalent radiation torque and the equivalent wave excitation torque at the hinge point, respectively. This represents the control torque exerted by the damper on the system. It is a time variable; The expression for the second-order linear system is as follows: ； in, Let be the state variable representing the rotation angle, and = , For rotation angle, Let be the state variable for angular velocity, and , Angular velocity, It is a linear function, which can be written as ,in, and The linear coefficients obtained for system identification. The first linear coefficient, The second linear coefficient, It is the input signal. For input time delay, This indicates the system output.

3. The time-delay compensation control method for wave energy converters according to claim 2, characterized in that, In step S2, the expression for constructing the auxiliary system is as follows: ； in, For the state variables of the first auxiliary controller, Let be the state variable of the second auxiliary controller, and and , and These are the control parameters of the design. The first control parameter, This is the second control parameter; The expression for defining the error variable is as follows: ； in, As the first error variable, As the second error variable, For virtual control laws; The expression for the virtual control law is as follows: ； in, This is the adjustment coefficient for the first error variable. It is the first derivative of the reference trajectory.

4. The time-delay compensation control method for wave energy converters according to claim 3, characterized in that, In S3, the expression for the actual control law is as follows: ； in, The feedback gain coefficient for the first error variable. The feedback gain coefficient for the second error variable. The feedback gain coefficient of the first auxiliary variable. The feedback gain coefficient of the second auxiliary variable. The first derivative of the virtual control law. It is a linear function.

5. A time-delay compensation control method for wave energy converters according to claim 4, characterized in that, In step S4, the expression for the characteristic equation is as follows: ； Input delay, and , The first linear coefficient, The second linear coefficient, The first control parameter, This is the second control parameter. For the constant term of the characteristic equation, These are characteristic roots. For the time delay term coefficient, The constant coefficient of the time delay term; The calculation expression for the critical time delay threshold of the wave energy converter system is as follows: ； in, For the imaginary part frequency, This is the critical time delay threshold.

6. The time-delay compensation control method for wave energy converters according to claim 5, characterized in that, In step S5, the step of outputting an effective combination of control parameters by comparing time delay values ​​specifically involves: 1) When Then the current control parameters and Effective; the wave energy converter system is controllable and outputs effective power. and Control parameters; 2) When Then the current control parameters and The stability of the wave energy converter system cannot be guaranteed; it is necessary to return to step S2 and readjust the control parameters. and .

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