CN110011303B - Photovoltaic multi-water-pump reachable set estimation and compensation coordination control method - Google Patents

Photovoltaic multi-water-pump reachable set estimation and compensation coordination control method Download PDF

Info

Publication number
CN110011303B
CN110011303B CN201910296953.XA CN201910296953A CN110011303B CN 110011303 B CN110011303 B CN 110011303B CN 201910296953 A CN201910296953 A CN 201910296953A CN 110011303 B CN110011303 B CN 110011303B
Authority
CN
China
Prior art keywords
formula
following
water pump
matrix
water
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
Application number
CN201910296953.XA
Other languages
Chinese (zh)
Other versions
CN110011303A (en
Inventor
汪星一
钟智雄
伍文才
万芳
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Minjiang University
Original Assignee
Minjiang University
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Minjiang University filed Critical Minjiang University
Priority to CN201910296953.XA priority Critical patent/CN110011303B/en
Publication of CN110011303A publication Critical patent/CN110011303A/en
Application granted granted Critical
Publication of CN110011303B publication Critical patent/CN110011303B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04B—POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
    • F04B17/00—Pumps characterised by combination with, or adaptation to, specific driving engines or motors
    • F04B17/006—Solar operated
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04B—POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS
    • F04B49/00—Control, e.g. of pump delivery, or pump pressure of, or safety measures for, machines, pumps, or pumping installations, not otherwise provided for, or of interest apart from, groups F04B1/00 - F04B47/00
    • F04B49/06—Control using electricity
    • 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
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

Landscapes

  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Evolutionary Computation (AREA)
  • General Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Power Engineering (AREA)
  • Computer Hardware Design (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Sustainable Development (AREA)
  • Sustainable Energy (AREA)
  • Control Of Positive-Displacement Pumps (AREA)
  • Control Of Electrical Variables (AREA)

Abstract

The invention provides a photovoltaic multi-water-pump reachable set estimation and compensation coordination control method. Firstly, a physical model of the photovoltaic multi-water pump system is built, and a neutral II type T-S fuzzy method is adopted to express the nonlinear dynamics of the system. Considering that each water pump is affected by different external environment interference factors, it is very difficult to inhibit different external environment interference by using a uniform qualitative and quantitative method. For this problem, an estimator is first designed to estimate the interference signal of each water pump. On the basis, a feedback controller based on compensation is adopted, so that the external interference signals can be eliminated and stable operation can be realized. The invention considers the real working conditions, and the designed photovoltaic multi-water-pump reachable set estimation and compensation coordination control method can eliminate the external interference signals and realize stable work.

Description

Photovoltaic multi-water-pump reachable set estimation and compensation coordination control method
Technical Field
The invention relates to the field of nonlinear control, in particular to a photovoltaic multi-water-pump reachable set estimation and compensation coordination control method.
Background
The photovoltaic water pump is a device for realizing water pumping by utilizing solar power generation to provide electric energy for the water pump, and is widely applied to remote places, drought water shortage, offshore floating bodies and other application occasions. Due to the nonlinear characteristic of the photovoltaic array and the fact that the factors of each water pump which are interfered by the external environment are different, it is very difficult to inhibit the interference of different external environments by using a uniform qualitative and quantitative method, and the stability problem of the photovoltaic water pump system is more and more prominent.
Disclosure of Invention
In view of this, the present invention provides a method for coordinated control of reachable set estimation and compensation of a photovoltaic multi-water pump, which can eliminate external interference signals of the photovoltaic multi-water pump and realize stable operation.
The invention is realized by adopting the following scheme: a photovoltaic multi-water-pump reachable set estimation and compensation coordination control method comprises the following steps:
step S1: providing a photovoltaic multi-water-pump physical system model;
step S2: establishing a nonlinear dynamic model of the photovoltaic multi-water pump physical system according to a physics principle and a neutral II type T-S fuzzy model;
step S3: establishing an estimation controller to estimate an external interference signal of the photovoltaic multi-water pump physical system model;
step S4: based on the external interference signal estimated by the estimation controller established in step S3, a compensation-based feedback controller is designed to enable the external interference signal to be suppressed and to achieve stable operation of the photovoltaic multi-water pump.
Further, the step S2 specifically includes the following steps:
step S21: establishing a photovoltaic single water pump nonlinear system model as shown in formula (1):
Figure BDA0002026544630000021
in the formula,
Figure BDA0002026544630000022
k6＝ωe-ωr；
Figure BDA0002026544630000023
Figure BDA0002026544630000024
Figure BDA0002026544630000025
isd、isqrepresents d-axis and q-axis currents;
Figure BDA0002026544630000026
respectively representing stator d-axis and q-axis magnetic chains;
Figure BDA0002026544630000027
respectively representing d-axis and q-axis magnetic chains of the rotor; omegarRepresenting the rotor angular velocity; u shapedcIs the photovoltaic power generation output voltage; t isLIs the load torque; omegaeRepresenting electromagnetic field angle velocity; l ismRepresenting armature mutual inductance;
Figure BDA0002026544630000028
showing a rotor time constant; l isrAnd RrRotor inductance and resistance, respectively; cdcIs a direct current side capacitor;
Figure BDA0002026544630000029
is the leakage inductance derivative; l issAnd RsRespectively representing the inductance and resistance of the stator; cdcRepresents the dc side capacitance; t iseRepresents an electromagnetic torque; p represents the number of pole pairs;
step S22: establishing a photovoltaic multi-water pump system, wherein each water pump system is defined as an angle mark i; according to kirchhoff's current theorem, the following results are obtained:
Figure BDA00020265446300000210
substituting the formula (2) into the formula (1) to obtain the following photovoltaic multi-water pump coupling nonlinear system,
Figure BDA0002026544630000031
in the formula,
Figure BDA0002026544630000032
Figure BDA0002026544630000033
Figure BDA0002026544630000034
Figure BDA0002026544630000035
k6(i)＝ωe(i)-ωr(i)；
Figure BDA0002026544630000036
Figure BDA0002026544630000037
Figure BDA0002026544630000038
Figure BDA0002026544630000039
Figure BDA00020265446300000310
Figure BDA00020265446300000311
step S23: will isd(i)，isq(i)，ωr(i)，udc(i)The interference involved in an output measurement channel is obtained as the output of a photovoltaic multi-water pump coupling nonlinear system, and is expressed as follows:
Figure BDA0002026544630000041
in the formula,
Figure BDA0002026544630000042
ωi(t) is the output measurement channel interference;
will be provided with
Figure BDA0002026544630000043
And (3) as a fuzzy front piece variable, and performing Euler discretization on the fuzzy front piece variable to obtain the following neutral II-type T-S fuzzy model of the photovoltaic multi-water pump system:
Figure BDA0002026544630000044
wherein,
Figure BDA0002026544630000045
Figure BDA0002026544630000046
Figure BDA0002026544630000047
are respectively non-linear Aii(t),Bi(t)Aij(t) function
Figure BDA0002026544630000048
A linearized parameter matrix;
Figure BDA0002026544630000049
is a fuzzy set of neutral type II.
Further, the step S3 specifically includes the following steps:
step S31: definition of
Figure BDA00020265446300000410
And introducing a variable
Figure BDA00020265446300000411
Figure BDA00020265446300000412
Substituting equation (5) yields:
Figure BDA00020265446300000413
in the formula,
Figure BDA0002026544630000051
introducing a fuzzy observer as follows:
Figure BDA0002026544630000052
in the formula,
Figure BDA0002026544630000053
Figure BDA0002026544630000054
is an auxiliary state vector that is,
Figure BDA0002026544630000055
Figure BDA0002026544630000056
is the observer gain; in order to ensure that the water-soluble organic acid,
Figure BDA0002026544630000057
Figure BDA0002026544630000058
in the formula, SiNon-singular matrices, resulting in:
Figure BDA0002026544630000059
obtained according to equations (6) to (10):
Figure BDA00020265446300000510
Figure BDA00020265446300000511
because of SiIs a non-singular matrix, so equation (11) is again expressed as:
Figure BDA00020265446300000512
in the formula,
Figure BDA00020265446300000513
step S32: the following lyapunov function is defined,
Figure BDA00020265446300000514
in the formula,
Figure BDA00020265446300000515
is a positive definite symmetric matrix; taking the difference of the Lyapunov functions to obtain:
Figure BDA0002026544630000061
due to the fact that
Figure BDA0002026544630000062
In the formula,
Figure BDA0002026544630000063
and scalar k > 0
Defining a positive definite symmetric matrix
Figure BDA0002026544630000064
Sum matrix
Figure BDA0002026544630000065
From equation (12):
Figure BDA0002026544630000066
in the formula,
Figure BDA0002026544630000067
let the performance indicator function:
Figure BDA0002026544630000071
wherein α∈ [0, 1].
According to the expressions (13) to (17), if j (t) <0 holds, the following inequality holds,
Figure BDA0002026544630000072
in the formula,
Figure BDA0002026544630000073
Figure BDA0002026544630000074
Figure BDA0002026544630000075
Figure BDA0002026544630000076
step S33: converting the inequality (18) into a linear matrix inequality, wherein the matrix is ordered
Figure BDA0002026544630000077
Comprises the following steps:
Figure BDA0002026544630000078
in the formula,
Figure BDA0002026544630000079
is a non-singular matrix;
substituting formula (20) for formula (18) to define
Figure BDA00020265446300000710
Extracting fuzzy advance variables to obtain:
Figure BDA00020265446300000711
in the formula, L ∈ Li,
Figure BDA00020265446300000712
Is a fuzzy rule that is a function of the rule,
Figure BDA00020265446300000713
Figure BDA00020265446300000714
Figure BDA0002026544630000081
Figure BDA0002026544630000082
step S34: j (k) <0 from inequality (21),
Vk+1)-1＜α(V(k)-1)； (23)
from equation (23):
V(k)＜αk(V(0)-1)+1, (24)
for the zero-initial case, we get:
Figure BDA0002026544630000083
in the formula,
Figure BDA0002026544630000084
Figure BDA0002026544630000085
the algorithm for establishing the solution estimation controller is as follows:
according to
Figure BDA0002026544630000086
And formula (21), wherein
Figure BDA0002026544630000087
The gains of the estimators are as follows:
Figure BDA0002026544630000088
further, the step S4 specifically includes the following steps:
step S41: the following compensation controller was set up:
Figure BDA0002026544630000089
in the formula,
Figure BDA00020265446300000810
Figure BDA00020265446300000811
and
Figure BDA00020265446300000812
is the compensation controller gain;
substituting the formula (27) into the formula (5) to obtain the following photovoltaic multi-water pump closed-loop control system:
Figure BDA0002026544630000091
in the formula,
Figure BDA0002026544630000092
Figure BDA0002026544630000093
step S42: the following Lyapunov function is defined:
Figure BDA0002026544630000094
in the formula,
Figure BDA0002026544630000095
is a positive definite symmetric matrix; by taking the difference of the lyapunov functions v (k), we obtain:
Figure BDA0002026544630000096
defining a positive definite symmetric matrix
Figure BDA0002026544630000097
Sum matrix
Figure BDA0002026544630000098
From equation (28) we obtain:
Figure BDA0002026544630000099
Figure BDA0002026544630000101
in the formula,
Figure BDA0002026544630000102
obtaining the result according to the step S34
Figure BDA0002026544630000103
The following performance indicator function is obtained:
Figure BDA0002026544630000104
wherein, β∈ [0, 1 ];
obtaining J (t) <0 according to formula (29) to formula (31),
Figure BDA0002026544630000105
in the formula,
Figure BDA0002026544630000106
Figure BDA0002026544630000107
is a symmetrical positive definite matrix and is characterized in that,
Figure BDA0002026544630000108
and
Figure BDA0002026544630000109
is a suitable dimension matrix, scalar β∈ [0, 1 [ ]]；
In order to ensure that the water-soluble organic acid,
Figure BDA0002026544630000111
and
Figure BDA0002026544630000112
obtaining the following result by adopting cone supplementary guiding and extracting fuzzy advancing variables:
Figure BDA0002026544630000113
Figure BDA0002026544630000114
in the formula,
Figure BDA0002026544630000115
Figure BDA0002026544630000116
Figure BDA0002026544630000117
Figure BDA0002026544630000118
Figure BDA0002026544630000119
Figure BDA00020265446300001110
Figure BDA00020265446300001111
Figure BDA00020265446300001112
step S43: inequalities (33) and (34) are established to result in J (k) <0,
Figure BDA00020265446300001113
in the formula,
Figure BDA00020265446300001114
Figure BDA00020265446300001115
for the zero-initial case, we get:
Figure BDA0002026544630000121
the algorithm of the feedback compensation controller is as follows:
according to
Figure BDA0002026544630000122
Formula (33) and formula (34),
Figure BDA0002026544630000123
wherein
Figure BDA0002026544630000124
Figure BDA0002026544630000125
And
Figure BDA0002026544630000126
is the gain of the controller.
Compared with the prior art, the invention has the following beneficial effects:
the invention can eliminate the external interference signal of the photovoltaic multi-water pump and realize stable work.
Drawings
FIG. 1 is a diagram of a photovoltaic multiple water pump physical system;
fig. 2 is a diagram of implementation steps of a photovoltaic multi-water-pump reachable set estimation and compensation coordination control method.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
As shown in fig. 1 and 2, the present embodiment provides a method for coordination control of estimation and compensation of an accessible set of a photovoltaic multi-water pump, including the following steps:
step S1: providing a photovoltaic multi-water-pump physical system model; the photovoltaic multi-water-pump physical system model comprises a photovoltaic, a plurality of DC/AC converters, a plurality of water pumps and a plurality of water pipes; each DC/AC converter is connected with a water pump; each water pump is connected with a water pipe; the photovoltaic provides electric energy for the plurality of DC/AC converters and the plurality of water pumps;
step S2: establishing a nonlinear dynamic model of the photovoltaic multi-water pump physical system according to a physics principle and a neutral II type T-S fuzzy model;
step S3: considering that each water pump is interfered by different external environments; it is very difficult to suppress different external environmental interferences by using a uniform qualitative and quantitative method. Designing an estimator for the problem to estimate an external interference signal of the photovoltaic multi-water pump physical system model;
step S4: based on the external interference signal estimated by the estimation controller established in step S3, a compensation-based feedback controller is designed to enable the external interference signal to be suppressed and to achieve stable operation of the photovoltaic multi-water pump.
In step S2, a fuzzy dynamic model of the photovoltaic multi-water pump physical system is established according to the physics principle and the expression method of the neutral type II T-S fuzzy model. The method comprises the following specific steps:
step S21, firstly, establishing a photovoltaic single water pump nonlinear system model as shown in formula (1):
Figure BDA0002026544630000131
in the formula,
Figure BDA0002026544630000132
k6＝ωe-ωr；
Figure BDA0002026544630000133
Figure BDA0002026544630000134
isd、isqrepresents d-axis and q-axis currents;
Figure BDA0002026544630000135
respectively representing stator d-axis and q-axis magnetic chains;
Figure BDA0002026544630000136
respectively representing d-axis and q-axis magnetic chains of the rotor; omegarRepresenting the rotor angular velocity; u shapedcIs the photovoltaic power generation output voltage; t isLIs the load torque; omegaeRepresenting electromagnetic field angle velocity; l ismRepresenting armature mutual inductance;
Figure BDA0002026544630000137
represents the rotor time constant; l isrAnd RrRotor inductance and resistance, respectively; cdcIs a direct current side capacitor;
Figure BDA0002026544630000138
is the leakage inductance derivative; l issAnd RsRespectively representing the inductance and resistance of the stator; cdcRepresents the dc side capacitance; t iseRepresents an electromagnetic torque; p represents the number of pole pairs.
Step S22: then, considering a photovoltaic multi-water pump system, and defining each water pump system as an angle mark i; according to kirchhoff's current theorem, the following results are obtained:
Figure BDA0002026544630000141
substituting the formula (2) into the formula (1) to obtain the following photovoltaic multi-water pump coupling nonlinear system,
Figure BDA0002026544630000142
in the formula,
Figure BDA0002026544630000143
Figure BDA0002026544630000144
Figure BDA0002026544630000145
Figure BDA0002026544630000146
k6(i)＝ωe(i)-ωr(i)；
Figure BDA0002026544630000147
Figure BDA0002026544630000148
step S23: will isd(i)，isq(i)，ωr(i)，udc(i)The method is characterized in that the method is selected as the output of a photovoltaic multi-water pump coupling nonlinear system, and the interference involved in an output measurement channel is considered, and is expressed as follows:
Figure BDA0002026544630000151
in the formula,
Figure BDA0002026544630000152
ωi(t) is the output measurement channel interference.
Selecting
Figure BDA0002026544630000153
And (3) as a fuzzy front piece variable, and performing Euler discretization on the fuzzy front piece variable to obtain the following neutral II-type T-S fuzzy model of the photovoltaic multi-water pump system:
Figure BDA0002026544630000154
wherein,
Figure BDA0002026544630000155
Figure BDA0002026544630000156
Figure BDA0002026544630000157
is non-linear Aii(t),Bi(t)Aij(t)Function(s)
Figure BDA0002026544630000158
A linearized parameter matrix;
Figure BDA0002026544630000159
Figure BDA00020265446300001510
is a fuzzy set of neutral type II.
In step S3, considering that each water pump is affected by different external environmental interference factors; it is very difficult to suppress different external environmental interferences by using a uniform qualitative and quantitative method. An estimator is designed to estimate these ambient interference signals for this problem. The specific implementation steps are as follows:
step S31: first, define
Figure BDA00020265446300001511
And introducing a variable
Figure BDA00020265446300001512
Figure BDA00020265446300001513
Then, with equation (5):
Figure BDA00020265446300001514
in the formula,
Figure BDA0002026544630000161
now introduce a fuzzy observer as follows:
Figure BDA0002026544630000162
in the formula,
Figure BDA0002026544630000163
and is
Figure BDA0002026544630000164
Is an auxiliary state vector that is,
Figure BDA0002026544630000165
Figure BDA0002026544630000166
is the observer gain to be designed.
Now, we further define
Figure BDA0002026544630000167
Figure BDA0002026544630000168
In the formula, SiIs a non-singular matrix, then we get:
Figure BDA0002026544630000169
following equations (6) - (10) we obtain:
Figure BDA00020265446300001610
because of SiIs a non-singular matrix, so the system (11) can be expressed again as:
Figure BDA00020265446300001611
in the formula,
Figure BDA00020265446300001612
step S32: the following lyapunov function is then defined,
Figure BDA0002026544630000171
in the formula,
Figure BDA0002026544630000172
is a positive definite symmetric matrix. Taking the difference of the Lyapunov functions to obtain:
Figure BDA0002026544630000173
due to the fact that
Figure BDA0002026544630000174
In the formula,
Figure BDA0002026544630000175
and scalar k > 0;
defining a positive definite symmetric matrixSum matrix
Figure BDA0002026544630000177
Then, from equation (12):
Figure BDA0002026544630000178
Figure BDA0002026544630000181
in the formula,
Figure BDA0002026544630000182
now, the following performance indicator function is defined:
Figure BDA0002026544630000183
wherein α∈ [0, 1].
Mixing (13) - (17), j (t) <0 holds, provided that the following inequality holds,
Figure BDA0002026544630000184
in the formula,
Figure BDA0002026544630000185
Figure BDA0002026544630000186
Figure BDA0002026544630000187
Figure BDA0002026544630000188
step S33: further, in order to convert the inequality (18) into a linear matrix inequality, a matrix is defined
Figure BDA0002026544630000189
Comprises the following steps:
Figure BDA00020265446300001810
in the formula,
Figure BDA00020265446300001811
is a non-singular matrix.
Now substitute (20) into (18) and define
Figure BDA00020265446300001812
And extracting the fuzzy advance variable to obtain:
Figure BDA0002026544630000191
in the formula, L ∈ Li,
Figure BDA0002026544630000192
Is a fuzzy rule that is a function of the rule,
Figure BDA0002026544630000193
Figure BDA0002026544630000194
Figure BDA0002026544630000195
then, if inequality (21) holds, J (k) <0 can be obtained, then
V(k+1)-1＜α(V(k)-1). (23)
From equation (23):
V(k)＜αk(V(0)-1)+1, (24)
for the zero-initial case, we get:
Figure BDA0002026544630000196
in the formula,
Figure BDA0002026544630000197
Figure BDA0002026544630000198
the algorithm for designing the solution estimation controller is as follows:
Figure BDA0002026544630000199
and (21), wherein
Figure BDA00020265446300001910
The gain of the estimator can be solved as follows:
Figure BDA00020265446300001911
in step S4, considering that each water pump is affected by different external environmental interference factors; it is very difficult to suppress different external environmental interferences by using a uniform qualitative and quantitative method. An estimator is designed to estimate these ambient interference signals for this problem. The specific implementation steps are as follows:
step S41: consider first the following compensation controller:
Figure BDA0002026544630000201
in the formula,
Figure BDA0002026544630000202
Figure BDA0002026544630000203
and
Figure BDA0002026544630000204
is the compensation controller gain to be designed.
Substituting the formula (27) into the formula (5) to obtain the following photovoltaic multi-water pump closed-loop control system:
Figure BDA0002026544630000205
in the formula,
Figure BDA0002026544630000206
Figure BDA0002026544630000207
step S42: next consider the following Lyapunov function:
Figure BDA0002026544630000208
in the formula,
Figure BDA0002026544630000209
is a positive definite symmetric matrix. Obtained by taking the difference of the lyapunov functions v (k):
Figure BDA00020265446300002010
defining a symmetric positive definite matrix
Figure BDA00020265446300002011
Sum matrix
Figure BDA00020265446300002012
As equation (28) yields:
Figure BDA0002026544630000211
in the formula,
Figure BDA0002026544630000212
following step S3
Figure BDA0002026544630000221
We further consider the following performance indicator function:
Figure BDA0002026544630000222
wherein β∈ [0, 1].
Blend (29) - (31), the following inequality holds, then J (t) <0 is guaranteed,
Figure BDA0002026544630000223
in the formula,
Figure BDA0002026544630000224
Figure BDA0002026544630000225
is a symmetrical positive definite matrix and is characterized in that,
Figure BDA0002026544630000226
and
Figure BDA0002026544630000227
is a suitable dimension matrix, scalar β∈ [0, 1 [ ]].
The definition of the method is that,
Figure BDA0002026544630000228
obtained by using the cone complement theorem and extracting the fuzzy advance variable:
Figure BDA0002026544630000229
Figure BDA00020265446300002210
in the formula,
Figure BDA00020265446300002211
Figure BDA00020265446300002212
Figure BDA00020265446300002213
Figure BDA0002026544630000231
Figure BDA0002026544630000232
step S43: inequalities (33) and (34) are established to result in J (k) <0,
Figure BDA0002026544630000233
in the formula,
Figure BDA0002026544630000234
Figure BDA0002026544630000235
for the zero-initial case, we get:
Figure BDA0002026544630000236
the algorithm for designing and solving the feedback compensation controller is as follows:
Figure BDA0002026544630000237
and (33) and (34),
Figure BDA0002026544630000238
wherein
Figure BDA0002026544630000239
Figure BDA00020265446300002310
And
Figure BDA00020265446300002311
the control method is the gain of the controller, so that the series of design steps can realize that the disturbance of the water pump is reversely compensated, and the stable work of the photovoltaic multi-water pump system is stabilized.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (1)

1. A photovoltaic multi-water-pump reachable set estimation and compensation coordination control method is characterized by comprising the following steps:
step S1: providing a photovoltaic multi-water-pump physical system model;
step S2: establishing a nonlinear dynamic model of the photovoltaic multi-water pump physical system according to a physics principle and a neutral II type T-S fuzzy model;
step S3: establishing an estimation controller to estimate an external interference signal of the photovoltaic multi-water pump physical system model;
step S4: designing a compensation-based feedback controller based on the external interference signal estimated by the estimation controller established in the step S3, so that the external interference signal can be suppressed and stable operation of the photovoltaic multi-water pump can be realized;
wherein, the step S2 specifically includes the following steps:
step S21: establishing a photovoltaic single water pump nonlinear system model as shown in formula (1):
Figure FDA0002452223050000011
in the formula,
Figure FDA0002452223050000012
k6＝ωe-ωr；
Figure FDA0002452223050000013
Figure FDA0002452223050000014
Figure FDA0002452223050000021
isd、isqrepresents d-axis and q-axis currents;
Figure FDA0002452223050000022
respectively representing stator d-axis and q-axis magnetic chains;
Figure FDA0002452223050000023
respectively representing d-axis and q-axis magnetic chains of the rotor; omegarRepresenting the rotor angular velocity; u shapedcIs the photovoltaic power generation output voltage; t isLIs the load torque; omegaeRepresenting electromagnetic field angle velocity; l ismRepresenting armature mutual inductance;
Figure FDA0002452223050000024
represents the rotor time constant; l isrAnd RrRotor inductance and resistance, respectively; cdcIs a direct current side capacitor;
Figure FDA0002452223050000025
is the leakage inductance derivative; l issAnd RsRespectively representing the inductance and resistance of the stator; p represents the number of pole pairs;
step S22: establishing a photovoltaic multi-water pump system, wherein each water pump system is defined as an angle mark i; according to kirchhoff's current theorem, the following results are obtained:
Figure FDA0002452223050000026
substituting the formula (2) into the formula (1) to obtain the following photovoltaic multi-water pump coupling nonlinear system,
Figure FDA0002452223050000027
in the formula,
Figure FDA0002452223050000028
Figure FDA0002452223050000029
Figure FDA00024522230500000210
Figure FDA0002452223050000031
k6(i)＝ωe(i)-ωr(i)；
Figure FDA0002452223050000032
Figure FDA0002452223050000033
Figure FDA0002452223050000034
Figure FDA0002452223050000035
Figure FDA0002452223050000036
Figure FDA0002452223050000037
step S23: will isd(i)，isq(i)，ωr(i)，udc(i)Coupling non-line used as photovoltaic multi-water pumpThe output of the sexual system, and the output measurement channel involvement interference is obtained, expressed as follows:
Figure FDA0002452223050000038
in the formula,
Figure FDA0002452223050000039
ωi(t) is the output measurement channel interference;
will be provided with
Figure FDA00024522230500000310
And (3) as a fuzzy front piece variable, and performing Euler discretization on the fuzzy front piece variable to obtain the following neutral II-type T-S fuzzy model of the photovoltaic multi-water pump system:
Figure FDA00024522230500000311
wherein,
Figure FDA00024522230500000312
Figure FDA00024522230500000313
Figure FDA00024522230500000314
are respectively non-linear Aii(t),Bi(t),Aij(t) function
Figure FDA00024522230500000315
A linearized parameter matrix;
Figure FDA00024522230500000316
is a fuzzy set of neutral type II;
wherein, the step S3 specifically includes the following steps:
step S31: definition of
Figure FDA00024522230500000317
And introducing a variable
Figure FDA00024522230500000318
Figure FDA0002452223050000041
Substituting equation (5) yields:
Figure FDA0002452223050000042
in the formula,
Figure FDA0002452223050000043
introducing a fuzzy observer as follows:
Figure FDA0002452223050000044
in the formula,
Figure FDA0002452223050000045
Figure FDA0002452223050000046
is an auxiliary state vector that is,
Figure FDA0002452223050000047
Figure FDA0002452223050000048
is the observer gain; wherein n isxi、nyiRespectively representing the vector order of the system state variable and the vector order of the system output variable; in order to ensure that the water-soluble organic acid,
Figure FDA0002452223050000049
Figure FDA00024522230500000410
Figure FDA00024522230500000411
in the formula, SiNon-singular matrices, resulting in:
Figure FDA00024522230500000412
obtained according to equations (6) to (10):
Figure FDA00024522230500000413
Figure FDA00024522230500000414
because of SiIs a non-singular matrix, so equation (11) is again expressed as:
Figure FDA0002452223050000051
in the formula,
Figure FDA0002452223050000052
step S32: the following lyapunov function is defined,
Figure FDA0002452223050000053
in the formula,
Figure FDA0002452223050000054
is a positive definite symmetric matrix; taking the difference of the Lyapunov functions to obtain:
Figure FDA0002452223050000055
due to the fact that
Figure FDA0002452223050000056
In the formula,
Figure FDA0002452223050000057
and scalar k is 0, RnA vector representing the order of n is shown,
Figure FDA0002452223050000058
and
Figure FDA0002452223050000059
all vectors of (a) are of order n;
defining a positive definite symmetric matrix
Figure FDA00024522230500000510
Sum matrix
Figure FDA00024522230500000511
From equation (12):
Figure FDA00024522230500000512
Figure FDA0002452223050000061
in the formula,
Figure FDA0002452223050000062
let the performance indicator function:
Figure FDA0002452223050000063
in the formula, α∈ [0, 1]
According to the expressions (13) to (17), if J (k) <0, the following inequality holds,
Figure FDA0002452223050000064
in the formula,
Figure FDA0002452223050000065
Figure FDA0002452223050000066
Figure FDA0002452223050000067
Figure FDA0002452223050000068
step S33: converting the inequality (18) into a linear matrix inequality, wherein the matrix is ordered
Figure FDA0002452223050000069
Comprises the following steps:
Figure FDA00024522230500000610
in the formula,
Figure FDA00024522230500000611
is a non-singular matrix;
substituting formula (20) for formula (18) to define
Figure FDA00024522230500000612
Extracting fuzzy advance variables to obtain:
Figure FDA0002452223050000071
in the formula, L ∈ Li,
Figure FDA0002452223050000072
Is a fuzzy rule that is a function of the rule,
Figure FDA0002452223050000073
Figure FDA0002452223050000074
Figure FDA0002452223050000075
Figure FDA0002452223050000076
step S34: j (k) <0 from inequality (21),
V(k+1)-1＜α(V(k)-1)； (23)
from equation (23):
V(k)＜αk(V(0)-1)+1, (24)
for the zero-initial case, we get:
Figure FDA0002452223050000077
in the formula,
Figure FDA0002452223050000078
Figure FDA0002452223050000079
the algorithm for establishing the estimation controller is as follows:
according to
Figure FDA00024522230500000710
And formula (21), wherein
Figure FDA00024522230500000711
The gains of the estimation controller are as follows:
Figure FDA00024522230500000712
wherein, the step S4 specifically includes the following steps:
step S41: the following compensation controller was set up:
Figure FDA0002452223050000081
in the formula,
Figure FDA0002452223050000082
Figure FDA0002452223050000083
and
Figure FDA0002452223050000084
is the compensation controller gain;
substituting the formula (27) into the formula (5) to obtain the following photovoltaic multi-water pump closed-loop control system:
Figure FDA0002452223050000085
in the formula,
Figure FDA0002452223050000086
Figure FDA0002452223050000087
step S42: the following Lyapunov function is defined:
Figure FDA0002452223050000088
in the formula,
Figure FDA0002452223050000089
is a positive definite symmetric matrix; by taking the difference of the lyapunov functions v (k), we obtain:
Figure FDA00024522230500000810
defining a positive definite symmetric matrix
Figure FDA00024522230500000811
Sum matrix
Figure FDA00024522230500000812
From equation (28) we obtain:
Figure FDA00024522230500000813
Figure FDA0002452223050000091
in the formula,
Figure FDA0002452223050000092
obtaining the result according to the step S34
Figure FDA0002452223050000093
The following performance indicator function is obtained:
Figure FDA0002452223050000094
wherein, β∈ [0, 1 ];
obtaining J (k) <0 according to formula (29) to formula (31),
Figure FDA0002452223050000095
in the formula,
Figure FDA0002452223050000101
Figure FDA0002452223050000102
is a symmetrical positive definite matrix and is characterized in that,
Figure FDA0002452223050000103
and
Figure FDA0002452223050000104
is a suitable dimension matrix, scalar β∈ [0, 1 [ ]]；
In order to ensure that the water-soluble organic acid,
Figure FDA0002452223050000105
and
Figure FDA0002452223050000106
obtaining the following result by adopting cone supplementary guiding and extracting fuzzy advancing variables:
Figure FDA0002452223050000107
Figure FDA0002452223050000108
in the formula,
Figure FDA0002452223050000109
Figure FDA00024522230500001010
Figure FDA00024522230500001011
Figure FDA00024522230500001012
Figure FDA00024522230500001013
Figure FDA00024522230500001014
Figure FDA00024522230500001015
Figure FDA00024522230500001016
step S43: inequalities (33) and (34) are established to result in J (k) <0,
Figure FDA00024522230500001017
in the formula,
Figure FDA00024522230500001018
Figure FDA0002452223050000111
for the zero-initial case, we get:
Figure FDA0002452223050000112
the algorithm of the compensation-based feedback controller is as follows:
according to
Figure FDA0002452223050000113
Formula (33) and formula (34),
Figure FDA0002452223050000114
wherein
Figure FDA0002452223050000115
Figure FDA0002452223050000116
And
Figure FDA0002452223050000117
is the gain of the controller.
CN201910296953.XA 2019-04-12 2019-04-12 Photovoltaic multi-water-pump reachable set estimation and compensation coordination control method Active CN110011303B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910296953.XA CN110011303B (en) 2019-04-12 2019-04-12 Photovoltaic multi-water-pump reachable set estimation and compensation coordination control method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910296953.XA CN110011303B (en) 2019-04-12 2019-04-12 Photovoltaic multi-water-pump reachable set estimation and compensation coordination control method

Publications (2)

Publication Number Publication Date
CN110011303A CN110011303A (en) 2019-07-12
CN110011303B true CN110011303B (en) 2020-07-07

Family

ID=67171661

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910296953.XA Active CN110011303B (en) 2019-04-12 2019-04-12 Photovoltaic multi-water-pump reachable set estimation and compensation coordination control method

Country Status (1)

Country Link
CN (1) CN110011303B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111244942B (en) * 2020-01-20 2021-07-27 闽江学院 Photovoltaic power generation system dynamic output feedback control method based on difference operator dispersion

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107069815A (en) * 2017-04-21 2017-08-18 厦门理工学院 A kind of fuzzy control method of wind power-generating grid-connected operation

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107069815A (en) * 2017-04-21 2017-08-18 厦门理工学院 A kind of fuzzy control method of wind power-generating grid-connected operation

Also Published As

Publication number Publication date
CN110011303A (en) 2019-07-12

Similar Documents

Publication Publication Date Title
Li et al. An adaptive sliding-mode observer for induction motor sensorless speed control
CN102411396B (en) Method and arrangement for tracking maximum power point of photovoltaic module
Tripathi et al. Design and control of LCL filter interfaced grid connected solar photovoltaic (SPV) system using power balance theory
Deniz RETRACTED ARTICLE: ANN-based MPPT algorithm for solar PMSM drive system fed by direct-connected PV array
CN113285593B (en) Direct-current buck converter system control method based on composite integral sliding mode control
CN107040138A (en) A kind of DC-DC down-converter recombination current about beam control method
CN110011303B (en) Photovoltaic multi-water-pump reachable set estimation and compensation coordination control method
Jenkal et al. Vector control of a Doubly Fed Induction Generator wind turbine
CN104578143A (en) Compensation method suitable for uncertain large time delay of new energy electric generator
CN104779873B (en) A kind of predictive functional control algorithm for PMSM servo-drive systems
CN110365045B (en) Network delay suppression method of wind-solar hybrid power generation system based on estimation and compensation control
Liu et al. Backstepping control with speed estimation of PMSM based on MRAS
CN111092580A (en) Improved MRAS control method based on limited memory least square method
Sharma et al. Single stage solar PV array fed field oriented controlled induction motor drive for water pump
Sharma et al. SyRG-PV-BES-based standalone microgrid using approximate multipliers based adaptive control algorithm
De et al. Implementation of designed PV integrated controlled converter system
CN115800844A (en) Permanent magnet synchronous motor model-free sliding mode control method based on reduced-order PI observer
Feng et al. Terminal sliding-mode control of induction motor speed servo systems
Dinakaran et al. Modelling and performance analysis of improved incremental conductance MPPT technique for water pumping system
Yuan et al. Improved H∞ repetitive controller for current harmonics suppression of PMSM control system
Tavan et al. Output Feedback Control of DC-DC Converters with Unknown Load: An Application of I&I Based Filtered Transformation
Bashir et al. Small Signal Modelling and Observer based Stability Analysis of Cuk Converter via Lyapunov's Direct Method
Zhang et al. Adaptive Sliding‐Mode Control in Bus Voltage for an Islanded DC Microgrid
CN109062316A (en) A kind of photovoltaic system maximum power tracking method and system
CN103279164A (en) Novel MPPT control method based on Buck class converters

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