CN109358509B - Rapid parameter identification method for chaotic ferromagnetic resonance system of coal mine power grid - Google Patents

Rapid parameter identification method for chaotic ferromagnetic resonance system of coal mine power grid Download PDF

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CN109358509B
CN109358509B CN201811336932.8A CN201811336932A CN109358509B CN 109358509 B CN109358509 B CN 109358509B CN 201811336932 A CN201811336932 A CN 201811336932A CN 109358509 B CN109358509 B CN 109358509B
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coal mine
power grid
ferromagnetic resonance
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马草原
李志杰
王法鑫
张勇
刘鹏娟
郑海广
智静茹
陈楚
张人懿
王伟
赵冬艳
许智恒
陈琦
闫龙
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China University of Mining and Technology CUMT
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Abstract

The invention provides a rapid parameter identification method for a chaotic ferromagnetic resonance system of a coal mine power grid, which is suitable for the field of electrical engineering. According to a fixed time stability theory and in combination with a traditional self-adaptive control method, a nonlinear controller is designed to enable a controlled variable to reach a neighborhood with an arbitrarily small reference value within a limited time, and the method specifically comprises the following steps: the method can identify the uncertain parameters of the chaotic ferromagnetic resonance system of the coal mine power grid in a limited time under the condition of not depending on an initial value; the time range of parameter identification can be ensured to have an upper bound, and the upper bound of the identification time can be calculated by the method provided by the invention; the method can quickly and accurately obtain the ferroresonance parameters, provide parameter support for preventing and controlling abnormal operation phenomena such as overvoltage and overcurrent of the transformer, and provide theoretical basis and technical support for safe operation research of a coal mine power grid.

Description

Rapid parameter identification method for chaotic ferromagnetic resonance system of coal mine power grid
Technical Field
The invention designs a rapid parameter identification method, and particularly relates to a rapid parameter identification method of a chaotic ferromagnetic resonance system of a coal mine power grid, which is suitable for the field of electrical engineering.
Background
Ferroresonance is a non-linear inductance and capacitance oscillation phenomenon in an electric power system, belongs to a complex electric phenomenon, and can occur in a loop formed by non-linear inductance elements and capacitance elements such as a power transformer or an electromagnetic voltage transformer (PT), a reactor with a core and the like. To date, researchers at home and abroad have a hundred years history on ferromagnetic resonance, but ferromagnetic resonance still frequently occurs in a power system, and various resonance elimination measures cannot completely eliminate ferromagnetic resonance. Mainly because the generation loops of the ferromagnetic resonance are extremely diversified, and the excitation condition is also extremely complicated. The complexity of the ferroresonance is not only expressed in the complexity of a generating circuit, but also in a very complex form, and in recent years, some researchers find that the ferroresonance with a chaotic effect may occur in a power system, and is also one of the expressions of the complexity of the ferroresonance. The resonance state has great harm to a coal mine power grid, and can cause the stability of an interconnected power system to be lost, so that the waveform distortion of circuit voltage and current, particularly the generation of overvoltage, causes the local serious instability of the system, and brings serious influence and harm to the coal mine power grid. And in the normal long-term operation of the transformer, parameters may change along with the change of temperature and humidity in the working environment. By parameter identification of the chaotic ferromagnetic resonance model, ferromagnetic resonance parameters can be obtained in time, parameter support is provided for preventing and controlling abnormal operation phenomena such as overvoltage and overcurrent of the transformer, theoretical basis and technical support are provided for safe operation research of a coal mine power grid, and therefore a rapid parameter identification method for a chaotic ferromagnetic resonance system of the coal mine power grid is necessary to research.
Most chaotic control methods are proposed based on the premise that system parameters are known. The coal mine power grid is complex in structure, certain parameters are difficult to accurately determine through online measurement, or system parameters are easy to drift and disturb in work due to the influence of the environment. In order to realize chaotic control and synchronization of the system, the common control methods have certain limitations. Therefore, the problem of parameter identification is an important issue in the field of chaotic system control and synchronization. In recent years, the problem of parameter identification of chaotic systems has attracted great attention of many scholars at home and abroad. The currently commonly used parameter identification methods mainly include an adaptive synchronous parameter identification method, a parameter identification method based on a synchronous parameter observer, a model identification method based on a fuzzy theory, and the like. In the parameter identification method, the identification method based on the synchronous observer does not need to copy the original chaotic system, and the controller is simple and easy to realize and has certain superiority. However, for the work of high-order power terms, sine terms, cosine terms and the like in the structure and multi-parameter synchronous identification of a complex system, the method has the problems of inaccurate identification, oscillation identification and the like, and has certain limitation in the application aspect. Therefore, the method for identifying the parameters of the conventional chaotic system is improved, and a better parameter identification scheme is found to become a main subject of chaotic parameter identification. Therefore, the scholars begin to apply the finite time stability theory and the fixed time stability theory to the chaotic recognition and combine the two theories with the traditional recognition method.
The finite time identification method can identify system parameters in finite time, but is limited by the limitation of finite time stability, namely the limitation is influenced by system initial conditions, and the accurate parameters are generally difficult to obtain in a coal mine power grid under the system initial conditions. The fixed time stability is an extension of the finite time stability, and compared with the identification method, the fixed time identification method can ensure that the identification time range has an upper bound and can identify the system parameters without depending on the initial condition.
Disclosure of Invention
Aiming at the technical problems, an error response system for constructing a chaotic ferromagnetic resonance system based on a synchronization idea is provided, and a self-adaptive fixed-time nonlinear controller is designed according to a fixed-time stability theory and by combining a traditional self-adaptive control method, so that the control quantity reaches the neighborhood with an arbitrarily small reference value within a limited time which does not depend on an initial value, the synchronization of a master system and a slave system is realized, and the rapid parameter identification method of the chaotic ferromagnetic resonance system of a coal mine power grid is realized more quickly and accurately.
In order to achieve the aim, the invention provides a method for quickly identifying parameters of a chaotic ferromagnetic resonance system of a coal mine power grid, which comprises the following steps:
a. collecting various data of a coal mine power grid, including transformer excitation inductance magnetic flux information, excitation inductance voltage information, resistance and capacitance information in a chaotic ferromagnetic resonance equivalent circuit, power supply voltage angular frequency, power supply voltage and magnetization characteristic parameters of the transformer excitation inductance, and establishing a second-order differential mathematical model of the chaotic ferromagnetic resonance system of the coal mine power grid by using the information;
b. based on a synchronization thought, aiming at error variables and uncertain parameters, establishing an error response system of the coal mine power grid chaotic ferromagnetic resonance through a second-order differential mathematical model of the coal mine power grid chaotic ferromagnetic resonance system;
c. aiming at an error response system, designing a nonlinear control law and an uncertain parameter self-adaptation law according to a fixed time stability theory, and realizing that the synchronous error of a controlled model and a reference model in fixed time is arbitrarily small;
d. designing a fixed time stability control rate and a self-adaptive law, realizing parameter identification and stability of a controlled model in a limited time, wherein the upper bound of identification time does not depend on an initial value;
e. and confirming the control parameters of the design control rate according to the Lyapunov stability theory.
The second-order differential mathematical model I of the chaotic ferromagnetic resonance system of the coal mine power grid is as follows:
Figure BDA0001861426840000021
in the formula: phi is the transformer excitation inductance magnetic flux, and V is the excitation inductance voltage; r is a resistor in the chaotic ferromagnetic resonance equivalent circuit, and C is a capacitor in the chaotic ferromagnetic resonance equivalent circuit; omega and E are respectively power supply voltage angular frequency and power supply voltage; a is0And b0Carrying out dimensionless treatment on the model I for the magnetization characteristic parameter of the transformer excitation inductance and t is time so that the chaotic ferromagnetic resonance system model of the coal mine power grid is equivalent to the following modelAs a master system model ii:
Figure BDA0001861426840000022
in the formula, a, b, c and d are uncertain parameters of coal mine power grid operation, but a magnetization characteristic parameter a of transformer excitation inductance0And b0Under the known condition, the specific values of the resistance R and the capacitance C of the transformer ferroresonance model with the chaotic dynamics behavior are determined by identifying the parameter C in the system model II, so that the parameters a and b can be obtained, and the parameter C is mainly identified in the parameter identification work.
The method for realizing the uncertain parameter synchronization comprises the following steps: the following system model iii was obtained according to formula ii:
Figure BDA0001861426840000031
wherein,
Figure BDA0001861426840000032
respectively, are estimated values of the system state variables,
Figure BDA0001861426840000033
respectively are estimated values of uncertain parameters, and u is the control input of the chaotic ferromagnetic resonance slave system of the coal mine power grid;
definition of
Figure BDA0001861426840000034
As a variable of the error, there is,
Figure BDA0001861426840000035
as the estimation error of the uncertain parameter, the difference between the formula iii and the formula ii is obtained to obtain the following error response system iv:
Figure BDA0001861426840000036
in the formula,
Figure BDA0001861426840000037
to relate to
Figure BDA0001861426840000038
And a polynomial of Φ.
The nonlinear control law designed according to the fixed time stability theory is as follows:
Figure BDA0001861426840000039
in the formula, alpha and beta are parameters to be designed of the system, alpha is more than 0 and less than 1, beta is more than 1, k is a terminal attractor feedback gain coefficient of a tuning parameter and meets the requirements,
the self-adaptive law of uncertain parameters is designed according to the self-adaptive control principle as follows:
Figure BDA00018614268400000310
in the formula, g is an arbitrary positive real number.
The calculation method for identifying the upper bound of the time range comprises the following steps: the nonlinear system is designed by using a fixed time stability theory as follows:
Figure BDA00018614268400000311
in the formula, x ∈ RnSetting f as unknown smooth nonlinear function for the state variable of the nonlinear system VII, if the abstract nonlinear system cannot be described in detail where T (x) is and the concrete expression has local bounded stable time function T (x) under the condition that the initial value of the nonlinear system is an arbitrary value, and the upper limit value T (x) of the bounded stable time function T (x)maxIndependent of the state variable x, i.e. when the initial conditions of the system take arbitrary values,
Figure BDA00018614268400000312
and TmaxIndependent of the state variable x, such that
Figure BDA00018614268400000313
And T > TmaxX (t) is ≡ 0. The nonlinear system VII is globally fixed and stable in time;
lesion 1-for any non-negative real number ξ1,ξ2,…,ξnAnd 0 < p.ltoreq.1, the following inequality holds:
Figure BDA0001861426840000041
for the nonlinear system VII, a continuous radial unbounded function V is assumed to exist: rn→R+∪ {0} satisfies:
Figure BDA0001861426840000042
any solution x (t) of the nonlinear system VII satisfies the inequality:
Figure BDA0001861426840000043
wherein alpha, beta, p, q, k is a real number larger than 0, pk <1, qk >1 is a simulation parameter, and at the moment, the overall fixed time of the origin of the nonlinear system VII is stable, V (x) is identical to 0 within the fixed time T, and the stable time is as follows:
Figure BDA0001861426840000044
the description is that a self-adaptive fixed time algorithm is designed to identify the cornerstone of uncertain parameters of the system in limited time, and a Lyapunov function is constructed according to the Lyapunov function stability theory:
Figure BDA0001861426840000045
the derivative of the Lyapunov candidate function of the error response system is obtained by using the designed controller u and the corresponding tuning parameter
Figure BDA0001861426840000051
Wherein,
Figure BDA0001861426840000052
the upper bound of the system settling time can thus be found to be:
Figure BDA0001861426840000053
this means that when t ≧ t1When the temperature of the water is higher than the set temperature,
Figure BDA0001861426840000054
and the master system II and the slave system III realize synchronization to obtain an uncertain parameter identification result.
Has the advantages that:
the invention discloses a method for quickly identifying parameters of a chaotic ferromagnetic resonance system of a coal mine power grid, which comprises the steps of firstly establishing a master-slave system model and an error response system model of the chaotic ferromagnetic resonance system of the coal mine power grid based on a synchronization thought, combining self-adaptive control with a fixed time stability theory, realizing uncertain parameter identification in a limited time under the condition of not depending on an initial value of a system parameter, quickly obtaining the upper bound of identification time, and preventing or controlling overvoltage and overcurrent phenomena through the identification parameters to achieve the aim of inhibiting ferromagnetic resonance.
Drawings
FIG. 1 is a schematic structural diagram of a chaotic ferromagnetic resonance system of a coal mine power grid adopted by the invention;
FIG. 2 is an equivalent circuit of the chaotic ferromagnetic resonance system of the coal mine power grid;
FIG. 3 is a flow chart of a method for identifying fast parameters of the chaotic ferroresonance system of the coal mine power grid according to the present invention;
FIG. 4(a) is the error system control result of the chaotic ferroresonant system of the present invention;
FIG. 4(b) is the error system control result of the chaotic ferroresonant system of the present invention;
FIG. 5 shows the identification result of the parameter c of the chaotic ferromagnetic resonance model of the coal mine power grid according to the present invention;
Detailed Description
Embodiments of the invention are further described below with reference to the accompanying drawings:
as shown in fig. 3, the method for rapidly identifying parameters of the chaotic ferromagnetic resonance system of the coal mine power grid comprises the following steps:
a. collecting various data of a coal mine power grid, including transformer excitation inductance magnetic flux information, excitation inductance voltage information, resistance and capacitance information in a chaotic ferromagnetic resonance equivalent circuit, power supply voltage angular frequency, power supply voltage and magnetization characteristic parameters of the transformer excitation inductance, and establishing a second-order differential mathematical model of the chaotic ferromagnetic resonance system of the coal mine power grid by using the information;
b. based on a synchronization thought, aiming at error variables and uncertain parameters, establishing an error response system of the coal mine power grid chaotic ferromagnetic resonance through a second-order differential mathematical model of the coal mine power grid chaotic ferromagnetic resonance system;
c. aiming at an error response system, designing a nonlinear control law and an uncertain parameter self-adaptation law according to a fixed time stability theory, and realizing that the synchronous error of a controlled model and a reference model in fixed time is arbitrarily small;
d. designing a fixed time stability control rate and a self-adaptive law, realizing parameter identification and stability of a controlled model in a limited time, wherein the upper bound of identification time does not depend on an initial value;
e. and confirming the control parameters of the design control rate according to the Lyapunov stability theory.
The method specifically comprises the following steps:
a. collecting various data of a coal mine power grid, including transformer excitation inductance magnetic flux information, excitation inductance voltage information, resistance and capacitance information in a chaotic ferromagnetic resonance equivalent circuit, power supply voltage angular frequency, power supply voltage and magnetization characteristic parameters of the transformer excitation inductance, and establishing a second-order differential mathematical model of the chaotic ferromagnetic resonance system of the coal mine power grid by using the information;
the coal mine power grid chaotic ferromagnetic resonance system and the equivalent circuit of the coal mine power grid chaotic ferromagnetic resonance system shown in the figure 2 are subjected to mathematical modeling, and a second-order differential mathematical model I of the coal mine power grid chaotic ferromagnetic resonance system is as follows:
Figure BDA0001861426840000071
in the formula: phi is the transformer excitation inductance magnetic flux, and V is the excitation inductance voltage; r is a resistor in the chaotic ferromagnetic resonance equivalent circuit, and C is a capacitor in the chaotic ferromagnetic resonance equivalent circuit; omega and E are respectively power supply voltage angular frequency and power supply voltage; a is0And b0Carrying out dimensionless treatment on the model I for the magnetization characteristic parameter of the transformer excitation inductance and t is time, so that the chaotic ferromagnetic resonance system model of the coal mine power grid is equivalent to the following system as a main system model II:
Figure BDA0001861426840000072
in the formula, a, b, c and d are uncertain parameters of coal mine power grid operation, but a magnetization characteristic parameter a of transformer excitation inductance0And b0Under the known condition, the specific values of the resistance R and the capacitance C of the transformer ferroresonance model with the chaotic dynamics behavior are determined by identifying the parameter C in the system model II, and the parameters a and b can be obtained, so that the parameter C is mainly identified in the parameter identification work;
b. based on a synchronization thought, aiming at error variables and uncertain parameters, establishing an error response system of the coal mine power grid chaotic ferromagnetic resonance through a second-order differential mathematical model of the coal mine power grid chaotic ferromagnetic resonance system;
to achieve synchronization of uncertain parameters in this embodiment, the following slave system model iii is obtained according to equation ii:
Figure BDA0001861426840000073
wherein,
Figure BDA0001861426840000074
are respectively system state variablesIs determined by the estimated value of (c),
Figure BDA0001861426840000075
respectively are estimated values of uncertain parameters, and u is the control input of the chaotic ferromagnetic resonance slave system of the coal mine power grid;
definition of
Figure BDA0001861426840000076
As a variable of the error, there is,
Figure BDA0001861426840000077
as the estimation error of the uncertain parameter, the difference between the formula iii and the formula ii is obtained to obtain the following error response system iv:
Figure BDA0001861426840000078
in the formula,
Figure BDA0001861426840000079
to relate to
Figure BDA00018614268400000710
And a polynomial of Φ;
c. aiming at an error response system, designing a nonlinear control law and an uncertain parameter self-adaptation law according to a fixed time stability theory, and realizing that the synchronous error of a controlled model and a reference model in fixed time is arbitrarily small;
the nonlinear control law is designed according to the fixed time stability theory as follows:
Figure BDA00018614268400000711
in the formula, alpha and beta are parameters to be designed of the system, alpha is more than 0 and less than 1, beta is more than 1, k is a terminal attractor feedback gain coefficient of a tuning parameter and meets the requirements,
the self-adaptive law of uncertain parameters is designed according to the self-adaptive control principle as follows:
Figure BDA0001861426840000081
wherein g is any positive real number;
d. designing a fixed time stability control rate and a self-adaptive law, realizing parameter identification and stability of a controlled model in a limited time, wherein the upper bound of identification time does not depend on an initial value;
the calculation method for identifying the upper bound of the time range comprises the following steps: the nonlinear system is designed by using a fixed time stability theory as follows:
Figure BDA0001861426840000082
in the formula, x ∈ RnSetting f as unknown smooth nonlinear function for the state variable of the nonlinear system VII, if the abstract nonlinear system cannot be described in detail where T (x) is and the concrete expression has local bounded stable time function T (x) under the condition that the initial value of the nonlinear system is an arbitrary value, and the upper limit value T (x) of the bounded stable time function T (x)maxIndependent of the state variable x, i.e. when the initial conditions of the system take arbitrary values,
Figure BDA0001861426840000083
and TmaxIndependent of the state variable x, such that
Figure BDA0001861426840000084
And T > TmaxX (t) is ≡ 0. The nonlinear system VII is globally fixed and stable in time;
lesion 1-for any non-negative real number ξ1,ξ2,…,ξnAnd 0 < p.ltoreq.1, the following inequality holds:
Figure BDA0001861426840000085
for the nonlinear system VII, a continuous radial unbounded function V is assumed to exist: rn→R+∪ {0} satisfies:
Figure BDA0001861426840000086
any solution x (t) of the nonlinear system VII satisfies the inequality:
Figure BDA0001861426840000087
wherein alpha, beta, p, q, k is a real number larger than 0, pk <1, qk >1 is a simulation parameter, and at the moment, the overall fixed time of the origin of the nonlinear system VII is stable, V (x) is identical to 0 within the fixed time T, and the stable time is as follows:
Figure BDA0001861426840000088
the description is that a self-adaptive fixed time algorithm is designed to identify the cornerstone of uncertain parameters of the system in limited time, and a Lyapunov function is constructed according to the Lyapunov function stability theory:
Figure BDA0001861426840000089
the derivative of the Lyapunov candidate function of the error response system is obtained by using the designed controller u and the corresponding tuning parameter
Figure BDA0001861426840000091
Wherein,
Figure BDA0001861426840000092
the upper bound of the system settling time can thus be found to be:
Figure BDA0001861426840000093
this means that when t ≧ t1When e is present1≡0,
Figure BDA0001861426840000094
The master system II and the slave system III realize synchronization to obtain uncertain parameter identificationThe result is;
e. and confirming the control parameters of the design control rate according to the Lyapunov stability theory.
Example (b): rapid parameter identification method for chaotic ferromagnetic resonance system of coal mine power grid
Mathematical modeling is carried out according to the coal mine power grid chaotic ferromagnetic resonance system shown in the figure 1 and the equivalent circuit of the coal mine power grid chaotic ferromagnetic resonance system shown in the figure 2, and the following steps are carried out:
Figure BDA0001861426840000101
wherein phi is a transformer excitation inductance magnetic flux, and V is an excitation inductance voltage; r and C are respectively a resistor and a capacitor in the chaotic ferromagnetic resonance equivalent circuit; omega and E are respectively power supply voltage angular frequency and power supply voltage; a is0And b0The magnetization characteristic parameter of the transformer excitation inductance is shown, and t is time. For convenience of derivation, the model is subjected to non-dimensionalization processing, so that the chaotic ferromagnetic resonance system model of the coal mine power grid is equivalent to the following system as a main system:
Figure BDA0001861426840000102
in the formula, a, b, c and d are uncertain parameters of system operation. But the magnetization characteristic parameter a of the transformer excitation inductance0And b0Under the known condition, the specific values of the resistance R and the capacitance C of the transformer ferroresonance model with the chaotic dynamics behavior can be determined by identifying the parameter C in the system (2), and the parameters a and b can be obtained.
To achieve synchronization of uncertain parameters in this embodiment, consider the following slave system according to equation (2):
Figure BDA0001861426840000103
wherein,
Figure BDA0001861426840000104
is an estimate of a state variable of the system,
Figure BDA0001861426840000105
and u is the control input of the chaotic ferroresonance slave system of the coal mine power grid as an estimation value of the uncertain parameter.
Definition of
Figure BDA0001861426840000106
As a variable of the error, there is,
Figure BDA0001861426840000107
as the estimation error of the uncertain parameter, the following error response system can be obtained by the difference between the formula (3) and the formula (2)
Figure BDA0001861426840000108
In the formula
Figure BDA0001861426840000109
To relate to
Figure BDA00018614268400001010
And a polynomial of Φ.
In order to realize the identification target, the nonlinear control law and the self-adaptive law of uncertain parameters of the designed error response system are as follows:
the nonlinear control law is designed according to the fixed time stability theory as follows:
Figure BDA00018614268400001011
wherein, alpha and beta are parameters to be designed of the system, alpha is more than 0 and less than 1, beta is more than 1, k is a terminal attractor feedback gain coefficient of the tuning parameter, and k is more than 0. In this embodiment, the parameter α is 0.5 and β is 1.5.
The self-adaptive law of uncertain parameters is designed according to the self-adaptive control principle as follows:
Figure BDA0001861426840000111
wherein g is any normal number. In this example, the parameter g is 0.3.
Determining an upper bound of a stability time range according to Lyapunov function stability analysis:
constructing a Lyapunov function:
Figure BDA0001861426840000112
by using the designed controller u and corresponding tuning parameters, the derivative of the Lyapunov function of the error response system is obtained:
Figure BDA0001861426840000113
wherein,
Figure BDA0001861426840000114
the upper bound of the system settling time can thus be found to be:
Figure BDA0001861426840000115
this means that when t ≧ t1When e is present1≡0,
Figure BDA0001861426840000116
And the master system and the slave system realize synchronization to obtain an uncertain parameter identification result.
All the parameters taken in the embodiment are taken in to obtain t130.35 or less, that is to say the upper bound of the system uncertainty parameter identification time is within 30.35s after the controller is applied.
The flow of the provided method for rapidly identifying the parameters of the chaotic ferromagnetic resonance system of the coal mine power grid is shown in fig. 3. 5. And performing data simulation on the MATLAB simulation platform according to the embodiment, and verifying the identification effect. This example begins withThe starting value is (Φ, V) ═ 0, 1.4142. Error e in chaotic ferromagnetic resonance system of coal mine power grid1，e2And the results of the identification of the uncertain parameter c are shown in fig. 4(a), fig. 4(b) and fig. 5. As shown in FIGS. 4(a)4(a) and (b), error e1，e2And stabilizing to 0, and realizing the synchronization of the master system and the slave system. As shown in fig. 5, the fixed time method based on the synchronization concept can identify the parameter c as the target value c-0.00122, and in the experiment with the time length of 50s, the adjustment time required for forcing the parameter identification curve to be within ± 3% of the stable region of the target value is tcThe overshoot of the identification curve is small and the identification curve is stable without buffeting when the time is 8.7 s.

Claims (1)

1. A method for quickly identifying parameters of a chaotic ferromagnetic resonance system of a coal mine power grid is characterized by comprising the following steps:
a. collecting various data of a coal mine power grid, including transformer excitation inductance magnetic flux information, excitation inductance voltage information, resistance and capacitance information in a chaotic ferromagnetic resonance equivalent circuit, power supply voltage angular frequency, power supply voltage and magnetization characteristic parameters of the transformer excitation inductance, and establishing a second-order differential mathematical model I of the chaotic ferromagnetic resonance system of the coal mine power grid by using the information;
the second-order differential mathematical model I of the chaotic ferromagnetic resonance system of the coal mine power grid is as follows:
Figure FDA0002531960810000011
in the formula: phi is the transformer excitation inductance magnetic flux, and V is the excitation inductance voltage; r is a resistor in the chaotic ferromagnetic resonance equivalent circuit, and C is a capacitor in the chaotic ferromagnetic resonance equivalent circuit; omega and E are respectively power supply voltage angular frequency and power supply voltage; a is0And b0Carrying out dimensionless treatment on the model I for the magnetization characteristic parameter of the transformer excitation inductance and t is time, so that the chaotic ferromagnetic resonance system model of the coal mine power grid is equivalent to the following system as a main system model II:
Figure FDA0002531960810000012
in the formula, a, b, c and d are uncertain parameters of coal mine power grid operation, but a magnetization characteristic parameter a of transformer excitation inductance0And b0Under the known condition, the specific values of the resistance R and the capacitance C of the transformer ferroresonance model with the chaotic dynamics behavior are determined by identifying the parameter C in the system model II, and then the parameters a and b can be obtained;
b. based on a synchronization thought, aiming at error variables and uncertain parameters, establishing an error response system IV of the coal mine power grid chaotic ferromagnetic resonance through a second-order differential mathematical model of the coal mine power grid chaotic ferromagnetic resonance system;
specifically, the method comprises the following steps:
the method for realizing the uncertain parameter synchronization comprises the following steps: obtaining a slave system model III according to the master system model II as follows:
Figure FDA0002531960810000013
wherein,
Figure FDA0002531960810000014
respectively, are estimated values of the system state variables,
Figure FDA0002531960810000015
respectively are estimated values of uncertain parameters, and u is the control input of the chaotic ferromagnetic resonance slave system of the coal mine power grid;
definition of
Figure FDA0002531960810000016
As a variable of the error, there is,
Figure FDA0002531960810000017
and as the estimation error of the uncertain parameters, obtaining the following error response system IV from the difference between the system model III and the system model II:
Figure FDA0002531960810000018
in the formula,
Figure FDA0002531960810000019
to relate to
Figure FDA00025319608100000110
And phi;
c. aiming at an error response system, designing a nonlinear control law and an uncertain parameter self-adaptation law according to a fixed time stability theory, and realizing that the synchronous error of a controlled model and a reference model in fixed time is arbitrarily small;
the nonlinear control law designed according to the fixed time stability theory is as follows:
Figure FDA0002531960810000021
in the formula, alpha and beta are parameters to be designed of the system, alpha is more than 0 and less than 1, beta is more than 1, k is a terminal attractor feedback gain coefficient of a tuning parameter,
the self-adaptive law of uncertain parameters is designed according to the self-adaptive control principle as follows:
Figure FDA0002531960810000022
wherein g is any positive real number;
d. designing a fixed time stability control rate and a self-adaptive law, realizing parameter identification and stability of a controlled model in a limited time, wherein the upper bound of identification time does not depend on an initial value;
the calculation method for identifying the upper bound of the time comprises the following steps: the nonlinear system is designed by using a fixed time stability theory as follows:
Figure FDA0002531960810000023
in the formula, x ∈ RnSetting f as unknown smooth nonlinear function for the state variable of the nonlinear system VII, if the abstract nonlinear system cannot be described in detail where T (x) is and the concrete expression has local bounded stable time function T (x) under the condition that the initial value of the nonlinear system is an arbitrary value, and the upper limit value T (x) of the bounded stable time function T (x)maxIndependent of the state variable x, i.e. when the initial conditions of the system take arbitrary values,
Figure FDA0002531960810000024
and TmaxIndependent of the state variable x, such that
Figure FDA0002531960810000029
And t is>TmaxX (t) is equal to 0, and the nonlinear system VII is stable in global fixed time;
lesion 1-for any non-negative real number ξ1，ξ2，…，ξnAnd 0<p is less than or equal to 1, the following inequality holds:
Figure FDA0002531960810000025
for the nonlinear system VII, a continuous radial unbounded function V is assumed to exist: rn→R+∪ {0} satisfies:
Figure FDA0002531960810000026
any solution x (t) of the nonlinear system VII satisfies the inequality:
Figure FDA0002531960810000027
V:Rn→R+∪ {0}, it is shown that the constructed function V is mapped from an n-dimensional vector to non-negative real numbers;
wherein alpha, beta, p, q, k is a real number larger than 0, pk <1, qk >1 is a simulation parameter, and at the moment, the overall fixed time of the origin of the nonlinear system VII is stable, V (x) is identical to 0 within the fixed time T, and the stable time is as follows:
Figure FDA0002531960810000028
the description is that a self-adaptive fixed time algorithm is designed to identify the cornerstone of uncertain parameters of the system in limited time, and a Lyapunov function is constructed according to the Lyapunov function stability theory:
Figure FDA0002531960810000031
the derivative of the Lyapunov candidate function of the error response system is obtained by using the designed controller u and the corresponding tuning parameter
Figure FDA0002531960810000032
Wherein,
Figure FDA0002531960810000033
Figure FDA0002531960810000034
is a parameter estimation value;
the upper bound of the system settling time can thus be found to be:
Figure FDA0002531960810000041
this means that when t ≧ t1When e is present1≡0,
Figure FDA0002531960810000042
The master system II and the slave system III realize synchronization to obtain an uncertain parameter identification result;
e. and confirming the control parameters of the design control rate according to the Lyapunov stability theory.
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