A control method for a two-body wave energy conversion device with nonlinear mooring force

Abstract

The present invention belongs to the technical field of marine power generation device control, and specifically discloses a control method for a two-body wave energy conversion device with nonlinear mooring force. The present invention is based on a pre-built two-body wave energy conversion device system, and establishes dynamic models of a float system and a column system respectively, and converts the dynamic models into state space models based on piecewise affine approximation technology; establishes a two-body wave energy conversion system model based on piecewise affine approximation and Markov partitioning rules; combines the state space model of the two-body wave energy conversion device with a state feedback piecewise affine controller to obtain a closed-loop system, and combines the piecewise Lyapunov function to calculate the performance index and controller gain that ensure the random stability of the wave energy conversion closed-loop system, and establishes a state feedback piecewise affine controller of the two-body wave energy conversion device, so as to realize the control of the two-body wave energy conversion device with nonlinear mooring force, and ensure that the closed-loop system has the random stability of performance.

Description

Technical Field

[0001] The invention belongs to the technical field of marine power generation device control, and in particular relates to a control method for a two-body wave energy conversion device with nonlinear mooring force. Background Art

[0002] As a clean energy, ocean energy has stronger advantages of being renewable, recyclable and reusable than coal, oil, and chemicals. Using ocean energy to generate electricity is an important application prospect in the current industrial development. Among them, wave energy conversion devices have received extensive attention and research from academia and industry due to their simple structure and easy maintenance. The working principle of the wave energy conversion device is mainly divided into two steps: first, the kinetic energy of sea waves is captured and converted into mechanical energy to complete the primary conversion; second, the power output device is used to convert the mechanical energy obtained in the primary conversion into electrical energy to complete the secondary conversion. According to the structure and operation mode, wave energy conversion devices can be summarized as overhead type, vibrating body type, point absorption type, oscillation type, etc.

[0003] In a two-body wave energy conversion device, the traditional linear relationship cannot accurately establish the dynamic model of all components. In the complex conduction process, there are quite a lot of nonlinear characteristics, such as the transfer process, conduction between different components, and the mooring force of the fixed device. Therefore, it is essential to study the nonlinear characteristics of the two-body wave energy conversion device, which has attracted great attention in the field of control and modeling. In order to overcome the difficulties brought by nonlinearity to system analysis and control, scholars have proposed some easy-to-handle approximation methods and techniques, such as linear approximation, nonlinear frequency domain method, quantitative measurement method, moment-based method, etc. In particular, a new piecewise affine technique can be used to approximate nonlinear terms more accurately. The nonlinear state space is divided into several sub-partitions by the piecewise affine technique, and the nonlinear terms in each sub-partition are approximated by the corresponding piecewise affine function. The more the piecewise affine partitions are divided, the denser the vertices of all the piecewise affine sub-functions are, and the smoother the trajectory of the piecewise affine function in the entire state space, so the approximation of the nonlinear function is more accurate. Due to its good accuracy, piecewise affine technology has important research value in both theoretical analysis and engineering application fields. However, in practice, there is no effective solution to how to use piecewise affine technology to solve the nonlinear problem of two-body wave energy conversion devices.

[0004] In addition, since the two-body wave energy conversion device can bring huge economic benefits, the research on the stability control of the two-body wave energy conversion device, the optimization control of the conversion process, and the fault-tolerant control to ensure fault operation has also received extensive attention and exploration from academia and industry. On the other hand, since the system state can switch between different piecewise affine partitions, it is necessary to optimize the switching path and process and establish switching rules. However, for the switching process rules, there is currently no effective mathematical representation to define the switching process from the current partition to the next random partition. Therefore, it is necessary to develop a new definition to visualize the switching process between different piecewise affine partitions. Summary of the invention

[0005] The purpose of the present invention is to propose a control method for a two-body wave energy conversion device with nonlinear mooring force, by using the piecewise affine technology to solve the nonlinear problem of the two-body wave energy conversion device, and by mathematically representing the switching rules between different piecewise affine partitions to ensure that the wave energy conversion closed-loop system has Random stability of performance.

[0006] In order to achieve the above object, the present invention adopts the following technical scheme:

[0007] A control method for a two-body wave energy conversion device with nonlinear mooring force is implemented based on a pre-built two-body wave energy conversion device system, wherein the two-body wave energy conversion device system includes a float system, a column system, and a power transmission module;

[0008] The control method of the two-body wave energy conversion device with nonlinear mooring force of the present invention comprises the following steps:

[0009] Step 1. Establish the dynamic models of the float system and the column system respectively, and then transform the established dynamic models into the state space model of the two-body wave energy conversion device based on the piecewise affine approximation technology; by designing a Markov partition rule, establish the two-body wave energy conversion system model based on the piecewise affine approximation and Markov partition rule;

[0010] Step 2. Based on the state space model of the two-body wave energy conversion device and the state feedback piecewise affine controller, the wave energy conversion closed-loop system is obtained, and the piecewise Lyapunov function calculation is combined to ensure the random stability of the wave energy conversion closed-loop system. performance indicators and controller gains, and establish a state feedback piecewise affine controller for a two-body wave energy conversion device;

[0011] Step 3. Use the state feedback piecewise affine controller of the two-body wave energy conversion device to control the two-body wave energy conversion device with nonlinear mooring force, and ensure that the wave energy conversion closed-loop system has Random stability of performance.

[0012] In addition, based on the control method of the two-body wave energy conversion device with nonlinear mooring force, the present invention also proposes a computer device, which includes a memory and one or more processors;

[0013] The memory stores executable codes, and when the processor executes the executable codes, the executable codes are used to implement the control method of the two-body wave energy conversion device with nonlinear mooring force mentioned above.

[0014] In addition, based on the above-mentioned control method of the two-body wave energy conversion device with nonlinear mooring force, the present invention also proposes a computer-readable storage medium on which a program is stored; when the program is executed by the processor, it is used to implement the above-mentioned control method of the two-body wave energy conversion device with nonlinear mooring force.

[0015] The present invention has the following advantages:

[0016] As described above, the present invention relates to a control method for a two-body wave energy conversion device with a nonlinear mooring force. First, the advantage of the good accuracy of the piecewise affine technology is utilized to provide an effective solution for approximating the nonlinear problem of the two-body wave energy conversion device, that is, the piecewise affine approximation technology is used to approximate the nonlinear mooring force in the wave energy conversion system, and the state space of the nonlinear mooring force is divided into a number of piecewise affine sub-partitions. The nonlinear function in each sub-partition is approximated by the corresponding piecewise affine function. The more piecewise affine partitions are divided, the more accurate the approximation of the nonlinear function is; then, in order to describe the system state in different piecewise affine sub-partitions, the nonlinear function is approximated by the corresponding piecewise affine function. The mathematical characteristics of the switching process between segmented affine partitions are studied. A novel segmented affine partition Markov partition rule is proposed in this paper. The process of the system state remaining in the current partition or reaching other partitions at the next moment is described by a class of quantitative probability forms. The switching process from the current partition to the next random partition is defined by an effective mathematical representation, and the switching process between different segmented affine partitions is visualized. Finally, in order to accurately adjust the state of the system in each segmented affine sub-partition, a state feedback segmented affine controller is designed, the segmented Lyapunov function is constructed, and a guarantee is established for the wave energy conversion closed-loop system. Sufficient conditions for the random stability of performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a control method of a two-body wave energy conversion device with nonlinear mooring force in an embodiment of the present invention;

[0018] Figure 2 It is a schematic diagram of the state trajectory of a two-body wave energy conversion device without a controller; Figure 2(a), (b), (c), and (d) represent the states , , , Schematic diagram of the state trajectory;

[0019] Figure 3 It is a schematic diagram of the state trajectory of a two-body wave energy conversion device with piecewise linear control; Figure 3 (a), (b), (c), and (d) represent the states , , , Schematic diagram of the state trajectory;

[0020] Figure 4 It is a schematic diagram of the state trajectory of a two-body wave energy conversion device controlled by piecewise affine; wherein, Figure 4 (a), (b), (c), and (d) represent the states , , , Schematic diagram of the state trajectory;

[0021] Figure 5 Schematic diagram of the change of the state of the two-body wave energy conversion device in different partitions in an embodiment of the present invention;

[0022] Figure 6 In the embodiment of the present invention, Performance indicators and optimal Performance Indicators Schematic diagram;

[0023] Figure 7 Schematic diagram of the structure of a two-body wave energy conversion device with nonlinear mooring force in an embodiment of the present invention. DETAILED DESCRIPTION

[0024] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0025] Example 1

[0026] This embodiment 1 describes a control method for a two-body wave energy conversion device with nonlinear mooring force. The method first converts the dynamic model of the two-body wave energy conversion device into a state space model, and uses the piecewise affine technology to approximate the nonlinear mooring force, and divides the mooring force state space into a number of sub-partitions. The nonlinear function in each sub-partition is approximated by the corresponding piecewise affine function; secondly, a novel Markov partition rule is designed to solve the mathematical representation problem of the switching process of the system state between different piecewise affine partitions; finally, based on the proposed mathematical model, with the help of the piecewise Lyapunov function method and the idea of ​​set, a state feedback piecewise affine controller is designed to achieve the two-body wave energy conversion device within the allowable error range. Control purpose, and calculate to ensure the random stability of the wave energy conversion closed-loop system Performance index: The method of the present invention can ensure that the wave energy conversion closed-loop system achieves random stability under the piecewise affine approximation and Markov partition rule.

[0027] Before introducing the control method of the two-body wave energy conversion device with nonlinear mooring force in the present invention, a two-body wave energy conversion device system is pre-built, which includes a float system, a column system and a power transmission module, such as Figure 7 shown.

[0028] The float system and the column system are connected by a power transmission module, a water tank is connected under the column system, and a mooring device is connected under the water tank. The float system performs vertical mechanical movement with the rise and fall of ocean waves, and the power transmission module converts the mechanical energy generated by the float system into electrical energy and inputs it into the storage unit in the column system. The power transmission module also includes a control unit, which controls the two-body wave energy conversion device. The water tank can not only maintain the vertical shape of the two-body wave energy conversion device, but also provide refrigeration and cooling effects. The mooring device can fix the two-body wave energy conversion device on the seabed to prevent the two-body wave energy conversion device from moving horizontally with the ocean current. In this embodiment, the mooring device is an eight-cable mooring configuration, which is a double-layer structure with four cables allocated to each layer.

[0029] like Figure 1 As shown, a control method for a two-body wave energy conversion device with nonlinear mooring force comprises the following steps:

[0030] Step 1. Establish the dynamic models of the float system and the column system respectively, and then transform the constructed dynamic models into the state space model of the two-body wave energy conversion device based on the piecewise affine approximation technology; by designing a Markov partition rule, establish a two-body wave energy conversion system model based on the piecewise affine approximation and Markov partition rule.

[0031] The established dynamic models of the float system and column system are shown in formula (1):

[0032] (1)

[0033] in, and denote the accelerations of the float and cylinder respectively; and represent the masses of the float and the cylinder respectively; Represents the control input of the power transmission module; and represent the wave excitation forces acting on the float and the column respectively; and denote the radiation forces of the float and the cylinder respectively; and represents the coupled radiation force; represents hydrostatic force; Represents the nonlinear mooring force that fixes the two-body wave energy conversion device to the seabed.

[0034] , , , , , The kinetic equations are expressed as:

[0035] (2)

[0036] in, and Represent the positions of the float and the cylinder respectively; and represent the velocities of the float and cylinder respectively; and denote the additional masses of the float and cylinder at infinite frequency respectively; represents the hydrostatic stiffness; and denote the radiation damping coefficients of the float and cylinder respectively; and Represent the conduction force of the float and the column respectively, based on the principle of fluid mechanics, The existing method uses an eight-cable mooring configuration to construct a nonlinear mooring force The mooring device can effectively anchor the two-body wave energy conversion device to the seabed and avoid translation with the ocean current. Eight cables extend from the mooring device in four directions and are evenly distributed in two groups on two layers at different heights. Represents the stiffness of a single cable; Indicates the length of the cable.

[0037] Nonlinear mooring force It can be approximated by a piecewise affine model:

[0038] (3)

[0039] in, and represents the piecewise affine parameter matrix, and Commonly depends on the change of cable force parameters, Represents a partition index, , represents the set of all piecewise affine partition indices, represents the total number of piecewise affine partition indices that satisfy ,in represents the set of piecewise affine partition indices containing the origin, represents the set of piecewise affine partition indices excluding the origin if , then .

[0040] In order to conduct an in-depth analysis of the two-body wave energy conversion device, it is necessary to establish a continuous time state space model based on piecewise affine approximation. After a simple mathematical transformation, the dynamic model of the float system and the column system described in formula (1), that is, the dynamic model of the two-body wave energy conversion device, is transformed into:

[0041] (4)

[0042] Then we need to eliminate the coupling term and , then equation (4) can be restated as:

[0043] (5)

[0044] in , .

[0045] Next, the state vector is defined as , express dimensional Euclidean space, and represents the initial condition, Represents a column matrix.

[0046] Combining the piecewise affine model given by formula (3) and formula (5), the state space model of the two-body wave energy conversion device based on piecewise affine approximation is expressed as:

[0047] (6)

[0048] in:

[0049] A i ≜ [ 0 1 0 0 − k 1 m e 1 − b 1 m e 1 A 1 2 F i m e 1 m e 2 2 A 1 2 b 2 m e 1 m e 2 2 0 0 0 1 A 2 1 k 1 m e 2 m e 1 1 A 2 1 b 1 m e 2 m e 1 1 − F i m e 2 − b 2 m e 2 ] , a i ≜ [ 0 A 1 2 ψ i m e 1 m e 2 2 0 − ψ i m e 2 ]  =   [ 0 A 1 2 m e 1 m e 2 2 0 − 1 m e 2 ]  ψ ;

[0050] B ≜ [ 0 1 m e 1 + A 1 2 m e 1 m e 2 2 0 − 1 m e 2 − A 2 1 m e 2 m e 1 1 ] ， B 1 ≜   [ 0 1 m e 1 0 − A 2 1 m e 2 m e 1 1 ] ， B 2 ≜ [ 0 − A 1 2 m e 1 m e 2 2 0 1 m e 2 ] ;

[0051] , , , .

[0052] represents the control input, and Wave excitation force and , both are considered as perturbation inputs.

[0053] Then formula (6) is rewritten as:

[0054] (7)

[0055] in, represents the measurement output, , express dimensional Euclidean space; represents the system matrix; where B ¯ ≜ [ B 1       B 2 ] , , .

[0056] Define the partition of a convex polyhedron as ,in and Represents a constant matrix.

[0057] definition Indicates piecewise affine partitioned state spaces, then all piecewise affine partitioned state spaces together constitute , and there is no intersection between the piecewise affine partitioned state spaces.

[0058] In addition, to handle the extra affine terms generated by the piecewise affine approximation technique, use The process combines the ellipsoid outer envelope approximation estimation method. Introducing the ellipsoid approximation set for:

[0059] (8)

[0060] if , , , then:

[0061] ;

[0062] in, and represents a constant, represents a matrix of suitable dimension.

[0063] In order to describe the random switching phenomenon of the state in the wave energy conversion system approximated by the piecewise affine model, a new switching rule based on the Markov process transition probability is constructed as follows:

[0064] (9)

[0065] in, Indicates the transfer process. Indicates piecewise affine partition state space, Represent the system state from piecewise affine partitions Switch to piecewise affine partitioning The transition probability, Indicates an instant in time, and Respectively represent the current moment and the next moment of the state.

[0066] If the current partition index is , then the next partition index may be ;

[0067] If the current partition index is , then the next partition index may be ;

[0068] If the current partition index is , then the next partition index may be .

[0069] Then given the transition probability matrix as follows:

[0070] (10)

[0071] in, , .

[0072] According to the properties of the transition probability matrix, the elements on the diagonal of the matrix represent the probability that the system state will not switch at the next moment, that is, the state is still in the current piecewise affine partition. The other elements represent the probability that the system state switches to other piecewise affine partitions at the next moment.

[0073] Step 2. Based on the state space model of the two-body wave energy conversion device and the state feedback piecewise affine controller, the wave energy conversion closed-loop system is obtained, and the piecewise Lyapunov function calculation is combined to ensure the random stability of the wave energy conversion closed-loop system. Performance indicators and controller gains are used to establish a state feedback piecewise affine controller for a two-body wave energy conversion device.

[0074] In order to ensure the stability of the continuous-time two-body wave energy conversion system based on the piecewise affine model approximation shown in formula (7), the following state feedback piecewise affine controller is designed:

[0075] (11)

[0076] in and denote the state feedback piecewise affine controller gain and affine gain to be calculated, respectively, and .if , then Combining formulas (7) and (11), the following wave energy conversion closed-loop system is obtained:

[0077] (12)

[0078] Considering the continuous-time two-body wave energy conversion system in equation (7) and the state feedback piecewise affine controller in equation (11), if there exists a matrix with suitable dimension , , , and scalar , , , and the following conditions hold:

[0079] (13)

[0080] [ Oh 1 , 1 Oh 1 , 2 e B ¯ ∗ Oh 2 , 2 0 ∗ ∗ − c 2 I c ] < 0 ,  i ∈ I 1 (14)

[0081] in, represents the transpose of a diagonal matrix;

[0082] (15)

[0083] in, and represents a matrix of suitable dimension, represents the identity matrix, Represent the system state from piecewise affine partitions Switch to piecewise affine partitioning The transition probability, , represents the sum of the target object itself and its transpose. Then the wave energy conversion closed-loop system of formula (12) is stochastically stable and satisfies Performance Indicators .

[0084] In addition, the state feedback piecewise affine controller gain is calculated as:

[0085] (16)

[0086] in, ;set up and , construct the following kind of piecewise Lyapunov function:

[0087] (17)

[0088] definition yes The infinitesimal operator of , we get:

[0089] ℒ V ( x ( t ) ) =  l i m D → 0 + 1 D [ E { P r { x ( t + D ) ∈ ℝ j ∣ x ( t ) ∈ ℝ i } x T ( t + D ) P j x ( t + D ) } − x T ( t ) P i x ( t ) ] =  H e { x T ( t ) P i ( A i x ( t ) + a i ) } + x T ( t ) ∑ j ∈ I π i j P j x ( t ) =  x T ( t ) X ^ ¯ i x ( t ) (18)

[0090] in , , , represents the mathematical expectation, Indicates the transfer process. Indicates piecewise affine partitions of the state space.

[0091] X ^ ¯ i = [ H e { P i A i } + ∑ j ∈ I π i j P j P i a i ∗ 0 ] (19)

[0092] To handle the affine terms, use The process is combined with the ellipsoid outer envelope approximation estimation method to obtain:

[0093] (20)

[0094] in:

[0095] P i = [ ℋ i T ℋ i ℋ i T h i ∗ h i T h i − 1 ] (twenty one)

[0096] Given a scalar , ,get:

[0097] (twenty two)

[0098] definition , Denote the minimum lower bound, and we get:

[0099] (twenty three)

[0100] ;

[0101] Further we get:

[0102] E { ∫ 0 ∞ | | x ( t ) | | 2 d t } ≤  − 1 ς X E { ∫ 0 ∞ ℒ V ( x ( t ) ) d t } =  − 1 ς X [ E { l i m t → ∞ V ( x ( t ) ) } − V ( x ( 0 ) ) ] =  1 ς X V ( x ( 0 ) ) < ∞ (twenty four)

[0103] Then we get:

[0104] (25)

[0105] In summary, the two-body wave energy conversion system based on the piecewise affine model approximation in formula (7) is stochastically stable.

[0106] According to the Lyapunov function shown in formula (17), , and infinitesimal operators ,get:

[0107] (26)

[0108] in .

[0109] X ^ i = [ X ^ 1 , 1 P i ( a i + B k i ) P i B ¯ ∗ 0 0 ∗ ∗ 0 ] (27)

[0110] (28)

[0111] By using the congruent transformation, we multiply the left and right sides of formula (27) by and its transpose. By setting and ,get:

[0112] L i = [ L 1 , 1 e a i  i , 2 + e B k i  i , 2 e B ¯ ∗ 0 0 ∗ ∗ 0 ] (29)

[0113] in:

[0114] (30)

[0115] Then we get the following Performance indicator function :

[0116] (31)

[0117] in represents the state of the system when time tends to infinity, represents the system state at time zero, represents the Lyapunov function as time approaches infinity, represents the Lyapunov function at time zero.

[0118] Next, use Affine partitioning , Make an approximation.

[0119] Ellipsoid It is expressed as:

[0120]  i = x T ( t ) [ ℋ i T ℋ i ℋ i T h i ∗ h i T h i − 1 ] x ( t ) = x ^ T ( t ) [ ℋ i T ℋ i ℋ i T h i 0 ∗ h i T h i − 1 0 ∗ ∗ 0 ] x ^ ( t ) (32)

[0121] By combining equations (29) to (32), we get , ,get:

[0122] (33)

[0123] X ˜ i = [ X ˜ 1 , 1 X ˜ 1 , 2 e B ¯ ∗ X ˜ 2 , 2 0 ∗ ∗ − c 2 I ] (34)

[0124] in, express Performance indicators, Represents the identity matrix.

[0125] (35)

[0126] definition , , , if inequality (14) is satisfied, then This means that the wave energy conversion closed-loop system in formula (12) is stochastically stable and satisfies Performance Indicators .

[0127] Furthermore, the state feedback piecewise affine controller gains are calculated as:

[0128] (36)

[0129] Step 3. Use the state feedback piecewise affine controller of the two-body wave energy conversion device to control the two-body wave energy conversion device with nonlinear mooring force, and ensure that the wave energy conversion closed-loop system has Random stability of performance.

[0130] In addition, in order to verify the feasibility of the control method proposed in the present invention, the following specific experiments are also given.

[0131] Table 1 Actual parameters of the two-body wave energy conversion device

[0132]

[0133] The actual parameters of the two-body wave energy conversion device are shown in Table 1. The state space of the two-body wave energy conversion device based on the piecewise affine technology approximation is divided into seven partitions, and its system matrix parameters are as follows:

[0134] A i =  [ 0 1 0 0 − 8 . 4 5 0 3 − 0 . 4 3 6 7  i , ( 2 , 3 ) 0 . 5 2 4 8 0 0 0 1 1 . 0 1 5 4 0 . 0 5 2 5  i , ( 4 , 3 ) − 1 6 . 6 6 1 2 ] ;

[0135] ;

[0136] a 1 = − a 7 [ 0 8 . 6 0 7 0 0 − 2 7 3 . 2 4 3 4 ] ， a 2 = − a 6 [ 0 2 . 6 2 4 1 0 − 8 3 . 3 0 5 9 ]      , a 3 =  − a 5   [ 0 0 . 5 2 4 8 0 − 1 6 . 6 6 1 2 ]     ,  a 4 =   [ 0 0 0 0 ]    ;

[0137] B =   [ 0 9 . 7 8 4 4 × 1 0 − 5 0 − 3 . 4 3 7 2 × 1 0 − 4 ]      , B 1 =     [ 0 8 . 7 3 4 8 × 1 0 − 5 0 − 1 . 0 4 9 6 × 1 0 − 5 ]    ,  B 2 =  [ 0 − 1 . 0 4 9 6 × 1 0 − 5 0 3 . 3 3 2 2 × 1 0 − 4 ] ， C = [ − 1 0 1 0 ] ;

[0138] in , .

[0139] Given the transition probability matrix P = [ π i j ] , The parameters are as follows:

[0140] P = [ 0 . 3 0 . 7 0 0 0 0 0 0 . 1 0 . 4 0 . 5 0 0 0 0 0 0 . 2 0 . 2 0 . 6 0 0 0 0 0 0 . 5 0 . 4 0 . 1 0 0 0 0 0 0 . 6 0 . 2 0 . 2 0 0 0 0 0 0 . 2 0 . 7 0 . 1 0 0 0 0 0 0 . 5 0 . 5 ] .

[0141] set up , in the initial condition Down, Figure 2 to Figure 4 The state trajectories of the two-body wave energy conversion device with no controller, state feedback piecewise linear controller, and state feedback piecewise affine controller are shown respectively.

[0142] in Figure 2 to Figure 4 middle, , , , They all represent state vectors.

[0143] Figure 5 The dynamic changes of the state of the two-body wave energy conversion device switching in different partitions are demonstrated.

[0144] from Figure 2 to Figure 5It can be clearly seen that under the change of partition, the state trajectory of the wave energy conversion open-loop system without a controller is divergent; although the state trajectory of the wave energy conversion closed-loop system can be converged by the state feedback piecewise linear controller, the state There is still a large jitter amplitude. In contrast, all state trajectories of the wave energy conversion closed-loop system using the state feedback piecewise affine controller of the present invention can converge quickly, which shows that the state feedback piecewise affine controller designed by the present invention has better applicability in the two-body wave energy conversion device than the state feedback piecewise linear controller.

[0145] In addition, the state feedback piecewise affine controller gain and , Calculate respectively:

[0146] K 1 =    [ 1 . 3 5 × 1 0 5 − 4 . 7 1 × 1 0 4 1 . 3 7 × 1 0 6 1 . 4 1 × 1 0 5 ] ;

[0147] K 2 =    [ 3 . 3 4 × 1 0 4 1 . 4 1 × 1 0 2 − 4 . 8 1 × 1 0 5 − 2 . 8 1 × 1 0 4 ] ;

[0148] K 3 =    [ 2 . 3 2 × 1 0 4 − 1 . 8 1 × 1 0 3 − 2 . 1 7 × 1 0 5 − 3 . 8 7 × 1 0 4 ] ;

[0149] K 4 =    [ 4 . 7 3 × 1 0 3 − 5 . 2 1 × 1 0 3 − 4 . 3 3 × 1 0 4 − 4 . 6 8 × 1 0 4 ] ;

[0150] K 5 =    [ 2 . 3 3 × 1 0 4 − 1 . 7 9 × 1 0 3 − 2 . 1 7 × 1 0 5 − 3 . 8 6 × 1 0 4 ] ;

[0151] K 6 =    [ 3 . 3 2 × 1 0 4 1 . 3 3 × 1 0 2 − 4 . 8 5 × 1 0 5 − 2 . 8 6 × 1 0 4 ] ;

[0152] K 7 =    [ 1 . 3 8 × 1 0 5 − 4 . 8 8 × 1 0 4 1 . 4 4 × 1 0 6 1 . 4 5 × 1 0 5 ] ;

[0153] ;

[0154] .

[0155] Then given the disturbance input as follows:

[0156] ;

[0157] pass Calculate sixteen sets of actual Performance indicators.

[0158] Figure 6 They showed the actual Performance indicators and optimal Performance Indicators .

[0159] Depend on Figure 6 It can be seen that the control method of the two-body wave energy conversion device with nonlinear mooring force proposed in the present invention has all practical The performance indicators are all less than the optimal value. This verifies the segmented affine Optimality of control schemes for a two-body wave energy conversion device approximated by piecewise affine technique.

[0160] Example 2

[0161] This embodiment 2 describes a computer device, which includes a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it is used to implement the steps of the control method of the two-body wave energy conversion device with nonlinear mooring force in the above embodiment 1.

[0162] In this embodiment, the computer device is any device or apparatus with data processing capability, which will not be described in detail here.

[0163] Example 3

[0164] This embodiment 3 describes a computer-readable storage medium having a program stored thereon, which, when executed by a processor, is used to implement the steps of the control method of the two-body wave energy conversion device with nonlinear mooring force in the above-mentioned embodiment 1.

[0165] The computer-readable storage medium may be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc., equipped on the device.

[0166] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the essential scope of this specification and should be protected by the present invention.

Claims

1. A control method for a two-body wave energy conversion device with nonlinear mooring force, which is implemented based on a pre-built two-body wave energy conversion device system, wherein the two-body wave energy conversion device system includes a float system, a column system, and a power transmission module; characterized in that: The control method of the two-body wave energy conversion device with nonlinear mooring force comprises the following steps: Step 1. Establish the dynamic models of the float system and the column system respectively, and then transform the established dynamic models into the state space model of the two-body wave energy conversion device based on the piecewise affine approximation technology; by designing a Markov partition rule, establish the two-body wave energy conversion system model based on the piecewise affine approximation and Markov partition rule; Step 2. Based on the state space model of the two-body wave energy conversion device and the state feedback piecewise affine controller, the wave energy conversion closed-loop system is obtained, and the H that ensures the random stability of the wave energy conversion closed-loop system is calculated by combining the piecewise Lyapunov function. ∞ performance indicators and controller gains, and establish a state feedback piecewise affine controller for a two-body wave energy conversion device; Step 3. Use the state feedback piecewise affine controller of the two-body wave energy conversion device to control the two-body wave energy conversion device with nonlinear mooring force, and ensure that the wave energy conversion closed-loop system has H ∞ Random stability of performance; In step 1, the dynamic models of the float system and the column system are as follows: in, and They represent the acceleration of the float and the cylinder respectively; m1 and m2 represent the mass of the float and the cylinder respectively; F PTO represents the control input of the power transmission module; F2 and F3 represent the wave excitation forces acting on the float and column respectively; F r1 and F r2 represent the radiation force of the float and the cylinder respectively; F r12 and F r21 represents the coupled radiation force; F h1 represents hydrostatic force; F m represents the nonlinear mooring force that fixes the two-body wave energy conversion device to the seabed; F r1 、F h1 、F r12 、F r2 、F r21 、F m The kinetic equations are expressed as: Among them, x and z represent the positions of the float and the cylinder respectively; and Represent the speed of the float and the cylinder respectively; A 11 and A 22 They represent the additional mass of the float and the column at infinite frequency respectively; k1 represents the hydrostatic stiffness; b1 and b2 represent the radiation damping coefficients of the float and the column respectively; A 12 and A 21 They represent the conduction force of the float and the column respectively. Based on the principle of fluid mechanics, A is obtained 12 ≡A 21 ; K NL Indicates the stiffness of a single cable; L NL Indicates the length of the cable; In step 1, the nonlinear mooring force F m It can be expressed as a piecewise affine model: F m (x)=Φ i x+ψ i ; Among them, Φ i and ψ i represents the piecewise affine parameter matrix, Φ i and ψ i They all depend on the change of the cable force parameters, i represents the partition index, i∈I, represents the set of all piecewise affine partition indices, represents the total number of piecewise affine partition indices and satisfies I = I0 ∪ I1, where I0 represents the set of piecewise affine partition indices containing the origin, and I1 represents the set of piecewise affine partition indices excluding the origin. If i∈I0, then ψ i ≡0; In step 1, the state space model of the two-body wave energy conversion device is: in: χ(t) represents the state vector and satisfies Indicates n χ dimensional Euclidean space; u(t) represents the control input; v(t) and w(t) represent the wave excitation forces F2 and F3 respectively, both of which are regarded as disturbance inputs; y(t) represents the measured output, Indicates n y dimensional Euclidean space; C represents the system matrix; Define the partition of a convex polyhedron as in and l i represents a constant matrix; definition represents the state space of the i-th piecewise affine partition, and all the piecewise affine partition state spaces together constitute And there is no intersection between the piecewise affine partitioned state spaces.

2. The control method of the two-body wave energy conversion device with nonlinear mooring force according to claim 1, characterized in that: In step 1, the switching rule based on the Markov process transition probability is as follows: Among them, Pr{} represents the transfer process, Indicates piecewise affine partition state space, Indicates that the system state switches from piecewise affine partition i to piecewise affine partition The transition probability of , Δ represents the instantaneous moment, χ(t) and χ(t+Δ) represent the current moment and the next moment of the state respectively; If the current partition index is i=1, then the next partition index is If the current partition index is Then the next partition index is If the current partition index is Then the next partition index is The given transition probability matrix Π is as follows: in, 3. The control method of the two-body wave energy conversion device with nonlinear mooring force according to claim 2, characterized in that: In step 2, the state feedback piecewise affine controller is as follows: u(t)=K i x(t)+k i ,i∈I; Among them, K i and κ i represent the state feedback piecewise affine controller gain and affine gain to be calculated respectively; If i∈I0, then κ i ≡0; Combining the state space model of the two-body wave energy conversion device and the state feedback piecewise affine controller, the following wave energy conversion closed-loop system is further obtained:

4. The control method of the two-body wave energy conversion device with nonlinear mooring force according to claim 3 is characterized in that: In step 2, the following piecewise Lyapunov function is constructed: V(x(t))=x T (t)P i x(t),i∈I1; in, ε is a scalar, represents a positive definite symmetric matrix; definition is an infinitesimal operator of {χ(t), t>0}, we get: Among them, E{} represents the mathematical expectation, He{} represents the sum of the target object itself and its transpose, represents the state space of the jth piecewise affine partition, represents a positive definite symmetric matrix; π ij represents the transition probability of the system state switching from piecewise affine partition i to piecewise affine partition j; col{} represents the column matrix; Where * represents the transpose of a diagonal matrix.

5. The control method of the two-body wave energy conversion device with nonlinear mooring force according to claim 4, characterized in that: In step 2, given the scalar λ i <0, i∈I1, we get the following H ∞ Performance indicator function: in, Indicates H ∞ Performance indicator function, Where γ represents H ∞ Performance index, I represents the identity matrix; in, represents the matrix, To handle the extra affine terms produced by the piecewise affine approximation technique, use The process combines the ellipsoid outer envelope approximation estimation method and introduces the ellipsoid approximation set as: if Then we have: Among them, θ and represents a constant, η i represents a matrix; definition Then the calculation formula of the state feedback piecewise affine controller gain is as follows:

6. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, the steps of the control method of the two-body wave energy conversion device with nonlinear mooring force as described in any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps of the control method of a two-body wave energy conversion device with nonlinear mooring force as claimed in any one of claims 1 to 5 are implemented.

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