Model predictive control method applicable to continuously adjustable damped wave energy devices

Abstract

A model predictive control method applicable to continuously adjustable damped wave energy devices is provided. The predictive control method includes the following steps: S3, analyzing the damping force and current of the continuously adjustable damper, clarifying the constraint boundary of the damping force, and establishing the correlation function between relative velocity, current, and damping force; introducing binary variables to convert the nonlinear constraints of the continuously adjustable damper into a combination of threshold conditions and logic conditions; S3, performing force analysis on the adjustable damped wave energy device and constructing the force dynamic equation of the hybrid logic dynamic system; setting the displacement parameters, velocity parameters, and external wave excitation parameters of the wave energy device as known conditions, and combining them with the system's motion equations to obtain the continuous state-space equation; establishing an objective function to maximize the energy capture efficiency of the wave energy device; updating the state vector of the wave energy device and the external wave excitation parameters at the next time step, constructing an input hybrid system model, and completing the overall model predictive control process.

Description

Technical fields:

[0001] This invention relates to a model predictive control method applicable to continuously adjustable damped wave energy devices. Background technology:

[0002] Wave energy has enormous potential as a renewable energy source, with a theoretical global annual power generation of 32,000 TWh. Developing and utilizing wave energy resources can help reduce carbon dioxide emissions and optimize the energy structure. Control strategies play an important role in improving the technical performance of wave energy devices. Specifically, an energy-maximizing control system can adjust wave energy devices to adapt to different wave conditions.

[0003] Mechanical energy conversion systems have the advantage of high energy conversion efficiency, but wave energy devices with mechanical energy conversion systems are difficult to control. Using a continuously adjustable damper to regulate an oscillating float wave energy device with a mechanical energy conversion system can effectively improve energy capture efficiency.

[0004] The introduction of continuously adjustable dampers leads to nonlinear characteristics in wave energy devices. Due to the change in velocity direction, logical variables are added to the wave energy system, resulting in a mixed state of logical and continuous variables. The constraint boundary also has a significant impact on the energy capture effect of the wave energy device. Therefore, predictive control of the mixed model has been widely used in the energy harvesting process of wave energy devices. Most existing predictive control methods are for linear systems, and the overall control process is too idealized. Control strategies for wave energy systems containing logical and continuous variables are still lacking, resulting in low energy conversion efficiency of wave energy devices and failing to meet the needs of practical applications. Summary of the Invention:

[0005] This invention provides a model predictive control method applicable to continuously adjustable damped wave energy devices. The method is rationally designed and can ensure the safe operation of the wave energy device in harsh marine environments while maintaining the constraints of the adjustable damper. At the same time, it constrains the system under extreme wave conditions, improves the energy conversion efficiency of the wave energy device, enhances the execution capability of the hybrid model predictive controller, and reduces the failure probability of the wave energy device. This improves the feasibility of hybrid model predictive control in the actual operation of wave energy devices. It can adjust the state of the continuously adjustable damper in a timely manner in a dynamically changing wave environment, enabling the device to achieve optimal energy capture effect and solving the problems existing in the prior art.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] A model predictive control method applicable to continuously adjustable damped wave energy devices, the predictive control method comprising the following steps:

[0008] S1, analyze the damping force and current of the continuously adjustable damper, clarify the constraint boundary of the damping force, and establish the correlation function between relative velocity, current and damping force;

[0009] S2, introduces a binary variable to convert the nonlinear constraint of the continuously adjustable damper into a combination of threshold conditions and logic conditions, and converts the combination of threshold conditions and logic conditions into linear constraints involving logic variables. At the same time, introduces an auxiliary continuous variable to convert the linear constraint of the logic variable into an integer linear inequality.

[0010] S3. Perform force analysis on the adjustable damping wave energy device and construct the force dynamic equation of the hybrid logic dynamic system as the discrete state space model of the wave energy device.

[0011] S4, set the displacement parameters, velocity parameters and external wave excitation parameters of the wave energy device as known conditions. The external wave excitation parameters are obtained by prediction. The displacement parameters and velocity parameters constitute the state vector of the wave energy device. Combined with the system's motion equation, the continuous state space equation is obtained.

[0012] S5. Establish the objective function to maximize the energy capture efficiency of the wave energy device, substitute the state vector into the state space model and the objective function, and propagate it in the prediction time domain to obtain the first value of the control force sequence as the optimal control force at the current moment.

[0013] S6. At the next moment, update the state vector of the wave energy device and the external wave excitation parameters, repeat step S5 above, construct the input hybrid system model, and complete the overall model predictive control process.

[0014] The constraint boundary and correlation function of the damping force are expressed as follows:

[0015]

[0016] Where u represents the control force, α and β are constraint boundary coefficients, v represents the relative velocity between the wave energy device's float and buoy, i is the driving current of the continuously adjustable damper, and F d The control force is represented by f, which is a function relating relative velocity, current, and damping force.

[0017] The combination of the threshold condition and the logical condition is:

[0018]

[0019] Among them, conjunctions It means "if and only if";

[0020] The logical variable δ vThe linear constraints are:

[0021]

[0022] Among them, v l and v u ε represents the lower and upper limits of the relative velocity v between the float and the floating body of the wave energy device; ε>0 represents the tolerance, usually computer precision.

[0023] Furthermore, the linear constraint of the damping force can be expressed as:

[0024]

[0025] Among them, z1, z2, and z3 all belong to the set of real numbers, are auxiliary continuous variables, and have constraints:

[0026] z1, z2, z3 > 0

[0027] The general "if-then-else" statement can be expressed as:

[0028] IFδTHEN z=a1x+b1u+f1

[0029] ELSE z=a²x+b²u+f²

[0030] Where δ∈{0,1}, z∈R, u∈R, a1, a2, b1, b2, f1 and f2 are constants with appropriate dimensions;

[0031] The integer linear inequality is:

[0032] (f2-F1)δ+z≤a2x+b2u+c2

[0033] (f1-F2)δ-z≤-a2x-b2u-c2

[0034] (f1-F2)(1-δ)+z≤a1x+b1u+c1

[0035] (f2-F1)(1-δ)-z≤-a1x-b1u-c1

[0036] Among them, f i and F i a i x+b i u+c i The lower and upper bounds of i∈{1,2}.

[0037] The dynamic equation for the force is:

[0038]

[0039] Where "1" and "2" represent the float and the buoy, respectively; m is the mass; x is the displacement relative to the equilibrium position; F exc Represents wave excitation force; F radij F is the radial force exerted on structure i due to the motion of structure j; b For still water restoring force; F pto For PTO force; F u For control;

[0040] The discrete state-space model is as follows:

[0041] p(k+1)=A d p(k)-B du F d (k)+B dδ δ v (k)+B dz z(k)+B de F exc

[0042] E2δ v (k)+E3z(k)≤E1F d (k)+E4p(k)+E5

[0043] Where p∈R is the state vector, F d ∈R is the control input, A d B du and B de B is the discrete system matrix in the discrete state-space equations; dδ and B dz All are zero matrices; E1, E2, E3, E4 and E5 are matrices with appropriate dimensions.

[0044] The wave excitation force includes regular wave excitation force and irregular wave excitation force, wherein the regular wave excitation force is:

[0045]

[0046] Where R represents the real part; H is the wave height; F exc (ω) represents the frequency-dependent complex amplitude of the wave excitation;

[0047] The irregular wave excitation force can be obtained by superimposing regular wave excitations within a certain frequency range, as follows:

[0048]

[0049] Among them, A j For frequency ω j wave amplitude, φ j The initial phase is random, and N is the frequency bandwidth;

[0050] The radiative force is:

[0051]

[0052] Where, μ ij For the added mass at infinite frequency, K rij Let be the radiation impulse response function;

[0053] The convolutional part of the radiative force is expressed in the form of a state-space equation as follows:

[0054]

[0055] Where q is the system's state vector;

[0056] The static water restoring force is:

[0057] F b =-ρgSx=-K H ·x

[0058] Where ρ is the density of seawater, g is the neutral acceleration, S is the seawater contact area of ​​the structure, and K H This is the hydrostatic stiffness coefficient;

[0059] The PTO is a linear mass-spring-damper energy conversion system, and the PTO force is:

[0060]

[0061] Where, m PTO PTO force equivalent mass; c pto For PTO system damping; k PTO For the stiffness of the PTO system.

[0062] The convolutional state space of the radiative force can be represented as:

[0063]

[0064] Among them, F c rad1 and F c rad2 These are the radiating forces acting on the float and the buoy, respectively:

[0065]

[0066] The system's equation of motion is then obtained as follows:

[0067]

[0068] in,

[0069]

[0070] The state vector is represented as:

[0071]

[0072] The continuous state-space equation is:

[0073]

[0074] Discretizing the continuous state-space equations using the zero-order preservation method yields the discrete state-space equations as follows:

[0075] p(k+1)=A d p(k)+B de F exc (k)+B du F u (k)=A d p(k)+B de F exc (k)-B du F d (k)

[0076] The sampling period is T s ;

[0077] in,

[0078] A d =e AT s

[0079]

[0080] The objective function to be maximized is:

[0081]

[0082] Where, N P To optimize the time domain length, the Q matrix is:

[0083] Q = N T N

[0084] N = [0 0 1 -1 0] T ]

[0085] The hybrid system model predictive control can be established as follows:

[0086]

[0087] Where p∈R is the state vector, F d ∈R is the control input, F excLet A be the wave excitation vector. d B du and B de B is the discrete system matrix in the discrete state-space equations; dδ and B dz All are zero matrices; E1, E2, E3, E4 and E5 are matrices with appropriate dimensions.

[0088] The wave energy device includes a ball screw, a screw nut, a gearbox, a generator, a battery pack, a float, a continuously adjustable damper, a float cylinder, a damping plate, an energy conversion system, and a floating body, all arranged in a coordinated manner.

[0089] The energy conversion system includes a ball screw, a screw nut, a gearbox, a generator, and a battery pack. The continuously adjustable damper is installed in parallel with the energy conversion system on the float and the float body. The relative motion between the float and the float body drives the screw nut to move up and down, which in turn drives the rotation of the ball screw. The speed is amplified by the gearbox, which drives the generator to generate electricity and store the electrical energy in the battery pack.

[0090] This invention employs the aforementioned method to analyze the damping force and current of a continuously adjustable damper, clarifying the constraint boundary of the damping force and establishing a correlation function between relative velocity, current, and damping force. By introducing binary variables, the nonlinear constraints of the continuously adjustable damper are transformed into a combination of threshold conditions and logical conditions, which are then converted into linear constraints involving logical variables. Force analysis of the adjustable damped wave energy device is performed to construct the dynamic equations of the hybrid logic dynamic system, serving as the discrete state-space model of the wave energy device. By establishing an objective function to maximize the energy capture efficiency of the wave energy device, the state vector is substituted into the state-space model and the objective function, and propagated within the prediction time domain to obtain the first value of the control force sequence as the optimal control force at the current moment. By improving upon the simple linear model predictive control method by considering the logical state transitions of the system, the execution capability of the hybrid model predictive controller is enhanced, enabling it to handle more complex wave energy devices and offering advantages of precision, efficiency, practicality, and reliability. Attached image description:

[0091] Figure 1 This is a schematic diagram of the wave energy device of the present invention.

[0092] Figure 2 This is a diagram showing the damping force-current relationship of the continuously adjustable damper of the present invention.

[0093] Figure 3 This is a graph showing the average output power in different prediction time domains under irregular waves, as presented in this invention.

[0094] In the diagram, 1. Ball screw; 2. Screw nut; 3. Gearbox; 4. Generator; 5. Battery pack; 6. Float; 7. Continuously adjustable damper; 8. Float; 9. Damping plate; 10. Energy conversion system; 11. Float body. Detailed implementation method:

[0095] To clearly illustrate the technical features of this solution, the invention will be described in detail below through specific implementation methods and in conjunction with the accompanying drawings.

[0096] like Figure 1-3 As shown, a model predictive control method applicable to continuously adjustable damped wave energy devices is described, the predictive control method comprising the following steps:

[0097] S1, analyze the damping force and current of the continuously adjustable damper, clarify the constraint boundary of the damping force, and establish the correlation function between relative velocity, current and damping force;

[0098] S2, introduces a binary variable to convert the nonlinear constraint of the continuously adjustable damper into a combination of threshold conditions and logic conditions, and converts the combination of threshold conditions and logic conditions into linear constraints involving logic variables. At the same time, introduces an auxiliary continuous variable to convert the linear constraint of the logic variable into an integer linear inequality.

[0099] S3. Perform force analysis on the adjustable damping wave energy device and construct the force dynamic equation of the hybrid logic dynamic system as the discrete state space model of the wave energy device.

[0100] S4, set the displacement parameters, velocity parameters and external wave excitation parameters of the wave energy device as known conditions. The external wave excitation parameters are obtained by prediction. The displacement parameters and velocity parameters constitute the state vector of the wave energy device. Combined with the system's motion equation, the continuous state space equation is obtained.

[0101] S5. Establish the objective function to maximize the energy capture efficiency of the wave energy device, substitute the state vector into the state space model and the objective function, and propagate it in the prediction time domain to obtain the first value of the control force sequence as the optimal control force at the current moment.

[0102] S6. At the next moment, update the state vector of the wave energy device and the external wave excitation parameters, repeat step S5 above, construct the input hybrid system model, and complete the overall model predictive control process.

[0103] The constraint boundary and correlation function of the damping force are expressed as follows:

[0104]

[0105] Where u represents the control force, α and β are constraint boundary coefficients, v represents the relative velocity between the wave energy device's float and buoy, i is the driving current of the continuously adjustable damper, and F d The control force is represented by f, which is a function relating relative velocity, current, and damping force.

[0106] The combination of the threshold condition and the logical condition is:

[0107]

[0108] Among them, conjunctions It means "if and only if";

[0109] The logical variable δ v The linear constraints are:

[0110]

[0111] Among them, v l and v u ε represents the lower and upper limits of the relative velocity v between the float and the floating body of the wave energy device; ε>0 represents the tolerance, usually computer precision.

[0112] Furthermore, the linear constraint of the damping force can be expressed as:

[0113]

[0114] Among them, z1, z2, and z3 all belong to the set of real numbers, are auxiliary continuous variables, and have constraints:

[0115] z1, z2, z3 > 0

[0116] The general "if-then-else" statement can be expressed as:

[0117] IFδTHEN z=a1x+b1u+f1

[0118] ELSE z=a²x+b²u+f²

[0119] Where δ∈{0,1}, z∈R, u∈R, a1, a2, b1, b2, f1 and f2 are constants with appropriate dimensions;

[0120] The integer linear inequality is:

[0121] (f2-F1)δ+z≤a2x+b2u+c2

[0122] (f1-F2)δ-z≤-a2x-b2u-c2

[0123] (f1-F2)(1-δ)+z≤a1x+b1u+c1

[0124] (f2-F1)(1-δ)-z≤-a1x-b1u-c1

[0125] Among them, f i and F i a i x+b i u+c i The lower and upper bounds of i∈{1,2}.

[0126] The dynamic equation for the force is:

[0127]

[0128] Where "1" and "2" represent the float and the buoy, respectively; m is the mass; x is the displacement relative to the equilibrium position; F exc Represents wave excitation force; F radij F is the radial force exerted on structure i due to the motion of structure j; b For still water restoring force; F pto For PTO force; F u For control;

[0129] The discrete state-space model is as follows:

[0130] p(k+1)=A d p(k)-B du F d (k)+B dδ δ v (k)+B dz z(k)+B de F exc

[0131] E2δ v (k)+E3z(k)≤E1F d (k)+E4p(k)+E5

[0132] Where p∈R is the state vector, F d ∈R is the control input, A d B du and B de B is the discrete system matrix in the discrete state-space equations; dδ and B dz All are zero matrices; E1, E2, E3, E4 and E5 are matrices with appropriate dimensions.

[0133] The wave excitation force includes regular wave excitation force and irregular wave excitation force, wherein the regular wave excitation force is:

[0134]

[0135] Where R represents the real part; H is the wave height; F exc (ω) represents the frequency-dependent complex amplitude of the wave excitation;

[0136] The irregular wave excitation force can be obtained by superimposing regular wave excitations within a certain frequency range, as follows:

[0137]

[0138] Among them, A j For frequency ω j wave amplitude, φ j The initial phase is random, and N is the frequency bandwidth;

[0139] The radiative force is:

[0140]

[0141] Where, μ ij For the added mass at infinite frequency, K rij Let be the radiation impulse response function;

[0142] The convolutional part of the radiative force is expressed in the form of a state-space equation as follows:

[0143]

[0144] Where q is the system's state vector;

[0145] The static water restoring force is:

[0146] F b =-ρgSx=-K H ·x

[0147] Where ρ is the density of seawater, g is the neutral acceleration, S is the seawater contact area of ​​the structure, and K H This is the hydrostatic stiffness coefficient;

[0148] The PTO is a linear mass-spring-damper energy conversion system, and the PTO force is:

[0149]

[0150] Where, m PTO PTO force equivalent mass; c pto For PTO system damping; k PTO For the stiffness of the PTO system.

[0151] The convolutional state space of the radiative force can be represented as:

[0152]

[0153] Among them, F c rad1 and F c rad2 These are the radiating forces acting on the float and the buoy, respectively:

[0154]

[0155] The system's equations of motion are then obtained as follows:

[0156]

[0157] in,

[0158]

[0159] The state vector is represented as:

[0160]

[0161] The continuous state-space equation is:

[0162]

[0163] Discretizing the continuous state-space equations using the zero-order preservation method yields the discrete state-space equations as follows:

[0164] p(k+1)=A d p(k)+B de F exc (k)+B du F u (k)=A d p(k)+B de F exc (k)-B du F d (k)

[0165] The sampling period is T s ;

[0166] in,

[0167] A d =e AT s

[0168]

[0169] The objective function to be maximized is:

[0170]

[0171] Where, N PTo optimize the time domain length, the Q matrix is:

[0172] Q = N T N

[0173] N = [0 0 1 -1 0] T ]

[0174] The hybrid system model predictive control can be established as follows:

[0175]

[0176] Where p∈R is the state vector, F d ∈R is the control input, F exc Let A be the wave excitation vector. d B du and B de B is the discrete system matrix in the discrete state-space equations; dδ and B dz All are zero matrices; E1, E2, E3, E4 and E5 are matrices with appropriate dimensions.

[0177] The wave energy device includes a ball screw, a screw nut, a gearbox, a generator, a battery pack, a float, a continuously adjustable damper, a float cylinder, a damping plate, an energy conversion system, and a floating body, all arranged in a coordinated manner.

[0178] The energy conversion system includes a ball screw, a screw nut, a gearbox, a generator, and a battery pack. The continuously adjustable damper is installed in parallel with the energy conversion system on the float and the float body. The relative motion between the float and the float body drives the screw nut to move up and down, which in turn drives the rotation of the ball screw. The speed is amplified by the gearbox, which drives the generator to generate electricity and store the electrical energy in the battery pack.

[0179] The working principle of the model predictive control method for continuously adjustable damped wave energy devices in this embodiment of the invention is as follows: Based on multiple computational models and algorithm formulas, it can ensure the safe operation of the wave energy device in harsh marine environments while ensuring the constraints of the adjustable damper. At the same time, it can constrain the system under extreme wave conditions, improve the energy conversion efficiency of the wave energy device, enhance the execution capability of the hybrid model predictive controller, reduce the failure probability of the wave energy device, and thus improve the feasibility of hybrid model predictive control in the actual operation of wave energy devices. It can adjust the state of the continuously adjustable damper in a timely manner in a dynamically changing wave environment, so that the device can achieve the optimal energy capture effect.

[0180] Furthermore, this application can construct a hybrid system model containing logical and continuous variables by analyzing the characteristics of wave energy devices. Under the constraint of the maximum limiting force of the continuously adjustable variable damper, the variable damping control can be used to maximize the energy capture efficiency of the wave energy device. At the same time, a prediction model and energy maximization objective function of the hybrid system wave energy device are constructed, and the dynamic response to complex wave environments can be achieved through the control of the continuously adjustable variable damper.

[0181] In the overall scheme, the predictive control method includes the following steps: analyzing the damping force and current of the continuously adjustable damper, clarifying the constraint boundary of the damping force, and establishing the correlation function between relative velocity, current, and damping force; introducing binary variables to convert the nonlinear constraints of the continuously adjustable damper into a combination of threshold conditions and logic conditions, and converting the combination of threshold conditions and logic conditions into linear constraints involving logic variables, while introducing auxiliary continuous variables to convert the linear constraints of logic variables into integer linear inequalities; performing force analysis on the adjustable damped wave energy device, constructing the force dynamic equation of the hybrid logic dynamic system as the discrete state space model of the wave energy device; and converting the wave energy device... The displacement parameters, velocity parameters, and external wave excitation parameters are set as known conditions. The external wave excitation parameters are obtained through prediction. The displacement parameters and velocity parameters constitute the state vector of the wave energy device. Combined with the system's equation of motion, a continuous state-space equation is obtained. An objective function to maximize the energy capture efficiency of the wave energy device is established. The state vector is substituted into the state-space model and the objective function, and propagated in the prediction time domain to obtain the first value of the control force sequence as the optimal control force at the current moment. At the next moment, the state vector of the wave energy device and the external wave excitation parameters are updated, and the above step S5 is executed again to construct the input hybrid system model and complete the overall model predictive control process.

[0182] Specifically, since the nonlinear damping force depends on the relative velocity and current between the hydraulic cylinder and the piston rod, and can be represented by five straight lines forming a bounded region, the constraint boundary and correlation function of the damping force are expressed as follows:

[0183]

[0184]

[0185] Where u represents the control force, α and β are constraint boundary coefficients, v represents the relative velocity between the wave energy device's float and buoy, i is the driving current of the continuously adjustable damper, and F d The control force is represented by f, which is a function relating relative velocity, current, and damping force.

[0186] Preferably, the combination of threshold condition and logical condition is as follows:

[0187]

[0188] Among them, conjunctions It means "if and only if";

[0189] The logical variable δ v The linear constraints are:

[0190]

[0191] Among them, v l and v u ε represents the lower and upper limits of the relative velocity v between the float and the floating body of the wave energy device; ε>0 represents the tolerance, usually computer precision.

[0192] Furthermore, the linear constraint of the damping force can be expressed as:

[0193]

[0194] Among them, z1, z2, and z3 all belong to the set of real numbers, are auxiliary continuous variables, and have constraints:

[0195] z1, z2, z3 > 0

[0196] The general "if-then-else" statement can be expressed as:

[0197] IFδTHEN z=a1x+b1u+f1

[0198] ELSE z=a²x+b²u+f²

[0199] Where δ∈{0,1}, z∈R, u∈R, a1, a2, b1, b2, f1 and f2 are constants with appropriate dimensions;

[0200] The integer linear inequality is:

[0201] (f2-F1)δ+z≤a2x+b2u+c2

[0202] (f1-F2)δ-z≤-a2x-b2u-c2

[0203] (f1-F2)(1-δ)+z≤a1x+b1u+c1

[0204] (f2-F1)(1-δ)-z≤-a1x-b1u-c1

[0205] Among them, f i and F i a i x+b i u+c iThe lower and upper bounds of i∈{1,2}, each "if-then-else" equation can be transformed into 4 linear inequality constraints, which facilitates data expansion, calculation and summarization.

[0206] Force analysis of the buoy of the wave energy device considers hydrodynamic effects such as hydrostatic restoring force, radiation force, wave excitation force, PTO force, and control force. Using Newton's second law, the dynamic equations of the forces acting on the wave energy device can be obtained as follows:

[0207]

[0208] Where "1" and "2" represent the float and the buoy, respectively; m is the mass; x is the displacement relative to the equilibrium position; F exc Represents wave excitation force; F radij F is the radial force exerted on structure i due to the motion of structure j; b For still water restoring force; F pto For PTO force; F u For control.

[0209] Specifically, the wave excitation force includes regular wave excitation force and irregular wave excitation force, wherein the regular wave excitation force is:

[0210]

[0211] Where R represents the real part; H is the wave height; F exc (ω) represents the frequency-dependent complex amplitude of the wave excitation;

[0212] The irregular wave excitation force can be obtained by superimposing regular wave excitations within a certain frequency range, as follows:

[0213]

[0214] Among them, A j For frequency ω j wave amplitude, φ j The initial phase is random, and N is the frequency bandwidth;

[0215] The radiative force is:

[0216]

[0217] Where, μ ij For the added mass at infinite frequency, K rij Let be the radiation impulse response function;

[0218] The convolutional part of the radiative force is expressed in the form of a state-space equation as follows:

[0219]

[0220] Where q is the system's state vector;

[0221] The static water restoring force is:

[0222] F b =-ρgSx=-K H ·x

[0223] Where ρ is the density of seawater, g is the neutral acceleration, S is the seawater contact area of ​​the structure, and K H This is the hydrostatic stiffness coefficient;

[0224] The PTO is a linear mass-spring-damper energy conversion system, and the PTO force is:

[0225]

[0226] Where, m PTO PTO force equivalent mass; c pto For PTO system damping; k PTO For the stiffness of the PTO system.

[0227] Based on the above calculation results, the discrete state-space model is obtained as follows:

[0228] p(k+1)=A d p(k)-B du F d (k)+B dδ δ v (k)+B dz z(k)+B de F exc

[0229] E2δ v (k)+E3z(k)≤E1F d (k)+E4p(k)+E5

[0230] Where p∈R is the state vector, F d ∈R is the control input, A d B du and B de B is the discrete system matrix in the discrete state-space equations; dδ and B dz All are zero matrices; E1, E2, E3, E4 and E5 are matrices with appropriate dimensions.

[0231] To facilitate calculations and improve accuracy, the radiative force is represented using a convolutional form. The convolutional state space of the radiative force can be represented as:

[0232]

[0233] Among them, F c rad1 and F c rad2 These are the radiating forces acting on the float and the buoy, respectively:

[0234]

[0235] The system's equations of motion are then obtained as follows:

[0236]

[0237] in,

[0238]

[0239] The state vector is represented as:

[0240]

[0241] The continuous state-space equation is:

[0242]

[0243] Discretizing the continuous state-space equations using the zero-order preservation method yields the discrete state-space equations as follows:

[0244] p(k+1)=A d p(k)+B de F exc (k)+B du F u (k)=A d p(k)+B de F exc (k)-B du F d (k)

[0245] The sampling period is T s ;

[0246] in,

[0247] A d =e AT s

[0248]

[0249] Furthermore, the displacement parameters, velocity parameters, and external wave excitation parameters of the wave energy device are set as known conditions. The displacement parameters and velocity parameters are combined to form the state vector of the wave energy device. Through the equation of motion, a continuous state space equation is obtained. Then, an objective function to maximize the energy capture efficiency of the wave energy device is established. The state vector is substituted into the state space model and the objective function to maximize the efficiency. The function is then propagated in the prediction time domain to obtain the first value of the control force sequence as the optimal control force at the current moment.

[0250] To maximize the objective function, specifically:

[0251]

[0252] Where, N P To optimize the time domain length, the Q matrix is:

[0253] Q = N T N

[0254] N = [0 0 1 -1 0] T ]

[0255] The hybrid system model predictive control can be established as follows:

[0256]

[0257] Where p∈R is the state vector, F d ∈R is the control input, F exc Let A be the wave excitation vector. d B du and B de B is the discrete system matrix in the discrete state-space equations; dδ and B dz All are zero matrices; E1, E2, E3, E4 and E5 are matrices with appropriate dimensions.

[0258] Upon reaching the next moment, update the system state of the wave energy device and the external wave excitation sequence, input the hybrid system model, and repeat the above steps.

[0259] In practical use, this invention takes into account the introduction of system logic variables, which enhances the model predictive controller's ability to regulate the system. It can adjust the state of the continuously adjustable damper in a timely manner in a dynamically changing wave environment, so that the system can achieve the optimal energy capture effect.

[0260] Specifically, via appendix Figure 3 The data comparison in the paper can verify the effectiveness of the present invention. It can be seen that under most wave conditions, the predictive control method of the present application can effectively improve the energy capture effect of the wave energy device.

[0261] It should be noted that the wave energy device of this application includes a ball screw, a screw nut, a gearbox, a generator, a battery pack, a float, a continuously adjustable damper, a float cylinder, a damping plate, an energy conversion system, and a float body, which are arranged in a coordinated manner. The energy conversion system includes a ball screw, a screw nut, a gearbox, a generator, and a battery pack. The continuously adjustable damper is installed in parallel with the energy conversion system on the float and the float body. The relative motion between the float and the float body drives the screw nut to move up and down, which drives the rotation of the ball screw. The speed is amplified by the gearbox, which drives the generator to generate electricity and store the electrical energy in the battery pack.

[0262] In summary, the model predictive control method for continuously adjustable damped wave energy devices in this embodiment of the invention is based on multiple computational models and algorithmic formulas. It can ensure the safe operation of wave energy devices in harsh marine environments while guaranteeing the constraints of the adjustable damper. At the same time, it can constrain the system under extreme wave conditions, improve the energy conversion efficiency of wave energy devices, enhance the execution capability of hybrid model predictive controllers, and reduce the failure probability of wave energy devices. This improves the feasibility of hybrid model predictive control in the actual operation of wave energy devices. It can also adjust the state of continuously adjustable dampers in a timely manner in dynamically changing wave environments, enabling the device to achieve optimal energy capture effect.

[0263] The above specific embodiments should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, any alternative improvements or modifications made to the embodiments of the present invention shall fall within the scope of protection of the present invention.

[0264] Any aspects of this invention not described in detail are well-known to those skilled in the art.

Claims

1. A model predictive control method applicable to continuously adjustable damped wave energy devices, characterized in that, The predictive control method Includes the following steps: S1, analyze the damping force and current of the continuously adjustable damper, clarify the constraint boundary of the damping force, and establish the correlation function between relative velocity, current and damping force; S2, introduces a binary variable to convert the nonlinear constraint of the continuously adjustable damper into a combination of threshold conditions and logic conditions, and converts the combination of threshold conditions and logic conditions into linear constraints involving logic variables. At the same time, introduces an auxiliary continuous variable to convert the linear constraint of the logic variable into an integer linear inequality. S3. Perform force analysis on the adjustable damped wave energy device and construct the force dynamic equation of the hybrid logic dynamic system as the discrete state space model of the wave energy device. S4, set the displacement parameters, velocity parameters and external wave excitation parameters of the wave energy device as known conditions. The external wave excitation parameters are obtained by prediction. The displacement parameters and velocity parameters constitute the state vector of the wave energy device. Combined with the system's motion equation, the continuous state space equation is obtained. S5. Establish the objective function to maximize the energy capture efficiency of the wave energy device, substitute the state vector into the state space model and the objective function, and propagate it in the prediction time domain to obtain the first value of the control force sequence as the optimal control force at the current moment. S6. At the next moment, update the state vector of the wave energy device and the external wave excitation parameters, repeat the above step S5, construct the input hybrid system model, and complete the overall model predictive control process. The dynamic equation for the force is: Where "1" and "2" represent the float and the buoy, respectively; m is the mass; x is the displacement relative to the equilibrium position; F exc Represents wave excitation force; F radij F is the radial force exerted on structure i due to the motion of structure j; b For still water restoring force; F pto For PTO force; F u For control; The discrete state-space model is as follows: p(k+1)=A d p(k)-B du F d (k)+B dδ δ v (k)+B dz z(k)+B de F exc E2δ v (k)+E3z(k))≤E1F d (k)+E4p(k)+E5 Where p∈R is the state vector, F d ∈R is the control input, A d B du and B de B is the discrete system matrix in the discrete state-space equations; dδ and B dz All are zero matrices; E1, E2, E3, E4 and E5 are matrices with appropriate dimensions; The objective function to be maximized is: Where, N P To optimize the time domain length, the Q matrix is: Q=N T N N＝[0 0 1 -1 0 T ] The hybrid system model predictive control can be established as follows: Where p∈R is the state vector, F d ∈R is the control input, F exc Let A be the wave excitation vector. d B du and B de B is the discrete system matrix in the discrete state-space equations; dδ and B dz All are zero matrices; E1, E2, E3, E4 and E5 are matrices with appropriate dimensions.

2. The model predictive control method for continuously adjustable damped wave energy devices according to claim 1, characterized in that, The constraint boundary and correlation function of the damping force are expressed as follows: Where u represents the control force, α and β are constraint boundary coefficients, v represents the relative velocity between the wave energy device's float and buoy, i is the driving current of the continuously adjustable damper, and F d The control force is represented by f, which is a function relating relative velocity, current, and damping force.

3. The model predictive control method for continuously adjustable damped wave energy devices according to claim 1, characterized in that, The combination of the threshold condition and the logical condition is: Among them, conjunctions It means "if and only if"; The logical variable δ v The linear constraints are: Among them, v l and v u ε represents the lower and upper limits of the relative velocity v between the float and the floating body of the wave energy device; ε>0 represents the tolerance, usually computer precision. Furthermore, the linear constraint of the damping force can be expressed as: Among them, z1, z2, and z3 all belong to the set of real numbers, are auxiliary continuous variables, and have constraints: z1, z2, z3 > 0 The general "if-then-else" statement can be expressed as: IFδTHEN z=a1x+b1u+f1 ELSE z=a²x+b²u+f² Where δ∈{0,1}, z∈R, u∈R, a1, a2, b1, b2, f1 and f2 are constants with appropriate dimensions; The integer linear inequality is: (f2-F1)δ+z≤a2x+b2u+c2 (f1-F2)δ-z≤-a2x-b2u-c2 (f1-F2)(1-δ)+z≤a1x+b1u+c1 (f2-F1)(1-δ)-z≤-a1x-b1u-c1 Among them, f i and F i a i x+b i u+c i The lower and upper bounds of i∈{1,2}.

4. The model predictive control method for continuously adjustable damped wave energy devices according to claim 1, characterized in that, The wave excitation force includes regular wave excitation force and irregular wave excitation force, wherein the regular wave excitation force is: Where R represents the real part; H is the wave height; F exc (ω) represents the frequency-dependent complex amplitude of the wave excitation; The irregular wave excitation force can be obtained by superimposing regular wave excitations within a certain frequency range, as follows: Among them, A j For frequency ω j wave amplitude, φ j The initial phase is random, and N is the frequency bandwidth; The radiative force is: Where, μ ij For the added mass at infinite frequency, K rij Let be the radiation impulse response function; The convolutional part of the radiative force is expressed in the form of a state-space equation as follows: Where q is the system's state vector; The static water restoring force is: F b =-ρgSx=-K H ·x Where ρ is the density of seawater, g is the neutral acceleration, S is the seawater contact area of ​​the structure, and K H This is the hydrostatic stiffness coefficient; The PTO is a linear mass-spring-damper energy conversion system, and the PTO force is: Where, m PTO PTO force equivalent mass; c pto For PTO system damping; k PTO For the stiffness of the PTO system.

5. The model predictive control method for continuously adjustable damped wave energy devices according to claim 4, characterized in that, The convolutional state space of the radiative force can be represented as: Among them, F c rad1 and F c rad2 These are the radiating forces acting on the float and the buoy, respectively: The system's equation of motion is then obtained as follows: in, The state vector is represented as: The continuous state-space equation is: Discretizing the continuous state-space equations using the zero-order preservation method yields the discrete state-space equations as follows: p(k+1)=A d p(k)+B de F exc (k)+B du F u (k) =A d p(k)+B de F exc (k)-B du F d (k) The sampling period is T s ; in, 6. The model predictive control method for continuously adjustable damped wave energy devices according to claim 1, characterized in that, The wave energy device includes a ball screw, a screw nut, a gearbox, a generator, a battery pack, a float, a continuously adjustable damper, a float cylinder, a damping plate, an energy conversion system, and a floating body, all arranged in a coordinated manner. The energy conversion system includes a ball screw, a screw nut, a gearbox, a generator, and a battery pack. The continuously adjustable damper is installed in parallel with the energy conversion system on the float and the float body. The relative motion between the float and the float body drives the screw nut to move up and down, which in turn drives the rotation of the ball screw. The speed is amplified by the gearbox, which drives the generator to generate electricity and store the electrical energy in the battery pack.

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