CN113090437B - Direct-drive wave energy power generation maximum wave energy accurate tracking control method based on spring resonance assistance - Google Patents
Direct-drive wave energy power generation maximum wave energy accurate tracking control method based on spring resonance assistance Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
- F03B—MACHINES OR ENGINES FOR LIQUIDS
- F03B13/00—Adaptations of machines or engines for special use; Combinations of machines or engines with driving or driven apparatus; Power stations or aggregates
- F03B13/12—Adaptations of machines or engines for special use; Combinations of machines or engines with driving or driven apparatus; Power stations or aggregates characterised by using wave or tide energy
- F03B13/14—Adaptations of machines or engines for special use; Combinations of machines or engines with driving or driven apparatus; Power stations or aggregates characterised by using wave or tide energy using wave energy
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
- F03B—MACHINES OR ENGINES FOR LIQUIDS
- F03B15/00—Controlling
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
- F05B2220/00—Application
- F05B2220/70—Application in combination with
- F05B2220/706—Application in combination with an electrical generator
- F05B2220/7066—Application in combination with an electrical generator via a direct connection, i.e. a gearless transmission
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- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/30—Energy from the sea, e.g. using wave energy or salinity gradient
Abstract
The invention provides a spring resonance-assisted direct-drive wave energy power generation maximum wave energy accurate tracking control method, which comprises the steps of constructing a mathematical model of a direct-drive wave energy power generation device; designing a mixed limited time tracking control strategy; and (5) performing stability analysis on the designed mixed limited time tracking control strategy. Aiming at the influence of the ocean complex environment on the power generation process, a limited-time disturbance observer is adopted to quickly compensate the environmental disturbance. Aiming at a motor control system, a d-axis current limited time rule and a nonsingular terminal sliding mode q-axis current controller based on a limited time disturbance observer are respectively designed so as to accurately realize resonance between a buoy of the direct-driven wave energy power generation device and waves in a complex environment and achieve maximum wave energy tracking. Simulation studies and comprehensive comparisons show that the proposed hybrid limited time tracking control strategy has significant fast adaptation and accurate maximum wave energy tracking performance in the presence of disturbances and spring resonance assist systems.
Description
Technical Field
The invention relates to the technical field of new energy application, in particular to a direct-drive wave energy power generation maximum wave energy accurate tracking control method based on spring resonance assistance.
Background
On the maximum wave energy tracking control execution device of the direct-driven wave energy power generation device, the wave energy absorption efficiency of the wave energy compensation system in the variable wave environment caused by the seasonality of the same sea area can be effectively improved by taking wave change caused by the seasonality of the seasonality into consideration. In the prior art, an Archimedes direct-drive wave power generation device is designed, and is a special air cylindrical cavity structure, and the gas volume can be changed according to wave pressure when the wave peaks and the wave valleys are in the process of moving along with the waves, so that the adverse effect caused by the large-scale change of the wave frequency can be well adapted. In addition, in the prior art, the designed hydraulic device realizes the latching and releasing of the float motion through a latching control strategy, and realizes the synchronization of the float speed and the wave force. In the control method, in the prior art, model Predictive Control (MPC) is applied to a wave energy power generation device, a controller capable of achieving maximum wave energy capture is designed, and a mathematical model adopted by the scheme can also consider that the actual condition of sea conditions is closer to the actual control effect. The disturbance observation method is applied to the wave power generation device, and the size of the applied step length can be adjusted according to the increase and decrease of the power, so that the maximum power point is achieved.
The tide effect compensation system does not consider the applicability problem of arranging large-span wave frequency changes in the sea area; compared with the change of wave frequency, the Archimedes direct-drive wave energy power generation device has slower air pressure change, is difficult to adapt to the change of large-span waves, and has more complex structure; the latch control strategy depends on the float latch time length, and the point in time of optimal release is not easily estimated accurately.
When the predictive control is applied to the wave power generation device, the dependence on a mathematical model is strong, modeling errors can affect the actual control effect, the kinematics of the PMLG (linear generator) are not taken into consideration, and the final control input is only in the level of the back electromagnetic force. The disturbance observation method is applied to the wave energy power generation device, the step length is not easy to select, the step length is too large to generate oscillation near the maximum power point, the step length is too small, the arrival speed is too slow, and the dynamic performance of the system is affected.
Disclosure of Invention
According to the technical problems, the direct-drive wave energy power generation maximum wave energy accurate tracking control method based on the spring resonance assistance is provided. The invention is mainly used for lifting direct-drive wave energy power generation maximum wave energy accurate tracking control, and a novel spring resonance auxiliary system mechanical device is designed aiming at a direct-drive wave energy power generation Device (DWEC). A control model is established based on a mechanical auxiliary system and a linear generator (PMLG) dynamics model, and a hybrid finite time tracking control (SR-HFTC) strategy is provided on the basis. First, for the influence of the ocean complex environment on the power generation process, a finite time disturbance observer (FDO) is adopted to rapidly compensate the environmental disturbance. Aiming at a motor control system, a d-axis current limited time rule and an FDO-based nonsingular terminal sliding mode (FDO-NTSM) q-axis current controller are respectively designed so as to accurately realize the DWEC buoy and wave resonance under a complex environment and achieve maximum wave energy tracking. Simulation studies and comprehensive comparisons show that the proposed SR-HFTC strategy has significant fast adaptation and accurate maximum wave energy tracking performance in the presence of disturbances and spring resonance assist systems.
The invention adopts the following technical means:
a direct-drive wave energy power generation maximum wave energy accurate tracking control method based on spring resonance assistance comprises the following steps:
s1, constructing a mathematical model of a direct-drive wave energy power generation device;
s2, designing a mixed finite time tracking control strategy;
s3, stability analysis is carried out on the designed mixed limited time tracking control strategy.
Further, the specific implementation method of the step S1 is as follows:
assuming that the direct-drive wave energy power generation device always operates in the vertical direction, under the drive of waves, the permanent magnet and the coil generate relative motion to convert wave mechanical energy into electric energy, and the kinematic equation of the direct-drive wave energy power generation device is as follows:
wherein m represents the mass of the direct-drive wave energy power generation device, x represents the mover displacement of the linear generator in the vertical direction, and f e Representing wave excitation force, f g Representing the back electromagnetic force of a linear generator,
R g representing internal damping, κ of a linear generator 2 Representing the elastic coefficient of the linear generator, f u Representing lumped unknowns, including unmodeled dynamics, uncertainty, turbulence, viscous forces, and friction forces, f r and fb Respectively the radiation force and the static buoyancy of the float,
f b ＝-κ 1 x+mg，m a represents an additional mass, R a Represents external damping, κ 1 ρgs represents the buoyancy coefficient, ρ represents the sea water density, g represents the gravitational acceleration, S represents the contact surface of the float with the wave;
in order to change the natural frequency of the direct-drive wave energy power generation device and adapt to the wave frequency of the laid sea area, a spring resonance auxiliary system is designed, the equivalent is a spring, and the expression is as follows:
f s ＝κ 3 x
the method combines the kinematic equation of the direct-driven wave energy power generation device, the radiation force, the static buoyancy of the floater and the back electromagnetic force of the linear generator to obtain the following components:
wherein m=m+m a Representing the total mass of the direct-drive wave energy power generation device;
calculating the output power of the direct-drive wave energy power generation device, wherein the output power is as follows:
output power P of direct-drive wave energy power generation device g Maximum output, let R a ＝R g ，κ 1 ＝-κ 2 By adjusting the spring constant k 3 ＝ω 2 M realizes the maximum wave energy capture of the direct-drive wave energy power generation device;
the dynamic equation of the direct-drive wave energy power generation device is constructed as follows:
wherein ,id and iq Current components of d and q axes, respectively;
the back electromagnetic force of the generator is expressed as follows:
wherein ,Ld and Lq The inductances of the d and q axes, respectively; from the above equation, the back electromagnetic force f can be changed by changing the current components of the d and q axes g ；
Taking a kinetic equation and a kinematic equation into consideration, constructing a control model of the direct-drive wave power generation device:
wherein ,
further, the specific implementation method of the step S2 is as follows:
s21, designing a finite-time disturbance observer:
assuming that the unknown complex marine disturbance d is continuous and delicate and bounded, i.e
L represents a positive bounded constant and is a finite constant,
the designed finite time disturbance observer is expressed as follows:
wherein ,vb、d and 
are respectively +.>
and />
Observed, sig α (x)＝|x| α sign (x) is a finite time transformation equation;
the following observed errors are defined:
the observed error dynamic equation is:
by selecting a suitable parameter lambda 1 ,λ 2 ,λ 3 And L, tracking error mu 1 ,μ 2 ,μ 3 Is settled to zero for a limited time, and:
s22, designing a d-axis current finite time rule:
according to vector control, a d-axis sliding mode control surface is designed as follows:
s d ＝i d +k id x e
wherein ,kid ＞0，x e ＝x-x d Representing displacement error, x d Representing a reference displacement;
the first derivative of the d-axis sliding mode control surface is calculated as follows:
s23, designing a d-axis voltage control law:
u d ＝L s (-l s i d +γ 2 vi q +k id v e +η 1 sign(s d ))
wherein ,η1 > 0 is the designed positive constant;
s24, designing a q-axis current tracking controller:
in combination with the q-axis current tracking system, the tracking error is defined as:
x e ＝x-x d ,v e ＝v-v d
wherein ,vd Representing a reference speed; the method comprises the following steps:
the current control law of the q axis is designed by adopting a back-stepping method, and is as follows:
then an error dynamic equation is derived as follows:
wherein ,
the q-axis nonsingular terminal sliding die surface is designed as follows:
wherein, beta is more than 0,1 is more than p/q is less than 2, and the beta is a designed normal number;
considering a q-axis current tracking system and a nonsingular terminal sliding mode surface, designing a q-axis voltage control law, and designing as follows:
further, the specific implementation method of the step S3 is as follows:
s31, assuming that the mixed limited time tracking control strategy meets the control model of the direct-drive wave power generation device, under the action of a disturbance observer and a control law, the lumped unknown disturbance of the direct-drive wave power generation device is observed in a limited time, and meanwhile, an error signal x is obtained e ,v e ,l qe Is stabilized to zero, and the actual state controller tracks the upper expected value;
s32, proving that the d-axis current converges to the sliding mode surface within a limited time, and gradually and stably converges to zero after the displacement, the speed tracking error and the q-axis current tracking error reach the designed nonsingular terminal sliding mode surface.
Further, the specific implementation method of the step S32 is as follows:
the first step: for the d-axis current tracking control subsystem, the following Lyapunov function is selected:
deriving the above method to obtain:
substituting the voltage control law into the above formula to obtain:
conclusion: the tracking error of the d-axis current tracking system converges to zero in a finite time;
and a second step of: for a q-axis current tracking system, the following Lyapunov function is established:
deriving the above method to obtain:
substituting the control law and the disturbance observation result into the above formula to obtain:
and a third step of: considering the maximum wave energy tracking control system of the whole direct-driven wave energy power generation device, designing a Lyapunov function:
V＝V d +V q
combining a disturbance observer and a control law to obtain:
thus, V (x) e (0),v e (0) Is bounded, V (x) e (t),v e (t)) is a non-increasing bounded function, then there are:
thus, the first and second substrates are bonded together,
is continuous all the time, guaranteed by selecting the appropriate parameters +.>
According to Lyapunov stability theory and Barbalat theorem, when t → infinity, x e and ve And the closed-loop direct-drive wave energy power generation device converges to zero, and the whole closed-loop direct-drive wave energy power generation device is gradually stable under the mixed limited time tracking control strategy.
Compared with the prior art, the invention has the following advantages:
1. the invention designs a novel spring resonance auxiliary system mechanical device aiming at a direct-driven wave energy power generation Device (DWEC). A control model is established based on a mechanical auxiliary system and a linear generator (PMLG) dynamic model, and resonance of the direct-driven wave energy power generation device under the regular change sea area caused by the monsoon is achieved through designing a spring coaxial with the rotor.
2. The invention provides a direct-drive wave energy power generation maximum wave energy accurate tracking control method based on spring resonance assistance, which is used for realizing tracking control of a closed loop system by respectively applying a finite time rule device and a nonsingular terminal sliding mode control (FDO-NTSM) device based on disturbance observation. The problem of maximum wave energy tracking control of a direct-driven wave energy power generation Device (DWEC) under the disturbed arrangement sea area is solved, and tracking of reference displacement and speed is realized.
Based on the reasons, the invention can be widely popularized in the fields of new energy application and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to the drawings without inventive effort to a person skilled in the art.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic structural diagram of a direct-drive wave energy power generation device according to an embodiment of the present invention.
Fig. 3 is a phase-contrast diagram of the speed and wave excitation force of the direct-drive wave power generation device according to the embodiment of the invention.
Fig. 4 is a diagram of an observation result of disturbance of the direct-drive wave power generation device according to the embodiment of the present invention.
Fig. 5 is a graph of displacement and velocity tracking results and error results of a direct-drive wave power generation device according to an embodiment of the present invention.
Fig. 6 is a graph of current tracking and tracking error results of a direct-drive wave power generation device according to an embodiment of the present invention.
Detailed Description
In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and the claims of the present invention and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the invention described herein may be implemented in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
As shown in fig. 1, the invention provides a direct-drive wave energy power generation maximum wave energy accurate tracking control method based on spring resonance assistance, which comprises the following steps:
s1, constructing a mathematical model of a direct-drive wave energy power generation device;
in specific implementation, as a preferred embodiment of the present invention, in this embodiment, as shown in fig. 2, the direct-drive wave power generation device is composed of four main parts, namely a floater, a permanent magnet linear generator, a spring resonance auxiliary system and a back-end control circuit, wherein the floater is directly connected with a permanent magnet of the Permanent Magnet Linear Generator (PMLG), and the spring resonance auxiliary system is designed between a PLMG rotor and a stator. Assuming that the direct-drive wave energy power generation device always operates in the vertical direction, under the drive of waves, the permanent magnet and the coil generate relative motion to convert wave mechanical energy into electric energy, and the kinematic equation of the direct-drive wave energy power generation device is as follows:
wherein m represents the mass of the direct-drive wave energy power generation device, x represents the mover displacement of the linear generator in the vertical direction, and f e Representing wave excitation force, f g Representing the back electromagnetic force of a linear generator,
R g representing internal damping, κ of a linear generator 2 Representing the elastic coefficient of the linear generator, f u Representing lumped unknowns, including unmodeled dynamics, uncertainty, turbulence, viscous forces, and friction forces, f r and fb Respectively the radiation force and the static buoyancy of the float,
f b ＝-κ 1 x+mg，m a represents an additional mass, R a Represents external damping, κ 1 ρgs represents the buoyancy coefficient, ρ represents the sea water density, g represents the gravitational acceleration, S represents the contact surface of the float with the wave;
in order to change the natural frequency of the direct-drive wave energy power generation device and adapt to the wave frequency of the laid sea area, a spring resonance auxiliary system is designed, the equivalent is a spring, and the expression is as follows:
f s ＝κ 3 x
the method combines the kinematic equation of the direct-driven wave energy power generation device, the radiation force, the static buoyancy of the floater and the back electromagnetic force of the linear generator to obtain the following components:
wherein m=m+m a Representing the total mass of the direct-drive wave energy power generation device;
calculating the output power of the direct-drive wave energy power generation device, wherein the output power is as follows:
output power P of direct-drive wave energy power generation device g Maximum output, let R a ＝R g ，κ 1 ＝-κ 2 By adjusting the spring constant k 3 ＝ω 2 M realizes the maximum wave energy capture of the direct-drive wave energy power generation device;
the dynamic equation of the direct-drive wave energy power generation device is constructed as follows:
wherein ,id and iq Current components of d and q axes, respectively;
the back electromagnetic force of the generator is expressed as follows:
wherein ,Ld and Lq The inductances of the d and q axes, respectively; from the above equation, the back electromagnetic force f can be changed by changing the current components of the d and q axes g ；
Taking a kinetic equation and a kinematic equation into consideration, constructing a control model of the direct-drive wave power generation device:
wherein ,
s2, designing a mixed finite time tracking control strategy;
in specific implementation, as a preferred embodiment of the present invention, the specific implementation method of the step S2 is as follows:
s21, designing a finite-time disturbance observer:
assuming that the unknown complex marine disturbance d is continuous and delicate and bounded, i.e
L represents a positive bounded constant and is a finite constant,
the designed finite time disturbance observer is expressed as follows:
wherein ,vb、d and 
are respectively +.>
and />
Observed, sig α (x)＝x α sign (x) is a finite time transformation equation;
the following observed errors are defined:
the observed error dynamic equation is:
by selecting a suitable parameter lambda 1 ,λ 2 ,λ 3 And L, tracking error mu 1 ,μ 2 ,μ 3 Is settled to zero for a limited time, and:
s22, designing a d-axis current finite time rule:
according to vector control, a d-axis sliding mode control surface is designed as follows:
s d ＝i d +k id x e
wherein ,kid ＞0，x e ＝x-x d Representing displacement error, x d Representing a reference displacement;
the first derivative of the d-axis sliding mode control surface is calculated as follows:
s23, designing a d-axis voltage control law:
wherein ,η1 > 0 is the designed positive constant;
s24, designing a q-axis current tracking controller:
in combination with the q-axis current tracking system, the tracking error is defined as:
x e ＝x-x d ,v e ＝v-v d
wherein ,vd Representing a reference speed; the method comprises the following steps:
the current control law of the q axis is designed by adopting a back-stepping method, and is as follows:
then an error dynamic equation is derived as follows:
wherein ,
the q-axis nonsingular terminal sliding die surface is designed as follows:
wherein, beta is more than 0,1 is more than p/q is less than 2, and the beta is a designed normal number;
considering a q-axis current tracking system and a nonsingular terminal sliding mode surface, designing a q-axis voltage control law, and designing as follows:
s3, stability analysis is carried out on the designed mixed limited time tracking control strategy.
In specific implementation, as a preferred embodiment of the present invention, the specific implementation method of the step S3 is as follows:
s31, assuming that the mixed limited time tracking control strategy meets the control model of the direct-drive wave power generation device, under the action of a disturbance observer and a control law, the lumped unknown disturbance of the direct-drive wave power generation device is observed in a limited time, and meanwhile, an error signal x is obtained e ,v e ,l qe Is stabilized to zero, and the actual state controller tracks the upper expected value;
s32, proving that the d-axis current converges to the sliding mode surface within a limited time, and gradually and stably converges to zero after the displacement, the speed tracking error and the q-axis current tracking error reach the designed nonsingular terminal sliding mode surface.
The first step: for the d-axis current tracking control subsystem, the following Lyapunov function is selected:
deriving the above method to obtain:
substituting the voltage control law into the above formula to obtain:
conclusion: the tracking error of the d-axis current tracking system converges to zero in a finite time;
and a second step of: for a q-axis current tracking system, the following Lyapunov function is established:
deriving the above method to obtain:
substituting the control law and the disturbance observation result into the above formula to obtain:
and a third step of: considering the maximum wave energy tracking control system of the whole direct-driven wave energy power generation device, designing a Lyapunov function:
V＝V d +V q
combining a disturbance observer and a control law to obtain:
thus, V (x) e (0),v e (0) Is bounded, V (x) e (t),v e (t)) is a non-increasing bounded function, then there are:
thus, the first and second substrates are bonded together,
is continuous all the time, guaranteed by selecting the appropriate parameters +.>
According to Lyapunov stability theory and Barbalat theorem, when t → infinity, x e and ve And the closed-loop direct-drive wave energy power generation device converges to zero, and the whole closed-loop direct-drive wave energy power generation device is gradually stable under the mixed limited time tracking control strategy.
Examples
The method of the present invention is compared with a method combining an equivalent circuit method and Sliding Mode Control (SMC) to verify the effectiveness of the control model and control scheme proposed by the present invention. The control scheme of the invention provides a high-order control model, and adopts a traditional equivalent circuit method to obtain the ideal value i of the q-axis current q * And the control process is converted into a virtual control quantity of a high-order model to directly control, so that the control accuracy of the device is improved. In this embodiment, reference displacements of the direct drive wave power generation Device (DWEC) are as follows:
x d ＝sin(0.2t+3)cos(0.5t+8)
the unknown disturbance is:
d＝20sin(2t/3+5)cos0.5tcos(t/3)/M
the parameters of the controller and observer are selected to be k id ＝2，k iq ＝3，η 1 ＝0.1，η 2 ＝0.2，p＝2，q＝3，l＝0.2，λ 1 ＝5.6，λ 2 ＝0.9，λ 3 ＝1.8。
As can be seen from fig. 3, SR-HFTC (hybrid finite time tracking control strategy) can achieve that the device mover velocity is in phase with the wave excitation force, i.e. the mover can be brought into resonance with the wave. Compared with SMC (sliding mode control), the method can realize more accurate tracking effect by considering the influence of unknown disturbance, and simultaneously proves the effectiveness of the control model and the control scheme.
Secondly, the SR-HFTC (hybrid finite time tracking control strategy) scheme proposed for wave verification of sea area large-span change has the following reference displacement of the direct-drive wave energy power generation device:
x d ＝2sintcos(0.5t)+cos(0.8t)cos(0.25t)
the parameters of the unknown disturbance, the controller and the disturbance observer are selected as k id ＝1.8，k iq ＝2，η 1 ＝0.3，η 2 ＝0.09，p＝2，q＝3，l＝0.1，λ 1 ＝9，λ 2 ＝2，λ 3 ＝2。
The simulation results are shown in fig. 4-6. As shown in fig. 4, a finite time disturbance observer (FDO) can accurately estimate the disturbance. As shown in fig. 5, the FDO-NTSM and SR-HFTC tracking effects are significantly better than NTSM, especially 16-20 seconds, for periodic waves in an interference environment, demonstrating that the disturbance observer employed herein can achieve effective rejection of interference. The SR-HFTC is better than FDO-NTSM in terms of error control, demonstrating that the spring resonance assisted system presented herein facilitates tracking of regular waves in a monsoon environment. As shown in fig. 6, DWEC under the SR-HFTC scheme can track the reference current more quickly and accurately. Taken together, the simulation results above demonstrate that the proposed SR-HFTC scheme can effectively achieve resonance of DWEC systems and track maximum wave energy in an deployment sea area.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (4)
1. A direct-drive wave energy power generation maximum wave energy accurate tracking control method based on spring resonance assistance is characterized by comprising the following steps:
s1, constructing a mathematical model of a direct-drive wave energy power generation device;
s2, designing a mixed finite time tracking control strategy; the specific implementation method of the step S2 is as follows:
s21, designing a finite-time disturbance observer:
assuming that the unknown complex marine disturbance d is continuous and delicate and bounded, i.e
L represents a positive bounded constant and is a finite constant,
the designed finite time disturbance observer is expressed as follows:
wherein ,vb、d and 
are respectively +.>
and />
Observed, sig α (x)＝|x| α sign (x) is a finite time transformation equation;
the following observed errors are defined:
the observed error dynamic equation is:
by selecting a suitable parameter lambda 1 ,λ 2 ,λ 3 And L, tracking error mu 1 ,μ 2 ,μ 3 Is settled to zero for a limited time, and:
s22, designing a d-axis current finite time rule:
according to vector control, a d-axis sliding mode control surface is designed as follows:
s d ＝i d +k id x e
wherein ,kid ＞0，x e ＝x-x d Representing displacement error, x d Representing a reference displacement;
the first derivative of the d-axis sliding mode control surface is calculated as follows:
s23, designing a d-axis voltage control law:
wherein ,η1 > 0 is the designed positive constant;
s24, designing a q-axis current tracking controller:
in combination with the q-axis current tracking system, the tracking error is defined as:
x e ＝x-x d ,v e ＝v-v d
wherein ,vd Representing a reference speed; the method comprises the following steps:
the current control law of the q axis is designed by adopting a back-stepping method, and is as follows:
then an error dynamic equation is derived as follows:
wherein ,
the q-axis nonsingular terminal sliding die surface is designed as follows:
wherein, beta is more than 0,1 is more than p/q is less than 2, and the beta is a designed normal number;
considering a q-axis current tracking system and a nonsingular terminal sliding mode surface, designing a q-axis voltage control law, and designing as follows:
s3, stability analysis is carried out on the designed mixed limited time tracking control strategy.
2. The method for precisely tracking and controlling the maximum wave energy of the direct-driven wave energy power generation based on the assistance of the spring resonance according to claim 1 is characterized in that the specific implementation method of the step S1 is as follows:
assuming that the direct-drive wave energy power generation device always operates in the vertical direction, under the drive of waves, the permanent magnet and the coil generate relative motion to convert wave mechanical energy into electric energy, and the kinematic equation of the direct-drive wave energy power generation device is as follows:
wherein m represents the mass of the direct-drive wave energy power generation device, x represents the mover displacement of the linear generator in the vertical direction, and f e Representing wave excitation force, f g Representing the back electromagnetic force of a linear generator,
R g representing internal damping, κ of a linear generator 2 Representing the elastic coefficient of the linear generator, f u Representing lumped unknowns, including unmodeled dynamics, uncertainty, turbulence, viscous forces, and friction forces, f r and fb Represents the radiation force and the static buoyancy of the float, respectively, +.>
f b ＝-κ 1 x+mg，m a Represents an additional mass, R a Represents external damping, κ 1 ρgs represents the buoyancy coefficient, ρ represents the sea water density, g represents the gravitational acceleration, S represents the contact surface of the float with the wave;
in order to change the natural frequency of the direct-drive wave energy power generation device and adapt to the wave frequency of the laid sea area, a spring resonance auxiliary system is designed, the equivalent is a spring, and the expression is as follows:
f s ＝κ 3 x
the method combines the kinematic equation of the direct-driven wave energy power generation device, the radiation force, the static buoyancy of the floater and the back electromagnetic force of the linear generator to obtain the following components:
wherein m=m+m a Representing the total mass of the direct-drive wave energy power generation device;
calculating the output power of the direct-drive wave energy power generation device, wherein the output power is as follows:
output power P of direct-drive wave energy power generation device g Maximum output, let R a ＝R g ，κ 1 ＝-κ 2 By adjusting the spring constant k 3 ＝ω 2 M realizes direct driveMaximum wave energy capture for a wave energy power plant;
the dynamic equation of the direct-drive wave energy power generation device is constructed as follows:
wherein ,id and iq Current components of d and q axes, respectively;
the back electromagnetic force of the generator is expressed as follows:
wherein ,Ld and Lq The inductances of the d and q axes, respectively; from the above equation, the back electromagnetic force f can be changed by changing the current components of the d and q axes g ；
Taking a kinetic equation and a kinematic equation into consideration, constructing a control model of the direct-drive wave power generation device:
wherein ,
3. the method for precisely tracking and controlling the maximum wave energy generated by direct-drive wave energy based on the assistance of spring resonance according to claim 1 is characterized in that the specific implementation method of the step S3 is as follows:
s31, assuming that the mixed limited time tracking control strategy meets the control model of the direct-drive wave power generation device, under the action of a disturbance observer and a control law, the lumped unknown disturbance of the direct-drive wave power generation device is observed in a limited time, and meanwhile, an error signal x is obtained e ,v e ,l qe Is stabilized to zero, and the actual state controller tracks the upper expected value;
s32, proving that the d-axis current converges to the sliding mode surface within a limited time, and gradually and stably converges to zero after the displacement, the speed tracking error and the q-axis current tracking error reach the designed nonsingular terminal sliding mode surface.
4. The method for precisely tracking and controlling the maximum wave energy generated by direct-drive wave energy based on the assistance of spring resonance according to claim 3, wherein the specific implementation method of the step S32 is as follows:
the first step: for the d-axis current tracking control subsystem, the following Lyapunov function is selected:
deriving the above method to obtain:
substituting the voltage control law into the above formula to obtain:
conclusion: the tracking error of the d-axis current tracking system converges to zero in a finite time;
and a second step of: for a q-axis current tracking system, the following Lyapunov function is established:
deriving the above method to obtain:
substituting the control law and the disturbance observation result into the above formula to obtain:
and a third step of: considering the maximum wave energy tracking control system of the whole direct-driven wave energy power generation device, designing a Lyapunov function:
V＝V d +V q
combining a disturbance observer and a control law to obtain:
thus, V (x) e (0),v e (0) Is bounded, V (x) e (t),v e (t)) is a non-increasing bounded function, then there are:
thus, the first and second substrates are bonded together,
is continuous all the time, guaranteed by selecting the appropriate parameters +.>
According to Lyapunov stability theory and Barbalat theorem, when t → infinity, x e and ve And the closed-loop direct-drive wave energy power generation device converges to zero, and the whole closed-loop direct-drive wave energy power generation device is gradually stable under the mixed limited time tracking control strategy. />
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