CN115903521A - Sliding mode control method of wind power generation system based on improved event trigger mechanism - Google Patents

Sliding mode control method of wind power generation system based on improved event trigger mechanism Download PDF

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CN115903521A
CN115903521A CN202310105925.1A CN202310105925A CN115903521A CN 115903521 A CN115903521 A CN 115903521A CN 202310105925 A CN202310105925 A CN 202310105925A CN 115903521 A CN115903521 A CN 115903521A
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sliding mode
wind power
power generation
generation system
mode control
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张莉
刘玉安
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Hefei University of Technology
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Abstract

The invention relates to a sliding mode control method of a wind power generation system based on an improved event trigger mechanism, which comprises the following steps: establishing a state space expression of a wind power generation system with a nonlinear permanent magnet synchronous motor; constructing a wind power generation system with a nonlinear permanent magnet synchronous motor into an interval two-type fuzzy singular perturbation system model; introducing an event trigger mechanism as a communication protocol; constructing an integral type sliding mode surface, establishing a global closed loop system for the interval two-type fuzzy singular perturbation system by using an equivalent control method, and synthesizing a second-order supercoiled sliding mode control law; deriving a stability criterion of the global closed-loop system, and analyzing the accessibility of an integral type sliding mode surface; evaluation and verification are performed. The invention adopts the interval two-type fuzzy idea to process the problem of the non-linear rotor rotating speed in the kinetic equation of the wind power generation system; the sliding modal motion of the system in a limited time is realized, and high-frequency buffeting caused by discontinuous control input is weakened.

Description

Sliding mode control method of wind power generation system based on improved event trigger mechanism
Technical Field
The invention relates to the technical field of control of wind power generation systems, in particular to a sliding mode control method of a wind power generation system based on an improved event trigger mechanism.
Background
Wind power has been greatly developed in recent years as one of the most potential energy sources, which has also driven the implementation of wind power generation systems. In particular to a wind power generation system with a permanent magnet synchronous generator, which is widely concerned due to the advantages of high efficiency, high power, convenient installation and the like. For the stabilization problem of a wind power generation system which is researched more, establishing an accurate mathematical model for the wind power generation system is considered firstly. At present, the T-S fuzzy idea is widely applied to nonlinear modeling of a wind power generation system. On the other hand, the mechanical and electromagnetic parts of a wind power system often exhibit different time scales in practice. For example, there are small circuit elements in the electromagnetic section, such as capacitors, inductors, etc., the presence of which introduces ill-conditioned problems into the system. Therefore, the singular perturbation theory is widely applied, and the core idea is to define a singular perturbation parameter and then skillfully eliminate or replace the parameter to avoid the influence.
Networked control is a development trend in the current control field, and has been widely researched, including some researches on the stabilization problem of the wind power generation system. For network control systems, how to select the appropriate communication protocol for each control module is a key issue. A suitable communication protocol provides both good control and transmission efficiency. For this reason, the classical event triggering mechanism is widely applied by virtue of its excellent idea, and also facilitates some improved methods such as the proposal and application of adaptive, dynamic and memory event triggering mechanisms.
Furthermore, in actual system operation, the system is usually affected by external interference, which may reduce system performance and even cause system instability. Common solutions are H-infinity control, sliding mode control, adaptive control, etc. Of these methods, sliding mode control is the most promising method and has been successfully used in the study of the calming problem of wind power generation systems, but most of the prior art focuses on control methods based on first-order sliding modes. Although the first-order sliding mode has strong robustness to external interference, the discontinuous control of the method inevitably causes the phenomenon of buffeting. The presence of chattering is disadvantageous for maintaining stable operation and good performance of the system, and particularly in many power systems, it is more desirable to provide a stable and high quality power supply. Recent work has shown that higher order sliding mode control is superior in reducing buffeting, and the higher order sliding mode theory utilizes the filtering effect of integration to reduce the buffeting effect by applying a discontinuous term to the higher order derivatives of the control law. However, due to the complexity of the high-order sliding mode theory, the research on the stabilization problem of the wind power generation system is still insufficient.
Disclosure of Invention
In order to solve the stabilization problem related to the wind power generation system at present, the invention aims to provide a sliding mode control method of the wind power generation system based on an improved event trigger mechanism, which not only realizes the sliding mode motion of the system in a limited time, but also weakens the high-frequency buffeting caused by discontinuous control input.
In order to realize the purpose, the invention adopts the following technical scheme: a sliding mode control method of a wind power generation system based on an improved event triggering mechanism, the method comprising the following sequential steps:
(1) Establishing a state space expression of a wind power generation system with a nonlinear permanent magnet synchronous motor;
(2) Constructing a wind power generation system with a nonlinear permanent magnet synchronous motor into an interval two-type fuzzy singular perturbation system model based on the constructed state space expression;
(3) Introducing an event trigger mechanism as a communication protocol;
(4) Constructing an integral type sliding mode surface, establishing a global closed loop system for the interval two-type fuzzy singular perturbation system by using an equivalent control method, and synthesizing a second-order supercoiled sliding mode control law;
(5) A stability criterion of the global closed-loop system is derived by utilizing a Lyapunov stability method, and the accessibility of an integral type sliding mode surface is analyzed based on a second-order supercoiled sliding mode control law;
(6) And evaluating and verifying the second-order supercoiled sliding mode control law.
The step (1) specifically comprises the following steps: the wind power generation system with the nonlinear permanent magnet synchronous motor is composed of a wind turbine, a transmission shaft, a converter and the permanent magnet synchronous motor, and based on aerodynamics, the energy generated by wind power is expressed as follows:
Figure BDA0004074793910000021
wherein, θ, R and v ω (t) represents air density, blade length and wind speed, respectively; c p (α (t), β) is a wind energy utilization coefficient, α (t) = v t (t)R/v ω (t) denotes tip speed ratio, β is helix angle, v t (t) represents the turbine speed, and the calculation formula of the tip speed ratio is as follows:
Figure BDA0004074793910000031
wherein:
Figure BDA0004074793910000032
ω m (t) represents the rotational speed of the wind turbine;
to obtain optimal energy, the wind turbine should be at the point of maximum power coefficient C Pmax (α (t), β) operation, in which case α (t) = α opt (t); the aerodynamic moment generated by the wind turbine is:
Figure BDA0004074793910000033
the dynamic system of the permanent magnet synchronous motor with parameter uncertainty is as follows:
Figure BDA0004074793910000034
wherein, P n Number of poles of the motor, omega g (t) rotor speed, R s And Δ R are the stator resistance and its uncertainty, L, respectively d And L q For the inductance of the stator in the d-Q axis, Q f Is a permanent magnetFlux, T e (t) is the generator torque, ω e (t)＝P n ω g (t)，U f (t) is an external disturbance, f 1 ,f 2 ,f 3 Is a disturbance parameter, and J and rho are respectively a moment of inertia and a friction coefficient;
establishing a state space expression of a wind power generation system with a nonlinear permanent magnet synchronous motor:
Figure BDA0004074793910000035
wherein the state vector x (t) = [ ω = [ ] g (t),i q (t),i d (t)] T Input vector u (t) = [ V ] q (t),V d (t)] T Output vector y (t) = [ ω ]) g (t),i q (t)] T The coefficient matrix is represented as:
Figure BDA0004074793910000041
Figure BDA0004074793910000042
wherein the content of the first and second substances,
Figure BDA0004074793910000043
is the uncertainty of the system matrix A, <' > is>
Figure BDA0004074793910000044
d is the upper bound of delta R and satisfies that | delta R | is less than or equal to d; Δ a satisfies a norm bounded condition:
Figure BDA0004074793910000045
wherein ν is greater than 0,
Figure BDA0004074793910000046
and
Figure BDA0004074793910000047
D 2 ＝[0 (2×1) ,diag{d,d}]。
the step (2) specifically comprises the following steps: when uncertainty
Figure BDA00040747939100000418
Upper and lower bounds->
Figure BDA0004074793910000048
When known, the upper membership function is established
Figure BDA0004074793910000049
And lower membership functionα 1 (x(t)),α 2 (x(t))：
Figure BDA00040747939100000410
The global membership function satisfies the following form:
Figure BDA00040747939100000411
wherein the content of the first and second substances,
Figure BDA00040747939100000412
is a weight function, satisfies->
Figure BDA00040747939100000413
And &>
Figure BDA00040747939100000414
Then, an interval type two fuzzy rule is established: if it is used
Figure BDA00040747939100000419
Is->
Figure BDA00040747939100000415
Then the
Figure BDA00040747939100000416
/>
Wherein the content of the first and second substances,
Figure BDA00040747939100000420
and &>
Figure BDA00040747939100000417
Respectively representing a precondition variable and an interval type two fuzzy set; epsilon ε ＝diag{I 1 ,εI 2 ε is a singular perturbation parameter; f (x (t)) = [ f 1 (x(t)),f 2 (x(t))] T Is a bounded non-linear signal present on the input channel that satisfies ∑ or ∑>
Figure BDA0004074793910000051
The system matrix is restated as:
Figure BDA0004074793910000052
wherein the content of the first and second substances,
Figure BDA0004074793910000053
and D 2i ＝[0 (2×1) ,diag{d}]And
Figure BDA0004074793910000054
establishing an interval two-type fuzzy singular perturbation system model for the wind power generation system with the permanent magnet synchronous motor by combining the defined membership functions (8) to (9):
Figure BDA0004074793910000055
the step (3) specifically comprises the following steps: for the ith fuzzy rule, an event triggering mechanism is proposed:
Figure BDA0004074793910000056
wherein:
Figure BDA0004074793910000057
m p (t)＝x(t l k+nk)-x(t l+1-p k)
Figure BDA0004074793910000058
wherein l is a positive integer, t l Is the sampling instant, k is the sampling period, theta i Is a trigger matrix, # p ∈[0,1]Is a weight parameter, satisfies
Figure BDA0004074793910000059
p is the amount of historical transmission data, and when p =1, equation (12) translates to a memoryless event-triggered mechanism; />
Figure BDA0004074793910000061
The dynamic threshold is a dynamic threshold, the dynamic characteristic of a memoryless event trigger mechanism is embodied by a hyperbolic tangent function tanh (-), and the dynamic threshold is evolved by the tanh (-), so as to adapt to the fluctuation degree of the system state; t is t l k is also the time at which the data reaches the zero order holder, and therefore, is asserted>
Figure BDA0004074793910000062
The step (4) specifically comprises the following steps: constructing integral type sliding mode surfaces:
Figure BDA0004074793910000063
wherein the content of the first and second substances,
Figure BDA0004074793910000064
is a shadow matrix, is selected>
Figure BDA0004074793910000065
Is a column full rank matrix, satisfies >>
Figure BDA0004074793910000066
For->
Figure BDA0004074793910000067
Satisfy->
Figure BDA0004074793910000068
For nominal control u 0 (t), design by model rules:
model rules: if it is not
Figure BDA00040747939100000619
Is->
Figure BDA0004074793910000069
Then the
Figure BDA00040747939100000610
Wherein, K εjp Is the controller gain to be solved, after defuzzification, the following are obtained:
Figure BDA00040747939100000611
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00040747939100000612
satisfies the following conditions:
Figure BDA00040747939100000613
according to an equivalent control method when
Figure BDA00040747939100000614
Obtaining equivalent control:
Figure BDA00040747939100000615
wherein the content of the first and second substances,
Figure BDA00040747939100000616
will u eq Substituting the interval two-type fuzzy singular perturbation system model to derive a global closed loop system for the fuzzy singular perturbation system model:
Figure BDA00040747939100000617
wherein the content of the first and second substances,
Figure BDA00040747939100000618
the second-order supercoiled sliding mode control law is as follows:
u(t)＝u 1 (t)+u 2 (t) (19)
wherein:
Figure BDA0004074793910000071
Figure BDA0004074793910000072
Figure BDA0004074793910000073
the step (5) specifically comprises the following steps: the stability analysis is carried out on the global closed loop system based on the Lyapunov method, and the analysis process is as follows:
theorem 1: known system matrix A i ,B i ,C i ,D i ,F i Given a number of scalars
Figure BDA0004074793910000074
And mu i Then for any i, j =1,2,/is combined>
Figure BDA0004074793910000075
If there is any symmetric matrix +>
Figure BDA0004074793910000076
And &>
Figure BDA0004074793910000077
And a matrix->
Figure BDA0004074793910000078
And &>
Figure BDA0004074793910000079
Scalar v i > 0 and theta i > 0, such that the following conditions hold, the global closed loop system is asymptotically stable and satisfies a given H-infinity performance level γ:
Figure BDA00040747939100000710
Figure BDA00040747939100000711
wherein:
Figure BDA00040747939100000712
Figure BDA00040747939100000713
Figure BDA00040747939100000714
Figure BDA00040747939100000715
and
Figure BDA0004074793910000081
Figure BDA0004074793910000082
Figure BDA0004074793910000083
Figure BDA0004074793910000084
Figure BDA0004074793910000085
the second-order supercoiled sliding mode control law is proved to be capable of driving the state track of the global closed-loop system to reach the sliding mode surface within a limited time, so that sliding mode motion is formed, and the second-order supercoiled sliding mode control law is substituted into an integral sliding mode surface to obtain the following expression:
Figure BDA0004074793910000086
wherein ξ 1 >0，
Figure BDA0004074793910000087
Figure BDA0004074793910000088
And &>
Figure BDA0004074793910000089
Is a given matrix in a sliding-mode surface, f (x (t)) is a non-linear function;
performing accessibility analysis based on a Lyapunov method:
theorem 2: given scalar ξ 1 ,ξ 2 The upper bound of the nonlinear function f (x (t)) is known
Figure BDA00040747939100000810
If the formula (24) holds, the interval type fuzzy singularity perturbation system withstands a finite time>
Figure BDA00040747939100000811
Converge internally to the origin, i.e.>
Figure BDA00040747939100000812
Figure BDA00040747939100000813
According to the technical scheme, the beneficial effects of the invention are as follows: firstly, aiming at a researched wind power generation system, the multi-time scale phenomenon existing in mechanical and electromagnetic components in the system is further considered, a more universal interval type fuzzy singular perturbation system model is established, and the interval type fuzzy idea is adopted to process the problem of the non-linear rotor rotating speed in the kinetic equation of the wind power generation system; secondly, in order to enhance the robustness of the actual operation of the wind power generation system, the invention provides H infinite sliding mode control comprising a second-order supercoiling control law, so that the sliding mode motion of the system in limited time is realized, and high-frequency buffeting caused by discontinuous control input is weakened compared with most of work depending on first-order sliding mode control; thirdly, based on the idea of network control, the invention provides a memory event trigger control with smoother dynamic threshold, which can utilize a plurality of current and historical transmission data to adjust the trigger condition.
Drawings
FIG. 1 is a control block diagram of a wind power generation system with a PMSM according to the present invention;
FIGS. 2 and 3 are graphs of the open loop state and the closed loop state under the supercoiled control of the two-type M fuzzy singular perturbation system;
FIGS. 4 and 5 are a state diagram and a control input diagram of the supercoiling control lower sliding die surface;
FIG. 6 is a diagram illustrating the release time and interval change of the event trigger mechanism in the present invention;
FIG. 7 is a threshold evolution scenario of the event trigger mechanism in the present invention.
Detailed Description
A sliding mode control method of a wind power generation system based on an improved event triggering mechanism, the method comprising the following sequential steps:
(1) Establishing a state space expression of a wind power generation system with a nonlinear permanent magnet synchronous motor;
(2) Constructing a wind power generation system with a nonlinear permanent magnet synchronous motor into an interval type two fuzzy singular perturbation system model based on the constructed state space expression;
(3) Introducing an event trigger mechanism as a communication protocol;
(4) Constructing an integral type sliding mode surface, establishing a global closed loop system for the interval two-type fuzzy singular perturbation system by using an equivalent control method, and synthesizing a second-order supercoiled sliding mode control law;
(5) A stability criterion of the global closed-loop system is derived by utilizing a Lyapunov stability method, and the accessibility of an integral type sliding mode surface is analyzed based on a second-order supercoiled sliding mode control law;
(6) And evaluating and verifying the second-order hyper-helical sliding mode control law.
As shown in fig. 1, the step (1) specifically includes: the wind power generation system with the nonlinear permanent magnet synchronous motor is composed of a wind turbine, a transmission shaft, a converter and a permanent magnet synchronous motor, and based on aerodynamics, the energy generated by wind power is expressed as follows:
Figure BDA0004074793910000101
wherein, θ, R and v ω (t) represents air density, blade length and wind speed, respectively; c p (α (t), β) is a wind energy utilization coefficient, α (t) = v t (t)R/v ω (t) denotes tip speed ratio, β is helix angle, v t (t) represents the turbine speed, and the calculation formula of the tip speed ratio is as follows:
Figure BDA0004074793910000102
wherein:
Figure BDA0004074793910000103
ω m (t) represents the rotational speed of the wind turbine;
to obtain optimal energy, the wind turbine should be at the point of maximum power coefficient C Pmax (α (t), β) operation, in which case α (t) = α opt (t); the aerodynamic moment generated by a wind turbine is:
Figure BDA0004074793910000104
the dynamic system of the permanent magnet synchronous motor with parameter uncertainty is as follows:
Figure BDA0004074793910000105
wherein, P n Number of poles of the motor, omega g (t) is the rotational speed of the rotor,R s and Δ R are the stator resistance and its uncertainty, L, respectively d And L q Inductance of stator in d-Q axis, Q f Is a permanent magnetic flux, T e (t) is the generator torque, ω e (t)＝P n ω g (t)，U f (t) is an external disturbance, f 1 ,f 2 ,f 3 Is a disturbance parameter, and J and rho are respectively a moment of inertia and a friction coefficient;
establishing a state space expression of a wind power generation system with a nonlinear permanent magnet synchronous motor:
Figure BDA0004074793910000111
/>
wherein the state vector x (t) = [ ω = [ ] g (t),i q (t),i d (t)] T Input vector u (t) = [ V ] q (t),V d (t)] T Output vector y (t) = [ ω ]) g (t),i q (t)] T The coefficient matrix is represented as:
Figure BDA0004074793910000112
Figure BDA0004074793910000113
wherein the content of the first and second substances,
Figure BDA0004074793910000114
is the uncertainty of the system matrix A, <' > is>
Figure BDA0004074793910000115
d is the upper bound of delta R and satisfies that | delta R | is less than or equal to d; Δ a satisfies a norm bounded condition:
Figure BDA0004074793910000116
wherein ν is greater than 0,
Figure BDA0004074793910000117
and
Figure BDA0004074793910000118
D 2 ＝[0 (2×1) ,diag{d,d}]。
for a nonlinear system, T-S fuzzy is a classical modeling method, and the main idea is to use a sector boundary method to construct a T-S fuzzy model, namely
Figure BDA0004074793910000119
Due to omega g (t) is placed in the established membership functions and the global non-linear model can be described as a combination of linear submodels. This is indeed an effective method, but note ω g The physical meaning of (t) is the rotor speed, which easily creates parameter uncertainty. It is assumed here that in the real case ω g (t) having parameter uncertainty>
Figure BDA00040747939100001112
Then->
Figure BDA00040747939100001113
Should have a true upper and lower bound->
Figure BDA00040747939100001110
In the form of (1). In this way, the coefficient matrix will contain this parameter uncertainty +>
Figure BDA00040747939100001114
In this case, the uncertainty parameter ≥ can be determined by means of the IT-2 ambiguity method>
Figure BDA00040747939100001115
Hidden in the upper and lower membership functions.
The step (2) specifically comprises the following steps: when uncertainty
Figure BDA00040747939100001116
Upper and lower bound>
Figure BDA00040747939100001111
When known, the upper membership function is established
Figure BDA0004074793910000121
And lower membership functionα 1 (x(t)),α 2 (x(t))：
Figure BDA0004074793910000122
The global membership function satisfies the following form:
Figure BDA0004074793910000123
/>
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0004074793910000124
is a weight function, satisfies->
Figure BDA0004074793910000125
And &>
Figure BDA0004074793910000126
Furthermore, consider the stator inductance L on the d-q axis of the electromagnetic subsystem q ,L d Is small, which will produce a multi-time scale phenomenon. In general, L d And L q Of the order of 10 -2 Thus, states of different orders of magnitude that exist in such a system can be described by introducing a singular perturbation parameter, for example, taking the perturbation parameter e =0.01.
Then, a zone two type fuzzy rule is established: if it is not
Figure BDA00040747939100001213
Is->
Figure BDA0004074793910000127
Then the
Figure BDA0004074793910000128
Wherein the content of the first and second substances,
Figure BDA00040747939100001214
and &>
Figure BDA0004074793910000129
Respectively representing a precondition variable and a two-type interval fuzzy set; epsilon ε ＝diag{I 1 ,εI 2 -wherein epsilon is a singular perturbation parameter; f (x (t)) = [ f 1 (x(t)),f 2 (x(t))] T Is a bounded nonlinear signal present on the input channel, satisfy->
Figure BDA00040747939100001210
The system matrix is restated as:
Figure BDA00040747939100001211
wherein the content of the first and second substances,
Figure BDA00040747939100001212
and D 2i ＝[0 (2×1) ,diag{d}]And
Figure BDA0004074793910000131
establishing an interval two-type fuzzy singular perturbation system model for the wind power generation system with the permanent magnet synchronous motor by combining the defined membership functions (8) to (9):
Figure BDA0004074793910000132
the step (3) specifically comprises the following steps: for the ith fuzzy rule, an event triggering mechanism is proposed:
Figure BDA0004074793910000133
wherein:
Figure BDA0004074793910000134
m p (t)＝x(t l k+nk)-x(t l+1-p k)
Figure BDA0004074793910000135
wherein l is a positive integer, t l Is the sampling instant, k is the sampling period, theta i Is a trigger matrix, # p ∈[0,1]Is a weight parameter, satisfies
Figure BDA0004074793910000136
p is the amount of historical transmission data, and when p =1, equation (12) translates to a memoryless event-triggered mechanism; />
Figure BDA0004074793910000137
The dynamic threshold is a dynamic threshold, the dynamic characteristic of a memoryless event trigger mechanism is embodied by a hyperbolic tangent function tanh (-), and the dynamic threshold is evolved by the tanh (-), so as to adapt to the fluctuation degree of the system state; in addition, the invention also assumes that the time delay phenomenon is not considered in the event triggering mechanism, t l k is also the time at which the data reaches the zero order holder, and therefore, is asserted>
Figure BDA0004074793910000138
The step (4) specifically comprises the following steps: constructing integral type sliding mode surfaces:
Figure BDA0004074793910000139
wherein the content of the first and second substances,
Figure BDA00040747939100001310
is a shooting matrix, in combination with a plurality of shooting units>
Figure BDA00040747939100001311
Is a column full rank matrix, satisfies->
Figure BDA00040747939100001312
For +>
Figure BDA00040747939100001313
Satisfy->
Figure BDA00040747939100001314
For nominal control u 0 (t), design by model rules:
model rules: if it is used
Figure BDA00040747939100001420
Is->
Figure BDA0004074793910000141
Then the
Figure BDA0004074793910000142
Wherein, K εjp Is the controller gain to be solved, and after defuzzification, the following are obtained:
Figure BDA0004074793910000143
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0004074793910000144
satisfies the following conditions:
Figure BDA0004074793910000145
according to an equivalent control method when
Figure BDA0004074793910000146
Obtaining equivalent control:
Figure BDA0004074793910000147
wherein the content of the first and second substances,
Figure BDA0004074793910000148
will u eq Substituting the interval two-type fuzzy singular perturbation system model to derive a global closed loop system for the fuzzy singular perturbation system model:
Figure BDA0004074793910000149
wherein the content of the first and second substances,
Figure BDA00040747939100001410
the second-order hyper-helical sliding mode control law is as follows:
u(t)＝u 1 (t)+u 2 (t) (19)
wherein:
Figure BDA00040747939100001411
Figure BDA00040747939100001412
Figure BDA00040747939100001413
the step (5) specifically comprises the following steps: the stability analysis is carried out on the global closed-loop system based on the Lyapunov method, and the analysis process is as follows:
theorem 1: known system matrix A i ,B i ,C i ,D i ,F i Given a number of scalars
Figure BDA00040747939100001414
And mu i Then for any i, j =1,2,/is>
Figure BDA00040747939100001415
If there is any symmetric matrix +>
Figure BDA00040747939100001416
And &>
Figure BDA00040747939100001417
And a matrix->
Figure BDA00040747939100001418
And &>
Figure BDA00040747939100001419
Scalar v i 0 and theta i > 0, such that the following conditions hold, the global closed loop system is asymptotically stable and satisfies a given H-infinity performance level γ:
Figure BDA0004074793910000151
Figure BDA0004074793910000152
wherein:
Figure BDA0004074793910000153
Figure BDA0004074793910000154
Figure BDA0004074793910000155
Figure BDA0004074793910000156
and
Figure BDA0004074793910000157
Figure BDA0004074793910000158
Figure BDA0004074793910000159
Figure BDA00040747939100001510
Figure BDA00040747939100001511
the second-order supercoiled sliding mode control law is proved to be capable of driving the state track of the global closed-loop system to reach the sliding mode surface within a limited time, so that sliding mode motion is formed, and the second-order supercoiled sliding mode control law is substituted into an integral sliding mode surface to obtain the following expression:
Figure BDA0004074793910000161
wherein ξ 1 ＞0，
Figure BDA0004074793910000168
ξ 2 ＞0，/>
Figure BDA0004074793910000162
And &>
Figure BDA0004074793910000163
Is a given matrix in a sliding-mode surface, f (x (t)) is a non-linear function;
performing accessibility analysis based on a Lyapunov method:
theorem 2: given scalar ξ 1 ，ξ 2 The upper bound of the nonlinear function f (x (t)) is known
Figure BDA0004074793910000164
If the formula (24) is true, the interval two-type fuzzy singular perturbation system holds at a finite time>
Figure BDA0004074793910000165
Internally converging to the origin, i.e. <' >>
Figure BDA0004074793910000166
Figure BDA0004074793910000167
The method is evaluated through a simulation model, and the verification proves that the method can be used for controlling the wind power generation system and has a better control effect.
This is further described below with reference to fig. 1 to 7.
As shown in fig. 1, table 1 below gives the values of the parameters of a wind power generation system with a nonlinear permanent magnet synchronous motor.
TABLE 1
Parameter(s) Value taking Parameter(s) Value taking
J
5×10 -3 N·m R 0.5m
θ 1.2kg/m 2 Q f 0.16Wb
ρ 6×10 -3 N·m·s/rad R s 1.13Ω
L d ＝L q 2.7×10 -3 H C p max 0.41
P n 8 D 1 -5
α opt (t) 8.1 D 2 5
In addition, the invention gives the parameters of the rest of the simulations: the upper and lower uncertain boundaries of the parameters of the nonlinear term are
Figure BDA00040747939100001712
Number of transmission history data>
Figure BDA0004074793910000171
Weight psi of historical data 1 ＝0.6,ψ 2 =0.4, event trigger related parameter κ i ＝0.05,μ i ＝8,/>
Figure BDA0004074793910000172
Uncertainty Δ R =0.5sin (t) and its upper bound d =0.5, h infinite performance level γ =2, singular perturbation parameter £ £ R>
Figure BDA0004074793910000173
Furthermore, for the upper and lower membership functions, the nonlinear weighting function is selected as
Figure BDA0004074793910000174
And &>
Figure BDA0004074793910000175
Then, χ ij ＝0.7,/>
Figure BDA00040747939100001713
The boundary conditions for the selected membership functions can be met. By solving the convex optimization problem for theorem 1, the following gain matrix can be obtained:
Figure BDA0004074793910000176
Figure BDA0004074793910000177
Figure BDA0004074793910000178
Figure BDA0004074793910000179
further, considering the influence of the environment, the disturbance function is set to ω (t) =2sin (t), and the nonlinear function is set to f (x (t)) = [2sin (2 t) x (t), 2cos (2 t) x (t)] T Projection matrix
Figure BDA00040747939100001710
Is set as an identity matrix of order 2,
Figure BDA00040747939100001711
setting an initial state to x T (0)＝[2,2,2]The sampling period is k =0.008, and then the operating environment of the model is built in MATLAB, resulting in the following simulation results.
First, as seen from fig. 2 and 3, the open loop state of the system is unstable when no controller is applied, but the state is well converged under the action of the designed supercoiled controller, which also indicates that the controller designed by the present invention can meet the stabilization requirement of the system. Secondly, according to fig. 4 and 5, the sliding mode surface state and the control input based on the supercoiling method both show good convergence. Then, as can be seen from fig. 6, with the introduction of the event trigger mechanism, the communication burden is greatly reduced, and the trigger threshold can be dynamically adjusted to adapt to the state fluctuation, and the dynamic adjustment process is shown in fig. 7.
Furthermore, the present invention compares the proposed method with the classical first order sliding mode for further significant advantages. Through testing, the first-order sliding mode control can achieve similar control targets, but certain fluctuation exists, which is probably caused by discontinuous control input in the first-order sliding mode, and the supercoiling method provided by the invention reduces the fluctuation, which is beneficial to the operation of a practical wind power generation system.
Furthermore, the present invention compares the proposed improved event triggering method with several classical event triggering methods. The index of comparison is the trigger rate, which can be calculated by the ratio between the number of transmitted data and the number of sampled data. Table 2 below shows the comparison results. Test results show that the improved event triggering method provided by the invention is superior to single and classical event triggering methods, probably because the proposed method has both memory and dynamic characteristics.
TABLE 2
Trigger rate k＝0.002 k＝0.004 k＝0.008 k＝0.01
Method of the invention 6.7％ 12.1％ 24.2％ 30.6％
Dynamic event triggering 8.5％ 17.8％ 35.8％ 40.2％
Memory event triggering 8.9％ 18.2％ 37.5％ 44.1％
Classical event triggering 11.8％ 23.5％ 47.6％ 56.7％
In conclusion, aiming at the researched wind power generation system, the invention further considers the multi-time scale phenomenon existing in mechanical and electromagnetic components in the system, establishes a more universal interval two-type fuzzy singular perturbation system model, and adopts the interval two-type fuzzy idea to process the problem of the non-linear rotor rotating speed in the kinetic equation of the wind power generation system; in order to enhance the robustness of the actual operation of the wind power generation system, the invention not only realizes the sliding mode motion of the system in limited time, but also weakens the high-frequency buffeting caused by discontinuous control input compared with the majority of work depending on first-order sliding mode control; based on the idea of network control, the invention can utilize a plurality of current and historical transmission data to adjust the triggering condition, and compared with a single method and a classical method, the method can more effectively reduce the communication pressure and has stronger practicability.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the invention and are not to be construed as limiting the embodiments of the present invention, and it will be apparent to those skilled in the art that other variations and modifications can be made on the basis of the above description.

Claims (6)

1. A sliding mode control method of a wind power generation system based on an improved event trigger mechanism is characterized by comprising the following steps: the method comprises the following steps in sequence:
(1) Establishing a state space expression of a wind power generation system with a nonlinear permanent magnet synchronous motor;
(2) Constructing a wind power generation system with a nonlinear permanent magnet synchronous motor into an interval two-type fuzzy singular perturbation system model based on the constructed state space expression;
(3) Introducing an event trigger mechanism as a communication protocol;
(4) Constructing an integral type sliding mode surface, establishing a global closed loop system for the interval two-type fuzzy singular perturbation system by using an equivalent control method, and synthesizing a second-order supercoiled sliding mode control law;
(5) A Lyapunov stability method is used for deriving a stability criterion of the global closed-loop system, and the accessibility of an integral type sliding mode surface is analyzed based on a second-order super-spiral sliding mode control law;
(6) And evaluating and verifying the second-order supercoiled sliding mode control law.
2. The sliding mode control method of the wind power generation system based on the improved event triggering mechanism according to claim 1, characterized in that: the step (1) specifically comprises the following steps: the wind power generation system with the nonlinear permanent magnet synchronous motor is composed of a wind turbine, a transmission shaft, a converter and the permanent magnet synchronous motor, and based on aerodynamics, the energy generated by wind power is expressed as follows:
Figure FDA0004074793900000011
wherein, θ, R and v ω (t) represents air density, blade length and wind speed, respectively; c p (alpha (t), beta) is wind energy benefitBy a factor, α (t) = v t (t)R/v ω (t) denotes tip speed ratio, β is helix angle, v t (t) represents the turbine speed, and the calculation formula of the tip speed ratio is as follows:
Figure FDA0004074793900000012
wherein:
Figure FDA0004074793900000013
ω m (t) represents the rotational speed of the wind turbine;
to obtain optimal energy, the wind turbine should be at the point of maximum power coefficient C Pmax (α (t), β) operation, in which case α (t) = α opt (t); the aerodynamic moment generated by a wind turbine is:
Figure FDA0004074793900000021
the dynamic system of the permanent magnet synchronous motor with parameter uncertainty is as follows:
Figure FDA0004074793900000022
wherein, P n Number of poles of the motor, omega g (t) is the rotor speed, R s And Δ R are the stator resistance and its uncertainty, L, respectively d And L q For the inductance of the stator in the d-Q axis, Q f Is a permanent magnetic flux, T e (t) is the generator torque, ω e (t)＝P n ω g (t)，U f (t) is an external disturbance, f 1 ,f 2 ,f 3 Is a disturbance parameter, and J and rho are respectively a moment of inertia and a friction coefficient;
establishing a state space expression of a wind power generation system with a nonlinear permanent magnet synchronous motor:
Figure FDA0004074793900000023
wherein the state vector x (t) = [ ω = g (t),i q (t),i d (t)] T Input vector u (t) = [ V ] q (t),V d (t)] T Output vector y (t) = [ ω ]) g (t),i q (t)] T The coefficient matrix is represented as:
Figure FDA0004074793900000024
Figure FDA0004074793900000025
wherein the content of the first and second substances,
Figure FDA0004074793900000026
is the uncertainty of the system matrix A, <' > is>
Figure FDA0004074793900000027
d is the upper bound of delta R and satisfies that | delta R | is less than or equal to d; Δ a satisfies a norm bounded condition:
Figure FDA0004074793900000031
wherein ν is greater than 0,
Figure FDA0004074793900000032
and
Figure FDA0004074793900000033
D 2 ＝[0 (2×1) ,diag{d,d}]。
3. the sliding mode control method of a wind power generation system based on an improved event triggering mechanism according to claim 1, characterized in that: the step (2) specifically comprises the following steps: when the upper and lower bounds of uncertainty l
Figure FDA0004074793900000034
When known, the upper membership function is established
Figure FDA0004074793900000035
And lower membership functionα 1 (x(t)),α 2 (x(t))：/>
Figure FDA0004074793900000036
The global membership functions satisfy the following form:
Figure FDA0004074793900000037
wherein the content of the first and second substances,
Figure FDA0004074793900000038
μ i (. Cndot.) is a weight function which satisfies +>
Figure FDA0004074793900000039
μ i (·)∈[0,1]And &>
Figure FDA00040747939000000310
Then, a zone two type fuzzy rule is established: if l ω g (t) is
Figure FDA00040747939000000311
Then the
Figure FDA00040747939000000312
Wherein, l ω g (t) and
Figure FDA00040747939000000313
respectively representing a precondition variable and an interval type two fuzzy set; epsilon ε ＝diag{I 1 ,εI 2 -wherein epsilon is a singular perturbation parameter; f (x (t)) = [ f 1 (x(t)),f 2 (x(t))] T Is a bounded non-linear signal present on the input channel that satisfies ∑ or ∑>
Figure FDA00040747939000000314
The system matrix is restated as:
Figure FDA00040747939000000315
wherein the content of the first and second substances,
Figure FDA0004074793900000041
and D 2i ＝[0 (2×1) ,diag{d}]And
Figure FDA0004074793900000042
establishing an interval two-type fuzzy singular perturbation system model for the wind power generation system with the permanent magnet synchronous motor by combining the defined membership functions (8) to (9):
Figure FDA0004074793900000043
4. the sliding mode control method of a wind power generation system based on an improved event triggering mechanism according to claim 1, characterized in that: the step (3) specifically comprises the following steps: for the ith fuzzy rule, an event trigger mechanism is proposed:
Figure FDA0004074793900000044
wherein:
Figure FDA0004074793900000045
m p (t)＝x(t l k+nk)-x(t l+1-p k)
Figure FDA0004074793900000046
wherein l is a positive integer, t l Is the sampling instant, k is the sampling period, theta i Is a trigger matrix, # p ∈[0,1]Is a weight parameter, satisfies
Figure FDA0004074793900000047
p is the amount of historical transmission data, and when p =1, equation (12) translates to a memoryless event-triggered mechanism; />
Figure FDA0004074793900000048
The dynamic threshold is a dynamic threshold, the dynamic characteristic of a memoryless event trigger mechanism is embodied by a hyperbolic tangent function tanh (-), and the dynamic threshold is evolved by the tanh (-), so as to adapt to the fluctuation degree of the system state; t is t l k is also the time at which the data reaches the zero order holder, and therefore, is asserted>
Figure FDA0004074793900000049
5. The sliding mode control method of a wind power generation system based on an improved event triggering mechanism according to claim 1, characterized in that: the step (4) specifically comprises the following steps: constructing integral type sliding mode surfaces:
Figure FDA0004074793900000051
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0004074793900000052
is a shadow matrix, is selected>
Figure FDA0004074793900000053
Is a column full rank matrix, satisfies
Figure FDA0004074793900000054
For->
Figure FDA0004074793900000055
Satisfy +>
Figure FDA0004074793900000056
For nominal control u 0 (t), design by model rules:
model rules: if l ω g (t) is
Figure FDA0004074793900000057
Then the
Figure FDA0004074793900000058
Wherein, K εjp Is the controller gain to be solved, after defuzzification, the following are obtained:
Figure FDA0004074793900000059
wherein the content of the first and second substances,
Figure FDA00040747939000000510
satisfies the following conditions:
Figure FDA00040747939000000511
according to an equivalent control method when
Figure FDA00040747939000000512
Obtaining equivalent control:
Figure FDA00040747939000000513
wherein the content of the first and second substances,
Figure FDA00040747939000000514
u is to be eq Substituting the interval two-type fuzzy singular perturbation system model into an interval two-type fuzzy singular perturbation system model, and deducing a global closed loop system for the fuzzy singular perturbation system model:
Figure FDA00040747939000000515
/>
wherein the content of the first and second substances,
Figure FDA00040747939000000516
the second-order supercoiled sliding mode control law is as follows:
u(t)＝u 1 (t)+u 2 (t) (19)
wherein:
Figure FDA0004074793900000061
Figure FDA0004074793900000062
Figure FDA0004074793900000063
6. the sliding mode control method of a wind power generation system based on an improved event triggering mechanism according to claim 1, characterized in that: the step (5) specifically comprises the following steps: the stability analysis is carried out on the global closed-loop system based on the Lyapunov method, and the analysis process is as follows:
theorem 1: known system matrix A i ,B i ,C i ,D i ,F i Given some scalar χ ij ,
Figure FDA0004074793900000064
ψ p ,/>
Figure FDA0004074793900000065
κ i And mu i Then for any i, j =1,2,/is>
Figure FDA0004074793900000066
If there is any symmetric matrix +>
Figure FDA0004074793900000067
And &>
Figure FDA0004074793900000068
And a matrix
Figure FDA0004074793900000069
And &>
Figure FDA00040747939000000610
Scalar v i > 0 and theta i > 0, such that the following conditions hold, the global closed loop system is asymptotically stable and satisfies a given H-infinity performance level γ:
Figure FDA00040747939000000611
Figure FDA00040747939000000612
wherein:
Figure FDA00040747939000000613
Figure FDA00040747939000000614
Figure FDA00040747939000000615
/>
Figure FDA00040747939000000616
and
Figure FDA0004074793900000071
Figure FDA0004074793900000072
Figure FDA0004074793900000073
Figure FDA0004074793900000074
Figure FDA0004074793900000075
the second-order supercoiled sliding mode control law is proved to be capable of driving the state track of the global closed-loop system to reach the sliding mode surface within a limited time, so that sliding mode motion is formed, and the second-order supercoiled sliding mode control law is substituted into an integral sliding mode surface to obtain the following expression:
Figure FDA0004074793900000076
wherein ξ 1 >0，
Figure FDA0004074793900000077
ξ 2 ＞0，/>
Figure FDA0004074793900000078
And &>
Figure FDA0004074793900000079
Is a given matrix in a sliding-mode surface, f (x (t)) is a non-linear function;
performing accessibility analysis based on a Lyapunov method:
theorem 2: given scalar ξ 1 ,ξ 2 The upper bound of the nonlinear function f (x (t)) is known
Figure FDA00040747939000000710
If the formula (24) is true, the interval two-type fuzzy singular perturbation system holds at a finite time>
Figure FDA00040747939000000711
Internally converging to the origin, i.e. <' >>
Figure FDA00040747939000000712
Figure FDA00040747939000000713
/>
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CN117039977A (en) * 2023-06-21 2023-11-10 淮阴工学院 Fuzzy supercoiled sliding mode observer inductance identification method based on predictive control condition
CN117193001A (en) * 2023-09-25 2023-12-08 南通大学 Hyperbolic approach law sliding mode control method based on integral reinforcement learning

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CN117039977A (en) * 2023-06-21 2023-11-10 淮阴工学院 Fuzzy supercoiled sliding mode observer inductance identification method based on predictive control condition
CN117039977B (en) * 2023-06-21 2024-06-11 淮阴工学院 Fuzzy supercoiled sliding mode observer inductance identification method based on predictive control condition
CN117193001A (en) * 2023-09-25 2023-12-08 南通大学 Hyperbolic approach law sliding mode control method based on integral reinforcement learning
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