A delay compensation control method for a double pendulum wave energy conversion device

Abstract

The application provides a delay compensation control method for a double pendulum wave energy conversion device, which comprises the following steps: numerical modeling and hydrodynamic analysis are performed on the double pendulum wave energy conversion device, time domain motion equations are established, a time delay function is introduced into the time domain motion equations to simulate control signal transmission delay, and partial differential equations are used to simulate the execution delay of the brake; state space equations of the device are established, the convolution items in the time domain motion equations are replaced by the state space equations, and the motion state of the device is calculated; a Hamilton function is defined to convert a constrained optimization problem into an unconstrained optimization problem, the optimal control criterion considering the control delay is obtained by solving the Hamilton function, and the maximization of energy capture under the optimal control criterion is realized. The application truly reflects the operation characteristics of the physical system by introducing the control delay, so that the closed-loop control method is effectively implemented in the actual physical device, and the energy capture efficiency of the wave energy conversion device and the reliability of the system operation are effectively improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wave energy generation, and particularly relates to a delay compensation control method for a double-oscillator wave energy conversion device. BACKGROUND

[0002] The overuse of traditional fossil energy (such as coal, oil and natural gas) not only leads to the gradual depletion of resources, but also causes serious environmental problems such as global warming and air pollution. These problems pose a threat to human health and the stability of the ecological system, so the development of sustainable and clean energy has become an urgent global demand. Among various forms of renewable energy, wind energy and solar energy have achieved a certain degree of development and application, but due to factors such as seasonality and intermittency, their energy supply is unstable. In contrast, wave energy, as a clean and renewable energy source, has higher development potential and application value due to its wide distribution, abundant reserves and high energy density.

[0003] A wave energy conversion device is a device that converts the energy of ocean waves into electrical energy. Although various types of wave energy conversion devices have been proposed and developed, such as differential pressure type, overtopping type and oscillating type, the overall wave energy capture efficiency is still low. In order to improve the power generation efficiency, researchers have proposed various control strategies, among which lock-in control is considered an important method that can effectively improve the energy extraction efficiency of wave energy conversion devices.

[0004] The implementation of lock-in control relies on the alternating locking and releasing of the physical brake to the float. In existing research, most scholars usually assume that the physical brake can be instantaneously loaded and released during the algorithm design and verification process, ignoring the delay effect of the brake in actual operation. In fact, the control delay of the physical brake is inevitable, mainly including two aspects: one is the transmission delay of the controller in sending control signals, and the other is the response delay of the brake itself in executing the loading and releasing actions. If this kind of delay factor is ignored, it will cause a deviation between the control strategy and the actual execution, thereby affecting the energy capture efficiency of the wave energy conversion device. SUMMARY

[0005] The purpose of the present application is to provide a delay compensation control method for a double-oscillator wave energy conversion device. The time delay function is introduced into the time-domain motion equation to simulate the control signal transmission delay, and the partial differential equation is used to simulate the execution delay of the brake, so as to truly reflect the running characteristics of the physical system and improve the energy capture efficiency of the wave energy conversion device and the reliability of the system operation.

[0006] The present application is implemented by adopting the following technical solutions:

[0007] Proposed is a delay compensation control method for a double pendulum wave energy converter, comprising;

[0008] S1: Numerical modeling of the double pendulum wave energy converter is performed, and hydrodynamic analysis is carried out;

[0009] S2: Time-domain motion equations of the double pendulum wave energy converter considering control delay are established:

[0010] ,

[0011] ;

[0012] wherein, and are the mass of the outer pendulum and the inner pendulum respectively; represents the added mass; denote the displacement of the outer pendulum, the displacement of the inner pendulum, the velocity of the outer pendulum, the velocity of the inner pendulum, the acceleration of the outer pendulum and the acceleration of the inner pendulum respectively; denotes a pulse response function representing radiative interaction, is a time variable; denote the viscous damping coefficient, the still water restoring stiffness, the spring damping coefficient and the spring stiffness coefficient respectively; denotes the wave excitation force;△ denotes the control signal transmission delay; is a control command; denotes the brake load of the brake, , denotes the execution delay index of the brake, is a brake load coefficient;

[0013] S3: State space equations of the double pendulum wave energy converter considering control delay are established, the convolution term of the time-domain motion equation is replaced by the state space equation, and the motion state of the double pendulum wave energy converter is calculated;

[0014] S4: Locking control considering control delay is implemented on the double pendulum wave energy converter to maximize the extraction of energy in the wave, comprising:

[0015] A Hamiltonian function is defined for the double pendulum wave energy converter ; wherein, is the motion equation of the double pendulum wave energy converter, is the motion state of the double pendulum wave energy converter; is the Lagrange multiplier, which follows the control equation ; T is a terminal time point defined for the control optimization problem;

[0016] Solving the Hamilton function according to the control equation of Lagrange multiplier, and obtaining the control criterion of the closed-loop control considering the transmission delay of the control signal and the execution delay of the brake according to the solving result 1 represents loading the double-oscillator wave energy conversion device, 0 represents unloading the double-oscillator wave energy conversion device; n is the order of the system.

[0017] In some embodiments of the application, the spatial state equation established by S3 is:

[0018] , ; wherein, ,

[0019] , ; p and q are calculated by the least square method:

[0020] ; wherein, is the radiation damping, is the outer array angular frequency, is the additional mass at infinite frequency;

[0021] The state space equation is brought into the time domain motion equation, and a new state variable is defined , the time domain motion equation is transformed into a linear differential equation:

[0022] ;

[0023] ; ;

[0024] The initial condition X(0)=0 is defined, the Runge-Kutta method is used to solve the linear differential equation, and the motion state X of the double-oscillator wave energy conversion device is calculated.

[0025] In some embodiments of the application, S4 solving the Hamilton function comprises: rewriting the Hamilton function H as ;

[0026] Expanding the Hamilton function:

[0027] ;

[0028] According to the control equation , the Lagrange multiplier is solved: ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] wherein the Hamiltonian is a linear function of the control commands, which reaches a maximum value when .

[0035] Compared with the prior art, the advantages and positive effects of the present application are that: in the lock control method considering the control delay of the double-oscillator wave energy conversion device proposed by the present application, the control delay factors of the brake, including the transmission delay of the control signal and the execution delay of the brake itself, are introduced into the designed time-domain motion equation, through the modeling and compensation of the two kinds of delays, the present application can more truly reflect the running characteristics of the physical system, so that the developed lock control method not only has feasibility in the theoretical level, but also can be effectively implemented in the actual physical device, effectively improving the energy capture efficiency of the wave energy conversion device and the reliability of the system operation.

[0036] Other features and advantages of the present application will become more apparent after reading the detailed description of the embodiments of the present application in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiment description will be briefly introduced below, and obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained according to these drawings without creative labor for those skilled in the art.

[0038] Figure 1 The delay compensation control algorithm for the double-oscillator wave energy conversion device proposed by the present application;

[0039] Figure 2 The overall structure of the double-oscillator wave energy conversion device in the present application is shown;

[0040] Figure 3 The numerical simulation model of the double-oscillator wave energy conversion device in the present application is shown;

[0041] Figure 4 The delay compensation control in the present application is shown;

[0042] Figure 5 The brake execution load in the present application is shown;

[0043] Figure 6 The specific implementation flow of the delay compensation control method in the present application is shown;

[0044] Figure 7 The figure shows the comparison between the delay compensation control method of the present application and the wave energy capture efficiency without the control algorithm. DETAILED DESCRIPTION

[0045] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0046] As shown in the figure, the lock control algorithm considering the control delay of the double-oscillator wave energy conversion device proposed in the present application has the following steps: Figure 1 S1: Numerical modeling of the double-oscillator wave energy conversion device and hydrodynamic analysis.

[0047] The double-oscillator wave energy conversion device is composed of three main parts: an outer oscillator, an inner oscillator, and a power take-off (PTO) system. The outer oscillator is directly affected by the incident wave and makes vertical reciprocating motion under wave excitation; the inner oscillator is connected to the outer oscillator through the PTO system and only moves in the heave direction. In the present application, the outer oscillator and the inner oscillator can be collectively referred to as the floater. The PTO system is installed inside the floater and is used to convert the relative motion between the two oscillators into electrical energy. The existing PTO systems have various forms, including hydraulic, mechanical transmission, hydraulic, pneumatic, linear motor, and hybrid hydraulic. In the present application, a hydraulic PTO system is selected, and its core components consist of a hydraulic cylinder, a hydraulic motor, and a generator. The piston rod of the hydraulic cylinder is connected to the device through a connecting rod. When the hydraulic cylinder moves under force, it pushes the hydraulic motor to rotate, which in turn drives the generator to output electrical energy.

[0048]

[0049] ​Furthermore, the working principle of the dual-oscillator wave energy conversion device is as follows: The outer oscillator is directly exposed to the incident wave environment and undergoes vertical heave motion under the periodic action of the waves. The inner oscillator is connected to the outer oscillator via a PTO and is only allowed to move relative to the outer oscillator in the heave direction. The relative displacement between the two is transmitted to the hydraulic cylinder through a connecting rod, causing the piston in the hydraulic cylinder to reciprocate, thereby compressing and releasing hydraulic oil to form a high-pressure oil flow, realizing the conversion of wave mechanical energy into hydraulic energy. Subsequently, the high-pressure hydraulic oil flows along the pipeline and drives the hydraulic motor to rotate. The hydraulic motor further converts the hydraulic energy into rotational mechanical energy (i.e., the torque and speed of the output shaft). The rotational motion of the output shaft then drives a three-phase permanent magnet synchronous generator to generate electricity, the principle of which is also based on the law of electromagnetic induction. When the rotor rotates under the action of mechanical energy, the permanent magnets on the rotor cut the magnetic field of the stator coils, generating three-phase alternating current in the three sets of stator coils with a phase difference of 120°. This power generation method ensures the synchronization between the output current and the rotor speed, enabling stable current output. Because permanent magnets do not require external excitation, three-phase permanent magnet synchronous generators are not only highly efficient but also simple in structure and low in maintenance costs, making them suitable for long-term operation in marine environments. Through the aforementioned energy conversion link, the dual-oscillator wave energy conversion device effectively achieves the efficient conversion from wave mechanical energy to electrical energy.

[0050] In this invention, combined Figure 2 As shown, the dual-oscillator wave energy conversion device mainly consists of an outer oscillator 1, an inner oscillator 2, and a PTO 3. The outer oscillator 1 is a hemispherical float with a radius of 5m and a draft of 5m. The inner oscillator 2 is a cylindrical structure with a radius of 2.5m. The PTO 3 adopts a hydraulic PTO system, mainly composed of a piston rod, a hydraulic cylinder, a hydraulic motor, and a generator. The hydraulic cylinder drives the hydraulic motor to operate, and the hydraulic motor drives the generator to generate electricity. Under the action of waves, the outer oscillator 1 reciprocates in the heave direction and is connected to the inner oscillator 2 through the PTO 3. The relative motion of the inner and outer oscillators drives the piston of the hydraulic cylinder to move up and down in the heave direction, increasing the pressure of the hydraulic oil in the hydraulic cylinder cavity. This process converts mechanical energy into hydraulic energy. The hydraulic oil then drives the hydraulic motor, converting the liquid pressure energy in the pipeline into the mechanical energy (torque and speed) of the output shaft, which then drives the generator at the back end to generate electrical energy. The generator adopts existing equipment: a three-phase permanent magnet synchronous motor.

[0051] Combination Figure 3As shown, the present application uses the GeniE module of the SESAM software to only establish a numerical model of the part of the double-pendulum wave energy converter below the waterline. In the GeniE module, a numerical model of the double-pendulum wave energy converter with a radius of 5 m and a draft of 5 m is first established, and the wet surface of the double-unit wave energy array is defined, then the wet surface of the double-pendulum wave energy converter is loaded, after the loading is completed, the grid is divided, and finally the.fem file can be obtained through calculation, and it is imported into the HydroD module. In the HydroD module, by completing a series of basic information such as defining the direction of the wave, the wave frequency, the panel model, etc., the hydrodynamic parameters of the double-pendulum wave energy converter can be calculated. The hydrodynamic parameters here mainly refer to the added mass, the radiation damping and the first-order wave force transfer function.

[0052] S2: Establishing the time-domain motion equation of the double-pendulum wave energy converter considering the control delay.

[0053] In order to more accurately describe the dynamic characteristics of the double-pendulum system, two coordinate systems are defined: a global coordinate system whose X-O-Y plane coincides with the calm water surface and the Z axis is vertically upward, used to describe the spatial position of the wave propagation direction and the whole floating body; a local coordinate system set at the geometric center of the inner pendulum and moving along the vertical direction with the heaving motion of the floating body, used to capture and describe the local motion characteristics of the inner pendulum relative to the outer pendulum.

[0054] In combination Figure 4 As shown, the control delay referred to in the present application includes control signal transmission delay and brake execution delay. Specifically, the controller sends a control signal, and the brake cannot obtain the control signal immediately, but obtains it after several time steps; after the brake obtains the control signal, in combination Figure 5 As shown, in the control model of the present application, due to the execution delay of the brake, the output brake force does not immediately reach the maximum value after receiving the control instruction, but gradually increases with time. When the control instruction is to lock or release the floater, the state of the floater will not change instantaneously, but will gradually complete the locking or releasing process after a delay. This feature can accurately reflect the dynamic response behavior of the actual brake.

[0055] The present application establishes the time-domain motion equation of the double-pendulum wave energy converter considering the control delay based on the impulse response theory as shown in the formula:

[0056] ,

[0057] ;

[0058] wherein, and are the masses of the outer pendulum and the inner pendulum, respectively; Represents added mass; These represent the displacement of the outer oscillator, the displacement of the inner oscillator, the velocity of the outer oscillator, the velocity of the inner oscillator, the acceleration of the outer oscillator, and the acceleration of the inner oscillator, respectively. This represents the impulse response function that represents the radiative interaction. It is a time variable; These represent the viscous damping coefficient, hydrostatic restoring stiffness, spring damping coefficient, and spring stiffness coefficient, respectively; △ Indicates the delay in control signal transmission; For control commands.

[0059] The wave excitation force is represented by the formula shown in the formula below. As shown;

[0060]

[0061] The braking load of the brake is represented by the formula shown in the formula below. As shown;

[0062]

[0063] in, This is the braking load coefficient; The delay index, This represents classic lockout control, where the lockout action occurs instantaneously, without considering control delay effects. As the delay exponent increases, the application of the braking force will be delayed accordingly, resulting in the oscillator being locked at a later time.

[0064] The aforementioned hydrodynamic parameters, such as added mass, radiation damping, and wave force transfer function, were all calculated using the hydrodynamic analysis software SESAM-HydroD.

[0065] S3: Establish the state-space equation of the dual-oscillator wave energy conversion device considering control delay, replace the convolution term of the time-domain motion equation with the state-space equation, and calculate the motion state of the dual-oscillator wave energy conversion device.

[0066] The convolution terms in the time-domain motion equations of the dual-oscillator wave energy conversion device, which considers control delay in step S2, are replaced with state-space equations to facilitate the implementation of the control algorithm.

[0067] The state-space equations are as follows: As shown:

[0068]

[0069] in, are used to approximate the convolution terms, respectively representing n x n, n x 1, 1 x n dimensional state space matrices, whose expansion formulae are as follows:

[0070]

[0071]

[0072] The vectors p and q can be calculated by least square method, whose formulae are as follows:

[0073]

[0074] where, is the radiation damping, is the outer array element angular frequency, is the added mass at infinite frequency.

[0075] Further, the established state space equation is brought into the time domain motion equation, and a new state variable is defined, the time domain motion equation is transformed into a linear differential equation, as shown in the formula

[0076]

[0077] The initial condition X(0)=0 is defined, and the Runge-Kutta method is used to solve the formula to calculate the motion state X of the double pendulum wave energy converter.

[0078] S4: Implement a latching control considering control delay for the double pendulum wave energy converter to maximize the energy extraction in the wave.

[0079] The latching control is essentially a phase control, and the brake works by controlling the command to alternately lock ( =1) and release ( =0) the floater, so that the phase of the floater's speed is consistent with the phase of the wave excitation force, thereby improving the wave energy capture efficiency.

[0080] The goal of controlling the double pendulum wave energy converter is to maximize the total energy capture of the double pendulum wave energy converter, and the constraint standard is the motion equation of the double pendulum wave energy converter , which is a constrained optimization problem and is not convenient to solve.​​​​​

[0081] Therefore, in the present application, a Hamiltonian function H is defined to transform the complex constrained optimization problem into an unconstrained optimization problem, which is a linear function of the control command β, and the Hamiltonian reaches the maximum value when it satisfies the formula , which can maximize the energy capture. The Hamiltonian function H is shown in the formula

[0082]

[0083] where, is the motion equation of the double pendulum wave energy converter, is the motion state of the double pendulum wave energy converter.

[0084] Further, the Hamiltonian function H can be written as the formula

[0085]

[0086] where, is the Lagrange multiplier, which follows the control equation

[0087]

[0088] T is the terminal time point defined by the control optimization problem.

[0089] By the control equation , the Lagrange multiplier can be solved, and then the control command β is updated by the Lagrange multiplier. The solving process is shown as follows:

[0090] (1) According to the state space equation of the double pendulum wave energy converter considering the control delay, the Hamiltonian function is expanded as follows:

[0091]

[0092] (2) According to the equation , the above Hamiltonian function is solved to calculate the Lagrange multiplier, which is shown as follows:

[0093]

[0094]

[0095]

[0096] ​​​​​​​ ;

[0097] ;

[0098] ;

[0099] wherein the Hamiltonian is a linear function of the control command, and the Hamiltonian reaches a maximum value when the formula is satisfied:

[0100]

[0101] The above, the present application solves the optimal control command by the Hamiltonian, and the optimal control command solved by the Hamiltonian Can maximize the energy capture Wherein, n is the order of the system.

[0102] Combined with Figure 6 It will be described in detail how the control delay algorithm is developed in matlab. Step 1 initializes the parameters, step 2 establishes the numerical model of the double pendulum wave energy conversion device, step 3 implements the closed-loop control algorithm considering the control delay for the double pendulum wave energy conversion device. When only considering the signal transmission delay, the optimal control command calculated at time t i Is not input to the actuator immediately, but is input at time t i+k After a delay of k time steps. When considering the execution delay of the actuator, the optimal control command generated at time t i Can be transmitted to the actuator immediately, but the response process of the actuator needs a certain time to complete gradually. In order to realize the modeling of this dynamic process, a differential equation varying with time is introduced in the closed-loop control algorithm to simulate the dynamic response of the actuator. When considering both the signal transmission delay and the execution delay of the actuator, the actuator still needs to go through a certain execution process after receiving the control command with a delay before completing the locking operation.

[0103] In a specific embodiment of the present application, for the double pendulum wave energy conversion device, as shown in Figure 7 , the wave energy conversion devices under two control methods (no control, delay control) are numerically simulated to compare their energy capture performance. The incident wave is described by JONSWAP spectrum, and three wave conditions are selected, condition one, the significant wave height is 1.54m, the spectral peak period is 7.79s, condition two, the significant wave height is 1.33m, the spectral peak period is 6.88s, condition three, the significant wave height is 2.39m, the spectral peak period is 8.18s. The total simulation time is 3600s, and the sampling time interval is 0.01s.

[0104] The lock control algorithm considering control delay in the application shows significant performance improvement in three typical working conditions, in which the capture efficiency is increased by about 15.2%, 7% and 20% compared with the state without control. The results fully show that the algorithm can stably improve the wave energy capture efficiency under different sea conditions, and has good adaptability and robustness.

[0105] It should be pointed out that the above description is not a limitation of the application, and the application is not limited to the above examples. Changes, modifications, additions or substitutions made by ordinary skilled in the art within the essential scope of the application should also be within the protection scope of the application.

Claims

1. A delay compensation control method for a double pendulum wave energy converter, characterized by, Comprising; S1: numerical modeling of the double pendulum wave energy converter and hydrodynamic analysis; S2: establishing time-domain motion equation of the double pendulum wave energy converter considering control delay; S3: establishing state space equation of the double pendulum wave energy converter considering control delay, replacing the convolution term of the time-domain motion equation with the state space equation, and calculating the motion state of the double pendulum wave energy converter; the control delay includes control signal transmission delay and brake execution delay; S4: implementing closed-loop control of the double pendulum wave energy converter considering control delay to maximize the extraction of energy in the wave; The time-domain motion equation established in S2 is: ， ； wherein, and mextand mlnare the mass of the outer and inner oscillators, respectively; mextand mlnare the mass of the outer and inner oscillators, respectively; respectively, are the displacement of the outer oscillator, the displacement of the inner oscillator, the velocity of the outer oscillator, the velocity of the inner oscillator, the acceleration of the outer oscillator and the acceleration of the inner oscillator, respectively; is a pulse response function representing the radiative interaction, is a time variable; respectively, are the viscous damping coefficient, the hydrostatic restoring stiffness, the spring damping coefficient and the spring stiffness coefficient, respectively; is the wave excitation force;△ is the control signal transmission delay; is the control command; is the brake load of the brake, satisfying , is the brake execution delay index, is the brake load coefficient; S4 specifically includes: Defining the Hamilton function for the double pendulum wave energy converter: ; wherein is the equation of motion of the double pendulum wave energy converter, is the motion state of the double pendulum wave energy converter; is a Lagrange multiplier, subject to the control equation T is a terminal time point defined for the control optimization problem; Solving the Hamilton function according to the control equation of Lagrange multiplier, and obtaining the control criterion of the closed-loop control considering the transmission delay of the control signal and the execution delay of the brake according to the solving result , 1 represents locking the double pendulum wave energy conversion device, 0 represents releasing the double pendulum wave energy conversion device; n is the order of the system.

2. The delay compensation control method for a twin-bobber wave energy converter according to claim 1, characterized in that, The space state equation established in S3 is: , ; wherein, , , ; p and q are calculated by least squares: ; wherein, is the radiation damping, is the outer array element angular frequency, is the added mass at infinite frequency; The state-space equations are brought into the time-domain motion equation, and new state variables are defined The time-domain motion equation is transformed into a linear differential equation: ； ； ； Defining the initial condition X(0)=0, solving the linear differential equation by the Runge-Kutta method, and calculating the motion state X of the double pendulum wave energy converter.

3. The delay compensation control method for a twin-bobber wave energy converter according to claim 2, characterized in that, S4 solving the Hamiltonian function comprises: rewriting the Hamiltonian function H as ; Expanding the Hamilton function: ； According to the control equation Solving the Lagrange multiplier: ; ； ； ； ； ； where the Hamiltonian is a linear function of the control commands, which reaches a maximum value when H = 1.

Images