CN112287618B - Finite time cascade tracking control method of direct-drive wave energy conversion device - Google Patents
Finite time cascade tracking control method of direct-drive wave energy conversion device Download PDFInfo
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- 238000013016 damping Methods 0.000 claims description 12
- 238000004804 winding Methods 0.000 claims description 11
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
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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
- G06F2113/00—Details relating to the application field
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- G—PHYSICS
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- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- 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 finite time cascade tracking control method of a direct-driven wave energy conversion device. The method comprises the following steps: constructing a kinetic equation of the direct-drive wave energy power generation device; establishing a mathematical model of a permanent magnet linear generator in a direct-driven wave energy power generation device, transforming the model of the linear generator under abc coordinates into a model under dq axis coordinates through Park transformation, establishing a cascade structure of a DWEC system, and independently designing d and q voltage cascade control laws; and a limited time observer is added on the DWEC cascade structure, a limited time cascade tracking controller is designed, and the tracking of the direct-drive wave energy power generation device on the maximum wave energy is completed. The invention has the characteristics of fast tracking and anti-interference. Through the cascade tracking control method, the phenomenon that the wave power generation system resonates with incident sea waves is realized, the maximum power tracking of wave energy is achieved, the energy conversion efficiency is greatly improved, and the defect of low efficiency in the field of offshore energy conversion is overcome.
Description
Technical Field
The invention relates to the technical field of wave energy, in particular to a finite time cascade tracking control method of a direct-drive wave energy conversion device.
Background
Wave energy is a specific form of ocean energy, and is one of the most important energy sources in ocean energy, and development and utilization of wave energy are very important for relieving energy crisis and reducing environmental pollution. The key technology of wave energy power generation is to improve the power capturing and energy conversion efficiency of a wave power generation system, namely the frequency of the wave system is equal to the frequency of sea waves, so that ideal wave energy capturing of wave energy is realized by achieving resonance. Due to the unstable frequency amplitude of ocean waves and the shortcomings of the prior art, the development of wave energy and wave energy capturing technology is not ideal, and the capturing of ideal wave energy cannot be realized for a long time.
Disclosure of Invention
According to the technical problems, the invention provides a maximum wave energy tracking control method, which is oriented to a direct-drive wave energy Device (DWEC), and the maximum wave energy tracking of the direct-drive wave energy power generation device is completed by designing a finite time cascade tracking control scheme. The invention adopts the following technical means:
a finite time cascade tracking control method of a direct-drive wave energy conversion device comprises the following steps:
step 1, only considering the force of wave force on the vertical direction of the floater to construct a kinetic equation of the direct-drive wave energy power generation device;
step 2, establishing a mathematical model of a permanent magnet linear generator in the direct-driven wave energy power generation device, converting the model of the linear generator under abc coordinates into a model under dq axis coordinates through Park conversion, establishing a cascade structure of a DWEC system, and independently designing d and q voltage cascade control laws;
and step 3, adding a limited time observer on the DWEC cascade structure, designing a limited time cascade tracking controller, and completing the tracking of the direct-driven wave energy power generation device on the maximum wave energy.
Further, in step 1, the kinetic equation of the direct-drive wave power generation device is:
wherein m is the total mass of the wave power generation system, x is the vertical position of the rotor of the wave power generation system, and f e (t) is wave excitation force, f r (t) is the radiation force, f b (t) is the static buoyancy of the float in the water, f v (t) is a viscous force, f f (t) isFriction force f g (t) is the electromagnetic force of the linear generator,
wherein ,
wherein ,ma For additional mass of system, R a Additional damping for the system;
wherein ,fb (t)=-Kx(t)+mg=-ρgSx(t)+mg
Wherein k=ρgs;
wherein ,
wherein ,Rg To reflect the damping coefficient, K, of the active power capacity of the linear generator g The elastic coefficient for reflecting the reactive power absorption capacity of the linear generator;
the final kinetic model is simplified as:
wherein m is the total mass of the wave power generation system; beta g Is the damping coefficient of the linear generator; beta w Is a hydrodynamic damping coefficient; k (k) s Is the coefficient of elasticity of the system.
Further, in step 2, the model of the linear motor under abc coordinates is specifically:
the stator flux linkage of the permanent magnet is as follows: psi phi type s =-Li abc +ψ PM-abc
ψ s =[ψ a ,ψ b ,ψ c ] T
wherein ,ΨPM-abc I is the three-phase current of the stator abc =[i a ,i b ,i c ] T L is an inductance matrix;
wherein lambda isThe pole distance of the permanent magnet linear generator; psi phi type PM A mover flux linkage that is a permanent magnet; l (L) ss Is the self-inductance of the stator winding; m is the mutual inductance between stator windings;
the stator voltage equation under abc coordinates is:
wherein ,us-abc Is a stator terminal voltage vector; r is a stator resistance matrix;
R=R=diag(R s ,R s ,R s ),R s is the resistance of the stator winding;
the transformation of the model in abc coordinates to the model in dq axis coordinates is specifically:
ψ dq =Dψ PM-abc
the stator voltage equation under dq coordinates is:
wherein A, S is a coefficient matrix;
the voltage equations for the d-axis and q-axis are:
wherein ω is the electrical angular velocity and λ is the polar distance;
ω=2πv/λ,L s =L ss -M。
further, the step 3 specifically includes the following steps:
step 31, designing a finite time observer, which specifically comprises the following steps:
wherein ,
ζ 1 =-λ 2 l 1/2 sig 1/2 (z 1 -ζ 0 )+z 2 ;
step 32, adopting limited time adjustment control as d-axis control to obtain a limited constant id; the q-axis is tracking controlled to obtain tracking errors xe, ve and iq.
The invention adds a finite time observer (FO) on the DWEC cascade structure obtained by dq conversion, and the FO is designed to ensure that concentrated unknown quantity can be accurately observed in a short time, thereby being beneficial to the decoupling design of the cascade controller. Meanwhile, the invention combines the finite time control and backstepping control technology, and the whole finite time cascade tracking control scheme is finally developed, so that the DWEC system can accurately track wave energy even in the condition that unmodeled dynamics and disturbance exist.
The invention has the characteristics of fast tracking and anti-interference. Through the cascade tracking control method, the phenomenon that the wave power generation system resonates with incident sea waves is realized, the maximum power tracking of wave energy is achieved, the energy conversion efficiency is greatly improved, and the defect of low efficiency in the field of offshore energy conversion is overcome.
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 schematic diagram of a DWEC system.
Fig. 2 is an overall system control block diagram based on a cascaded tracking control method.
Fig. 3 is a schematic diagram of the expected and actual states of x and v in a DWEC system.
FIG. 4 x in DWEC system c and vc Is a tracking error diagram of (a).
FIG. 5 i in DWEC system q and id Is a schematic diagram of the expected and actual states of (a).
FIG. 6 u in DWEC system d and uq Is a control input schematic of (a).
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 2, the direct-drive wave energy power generation device mainly comprises a floater, a permanent magnet linear generator and a fixed anchor chain. Wherein, the floater is connected with the rotor of the permanent magnet linear generator to realize synchronous motion. The stator of the generator is connected to the seabed by a fixed anchor chain.
A finite time cascade tracking control method of a direct-drive wave energy conversion device comprises the following steps:
in the step 1, the force of the wave acting on the floater is multidimensional, and only the force of the wave force on the floater in the vertical direction is considered, so that the wave energy conversion device is equivalent to a vibration structure formed by a spring and a mass block, and the vibration structure is converted into a mechanical energy form by the elastic potential energy of the spring deformation and the kinetic energy of the movement of the mass block. According to Newton's second law, constructing a kinetic equation of the direct-drive wave energy power generation device;
step 2, establishing a mathematical model of a permanent magnet linear generator in the direct-driven wave energy power generation device, converting the model of the linear generator under abc coordinates into a model under dq axis coordinates through Park conversion, establishing a cascade structure of a DWEC system, and independently designing d and q voltage cascade control laws;
and step 3, adding a limited time observer on the DWEC cascade structure, designing a limited time cascade tracking controller, and completing the tracking of the direct-driven wave energy power generation device on the maximum wave energy.
As shown in fig. 1, in step 1, the kinetic equation of the direct-drive wave power generation device is:
wherein m is the total mass of the wave power generation system, x is the vertical position of the rotor of the wave power generation system, and f e (t) is wave excitation force, f r (t) is the radiation force, f b (t) is the static buoyancy of the float in the water, f v (t) is a viscous force, f f (t) is friction force, f g (t) is the electromagnetic force of the linear generator,
wherein ,
wherein ,ma For additional mass of system, R a For additional damping of the system, ω is the angular velocity of the incident wave;
wherein ,fb (t)=-Kx(t)+mg=-ρgSx(t)+mg
Wherein k=pgs, ρ is water density, S is contact area of the float and seawater;
neglecting viscous and frictional forces can result in:
the electromagnetic force of a linear generator can be expressed as a linear combination of speed and displacement, namely: wherein,
wherein ,Rg To reflect the damping coefficient, K, of the active power capacity of the linear generator g The elastic coefficient for reflecting the reactive power absorption capacity of the linear generator;
the electromagnetic loss of the linear generator is ignored, and the output instantaneous power is as follows:
the final kinetic model is simplified as:
wherein m is the total mass of the wave power generation system; beta g Is the damping coefficient of the linear generator; beta w Is a hydrodynamic damping coefficient; k (k) s Is the coefficient of elasticity of the system.
In the step 2, the stator of the linear generator makes reciprocating motion, and the speed and the direction are changed. To build a mathematical model of a permanent magnet linear generator, the following basic assumptions are made:
(1) The rotor and the permanent magnet are provided with undamped windings;
(2) Neglecting the influence of saturation, eddy current, hysteresis and end effect on motor parameters;
(3) The magnetomotive force of the permanent magnet is kept constant;
(4) The armature resistance and the armature inductance of each winding of the three phases of the motor stator are equal.
The model of the linear motor under the abc coordinates is specifically:
the stator flux linkage of the permanent magnet is as follows: psi phi type s =-Li abc +ψ PM-abc
ψ s =[ψ a ,ψ b ,ψ c ] T
Wherein, iabc is stator three-phase current, i abc =[i a ,i b ,i c ] T L is an inductance matrix;
wherein lambda is the pole pitch of the permanent magnet linear generator; psi phi type PM A mover flux linkage that is a permanent magnet; l (L) ss Is the self-inductance of the stator winding; m is the mutual inductance between stator windings;
the stator voltage equation under abc coordinates is:
wherein ,us-abc Is a stator terminal voltage vector; r is a stator resistance matrix;
R=R=diag(R s ,R s ,R s ),R s is the resistance of the stator winding;
the transformation of the model in abc coordinates to the model in dq axis coordinates is specifically:
ψ dq =Dψ PM-abc
in steady state, the rotation speed and rotation direction of the dq coordinate used for modeling the synchronous generator are kept unchanged, and the dq coordinate is fixed on the mover of the linear generator and reciprocates back and forth along with the mover of the linear generator, so that the movement speed and direction of the dq coordinate are changed with time.
Equation U of voltage s-abc The stator voltage equation under dq coordinates can be obtained by multiplying the left side and the right side by the transformation matrix D:
wherein ,Ls The inductance of the stator is A, S is a coefficient matrix;
substituting A and S into the above formula: the voltage equations for the d-axis and q-axis are:
wherein ω is the electrical angular velocity and λ is the polar distance;
ω=2πv/λ,L s =L ss -M。
the voltage and current induced by the magnetic field cutting stator flux linkage are the same in amplitude and opposite in direction no matter whether the mover moves forward or backward, displacement, and the like.
The method adopts the finite time cascade tracking control, and has the characteristics that 1) d-axis current dynamics are finely considered, a cascade structure of a DWEC system is established, and accurate tracking of wave energy is realized by independently designing d and q-voltage cascade control laws; 2) In order to accurately compensate complex unknowns including unmodeled dynamics and disturbances, a finite time observer (FO) is designed in the cascade structure, so that the cascade controller is convenient to synthesize, and the backbone can be reasonably decoupled; 3) In the whole finite time cascade tracking control scheme, the d-axis current tracking dynamics can be fully solved, so that the tracking accuracy of wave energy is remarkably improved.
In view of the above-mentioned problems of mover dynamics
wherein and />The following subsystems are constructed
S 1 :
S 2 :
wherein ,Fu =f u /M。
Based on this, a finite time observer (FO) is designed as follows:
ζ 1 =-λ 2 l 1/2 sig 1/2 (z 1 -ζ 0 )+z 2
(2) The d-axis control adopts limited time adjustment control:
first introducing an quotation; consider d-axis control law of S2 subsystem
The above formula is brought into the S2 subsystem,
obtaining
Establishing a Lyapunov equation:
and using the quotients to derive:t<T 1 |i d (t)|≡0,t≥T 1
the finite constant id can be derived from the following equation:
finally, as can be seen from the above demonstration, the d-axis current can converge to zero in a limited time.
(3) Tracking control adopted by q axis:
consider the s1 subsystem and coordinate transformation:
x e =x-x d ,
the reference control signal for the iq axis setting is as follows:
the continuous simplification and the bringing into the formula can be obtained:
introduction of the quotation: the q-axis control law may be nominally referred to as S1 subsystem:
accurately tracking the expected displacement x, converging the global index, and bringing the simplified equation into the quotation:
consider the following Lyapunov function:
using the young's inequality can be further derived:
a proof can be obtained by combining the above formulas;
(4) As shown in fig. 3-6, the stability analysis results show that when id is adjusted for a limited time, the tracking errors xe, ve and iq all converge to zero at an exponential rate, proving that the system is stable.
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 (1)
1. The finite time cascade tracking control method of the direct-drive wave energy conversion device is characterized by comprising the following steps of:
step 1, only considering the force of wave force on the vertical direction of the floater to construct a kinetic equation of the direct-drive wave energy power generation device;
step 2, establishing a mathematical model of a permanent magnet linear generator in the direct-driven wave energy power generation device, converting the model of the linear generator under abc coordinates into a model under dq axis coordinates through Park conversion, establishing a cascade structure of a DWEC system, and independently designing d and q voltage cascade control laws;
step 3, adding a limited time observer on the DWEC cascade structure, designing a limited time cascade tracking controller, and completing tracking of the maximum wave energy by the direct-driven wave energy generating device;
in the step 1, the kinetic equation of the direct-drive wave energy power generation device is as follows:
wherein m is the total mass of the wave power generation system, x is the vertical position of the rotor of the wave power generation system, and f e (t) is wave excitation force, f r (t) is the radiation force, f b (t) is the static buoyancy of the float in the water, f v (t) is a viscous force, f f (t) is friction force, f g (t) is the electromagnetic force of the linear generator,
wherein ,
wherein ,ma For additional mass of system, R a For additional damping of the system, ω is the angular velocity of the incident wave;
wherein ,fb (t)=-Kx(t)+mg=-ρgSx(t)+mg
Wherein k=pgs, ρ is water density, S is contact area of the float and seawater;
wherein ,
wherein ,Rg To reflect the damping coefficient, K, of the active power capacity of the linear generator g The elastic coefficient for reflecting the reactive power absorption capacity of the linear generator;
the final kinetic model is simplified as:
wherein m is the total wave power generation systemQuality; beta g Is the damping coefficient of the linear generator; beta w Is a hydrodynamic damping coefficient; k (k) s Is the system elastic coefficient;
in step 2, the model of the linear motor under abc coordinates is specifically:
the stator flux linkage of the permanent magnet is as follows: psi phi type s =-Li abc +ψ PM-abc
ψ s =[ψ a ,ψ b ,ψ c ] T
Wherein, iabc is stator three-phase current, i abc =[i a ,i b ,i c ] T L is an inductance matrix;
wherein lambda is the pole pitch of the permanent magnet linear generator; psi phi type PM A mover flux linkage that is a permanent magnet; l (L) ss Is the self-inductance of the stator winding; m is the mutual inductance between stator windings;
the stator voltage equation under abc coordinates is:
wherein ,us-abc Is a stator terminal voltage vector; r is a stator resistance matrix;
R=R=diag(R s ,R s ,R s ),R s is the resistance of the stator winding;
the transformation of the model in abc coordinates to the model in dq axis coordinates is specifically:
v dq =Dψ PM-abc
the stator voltage equation under dq coordinates is:
wherein ,Ls The inductance of the stator is A, S is a coefficient matrix;
the voltage equations for the d-axis and q-axis are:
wherein ω is the electrical angular velocity and λ is the polar distance;
ω=2πv/λ,L s =L ss -M;
the step 3 specifically comprises the following steps:
step 31, designing a finite time observer, which specifically comprises the following steps:
wherein ,
ζ 1 =-λ 2 l 1/2 sig 1/2 (z 1 -ζ 0 )+z 2 ;
step 32, adopting limited time adjustment control as d-axis control to obtain a limited constant id; the q-axis is tracking controlled to obtain tracking errors xe, ve and iq.
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EP2535557A2 (en) * | 2011-06-17 | 2012-12-19 | Robert Bosch GmbH | Method for operating a wave energy converter and wave energy converter |
CN110134170A (en) * | 2019-03-29 | 2019-08-16 | 广东工业大学 | A kind of reference current tracking based on sea wave power generation system |
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EP2535557A2 (en) * | 2011-06-17 | 2012-12-19 | Robert Bosch GmbH | Method for operating a wave energy converter and wave energy converter |
CN110134170A (en) * | 2019-03-29 | 2019-08-16 | 广东工业大学 | A kind of reference current tracking based on sea wave power generation system |
CN110311607A (en) * | 2019-07-24 | 2019-10-08 | 大连海事大学 | A kind of contragradience sliding formwork maximum wave energy catching method |
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