Wave energy extraction power maximization control method based on improved model predictive control

Abstract

The invention discloses a wave energy extraction power maximization control method based on improved model prediction control. The method comprises a wave module, a Kalman filter module, a model prediction control module based on an APO algorithm and a WEC module. An adaptive noise covariance estimation method is introduced into the Kalman filter, and covariance matrixes of process noise and measurement noise are dynamically adjusted to output more accurate wave excitation force. Model prediction is utilized to control MPC online optimization so that the MPC can adapt to changes of system dynamic characteristics, meanwhile, an MPC module calculates optimal sampling time, a prediction time domain and a control time domain at the current moment through an APO algorithm, better control input is generated to be used for adjusting the running state of a wave energy converter WEC, movement of the WEC is matched with waves, and power absorption is maximized. The method has the advantages that the absorption power of the wave energy converter of irregular waves is controlled and maximized by improving the model prediction module, so that the power can be maximized.

Description

Technical Field

[0001] The present invention relates to the technical field of ocean energy development, and in particular to a wave energy extraction power maximization control method based on improved model predictive control. Background Art

[0002] Wave energy is essentially converted from wind energy, which is primarily derived from solar energy. Through this layered energy conversion process, wave energy has become a form of energy with enormous potential. Energy harvesting technology plays a crucial role in its practical utilization. The primary task of a wave energy converter is to maximize the energy extracted from ocean waves. Leveraging wave energy is undoubtedly an excellent way to effectively reduce excessive fossil fuel consumption. However, the greatest challenge in effectively utilizing the extracted wave energy lies in precisely controlling the wave energy converter. Furthermore, it is crucial to ensure optimal performance and minimize the risk of equipment damage.

[0003] Since 2010, various control strategies have been applied to wave energy converters (WECs), primarily aiming to improve their efficiency. These strategies include complex conjugate control (proposed by Fusco and Ringwood in 2013), locking control (proposed by Kara in 2010), and breakaway control (proposed by Schoen in 2011). Comparisons between fuzzy and robust controllers have shown that robust controllers can more effectively minimize the errors caused by unknown parameters and extract more energy than fuzzy controllers. Model predictive control (MPC) is another controller with specific characteristics that makes it highly practical. MPC is an online constrained optimization technique. In addition to using a suitable controller, MPC requires predicting the wave excitation forces. Various techniques have been explored for predicting these forces. Kalman filters, due to their simplicity, robustness, and suitability for real-time implementation, have been used to predict linear and nonlinear systems. They have also been used to predict waves in two-body reflexive devices. Among the fundamental parameters of MPC, prediction horizon, control horizon, and sampling time have a significant impact on controller performance. Therefore, exploring the optimal values ​​of these parameters has become a new idea to further improve controller performance. Summary of the Invention

[0004] Purpose of the invention: In response to the problems existing in the prior art, the present invention discloses a wave energy extraction power maximization control method based on improved model predictive control, which is used to improve the efficiency of searching for the optimal solution under irregular wave conditions.

[0005] Technical solution: The present invention discloses a wave energy extraction power maximization control method based on improved model predictive control, comprising the following steps:

[0006] Step 1: Establish a wave model, use Gaussian white noise w(k) as process noise input to simulate the wave motion state, and add measurement noise v(k) to generate the wave excitation force f ex [k];

[0007] Step 2: Use Kalman filter to make the best estimate of the wave excitation force, filter out the measurement noise interference, and output a more accurate wave excitation force F ex [k];

[0008] Step 3: For the model predictive control MPC, the optimal sampling time Ts, prediction time domain P, and control time domain M at the current moment are calculated by the APO algorithm to obtain the optimized model predictive control MPC;

[0009] Step 4: Using the wave excitation force output in step 2 and the system feedback signal as input, the optimized model predictive control (MPC) is used to predict the optimal control input signal u in the future.

[0010] Step 5: The optimal control signal u output by the optimized model predictive control MPC is added with the external unmeasurable disturbance d to adjust the operating state of the wave energy converter WEC, convert the kinetic energy and potential energy of the wave into electrical energy, and output the estimated value The final system feedback signal y(k) is obtained by superimposing it with the external input electrical noise z(k);

[0011] Step 6: The system feedback signal y(k) output in step 5 is fed back to the model predictive control MPC and compared with the desired set value to form an error signal. The error signal is used by the model predictive control MPC to recalculate the control signal u to form a closed-loop control.

[0012] Furthermore, the wave model adopts an oscillating float structure, including a state space model of the incident wave, a floating body moving in the heave direction of the target water level, and a power take-off device (PTO) responsible for converting the movement of the floating body into electrical energy. The wave model incorporates the natural frequency ω and damping coefficient λ of the wave into state variables for wave prediction. The established wave model sets a discrete state space model of irregular waves:

[0013]

[0014] f ex [k]=[OC F OO]x[k]+v[k] (2)

[0015] Where k represents a discrete time point, represents the state vector at the current moment; x[k+1] is the displacement of the float; u[k+1] is the velocity of the float; C FIs the force-speed conversion coefficient; output matrix [OC F OO] means that only the velocity component of the state vector will pass through C F The coefficient contributes to the output excitation force f ex [k]; v[k] is the measurement noise;

[0016] Based on continuous time, the motion equation of the floating body moving in the heave direction is established:

[0017]

[0018] Among them, M m Represents the mass of the floating body; represents the acceleration of the floating body; x(t) and v1(t) represent the position and velocity of the floating body at the current moment respectively; z(t-τ) is the kernel function, which represents the delayed response of the fluid to the floating body motion; v1(τ) is the floating body velocity at the historical moment, k f is the friction constant used in modeling; k s is the stiffness coefficient; f PTO (t) is the force applied by the power take-off device to the wave energy converter; the wave excitation force f ex (t) is the dynamic force generated by the incident wave acting on the floating body, which is related to the wave surface height η(t) and is a non-causal transfer function.

[0019] Furthermore, the wave excitation force f output by the wave model is ex [k] Use Kalman filter to filter out measurement noise interference and output more accurate wave excitation force F ex [k], as follows:

[0020] Assume that the process noise w(k) and the measurement noise v(k) are Gaussian white noise, the discrete state space model of the incident wave is as described in formula (6) and formula (7), u and f ex [k] is considered as the input of the Kalman filter, which outputs the optimal estimate of the measurement F ex [k], so that F ex [k] is more accurate and input to the MPC module.

[0021] w(k)~N(0,δ) (4)

[0022] v(k)~N(0,μ) (5)

[0023] x(k+1)=Ax(k)+B u u(k)+B w w(k) (6)

[0024] f ex [k]=Cx(k)+v(k) (7)

[0025]

[0026] Where δ is the covariance matrix of process noise, μ is the covariance matrix of measurement noise, A is the state transition matrix, and B u and B w is the control input matrix, C is the output matrix, is the current state estimate.

[0027] Furthermore, an adaptive noise covariance estimation method is introduced into the Kalman filter, which dynamically adjusts the covariance matrices δ and μ of the process noise and the measurement noise, including the following steps:

[0028] Step 2.1: Set the initial δ(0), μ(0) and window length N;

[0029] Step 2.2: Calculate the residual r k and calculate the real-time covariance of the residuals

[0030]

[0031] Among them, the residual r k It represents the difference between the observed value and the filter prediction value, p k is the actual observation value, H is the observation matrix, For the predicted state estimate;

[0032] Step 2.3: Derive the theoretical residual covariance S k And define the minimum actual residual covariance and the theoretical covariance S k The difference is the loss value:

[0033] S k =HP k|k-1 H T +R k (11)

[0034]

[0035] Among them, P k|k-1 is the prediction error covariance matrix, R k is the current measurement noise covariance;

[0036] Step 2.4: Adjust the covariance matrix of process noise and measurement noise by gradient descent method, and update along the negative gradient direction of the objective function:

[0037]

[0038] Where η is the adaptive learning rate;

[0039] Step 2.5: Update the covariance matrices δ and μ, and generate new w(k) and v(k) according to formulas (4) and (5);

[0040] Step 2.6: Repeat steps 2.2 to 2.4 until the loss value stabilizes.

[0041] Furthermore, the model predictive control (MPC) is optimized by the artificial protozoan optimizer algorithm (APO), which adopts an ordinal method to select candidate solutions as reference positions, focusing on the relative order of the index in the population, and selecting each candidate solution as the reference position in sequence; at the same time, it combines the update iteration mechanism based on the fitness value to define the new population and select appropriate and optimized Ts, P and M values.

[0042] Furthermore, the model predictive control (MPC) is optimized by the artificial protozoan optimizer (APO), specifically:

[0043] Step 3.1: First, detect the Ts, P, and M values, randomly sample and initialize them, and set the value X as the initial position;

[0044] Step 3.2: After generating the initial values, the fitness value of each candidate solution will be evaluated;

[0045] Step 3.3: Use the ordinal method to select candidate solutions as reference positions in the search space to provide a reference for subsequent individual updates;

[0046] Step 3.4: Classify the protozoa based on their fitness values ​​to distinguish between better and worse individuals;

[0047] Step 3.5: After classification, determine whether the protozoan's behavior is in a foraging state;

[0048] Step 3.6: When the protozoa is in the foraging state, first determine whether the individual is autotrophic. For autotrophic individuals, the output expression is:

[0049]

[0050] in, and X i represent the updated position and original position of the i-th protozoan, X j represents the randomly selected j-th protozoan, X k- represents a randomly selected protozoan with a ranking index less than i in the kth pair of neighbors; X k+ represents a randomly selected protozoan with a ranking index greater than i among the kth pair of neighbors; in particular, if X i It's X ps , then X k+ Also set to X ps, ps refers to the population size; f represents the foraging factor, np represents the number of neighbor pairs in the external factor, ω a is the weight factor in the autotrophic model, Θ represents the Hadamard product, M f is the mapping vector used for foraging, with a size of 1×dim, where each element is 0 or 1;

[0051] If the individual is not autotrophic, the output expression is:

[0052]

[0053] Among them, X near Indicates a nearby location, X i-k represents the (ik)th protozoan selected from the kth pair of neighbors, with a ranking index of ik; X i+k represents the (i+k)th protozoan selected from the kth pair of neighbors, whose ranking index is i+k; if X i It's X ps , ps refers to the population size, then X i+k Also set to X ps ;ω h is the weight factor under non-autotrophic type;

[0054] When the protozoa is not in the foraging state, it is first determined whether the individual is in a dormant state. The output expression of the dormant individual is:

[0055]

[0056] Among them, X max and X min Represent the upper and lower limit vectors respectively, Rand is a random vector whose elements are in the interval [0,1];

[0057] If the individual is not in a dormant state, its output expression is:

[0058]

[0059] Among them, “±” indicates whether the perturbation is forward or reverse, rand represents a random number in the interval [0,1], and M r Represents the mapping vector in the non-foraging process, with a size of 1×dim, where each element is 0 or 1;

[0060] Step 3.7: Evaluate the newly generated individual and update the individual's status;

[0061] Step 3.8: Update the global optimal solution X ibest ;

[0062] Step 3.9: Determine whether the maximum number of function evaluations has been reached. If not, return to step 3.3. If completed, output the optimized Ts, P, and M values. MPC generates the optimal control input sequence and applies the control signal u to the WEC module.

[0063] Beneficial effects:

[0064] 1. The present invention uses a Kalman filter to filter out measurement noise interference, assuming that process noise and measurement noise are Gaussian noise, to minimize the mean square error of all estimated parameters, and introduces an adaptive noise covariance estimation method to address the problem that noise characteristics in actual systems change with time or environment, thereby improving the robustness of the filter and the accuracy of state estimation.

[0065] 2. The present invention combines the model predictive control system. When the system has multiple outputs and each output has different constraints, the model predictive control (MPC) can take into account the output constraints.

[0066] 3. The present invention uses the APO algorithm and combines it with the model prediction module to optimize the three important parameters: sampling time Ts, prediction time domain P, and control time domain M. It adopts the ordinal method and the update iteration mechanism based on the fitness value to improve the search efficiency and avoid falling into the local optimal solution, thereby improving the performance of WEC under MPC control.

[0067] 4. The APO algorithm can be combined with an adaptive mechanism to improve search efficiency and avoid falling into local optimal solutions. It is mainly suitable for complex, multi-dimensional optimization problems. First, for the sampling time Ts: selecting the Ts value optimized by the APO algorithm allows the controller to frequently update the control signal, which is conducive to ensuring the stability and robustness of the system, while being able to track the set point r faster. Secondly, for the prediction time domain P: selecting the P value optimized by the APO algorithm means that MPC can consider more distant future states, which helps to better handle the dynamic characteristics of the system. Finally, for the control time domain M: selecting the M value optimized by the APO algorithm means that only the input signal within a short time period needs to be adjusted each time, which can speed up the system's response speed and reduce the amount of calculation. The optimized parameters enable MPC to more accurately predict F ex The dynamic characteristics of [k] are optimized to generate a better u, matching the motion of the wave energy converter (WEC) with the waves and maximizing power absorption. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A block diagram of a wave energy extraction power maximization control method based on improved model predictive control according to the present invention;

[0069] Figure 2 This is a block diagram of the model prediction system module and the WEC module of the present invention;

[0070] Figure 3 APO algorithm flow chart of the present invention;

[0071] Figure 4 Schematic diagram of the wave model of the present invention;

[0072] Figure 5 It is the control input signal received by the WEC module in one cycle;

[0073] Figure 6 is the heave displacement trajectory of the WEC at this time in the embodiment of the present invention;

[0074] Figure 7 is the heave speed of the WEC at this time in the embodiment of the present invention;

[0075] Figure 8 is the absorbed power of the WEC module under the action of MPC parameters before APO algorithm optimization;

[0076] Figure 9 The absorbed power of the WEC module under the action of the MPC parameters optimized by the APO algorithm according to the embodiment of the present invention;

[0077] Figure 10 The absorbed energy of the WEC module under different MPC parameters before and after APO algorithm optimization. DETAILED DESCRIPTION

[0078] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0079] The present invention provides a wave energy extraction power maximization control method based on an improved model predictive control, comprising the following steps:

[0080] Step 1: Establish a wave model, use Gaussian white noise w(k) as process noise input to simulate the wave motion state, and add measurement noise v(k) to generate the wave excitation force f ex [k].

[0081] Step 2: Use Kalman filter to make the best estimate of the wave excitation force, filter out the measurement noise interference, and output a more accurate wave excitation force F ex [k].

[0082] Step 3: For the model predictive control MPC, the APO algorithm is used to calculate the optimal sampling time Ts, prediction time domain P, and control time domain M at the current moment to obtain the optimized model predictive control MPC.

[0083] Step 4: Using the wave excitation force output in step 2 and the system feedback signal as input, the optimized model predictive control (MPC) is used to predict the optimal control input signal u in the future.

[0084] Step 5: The optimal control signal u output by the optimized model predictive control MPC is added with the external unmeasurable disturbance d to adjust the operating state of the wave energy converter WEC, convert the kinetic energy and potential energy of the wave into electrical energy, and output the estimated value The final system feedback signal y(k) is obtained by superimposing it with the external input electrical noise z(k).

[0085] Step 6: The system feedback signal y(k) output in step 5 is fed back to the model predictive control MPC and compared with the desired set value to form an error signal. The error signal is used by the model predictive control MPC to recalculate the control signal u to form a closed-loop control.

[0086] in, Figure 4 The wave model in

[15] adopts a traditional oscillating float structure, including a state-space model of the incident wave, a float moving in the heave direction of the target water level, and a power take-off device (PTO) responsible for converting the movement of the float into electrical energy. The wave model incorporates the natural frequency ω and damping coefficient λ of the wave into state variables for wave prediction. The established wave model sets a discrete state-space model for irregular waves:

[0087]

[0088] f ex [k]=[OC F OO]x[k]+v[k] (2)where, represents the state vector at the current moment; v[k+1] is the displacement of the float; u[k+1] is the velocity of the float; C F Is the force-speed conversion coefficient; output matrix [OC F OO] means that only the velocity component of the state vector will pass through C F The coefficient contributes to the output excitation force f ex [k]; v[k] is the measurement noise.

[0089] Based on continuous time, the motion equation of the floating body moving in the heave direction is established:

[0090]

[0091] Among them, M m Represents the mass of the floating body; represents the acceleration of the floating body; x(t) and v1(t) represent the position and velocity of the floating body at the current moment respectively; z(t-τ) is the kernel function, which represents the delayed response of the fluid to the floating body motion; v1(τ) is the floating body velocity at the historical moment, k f is the friction constant used in modeling; k s is the stiffness coefficient; f PTO (t) is the force applied by the power take-off device to the wave energy converter; the wave excitation force f ex (t) is the dynamic force generated by the incident wave acting on the floating body, which is related to the wave surface height η(t) and is a non-causal transfer function.

[0092] The wave excitation force f output by the wave model ex [k] Use Kalman filter to filter out measurement noise interference and output more accurate wave excitation force f ex [k], as follows:

[0093] Assume that the process noise w(k) and the measurement noise v(k) are Gaussian noises, the discrete state space model of the incident wave is as described in formula (6) and formula (7), u and f ex [k] is considered as the input of the Kalman filter, which outputs the optimal estimate of the measurement F ex [k], so that F ex [k] is more accurate and input to the MPC module.

[0094] w(k)~N(0,δ) (4)

[0095] v(k)~N(0,μ) (5)

[0096] x(k+1)=Ax(k)+B u u(k)+B w w(k) (6)

[0097] f ex [k]=Cx(k)+v(k) (7)

[0098]

[0099] Where δ is the covariance matrix of process noise, μ is the covariance matrix of measurement noise, A is the state transition matrix, and B u and B w is the control input matrix, C is the output matrix, is the current state estimate.

[0100] Among them, an adaptive noise covariance estimation method is introduced into the Kalman filter, and the covariance matrices δ and μ of process noise and measurement noise are dynamically adjusted, including the following steps:

[0101] Step 1: Set the initial δ(0), μ(0) and window length N;

[0102] Step 2: Calculate the residual r k and calculate the real-time covariance of the residuals

[0103]

[0104] Among them, the residual r k It represents the difference between the observed value and the filter prediction value, p k is the actual observation value, H is the observation matrix, For the predicted state estimate;

[0105] Step 3: Derive the theoretical residual covariance S k And define the minimum actual residual covariance and the theoretical covariance S k The difference is the loss value:

[0106] S k =HP k|k-1 H T +R k (11)

[0107]

[0108] Among them, P k|k-1 is the prediction error covariance matrix, R k is the current measurement noise covariance;

[0109] Step 4: Adjust the covariance matrix by gradient descent method and update along the negative gradient direction of the objective function:

[0110]

[0111] Where η is the adaptive learning rate;

[0112] Step 5: Update the covariance matrices δ and μ, and generate new w(k) and v(k) according to formulas (4) and (5).

[0113] Step 6: Repeat steps 2.2 to 2.4 until the loss value stabilizes.

[0114] in, Figure 2 The block diagram of MPC implementation is shown. Model Predictive Control (MPC) optimizes the problem through the Artificial Protozoa Optimizer (APO) algorithm. On the one hand, the MPC module receives the F ex[k], and on the other hand, it receives the feedback signal y(k) of the system. Through model predictive control, the behavior of the system in the future is predicted, and the APO algorithm is introduced to calculate the optimal sampling time Ts, prediction time domain P, and control time domain M at the current moment. The APO algorithm can be combined with an adaptive mechanism to improve search efficiency and avoid falling into local optimal solutions. It is mainly suitable for complex, multi-dimensional optimization problems. First, for the sampling time Ts: selecting the Ts value optimized by the APO algorithm allows the controller to frequently update the control signal, which is conducive to ensuring the stability and robustness of the system, while being able to track the set point r faster; secondly, for the prediction time domain P: selecting the P value optimized by the APO algorithm means that MPC can consider more distant future states, which helps to better handle the dynamic characteristics of the system; finally, for the control time domain M: selecting the M value optimized by the APO algorithm means that only the input signal in a short time period needs to be adjusted each time, which can speed up the system's response speed and reduce the amount of calculation. The optimized parameters enable MPC to more accurately predict F ex The dynamic characteristics of [k] are optimized to generate a better u, matching the motion of the wave energy converter (WEC) with the waves and maximizing power absorption.

[0115] Among them, the wave energy extraction power maximization control method based on the improved model predictive control is characterized by the artificial protozoan optimizer algorithm (APO) adopted by the MPC module. This algorithm adopts an ordinal method to select candidate solutions as reference positions. This selection focuses on the relative order of the index in the population, and each candidate solution is selected as the reference position in sequence. At the same time, an update iteration mechanism based on fitness value is combined to define a new population, thereby improving search efficiency and avoiding falling into local optimal solutions, thereby improving the performance of MPC, selecting appropriate and optimized Ts, P and M values, and inputting the optimal solution u into the WEC module. The specific algorithm flow can be expressed as:

[0116] Step 1: First detect the Ts, P and M values, randomly sample and initialize them, and set the value X as the initial position.

[0117] Step 2: After generating the initial values, the fitness value of each candidate solution is evaluated.

[0118] Step 3: Use the ordinal method to select candidate solutions as reference positions in the search space to provide a reference for subsequent individual updates.

[0119] Step 4: Classify the protozoa based on their fitness values ​​to distinguish between better and worse individuals.

[0120] Step 5: After classification, determine whether the protozoan's behavior is in a foraging state.

[0121] Step 6: When the protozoa is in the foraging state, first determine whether the individual is autotrophic. For autotrophic individuals, the output expression is:

[0122]

[0123] in, and X i represent the updated position and original position of the i-th protozoan, X j represents the randomly selected j-th protozoan, X k- represents a randomly selected protozoan with a ranking index less than i in the kth pair of neighbors; X k+ represents a randomly selected protozoan with a ranking index greater than i among the kth pair of neighbors; in particular, if X i It's X ps , then X k+ Also set to X ps , ps refers to the population size; f represents the foraging factor, np represents the number of neighbor pairs in the external factor, ω a is the weight factor in the autotrophic model, Θ represents the Hadamard product, M f is the mapping vector used for foraging, of size 1×dim, where each element is either 0 or 1.

[0124] If the individual is not autotrophic, the output expression is:

[0125]

[0126] Among them, X near Indicates a nearby location, X i-k represents the (ik)th protozoan selected from the kth pair of neighbors, with a ranking index of ik; X i+k represents the (i+k)th protozoan selected from the kth pair of neighbors, whose ranking index is i+k; if X i It's X ps , ps refers to the population size, then X i+k Also set to X ps ;ω h is the weight factor under non-autotrophic type.

[0127] When the protozoa is not in the foraging state, it is first determined whether the individual is in a dormant state. The output expression of the dormant individual is:

[0128]

[0129] Among them, X max and X min Represent the upper and lower limit vectors respectively, Rand is a random vector whose elements are in the interval [0,1];

[0130] If the individual is not in a dormant state, its output expression is:

[0131]

[0132] Among them, “±” indicates whether the perturbation is forward or reverse, rand represents a random number in the interval [0,1], and M r Represents the mapping vector in the non-foraging process, with a size of 1×dim, where each element is 0 or 1.

[0133] Step 7: Evaluate the newly generated individual and update the individual's status.

[0134] Step 8: Update the global optimal solution X ibest .

[0135] Step 9: Determine whether the maximum number of function evaluations has been reached. If not, return to step 3. If completed, output the optimized Ts, P, and M values. MPC generates the optimal control input sequence and applies the control signal u to the WEC module. Under the action of the maximum PTO force, the efficiency of converting wave energy into electrical energy is maximized, and the maximum energy will be transmitted to the grid.

[0136] The following simulation experiment is conducted for the above method. In MATLAB 2024a, the input of the WEC module in one cycle, the operating status of the WEC module in the cycle, the absorbed power and absorbed energy of the WEC module before and after the APO algorithm optimization are shown. The cycle is set to 30s.

[0137] like Figure 5 As shown in Figure 2, the control input signal received by the WEC module in one cycle is shown. Figure 6 The vertical displacement trajectory of WEC at this time is shown. Figure 7 It shows the vertical speed of WEC at this time. Figure 8 The absorbed power of the WEC module under the action of MPC parameters before APO algorithm optimization is shown.

[0138] Figure 9 The absorbed power of the WEC module is shown under the MPC parameters optimized by the APO algorithm. Figure 10 The energy absorption of the WEC module under different MPC parameters before and after APO algorithm optimization is compared. As shown in the figure, the optimized MPC parameters significantly increase the instantaneous power absorption of the WEC module, making the system more efficient in energy absorption. This verifies that the parameter combination optimized by APO balances system response speed and stability, enabling the WEC module to achieve maximum power output within physical constraints.

[0139] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made in accordance with the spirit of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. A wave energy extraction power maximization control method based on improved model predictive control, characterized in that: The following steps are involved: Step 1: Establish a wave model, use Gaussian white noise w(k) as process noise input to simulate the wave motion state, and add measurement noise v(k) to generate the wave excitation force f ex [k]; Step 2: Use Kalman filter to make the best estimate of the wave excitation force, filter out the measurement noise interference, and output a more accurate wave excitation force F ex [k]; Step 3: For the model predictive control MPC, the optimal sampling time Ts, prediction time domain P, and control time domain M at the current moment are calculated by the APO algorithm to obtain the optimized model predictive control MPC; Step 4: Using the wave excitation force output in step 2 and the system feedback signal as input, the optimized model predictive control (MPC) is used to predict the optimal control input signal u in the future. Step 5: The optimal control signal u output by the optimized model predictive control MPC is added with the external unmeasurable disturbance d to adjust the operating state of the wave energy converter WEC, convert the kinetic energy and potential energy of the wave into electrical energy, and output the estimated value The final system feedback signal y(k) is obtained by superimposing it with the external input electrical noise z(k); Step 6: The system feedback signal y(k) output in step 5 is fed back to the model predictive control MPC and compared with the desired set value to form an error signal. The error signal is used by the model predictive control MPC to recalculate the control signal u to form a closed-loop control.

2. The wave energy extraction power maximization control method based on improved model predictive control according to claim 1 is characterized in that: The wave model uses an oscillating float structure, including a state-space model of the incident wave and a float moving in the heave direction of the target water level. The power take-off (PTO) is responsible for converting the movement of the float into electrical energy. The wave model incorporates the natural frequency ω and damping coefficient λ of the wave into state variables for wave prediction. The established wave model sets a discrete state-space model for irregular waves: f ex [k]=[OC F OO]x[k]+v[k] (2) Where k represents a discrete time point, represents the state vector at the current moment; x[k+1] is the displacement of the float; u[k+1] is the velocity of the float; C F Is the force-speed conversion coefficient; output matrix [OC F OO] means that only the velocity component of the state vector will pass through C F The coefficient contributes to the output excitation force f ex [k]; v[k] is the measurement noise; Based on continuous time, the motion equation of the floating body moving in the heave direction is established: Among them, M m Represents the mass of the floating body; represents the acceleration of the floating body; x(t) and v1(t) represent the position and velocity of the floating body at the current moment respectively; z(t-τ) is the kernel function, which represents the delayed response of the fluid to the floating body motion; v1(τ) is the floating body velocity at the historical moment, k f is the friction constant used in modeling; k s is the stiffness coefficient; f PTO (t) is the force applied by the power take-off device to the wave energy converter; the wave excitation force f ex (t) is the dynamic force generated by the incident wave acting on the floating body, which is related to the wave surface height η(t) and is a non-causal transfer function.

3. The wave energy extraction power maximization control method based on improved model predictive control according to claim 1 is characterized in that: The wave excitation force f output by the wave model ex [k] Use Kalman filter to filter out measurement noise interference and output more accurate wave excitation force F ex [k], as follows: Assume that the process noise w(k) and the measurement noise v(k) are Gaussian white noise, the discrete state space model of the incident wave is as described in formula (6) and formula (7), u and f ex [k] is considered as the input of the Kalman filter, which outputs the optimal estimate of the measurement F ex [k], so that F ex [k] is more accurate and input to the MPC module. w(k)~N(0,δ) (4) v(k)~N(0,μ) (5) x(k+1)=Ax(k)+B u u(k)+B w w(k) (6) f ex [k]=Cx(k)+v(k) (7) Where δ is the covariance matrix of process noise, μ is the covariance matrix of measurement noise, A is the state transition matrix, and B u and B w is the control input matrix, C is the output matrix, is the current state estimate.

4. The wave energy extraction power maximization control method based on improved model predictive control according to claim 3 is characterized in that: An adaptive noise covariance estimation method is introduced into the Kalman filter, which dynamically adjusts the covariance matrices δ and μ of process noise and measurement noise, including the following steps: Step 2.1: Set the initial δ(0), μ(0) and window length N; Step 2.2: Calculate the residual r k and calculate the real-time covariance of the residuals Among them, the residual r k It represents the difference between the observed value and the filter prediction value, p k is the actual observation value, H is the observation matrix, For the predicted state estimate; Step 2.3: Derive the theoretical residual covariance S k And define the minimum actual residual covariance and the theoretical covariance S k The difference is the loss value: S k =HP k|k-1 H T +R k (11) Among them, P k|k-1 is the prediction error covariance matrix, R k is the current measurement noise covariance; Step 2.4: Adjust the covariance matrix of process noise and measurement noise by gradient descent method, and update along the negative gradient direction of the objective function: Where η is the adaptive learning rate; Step 2.5: Update the covariance matrices δ and μ, and generate new w(k) and v(k) according to formulas (4) and (5); Step 2.6: Repeat steps 2.2 to 2.4 until the loss value stabilizes.

5. The wave energy extraction power maximization control method based on improved model predictive control according to claim 1 is characterized in that: The model predictive control (MPC) is optimized by the artificial protozoan optimizer algorithm (APO). The ordinal method is used to select candidate solutions as reference positions, focusing on the relative order of the index in the population, and each candidate solution is selected as the reference position in sequence. At the same time, an update iterative mechanism based on fitness value is combined to define a new population and select appropriate and optimized Ts, P and M values.

6. The wave energy extraction power maximization control method based on improved model predictive control according to claim 5 is characterized in that: The model predictive control (MPC) is optimized using the artificial protozoan optimizer (APO) algorithm, specifically: Step 3.1: First, detect the Ts, P, and M values, randomly sample and initialize them, and set the value X as the initial position; Step 3.2: After generating the initial values, the fitness value of each candidate solution will be evaluated; Step 3.3: Use the ordinal method to select candidate solutions as reference positions in the search space to provide a reference for subsequent individual updates; Step 3.4: Classify the protozoa based on their fitness values ​​to distinguish between better and worse individuals; Step 3.5: After classification, determine whether the protozoan's behavior is in a foraging state; Step 3.6: When the protozoa is in the foraging state, first determine whether the individual is autotrophic. For autotrophic individuals, the output expression is: in, and X i represent the updated position and original position of the i-th protozoan, X j represents the randomly selected j-th protozoan, X k- represents a randomly selected protozoan with a ranking index less than i in the kth pair of neighbors; X k+ represents a randomly selected protozoan with a ranking index greater than i among the kth pair of neighbors; in particular, if X i It's X ps , then X k+ Also set to X ps , ps refers to the population size; f represents the foraging factor, np represents the number of neighbor pairs in the external factor, ω a is the weight factor in the autotrophic model, Θ represents the Hadamard product, M f is the mapping vector used for foraging, with a size of 1×dim, where each element is 0 or 1; If the individual is not autotrophic, the output expression is: Among them, X near Indicates a nearby location, X i-k represents the (ik)th protozoan selected from the kth pair of neighbors, with a ranking index of ik; X i+k represents the (i+k)th protozoan selected from the kth pair of neighbors, whose ranking index is i+k; if X i It's X ps , ps refers to the population size, then X i+k Also set to X ps ;ω h is the weight factor under non-autotrophic type; When the protozoa is not in the foraging state, it is first determined whether the individual is in a dormant state. The output expression of the dormant individual is: Among them, X max and X min Represent the upper and lower limit vectors respectively, Rand is a random vector whose elements are in the interval [0,1]; If the individual is not in a dormant state, its output expression is: Among them, "±" indicates whether the perturbation is forward or reverse, rand represents a random number in the interval [0,1], and M r Represents the mapping vector in the non-foraging process, with a size of 1×dim, where each element is 0 or 1; Step 3.7: Evaluate the newly generated individual and update the individual's status; Step 3.8: Update the global optimal solution X ibest ; Step 3.9: Determine whether the maximum number of function evaluations has been reached. If not, return to step 3.

3. If completed, output the optimized Ts, P, and M values. MPC generates the optimal control input sequence and applies the control signal u to the WEC module.

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