CN112287618A - Finite time cascade tracking control method of direct drive type wave energy conversion device - Google Patents

Finite time cascade tracking control method of direct drive type wave energy conversion device Download PDF

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CN112287618A
CN112287618A CN202011205785.8A CN202011205785A CN112287618A CN 112287618 A CN112287618 A CN 112287618A CN 202011205785 A CN202011205785 A CN 202011205785A CN 112287618 A CN112287618 A CN 112287618A
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CN112287618B (en
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王宁
付水
贾玉森
白超
刘宇玲
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Abstract

The invention provides a finite time cascade tracking control method of a direct-drive wave energy conversion device. The method comprises the following steps: constructing a dynamic equation of the direct-drive wave power generation device; establishing a mathematical model of a permanent magnet linear generator in a direct drive type 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; a finite time observer is added to a DWEC cascade structure, and a finite time cascade tracking controller is designed to complete the tracking of the direct-drive wave energy power generation device on the maximum wave energy. The invention has the characteristics of rapid tracking and anti-interference. Through the cascade tracking control method, the phenomenon that the wave power generation system resonates with incident waves is achieved, 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

Finite time cascade tracking control method of direct drive type wave energy conversion device
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 the development and utilization of the wave energy are very important for relieving the energy crisis and reducing the environmental pollution. The key technology of wave energy power generation is to improve the power capture 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 resonance is achieved to realize ideal wave energy capture of wave energy. Due to unstable frequency amplitude of sea waves and the defects of the prior art, the development of wave energy capturing technology is not ideal, and ideal wave energy capturing 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 Converter (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 technical means adopted by the invention are as follows:
a finite time cascade tracking control method of a direct drive type wave energy conversion device comprises the following steps:
step 1, only considering the force of wave force on the floater in the vertical direction, and constructing a dynamic equation of the direct-drive wave power generation device;
step 2, establishing a mathematical model of a permanent magnet linear generator in the direct drive type 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 3, adding a finite time observer to the DWEC cascade structure, and designing a finite time cascade tracking controller to complete the tracking of the direct-drive 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 as follows:
Figure BDA0002757000760000021
wherein m is the total mass of the wave power generation system, x is the vertical position of a rotor of the wave power generation system, and fe(t) is the excitation force of sea waves, fr(t) is radiation force, fb(t) is the static buoyancy of the float in water, fv(t) is viscosity, ff(t) is the friction force, fg(t) is the electromagnetic force of the linear generator,
wherein ,
Figure BDA0002757000760000022
wherein ,maAs an additional mass of the system, RaAdditional damping for the system;
wherein ,fb(t)＝-Kx(t)+mg＝-ρgSx(t)+mg
Wherein K ═ ρ gS;
wherein ,
Figure BDA0002757000760000023
wherein ,RgDamping coefficient, K, for reflecting the active power capability of a linear generatorgThe elastic coefficient for the reactive power absorbing capability of the reactive linear generator;
the final kinetic model is simplified to:
Figure BDA0002757000760000024
wherein m is the total mass of the wave power generation system; beta is agIs a straight lineA generator damping coefficient; beta is awIs the hydrodynamic damping coefficient; k is a radical ofsIs the system elastic coefficient.
Further, in step 2, the model of the linear motor under the abc coordinates is specifically:
the stator flux linkage of the permanent magnet is: psis＝-Liabc+ψPM-abc
ψs＝[ψa,ψb,ψc]T
wherein ,ΨPM-abcFor stator three-phase currents iabc＝[ia,ib,ic]TL is an inductance matrix;
Figure BDA0002757000760000025
wherein, λ is the pole pitch of the permanent magnet linear generator; psiPMA rotor flux linkage which is a permanent magnet; l isssIs the self-inductance of the stator winding; m is the mutual inductance between the stator windings;
the stator voltage equation under abc coordinates is:
Figure BDA0002757000760000026
wherein ,us-abcIs a stator terminal voltage vector; r is a stator resistance matrix;
R＝R＝diag(Rs,Rs,Rs)，Rsresistance of the stator winding;
the transformation of the model in abc coordinates into the model in dq axis coordinates is specifically as follows:
ψdq＝DψPM-abc
Figure BDA0002757000760000031
Figure BDA0002757000760000032
the stator voltage equation in dq coordinates is:
Figure BDA0002757000760000033
wherein, A and S are coefficient matrixes;
Figure BDA0002757000760000034
the voltage equations for the d-axis and q-axis are:
Figure BDA0002757000760000035
Figure BDA0002757000760000036
wherein ω is the electrical angular velocity and λ is the polar distance;
ω＝2πv/λ,Ls＝Lss-M。
further, the step 3 specifically includes the following steps:
step 31, designing a finite time observer, specifically:
Figure BDA0002757000760000037
wherein ,
Figure BDA0002757000760000038
Figure BDA0002757000760000039
ζ1＝-λ2l1/2sig1/2(z1-ζ0)+z2；
Figure BDA00027570007600000310
Figure BDA0002757000760000041
step 32, adopting limited time adjustment control as control of a d axis to obtain a limited constant id; and tracking control is adopted for the q axis, and tracking errors xe, ve and iq are obtained.
The invention adds a finite time observer (FO) to the DWEC cascade structure obtained by dq transformation, and the FO is designed to ensure that the concentrated unknown quantity can be accurately observed in a short time, thereby being beneficial to the decoupling design of a cascade controller. Meanwhile, the invention combines the finite time control and the backstepping control technology, and the whole finite time cascade tracking control scheme is finally developed, so that the DWEC system can accurately track the wave energy even under the condition that unmodeled dynamics and disturbance exist.
The invention has the characteristics of rapid tracking and anti-interference. Through the cascade tracking control method, the phenomenon that the wave power generation system resonates with incident waves is achieved, 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.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of a DWEC system.
Fig. 2 is a block diagram of the overall system control based on the cascaded trace control method.
FIG. 3 is a schematic diagram of the expected and actual states of x and v in a DWEC system.
X in DWEC system of FIG. 4c and vcSchematic diagram of tracking error of (1).
FIG. 5DWEC System iq and idSchematic diagram of expected and actual states of (c).
FIG. 6DWEC System ud and uqSchematic control input diagram of (1).
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 2, the direct-drive wave 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 type wave energy conversion device comprises the following steps:
step 1, the force of the waves acting on the floater is multidimensional, the wave energy conversion device is equivalent to a vibration structure formed by a spring and a mass block only by considering the force of the wave force on the floater in the vertical direction, and the vibration structure is converted into a mechanical energy form of elastic potential energy of spring deformation and kinetic energy of mass block movement. According to a Newton second law, a dynamic equation of the direct-drive wave power generation device is constructed;
step 2, establishing a mathematical model of a permanent magnet linear generator in the direct drive type 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 3, adding a finite time observer to the DWEC cascade structure, and designing a finite time cascade tracking controller to complete the tracking of the direct-drive 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 energy power generation device is as follows:
Figure BDA0002757000760000051
wherein m is the total mass of the wave power generation system, x is the vertical position of a rotor of the wave power generation system, and fe(t) is the excitation force of sea waves, fr(t) is radiation force, fb(t) is the static buoyancy of the float in water, fv(t) is viscosity, ff(t) is the friction force, fg(t) is the electromagnetic force of the linear generator,
wherein ,
Figure BDA0002757000760000052
wherein ,maAs an additional mass of the system, RaFor 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 is rho gS, rho is water density, and S is the contact area of the floater and the seawater;
neglecting viscous and frictional forces can yield:
Figure BDA0002757000760000061
the electromagnetic force of a linear generator can be expressed as a linear combination of speed and displacement, namely: wherein,
Figure BDA0002757000760000062
wherein ,RgDamping coefficient, K, for reflecting the active power capability of a linear generatorgThe elastic coefficient for the reactive power absorbing capability of the reactive linear generator;
Figure BDA0002757000760000063
neglecting the electromagnetic loss of the linear generator, the output instantaneous power is:
Figure BDA0002757000760000064
the final kinetic model is simplified to:
Figure BDA0002757000760000065
wherein m is the total mass of the wave power generation system; beta is agIs the damping coefficient of the linear generator; beta is awIs the hydrodynamic damping coefficient; k is a radical ofsIs the system elastic coefficient.
In the step 2, the stator of the linear generator does reciprocating motion, and the speed and the direction of the stator of the linear generator are changed. To establish a mathematical model of a permanent magnet linear generator, the following basic assumptions are made:
(1) the rotor and the permanent magnet are both provided with no damping winding;
(2) neglecting the influence of saturation, eddy current, magnetic hysteresis and end effect on the motor parameters;
(3) the magnetomotive force of the permanent magnet keeps 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 as follows:
the stator flux linkage of the permanent magnet is: psis＝-Liabc+ψPM-abc
ψs＝[ψa,ψb,ψc]T
Wherein iabc is stator three-phase current, iabc＝[ia,ib,ic]TL is an inductance matrix;
Figure BDA0002757000760000066
wherein, λ is the pole pitch of the permanent magnet linear generator; psiPMA rotor flux linkage which is a permanent magnet; l isssIs the self-inductance of the stator winding; m is the mutual inductance between the stator windings;
the stator voltage equation under abc coordinates is:
Figure BDA0002757000760000067
wherein ,us-abcIs a stator terminal voltage vector; r is a stator resistance matrix;
R＝R＝diag(Rs,Rs,Rs)，Rsresistance of the stator winding;
Figure BDA0002757000760000071
the transformation of the model in abc coordinates into the model in dq axis coordinates is specifically as follows:
ψdq＝DψPM-abc
Figure BDA0002757000760000072
Figure BDA0002757000760000073
in a steady state situation, the rotation speed and the rotation direction of the dq coordinate used for modeling the synchronous generator are kept unchanged, and the dq coordinate is fixed on the rotor of the linear generator and reciprocates back and forth along with the rotor of the linear generator, so that the magnitude and the direction of the movement speed of the dq coordinate change along with time.
Equation of voltage Us-abcThe stator voltage equation under dq coordinates obtained by multiplying the left side and the right side by the transformation matrix D is as follows:
Figure BDA0002757000760000074
wherein ,LsThe inductance of the stator is shown, A and S are coefficient matrixes;
Figure BDA0002757000760000075
Figure BDA0002757000760000076
substituting A and S into the formula: the voltage equations for the d-axis and q-axis are:
Figure BDA0002757000760000077
Figure BDA0002757000760000078
wherein ω is the electrical angular velocity and λ is the polar distance;
ω＝2πv/λ,Ls＝Lss-M。
when the displacement is equal whether the rotor moves in the forward direction or the reverse direction, the voltage and the current induced by the magnetic field cutting the stator flux linkage have the same amplitude and opposite directions.
The method adopts a finite time cascade tracking control method, and has the following characteristics that 1) d-axis electrodynamics is considered finely, a cascade structure of a DWEC system is established, and accurate tracking of wave energy is realized by independently designing a d and q voltage cascade control law; 2) in order to accurately compensate complex unknown quantities including unmodeled dynamics and disturbance, a finite time observer (FO) is designed in the cascade structure, so that the cascade controller is convenient to synthesize, and a main trunk 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 precision of wave energy is obviously improved.
Considering the above-mentioned mover dynamics problems
Figure BDA0002757000760000081
wherein
Figure BDA0002757000760000082
and
Figure BDA0002757000760000083
Construct the following subsystems
S1:
Figure BDA0002757000760000084
S2:
Figure BDA0002757000760000085
wherein ,Fu＝fu/M。
Based on this, a finite time observer (FO) is designed, as follows:
Figure BDA0002757000760000086
Figure BDA0002757000760000087
Figure BDA0002757000760000088
ζ1＝-λ2l1/2sig1/2(z1-ζ0)+z2
Figure BDA0002757000760000089
(2) the d-axis control adopts finite time regulation control:
first, a lemma is introduced; considering the d-axis control law of the S2 subsystem
Figure BDA0002757000760000091
The above formula is substituted into the S2 subsystem,
to obtain
Figure BDA0002757000760000092
Establishing a Lyapunov equation:
Figure BDA0002757000760000093
and using the lemma to obtain:
Figure BDA0002757000760000094
t＜T1|id(t)|≡0,t≥T1
the finite constant id can be given by:
Figure BDA0002757000760000095
finally, it can be concluded from the above-mentioned proof that the d-axis current can converge to zero within a limited time.
(3) Tracking control adopted for the q axis:
considering the s1 subsystem and the coordinate transformation:
xe＝x-xd,
Figure BDA0002757000760000096
Figure BDA0002757000760000097
Figure BDA0002757000760000098
Figure BDA0002757000760000099
the reference control signal for the iq axis setting is as follows:
Figure BDA00027570007600000910
the above is continuously simplified and carried into the above formula to obtain:
Figure BDA0002757000760000101
Figure BDA0002757000760000102
Figure BDA0002757000760000103
introduction and leading: the q-axis control law may be referred to as the S1 subsystem:
Figure BDA0002757000760000104
Figure BDA0002757000760000105
Figure BDA0002757000760000106
accurately tracking the expected displacement x, converging the global index, and bringing the simplified formula into the theorem:
Figure BDA0002757000760000107
Figure BDA0002757000760000108
Figure BDA0002757000760000109
consider the following Lyapunov function:
Figure BDA00027570007600001010
Figure BDA00027570007600001011
further derived using the young inequality:
Figure BDA00027570007600001012
the above formula can be combined to obtain a proof;
Figure BDA00027570007600001013
Figure BDA00027570007600001014
(4) as shown in FIGS. 3-6, the stability analysis result shows that when id is adjusted for a finite time, the tracking errors xe, ve and iq all converge to zero at an exponential rate, which proves that the system is stable.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (4)

1. A finite time cascade tracking control method of a direct drive type wave energy conversion device is characterized by comprising the following steps:
step 1, only considering the force of wave force on the floater in the vertical direction, and constructing a dynamic equation of the direct-drive wave power generation device;
step 2, establishing a mathematical model of a permanent magnet linear generator in the direct drive type 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 3, adding a finite time observer to the DWEC cascade structure, and designing a finite time cascade tracking controller to complete the tracking of the direct-drive wave energy power generation device on the maximum wave energy.
2. The finite time cascade tracking control method of the direct drive wave energy conversion device according to claim 1, wherein in step 1, the kinetic equation of the direct drive wave energy power generation device is as follows:
Figure FDA0002757000750000011
wherein m is the total mass of the wave power generation system, x is the vertical position of a rotor of the wave power generation system, and fe(t) is the excitation force of sea waves, fr(t) is radiation force, fb(t) is the static buoyancy of the float in water, fv(t) is viscosity, ff(t) is the friction force, fg(t) is the electromagnetic force of the linear generator,
wherein ,
Figure FDA0002757000750000012
wherein ,maAs an additional mass of the system, RaFor 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 is rho gS, rho is water density, and S is the contact area of the floater and the seawater;
wherein ,
Figure FDA0002757000750000013
wherein ,RgDamping coefficient, K, for reflecting the active power capability of a linear generatorgThe elastic coefficient for the reactive power absorbing capability of the reactive linear generator;
the final kinetic model is simplified to:
Figure FDA0002757000750000014
wherein m is the total mass of the wave power generation system; beta is agIs the damping coefficient of the linear generator; beta is awIs the hydrodynamic damping coefficient; k is a radical ofsIs the system elastic coefficient.
3. The finite time cascade tracking control method of the direct drive wave energy conversion device according to claim 2, wherein in the step 2, the model of the linear motor under abc coordinates is specifically:
the stator flux linkage of the permanent magnet is: psis＝-Liabc+ψPM-abc
ψs＝[ψa,ψb,ψc]T
wherein ,iabcFor stator three-phase currents iabc＝[ia,ib,ic]TL is an inductance matrix;
Figure FDA0002757000750000021
wherein, λ is the pole pitch of the permanent magnet linear generator; psiPMA rotor flux linkage which is a permanent magnet; l isssIs the self-inductance of the stator winding; m is the mutual inductance between the stator windings;
the stator voltage equation under abc coordinates is:
Figure FDA0002757000750000022
wherein ,us-abcIs a stator terminal voltage vector; r is a stator resistance matrix;
R＝R＝diag(Rs,Rs,Rs)，Rsresistance of the stator winding;
the transformation of the model in abc coordinates into the model in dq axis coordinates is specifically as follows:
ψdq＝DψPM-abc
Figure FDA0002757000750000023
Figure FDA0002757000750000024
the stator voltage equation in dq coordinates is:
Figure FDA0002757000750000025
wherein ,LsThe inductance of the stator is shown, A and S are coefficient matrixes;
Figure FDA0002757000750000026
Figure FDA0002757000750000031
the voltage equations for the d-axis and q-axis are:
Figure FDA0002757000750000032
Figure FDA0002757000750000033
wherein ω is the electrical angular velocity and λ is the polar distance;
ω＝2πv/λ,Ls＝Lss-M。
4. the finite time cascade tracking control method of the direct drive wave energy conversion device according to claim 3, wherein the step 3 specifically comprises the following steps:
step 31, designing a finite time observer, specifically:
Figure FDA0002757000750000034
wherein ,
Figure FDA0002757000750000035
Figure FDA0002757000750000036
ζ1＝-λ2l1/2sig1/2(z1-ζ0)+z2；
Figure FDA0002757000750000037
Figure FDA0002757000750000038
step 32, adopting limited time adjustment control as control of a d axis to obtain a limited constant id; and tracking control is adopted for the q axis, and tracking errors xe, ve and iq are obtained.
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