CN118760027B - A control method for a two-body wave energy conversion device with nonlinear mooring force - Google Patents
A control method for a two-body wave energy conversion device with nonlinear mooring force Download PDFInfo
- Publication number
- CN118760027B CN118760027B CN202411236972.0A CN202411236972A CN118760027B CN 118760027 B CN118760027 B CN 118760027B CN 202411236972 A CN202411236972 A CN 202411236972A CN 118760027 B CN118760027 B CN 118760027B
- Authority
- CN
- China
- Prior art keywords
- energy conversion
- wave energy
- affine
- conversion device
- body wave
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000006243 chemical reaction Methods 0.000 title claims abstract description 118
- 238000000034 method Methods 0.000 title claims abstract description 80
- PXFBZOLANLWPMH-UHFFFAOYSA-N 16-Epiaffinine Natural products C1C(C2=CC=CC=C2N2)=C2C(=O)CC2C(=CC)CN(C)C1C2CO PXFBZOLANLWPMH-UHFFFAOYSA-N 0.000 claims abstract description 107
- 238000005516 engineering process Methods 0.000 claims abstract description 9
- 238000004364 calculation method Methods 0.000 claims abstract description 3
- 238000005192 partition Methods 0.000 claims description 70
- 239000011159 matrix material Substances 0.000 claims description 25
- 230000006870 function Effects 0.000 claims description 24
- 230000008569 process Effects 0.000 claims description 20
- 230000005540 biological transmission Effects 0.000 claims description 9
- 230000007704 transition Effects 0.000 claims description 9
- 230000005855 radiation Effects 0.000 claims description 5
- 230000002706 hydrostatic effect Effects 0.000 claims description 4
- 238000005259 measurement Methods 0.000 claims description 4
- 238000012946 outsourcing Methods 0.000 claims description 4
- 230000008878 coupling Effects 0.000 claims description 3
- 238000010168 coupling process Methods 0.000 claims description 3
- 238000005859 coupling reaction Methods 0.000 claims description 3
- 238000012546 transfer Methods 0.000 claims description 3
- 230000001133 acceleration Effects 0.000 claims description 2
- 238000013016 damping Methods 0.000 claims description 2
- 230000005284 excitation Effects 0.000 claims description 2
- 239000012530 fluid Substances 0.000 claims description 2
- 238000000638 solvent extraction Methods 0.000 abstract description 5
- 238000010248 power generation Methods 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 6
- 230000008901 benefit Effects 0.000 description 4
- 238000012512 characterization method Methods 0.000 description 4
- 230000008859 change Effects 0.000 description 3
- 238000012545 processing Methods 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 3
- 238000004458 analytical method Methods 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 238000010521 absorption reaction Methods 0.000 description 1
- 239000003245 coal Substances 0.000 description 1
- 238000001816 cooling Methods 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000005611 electricity Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000010921 in-depth analysis Methods 0.000 description 1
- 238000012423 maintenance Methods 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 239000003208 petroleum Substances 0.000 description 1
- 238000005057 refrigeration Methods 0.000 description 1
- 239000013535 sea water Substances 0.000 description 1
- 230000006641 stabilisation Effects 0.000 description 1
- 238000011105 stabilization Methods 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
- 238000000844 transformation Methods 0.000 description 1
- 238000013519 translation Methods 0.000 description 1
- 238000012800 visualization Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/04—Programme control other than numerical control, i.e. in sequence controllers or logic controllers
- G05B19/042—Programme control other than numerical control, i.e. in sequence controllers or logic controllers using digital processors
- G05B19/0428—Safety, monitoring
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/20—Pc systems
- G05B2219/24—Pc safety
- G05B2219/24024—Safety, surveillance
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
本发明属于海洋发电装置控制技术领域，具体公开了一种具有非线性系泊力的两体波能转换装置的控制方法。本发明基于预先搭建的两体波能转换装置系统，分别建立浮子系统和柱体系统的动力学模型，基于分段仿射近似技术将动力学模型转化为状态空间模型；建立基于分段仿射近似和Markov分区规则的两体波能转换系统模型；将两体波能转换装置的状态空间模型和状态反馈分段仿射控制器组合得到的闭环系统，结合分段Lyapunov函数计算保证波能转换闭环系统随机稳定的性能指标和控制器增益，建立两体波能转换装置的状态反馈分段仿射控制器，实现对具有非线性系泊力的两体波能转换装置的控制，并保证闭环系统具有性能的随机稳定性。
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 calculation to ensure the random stability of the wave energy conversion closed-loop system The performance index and controller gain are used to establish a state feedback piecewise affine controller for the two-body wave energy conversion device, realize the control of the two-body wave energy conversion device with nonlinear mooring force, and ensure that the closed-loop system has Random stability of performance.
Description
Technical Field
The invention belongs to the technical field of ocean power generation device control, and particularly relates to a control method of a two-body wave energy conversion device with nonlinear mooring force.
Background
The ocean energy is used as a clean energy source, has the advantages of being more renewable, recyclable and reusable than coal, petroleum, chemical industry and the like, and the ocean energy source is used for generating electricity, so that the ocean energy source is an important application prospect in the current industrial development. Among them, the wave energy conversion device has received extensive attention and research in academia and industry because of its simple structure and convenient maintenance. The working principle of the wave energy conversion device mainly comprises the steps of firstly capturing the kinetic energy of sea water waves, converting the kinetic energy into mechanical energy to finish primary conversion, and secondly converting the mechanical energy obtained in the primary conversion into electric energy by utilizing the power output device to finish secondary conversion. The wave energy conversion device can be classified into a top passing type, a vibrating type, a point absorption type, a vibrating type and the like according to the structure and the operation mode.
In a two-body wave energy conversion device, the conventional linear relationship cannot accurately establish a kinetic model of all components. In complex conduction processes there are considerable non-linear features such as the transmission process, conduction between different components, mooring forces of the fastening device, etc. Therefore, it is indispensable to study the nonlinear characteristics of the two-body wave energy conversion device, which has attracted extremely high attention in the field of control and modeling. To overcome the difficulties of non-linearity in system analysis and control, scholars have proposed some approximation methods and techniques that are easy to handle, such as linear approximation, non-linear frequency domain, quantitative measurement, moment-based methods, etc. In particular, a new piecewise affine technique can be used to more accurately approximate nonlinear terms. The nonlinear state space is divided into a plurality of sub-partitions by piecewise affine techniques, and nonlinear terms in each sub-partition are approximated by a corresponding piecewise affine function. The more the piecewise affine partitions are divided, the denser the vertices of all piecewise affine sub-functions are, the smoother the trajectories of the piecewise affine functions in the whole state space are, and therefore the more accurate the approximation of the nonlinear function is. Because of its good precision, the piecewise affine technique has important research value in both theoretical analysis and engineering application fields, however, in practice, how to solve the nonlinear problem of the two-body wave energy conversion device by using the piecewise affine technique has not yet emerged as an effective solution.
In addition, as the two-body wave energy conversion device can bring great economic benefit, the research on the aspects of stability control, optimal control of the conversion process, fault tolerance control for ensuring fault operation and the like of the two-body wave energy conversion device is also widely focused and explored in academia and industry. On the other hand, since the system state can be switched between different piecewise affine partitions, it is necessary to optimize the switching paths and procedures and establish switching rules. However, for the handover procedure rules, no effective mathematical characterization has yet emerged to define the handover procedure 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 segmented affine partitions.
Disclosure of Invention
The invention aims to provide a control method of a two-body wave energy conversion device with nonlinear mooring force, which solves the problem of nonlinearity of the two-body wave energy conversion device by utilizing a piecewise affine technology, and defines switching rules among different piecewise affine partitions by mathematical characterization so as to ensure that a wave energy conversion closed-loop system hasRandom stability of performance.
In order to achieve the above purpose, the invention adopts the following technical scheme:
The control method of the two-body wave energy conversion device with the nonlinear mooring force is realized based on a two-body wave energy conversion device system built in advance, and the two-body wave energy conversion device system comprises a floater system, a cylinder system and a power transmission module;
the invention relates to a control method of a two-body wave energy conversion device with nonlinear mooring force, which comprises the following steps:
Step 1, respectively establishing dynamic models of a float system and a column system, and then converting the established dynamic models into a state space model of a two-body wave energy conversion device based on a piecewise affine approximation technology;
Step 2, obtaining a wave energy conversion closed-loop system based on the combination of a state space model and a state feedback segmented affine controller of the two-body wave energy conversion device, and combining the segmented Lyapunov function to calculate and ensure random stability of the wave energy conversion closed-loop system The performance index and the controller gain establish a state feedback piecewise affine controller of the two-body wave energy conversion device;
step 3, realizing control of the two-body wave energy conversion device with nonlinear mooring force by using a state feedback piecewise affine controller of the two-body wave energy conversion device, and ensuring that a wave energy conversion closed-loop system has Random stability of performance.
In addition, on the basis of the control method of the two-body wave energy conversion device with the nonlinear mooring force, the invention also provides a computer device, which comprises a memory and one or more processors;
the memory stores executable code, and the processor is used for realizing the control method of the two-body wave energy conversion device with the nonlinear mooring force when executing the executable code.
In addition, on the basis of the control method of the two-body wave energy conversion device with the nonlinear mooring force, the invention further provides a computer readable storage medium, wherein a program is stored in the computer readable storage medium, and the program is used for realizing the control method of the two-body wave energy conversion device with the nonlinear mooring force when being executed by a processor.
The invention has the following advantages:
As described above, the present invention provides a control method of a two-body wave energy conversion device with nonlinear mooring force, firstly, utilizing the advantage of piecewise affine technology to have good precision, providing an effective solution for approximating the nonlinear problem of the two-body wave energy conversion device, namely, adopting piecewise affine approximation technology to approximate the nonlinear mooring force in a wave energy conversion system, dividing the state space of the nonlinear mooring force into a plurality of piecewise affine sub-partitions, approximating the nonlinear function in each sub-partition by a corresponding piecewise affine function, the more divided piecewise affine sub-partitions are approximated, the more the approximation of the nonlinear function is accurate, then, in order to describe the mathematical characteristics of the switching process of the system state between different piecewise affine sub-partitions, the present invention provides a novel piecewise affine partition dividing rule, the process of maintaining the system state at the current partition or reaching other partitions at the next moment is described by a certain quantitative probability form, the switching process from the current partition to the next random partition is defined by effective mathematical characterization, the visualization of the switching process between different piecewise affine sub-partitions is realized, finally, the piecewise affine function is adjusted to ensure that the closed-loop affine system has a closed-loop control structure for the precise state of each piecewise affine function is established Adequate conditions for random stability of performance.
Drawings
FIG. 1 is a flow chart of a method of controlling a two-body wave energy conversion device with non-linear mooring force in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram showing the state trace of a two-body wave energy conversion device without a controller, wherein (a), (b), (c) and (d) in FIG. 2 respectively show the states 、、、Is a state trace schematic of (1);
FIG. 3 is a schematic diagram showing the state trace of a piecewise linear controlled two-body wave energy conversion device, wherein (a), (b), (c) and (d) in FIG. 3 respectively show the states 、、、Is a state trace schematic of (1);
FIG. 4 is a schematic diagram showing the state trace of a segmented affine controlled two-body wave energy conversion device, wherein (a), (b), (c) and (d) in FIG. 4 respectively show the states 、、、Is a state trace schematic of (1);
FIG. 5 is a schematic diagram showing the change of the state of the two-body wave energy conversion device in different partitions according to an embodiment of the present invention;
FIG. 6 shows an actual embodiment of the present invention Performance index and optimizationPerformance indexA schematic diagram;
fig. 7 is a schematic structural diagram of a two-body wave energy conversion device with nonlinear mooring force according to an embodiment of the invention.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and detailed description:
Example 1
The embodiment 1 describes a control method of a two-body wave energy conversion device with nonlinear mooring force, which comprises firstly converting a dynamic model of the two-body wave energy conversion device into a state space model, approximating the nonlinear mooring force by a piecewise affine technique, dividing the mooring force state space into a plurality of sub-partitions, approximating the nonlinear function in each sub-partition by a corresponding piecewise affine function, secondly designing a novel Markov partition rule for solving the mathematical characterization problem of the switching process of the system state between different piecewise affine partitions, and finally designing a state feedback piecewise affine controller by means of the piecewise Lyapunov function method and the concept of the set based on the proposed mathematical model to realize the two-body wave energy conversion device within the allowable error rangeControl purpose and calculate to ensure random stabilization of wave energy conversion closed loop systemPerformance index. The method can ensure that the wave energy conversion closed-loop system realizes random stability under the piecewise affine approximation and Markov partition rule.
Before describing the control method of the two-body wave energy conversion device with nonlinear mooring force in the invention, a two-body wave energy conversion device system is built in advance, and the two-body wave energy conversion device system comprises a floater system, a cylinder system and a power transmission module, as shown in fig. 7.
The float system is connected with the column system through a power transmission module, a water tank is connected below the column system, and a mooring device is connected below the water tank. The float system moves vertically along with the fluctuation of ocean waves, and the power transmission module converts mechanical energy generated by the float system into electric energy to be input into the storage unit of the cylinder system. The power transmission module further comprises a control unit, and the control of the two-body wave energy conversion device is realized through the control unit. The water tank not only can keep the vertical form of the two-body wave energy conversion device, but also can provide refrigeration and cooling functions. The mooring device can fix the two-body wave energy conversion device on the sea bottom, and the two-body wave energy conversion device is prevented from horizontally moving along with ocean currents. The mooring device in this embodiment is an eight-cable mooring configuration that is a double-deck structure, with four cables distributed to each deck.
As shown in fig. 1, the control method of the two-body wave energy conversion device with nonlinear mooring force comprises the following steps:
And 1, respectively establishing dynamic models of a float system and a column system, then converting the established dynamic models into a state space model of the two-body wave energy conversion device based on a piecewise affine approximation technology, and establishing the two-body wave energy conversion system model based on the piecewise affine approximation and the Markov partitioning rule by designing a Markov partitioning rule.
The established kinetic models of the float system and the column system are shown in the formula (1):
(1)
Wherein, AndThe accelerations of the float and the cylinder, respectively; And Representing the mass of the float and the cylinder, respectively; a control input representing a power transmission module; And Representing the wave-induced forces acting on the float and the cylinder, respectively; And The radiant forces of the float and cylinder, respectively; And Representing the coupling radiation force; Representing hydrostatic forces; representing the nonlinear mooring forces securing the two-body wave energy conversion device to the sea floor.
、、、、、The kinetic equations of (2) are expressed as:
(2)
Wherein, AndIndicating the positions of the float and the cylinder, respectively; And Indicating the speeds of the float and the cylinder, respectively; And Representing the additional mass of the float and column, respectively, at infinite frequency; Representing the hydrostatic stiffness; And The radiation damping coefficients of the float and the cylinder are respectively represented; And Representing the conductive forces of the float and the cylinder, respectively, based on the principles of fluid mechanics. In the prior method, eight-cable mooring configuration is used to construct nonlinear mooring forceThe mooring device can effectively anchor the two-body wave energy conversion device to the sea floor, avoiding translation with ocean currents. Eight cables extend from the mooring device in four directions and are evenly distributed in two groups on two layers of different heights.Representing the stiffness of a single cable; Indicating the length of the cable.
Nonlinear mooring forceThe approximation with the piecewise affine model is expressed as:
(3)
Wherein, AndRepresenting a matrix of piecewise affine parameters,AndIn common with the variation of the cable force parameter,The index of the partition is represented and,,Representing a set of all segmented affine partition indices,Represents the total number of segmented affine partition indexes and satisfiesWhereinRepresenting a set of segmented affine partition indices containing the origin,Representing a set of segmented affine partition indices that do not contain an origin, ifThen there is。
In order to be able to perform an in-depth analysis of the two-body wave energy conversion device, it is necessary to build a continuous time state space model based on piecewise affine approximation. After simple mathematical transformation, the dynamic model of the float system and the column system described in the formula (1), namely the dynamic model of the two-body wave energy conversion device, is deformed into:
(4)
then the coupling term needs to be eliminated AndEquation (4) is restated as:
(5)
Wherein the method comprises the steps of ,。
Next, define the state vector as,Representation ofA Willide space, andThe initial conditions are indicated to be such that,Representing a column matrix.
The state space model of the two-body wave energy conversion device based on the piecewise affine approximation is expressed as follows in combination with the piecewise affine model given by the formula (3) and the formula (5):
(6)
Wherein:
,;
;
,,,。
the control input is represented as such, AndRespectively represent wave excitation forceAndBoth are considered disturbance inputs.
Then equation (6) is rewritten as:
(7)
Wherein, The measurement output is represented by a representation of the measurement output,,Representation ofA wieuclidean space; representing a system matrix, wherein ,,。
Defining convex polyhedron partitions asWhereinAndRepresenting a constant matrix.
Definition of the definitionRepresent the firstThe state space of each segmented affine partition, then all segmented affine partition state spaces are combinedAnd there is no intersection between the individual piecewise affine partition state spaces.
In addition, to process additional affine terms generated by piecewise affine approximation techniques, use is made ofThe process combines an ellipsoid outsourcing approximate estimation method. Introducing an ellipsoidal approximation setThe method comprises the following steps:
(8)
If it is ,,The following steps are:
;
Wherein, AndThe constant is represented by a value that is a function of,Representing a matrix of suitable dimensions.
In order to describe the random switching phenomenon of states in the wave energy conversion system approximated by the piecewise affine model, a new switching rule based on Markov process transition probability is constructed as follows:
(9)
Wherein, The transfer process is indicated as such,Represent the firstThe state space of the affine partition is segmented,Representing system state slave segment affine partitionsSwitching to segmented affine partitioningIs used for the transition probability of (1),The instant of time is indicated and the time of day,AndThe current time and the next time of the state are represented respectively.
If the current partition index isThen the next partition index may be;
If the current partition index isThen the next partition index may be;
If the current partition index isThen the next partition index may be。
Then giving a transition probability matrixThe following are provided:
(10)
Wherein, ,。
According to the nature of the transition probability matrix, the elements on the diagonal of the matrix represent the probability that the system state does not switch at the next moment, i.e. the state is still in the current piecewise affine partition. Other elements represent the probability of the system state switching to other piecewise affine partitions at the next time.
Step 2, obtaining a wave energy conversion closed-loop system based on the combination of a state space model and a state feedback segmented affine controller of the two-body wave energy conversion device, and combining the segmented Lyapunov function to calculate and ensure random stability of the wave energy conversion closed-loop systemAnd (3) setting up a state feedback piecewise affine controller of the two-body wave energy conversion device by using the performance index and the controller gain.
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 the formula (7), a state feedback piecewise affine controller is designed as follows:
(11)
Wherein the method comprises the steps of AndRepresenting the state feedback segmented affine controller gain and affine gain to be calculated, respectively, and. If it isThen there is. Combining equations (7) and (11) yields the following wave energy conversion closed loop system:
(12)
Considering the continuous-time two-body wave energy conversion system in equation (7) and the state feedback segmented affine controller of equation (11), if a matrix with appropriate dimensions is present 、、,And scalar quantity、,And the following condition holds:
(13)
(14)
Wherein, A transpose item representing a diagonal matrix;
(15)
Wherein, AndRepresenting a matrix having a suitable dimension number,Representing the identity matrix of the cell,Representing system state slave segment affine partitionsSwitching to segmented affine partitioningIs used for the transition probability of (1),,Representing the sum of the target object itself and its transpose. The wave energy conversion closed loop system of equation (12) is randomly stable and satisfiesPerformance index。
Further, the state feedback piecewise affine controller gain is calculated as:
(16)
Wherein, Setting upAndThe following type of piecewise Lyapunov function is constructed:
(17)
Definition of the definition Is thatIs an infinitesimal operator, resulting in:
(18)
Wherein the method comprises the steps of ,,,Representing the mathematical expectation that the data will be,The transfer process is indicated as such,Represent the firstThe state space of the affine partition is segmented.
(19)
To process affine items, by usingThe process is combined with an ellipsoid outsourcing approximate estimation method to obtain:
(20)
Wherein:
(21)
Given scalar quantity ,The method comprises the following steps of:
(22)
Definition of the definition ,Representing the minimum lower bound, yields:
(23)
;
The method further comprises the following steps:
(24)
Then, the following steps are obtained:
(25)
to sum up, the two-body wave energy conversion system based on the piecewise affine model approximation in the formula (7) is randomly stable.
According to the Lyapunov function shown in equation (17),,Sum infinity operatorThe method comprises the following steps of:
(26)
Wherein the method comprises the steps of 。
(27)
(28)
Multiplying the left and right sides of equation (27) by respectively using congruent transformationsAnd its transpose. By setting upAndThe method comprises the following steps of:
(29)
Wherein:
(30)
Then the following is obtained Performance index function:
(31)
Wherein the method comprises the steps ofRepresenting the state of the system when the time goes to infinity,Indicating the state of the system at time zero,Representing the Lyapunov function when time tends to infinity,Representing the Lyapunov function at time zero.
Next, use is made ofAffine partition by combining process with ellipsoid outsourcing approximate estimation method,And performing approximation.
Ellipsoid bodyExpressed as:
(32)
by combining formulas (29) to (32), given ,The method comprises the following steps of:
(33)
(34)
Wherein, Representation ofThe performance index of the product is that,Representing the identity matrix.
(35)
Definition of the definition,,If inequality (14) is satisfied, there isEstablishment indicates that the wave energy conversion closed loop system in equation (12) is randomly stable and satisfiesPerformance index。
Further, the state feedback piecewise affine controller gains are calculated as:
(36)
step 3, realizing control of the two-body wave energy conversion device with nonlinear mooring force by using a state feedback piecewise affine controller of the two-body wave energy conversion device, and ensuring that a wave energy conversion closed-loop system has Random stability of performance.
In addition, in order to verify the feasibility of the control method proposed by the present invention, the following specific experiments are also presented.
Table 1 actual parameters of two-body wave energy conversion device
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 approximated based on the piecewise affine technology is divided into seven partitions, and the system matrix parameters are as follows:
;
;
;
;
Wherein the method comprises the steps of ,。
Given transition probability matrix,The parameters of (2) are as follows:
。
Setting up Under initial conditionsNext, fig. 2 to 4 show the state trajectories of the two-body wave energy conversion device respectively acted on by the no-controller, the state feedback piecewise linear controller, and the state feedback piecewise affine controller.
In which in figures 2 to 4,、、、All representing a state vector.
Fig. 5 shows the dynamic change of the state of the two-body wave energy conversion device in different partition switching.
As can be clearly seen from fig. 2 to 5, the state trace of the wave energy conversion open loop system is divergent without the controller under the change of partition, while the state trace of the wave energy conversion closed loop system can be converged by the state feedback piecewise linear controller, the stateStill a large jitter amplitude exists. In contrast, all state trajectories of the wave energy conversion closed-loop system adopting the state feedback piecewise affine controller can be converged rapidly, which shows that the state feedback piecewise affine controller designed by the invention has better applicability than a state feedback piecewise linear controller in a two-body wave energy conversion device.
Furthermore, state feedback piecewise affine controller gainAnd,And respectively calculating to obtain:
;
;
;
;
;
;
;
;
。
then given disturbance input The following are provided:
;
By passing through Sixteen actual sets of calculationsPerformance index.
FIG. 6 shows the actual results respectivelyPerformance index and optimizationPerformance index。
As can be seen from fig. 6, the control method of the two-body wave energy conversion device with nonlinear mooring force according to the present invention is all practicalThe performance index is less than the optimal value. Thereby verifying the piecewise affine of the inventive designThe control scheme is optimal for the two-body wave energy conversion device based on piecewise affine technology approximation.
Example 2
Embodiment 2 describes a computer device including a memory and one or more processors. The memory stores executable codes, which when executed by the processor, are used to implement the steps of the control method of the two-body wave energy conversion device with nonlinear mooring force in the above-described embodiment 1.
In this embodiment, the computer device is any device or apparatus having data processing capability, which is not described herein.
Example 3
Embodiment 3 describes a computer-readable storage medium having a program stored thereon, which when executed by a processor, is configured to implement the steps of the control method of the two-body wave energy conversion device with nonlinear mooring force in embodiment 1 described above.
The computer readable storage medium may be any internal storage unit of a device or apparatus having data processing capability, such as a hard disk or a memory, or may be any external storage device of a device having data processing capability, such as a plug-in hard disk, a smart memory card (SMART MEDIA CARD, SMC), an SD card, a flash memory card (FLASH CARD), or the like, provided on the device.
The foregoing description is, of course, merely illustrative of preferred embodiments of the present invention, and it should be understood that the present invention is not limited to the above-described embodiments, but is intended to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.
Claims (7)
1. The control method of the two-body wave energy conversion device with the nonlinear mooring force is realized based on a two-body wave energy conversion device system built in advance, and the two-body wave energy conversion device system comprises a floater system, a column system and a power transmission module, and is characterized by comprising the following steps of:
Step 1, respectively establishing dynamic models of a float system and a column system, and then converting the established dynamic models into a state space model of a two-body wave energy conversion device based on a piecewise affine approximation technology;
Step 2, based on a state space model of the two-body wave energy conversion device and a state feedback segmented affine controller, a wave energy conversion closed-loop system is obtained, an H ∞ performance index and a controller gain which ensure random stability of the wave energy conversion closed-loop system are calculated by combining a segmented Lyapunov function, and a state feedback segmented affine controller of the two-body wave energy conversion device is established;
Step 3, utilizing a 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 ensuring that a wave energy conversion closed-loop system has random stability of H ∞ performance;
In the step 1, the dynamic models of the float system and the cylinder system are respectively as follows:
Wherein, AndRespectively, the accelerations of the float and the column, m 1 and m 2 respectively, the masses of the float and the column, F PTO for the control input of the power transmission module, F 2 and F 3 for the wave excitation forces acting on the float and the column, F r1 and F r2 for the radiation forces of the float and the column, F r12 and F r21 for the coupling radiation forces, F h1 for the hydrostatic forces, and F m for the nonlinear mooring forces securing the two-body wave energy conversion device to the sea floor;
The kinetic equation for F r1、Fh1、Fr12、Fr2、Fr21、Fm is expressed as:
wherein x and z represent the positions of the float and cylinder, respectively; And Respectively, the speeds of the float and the column, A 11 and A 22 respectively, the additional mass of the float and the column at infinite frequency, k 1, the hydrostatic stiffness, b 1 and b 2 respectively, the radiation damping coefficient of the float and the column, A 12 and A 21 respectively, the conductivity of the float and the column, A 12≡A21;KNL based on the fluid mechanics principle, the stiffness of a single cable, L NL the length of the cable;
In the step 1, the nonlinear mooring force F m is expressed as a piecewise affine model:
Fm(x)＝Φix+ψi;
where Φ i and ψ i represent a segmented affine parameter matrix, Φ i and ψ i together depend on the variation of the cable force parameters, I represents the partition index, I e I, Representing a set of all segmented affine partition indices,Representing the total number of segmented affine partition indices and satisfying i=i 0∪I1, where I 0 represents the set of segmented affine partition indices containing the origin, I 1 represents the set of segmented affine partition indices not containing the origin, if I e I 0, then there is ψ i ≡0;
In the step 1, the state space model of the two-body wave energy conversion device is as follows:
Wherein:
χ (t) represents a state vector and satisfies Representing n χ -dimensional euclidean space, u (t) representing the control input, v (t) and w (t) representing the wave-induced forces F 2 and F 3, respectively, both being considered disturbance inputs, y (t) representing the measurement output,Represents an n y dimensional Euclidean space;
Defining convex polyhedron partitions as Wherein the method comprises the steps ofAnd l i denotes a constant matrix;
Definition of the definition Representing the state space of the ith piecewise affine partition, all piecewise affine partition state spaces being co-composedAnd the respective piecewise affine partition state spaces do not have any intersection between them.
2. The method for controlling a two-body wave energy conversion device with nonlinear mooring force according to claim 1, wherein in step 1, the switching rule based on Markov process transition probability is as follows:
wherein Pr { } represents the transfer process, Represent the firstThe state space of the affine partition is segmented,Representing a system state switch from segmented affine partition i to segmented affine partitionDelta represents the instant moment, χ (t) and χ (t+delta) represent the current and 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 isThen the next partition index is
If the current partition index isThen the next partition index is
The given transition probability matrix pi is as follows:
Wherein,
3. The method for controlling a two-body wave energy conversion device with nonlinear mooring force according to claim 2, wherein in step 2, the state feedback piecewise affine controller is as follows:
u(t)=Kiχ(t)+κi,i∈I;
Wherein K i and κ i represent the state feedback segmented affine controller gain and affine gain to be calculated, respectively;
If I ε I 0, then there is κ i ≡0;
The state space model and the state feedback piecewise affine controller of the two-body wave energy conversion device are combined to further obtain the following wave energy conversion closed-loop system:
4. a method of controlling a two-body wave energy conversion device with non-linear mooring force according to claim 3, wherein in step 2, the following piecewise Lyapunov function is constructed:
V(χ(t))=χT(t)Piχ(t),i∈I1;
Wherein, Epsilon is a scalar quantity and is,Representing a positive definite symmetry matrix;
Definition of the definition Is an infinitely small operator { χ (t), t >0} resulting in:
where E { } represents a mathematical expectation, he { } represents the sum of the target object itself and its transpose, Representing the state space of the j-th piecewise affine partition,Representing a positive definite symmetry matrix; pi ij represents the transition probability of the system state from segment affine partition i to segment affine partition j;
where x represents the transpose term of the diagonal matrix.
5. The method of controlling a two-body wave energy conversion device with non-linear mooring force according to claim 4, wherein in step 2, given a scalar λ i＜0,i∈I1, the following H ∞ performance index function is obtained:
Wherein, Represents the performance index function of the H ∞,
Wherein, gamma represents H ∞ performance index, I represents identity matrix;
Wherein, The matrix is represented by a representation of the matrix,
To process additional affine terms generated by piecewise affine approximation techniques, use is made ofThe process combines an ellipsoid outsourcing approximate estimation method, and introduces an ellipsoid approximate set as follows:
If it is Then there are:
Wherein θ and Representing a constant, η i representing a matrix;
Definition of the definition 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, the memory having executable code stored therein, wherein the processor, when executing the executable code, performs the steps of the method of controlling a two-body wave energy conversion device with non-linear mooring force as defined in any of claims 1 to 5.
7. A computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of the control method of the two-body wave energy conversion device with nonlinear mooring force as defined in any one of claims 1 to 5.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202411236972.0A CN118760027B (en) | 2024-09-05 | 2024-09-05 | A control method for a two-body wave energy conversion device with nonlinear mooring force |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202411236972.0A CN118760027B (en) | 2024-09-05 | 2024-09-05 | A control method for a two-body wave energy conversion device with nonlinear mooring force |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN118760027A CN118760027A (en) | 2024-10-11 |
| CN118760027B true CN118760027B (en) | 2025-02-07 |
Family
ID=92949433
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202411236972.0A Active CN118760027B (en) | 2024-09-05 | 2024-09-05 | A control method for a two-body wave energy conversion device with nonlinear mooring force |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN118760027B (en) |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110597055A (en) * | 2019-08-05 | 2019-12-20 | 海南师范大学 | Anti-uncertainty 2D piecewise affine batch process min-max optimization predictive control method |
| CN118148819A (en) * | 2024-03-12 | 2024-06-07 | 中国海洋大学 | Wave energy converter control method based on wave prediction |
Family Cites Families (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6714899B2 (en) * | 1998-09-28 | 2004-03-30 | Aspen Technology, Inc. | Robust steady-state target calculation for model predictive control |
| GB2529210B (en) * | 2014-08-13 | 2018-01-31 | Gregory Bruce | Improved wave energy converter |
| CN104921851B (en) * | 2015-05-25 | 2016-09-07 | 河北工业大学 | The kneed forecast Control Algorithm of active above-knee prosthesis |
| CN107423486B (en) * | 2017-06-16 | 2020-09-11 | 哈尔滨工程大学 | Modeling simulation method for floating-in-ship installation operation model in ship-entering stage |
| CN117574599A (en) * | 2023-10-08 | 2024-02-20 | 上海交通大学 | Extreme force prediction method of wave energy generator based on adaptive kernel density estimation |
| CN118244770B (en) * | 2024-05-28 | 2024-08-02 | 山东科技大学 | Repeated learning composite disturbance-resistant error-tolerant control method for unmanned ship |
-
2024
- 2024-09-05 CN CN202411236972.0A patent/CN118760027B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110597055A (en) * | 2019-08-05 | 2019-12-20 | 海南师范大学 | Anti-uncertainty 2D piecewise affine batch process min-max optimization predictive control method |
| CN118148819A (en) * | 2024-03-12 | 2024-06-07 | 中国海洋大学 | Wave energy converter control method based on wave prediction |
Also Published As
| Publication number | Publication date |
|---|---|
| CN118760027A (en) | 2024-10-11 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Clément et al. | Discrete control of resonant wave energy devices | |
| Moarefdoost et al. | Layouts for ocean wave energy farms: Models, properties, and optimization | |
| Parrinello et al. | An adaptive and energy-maximizing control optimization of wave energy converters using an extremum-seeking approach | |
| CN113673076B (en) | Dynamic response solving method suitable for ocean floating structure | |
| Hals | Modelling and phase controlof wave-energy converters | |
| Herber | Dynamic system design optimization of wave energy converters utilizing direct transcription | |
| Sun et al. | High‐performance control for a permanent‐magnet linear synchronous generator using state feedback control scheme plus grey wolf optimisation | |
| Haider et al. | Application of real‐time nonlinear model predictive control for wave energy conversion | |
| Sprague et al. | FAST modular framework for wind turbine simulation: New algorithms and numerical examples | |
| CN110601172B (en) | Multi-direct-current coordination controller design method based on convex polyhedron uncertainty | |
| Teruel et al. | Metrics for wave energy converter hull geometry optimisation | |
| Gunasekaran et al. | Exponential sampled‐data fuzzy stabilization of nonlinear systems and its application to basic buck converters | |
| Haessig et al. | Computing an optimal control policy for an energy storage | |
| Yavuz | On control of a pitching and surging wave energy converter | |
| Wahyudie et al. | Maximising power conversion for heaving point absorbers using a reference‐based control technique | |
| CN118760027B (en) | A control method for a two-body wave energy conversion device with nonlinear mooring force | |
| Tang et al. | Electrical power prediction of proton exchange membrane fuel cell by using support vector regression | |
| Cavaglieri et al. | Model Predictive Control leveraging Ensemble Kalman forecasting for optimal power take-off in wave energy conversion systems | |
| Jia et al. | Data-driven economic MPC of a point absorber wave energy converter | |
| Zhu et al. | Model predictive current control based on hybrid control set for permanent magnet synchronous motor drives | |
| Patel et al. | Optimized cascade fractional‐order 3DOF‐controller for frequency regulation of a hybrid power system using marine predators algorithm | |
| Li et al. | Data‐driven optimal PEMFC temperature control via curriculum guidance strategy‐based large‐scale deep reinforcement learning | |
| Yagi | Matched‐pole–zero discrete‐time model in the state‐space representation | |
| CN114329960B (en) | Feasible domain projection equivalence method and system | |
| Zuo et al. | Fast nonlinear model predictive control parallel design using QPSO and its applications on trajectory tracking of autonomous vehicles |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |