CN112664468A - Fan control system fault-tolerant control method considering random time delay - Google Patents

Fan control system fault-tolerant control method considering random time delay Download PDF

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CN112664468A
CN112664468A CN202011360933.3A CN202011360933A CN112664468A CN 112664468 A CN112664468 A CN 112664468A CN 202011360933 A CN202011360933 A CN 202011360933A CN 112664468 A CN112664468 A CN 112664468A
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matrix
control system
fault
tolerant
controller
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王雅宾
孙晓刚
褚孝国
翁存兴
王传鑫
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Huaneng Group Technology Innovation Center Co Ltd
Beijing Huaneng Xinrui Control Technology Co Ltd
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Huaneng Group Technology Innovation Center Co Ltd
Beijing Huaneng Xinrui Control Technology Co Ltd
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Abstract

A fan control system fault-tolerant control method considering random time delay comprises the following steps: considering the influence of external disturbance, establishing a state space equation of a fan torque control system, considering the faults of an actuator in a network control system, and obtaining an improved system state equation by applying input time lag and Bernoulli distribution; obtaining a constraint condition matrix of the controller by adopting a Lyapunov stability analysis method; obtaining state feedback controller gain matrix by matrix inequality calculation
Figure DDA0002803896070000011
The invention considers a fan torque control system with actuator faults and random time lag, establishes a closed-loop control system model and provides a solution for asymptotic stability and fault-tolerant control of the closed-loop system; a Lyapunov-Classkiky function containing random time lag information is established, and the random time lag information is complementary based on expansionThe convex optimization matrix method analyzes and processes the time lag to obtain sufficient conditions for stabilizing the system, and the conservation of the system is obviously reduced; good performance characteristics are obtained.

Description

Fan control system fault-tolerant control method considering random time delay
Technical Field
The invention relates to the field of fan control system control, in particular to a sampled data control method of a fan control system considering random time delay and actuator faults.
Background
The fan control system connects the sensors, the controller, the controlled object and other units through a communication network. Various disturbances are inevitably encountered in the fan control system, which may lead to system instability and performance degradation. The traditional control method is realized by continuous time signals, and digital signals are often needed in a fan control system. It is known that most controllers in practical systems are designed using digital technology. Therefore, a sampling data control method capable of directly designing a digital controller for a continuous time system is widely used. There are currently three main approaches to studying sampled data control: discretization methods, pulse model methods, and input time-lag methods. Compared with the former two methods, the input time-delay method reconstructs the traditional sampling data system into a time-delay system, and has the advantage that the sampling interval does not need to be constant. For sample control systems with input skew, researchers have proposed many advanced matrix inequalities to establish the stability condition of the system. Of these methods, the complementary convex matrix inequality obtains an accurate convex inequality by merging non-convex terms into one expression, which has proven to be an effective method for improving the stability criterion.
It is noted that existing sampling control methods are designed under the assumption that deterministic sampling and the system is not faulty. But due to various external random factors or communication interference in the actual control system, the time lag occurs in a random fashion in practice. Moreover, the structure of the system cannot be fixed, because the occurrence of faults in the fan control system is inevitable and difficult to predict, which can lead to system instability and performance degradation.
In summary, how to design a controller to make a closed-loop system asymptotically stable and make the controlled output and the external input lower than the specified indexes of performance, so that the fan torque control system is stable when a fault occurs, and has good robust performance and lower conservatism becomes a technical problem to be solved in the prior art.
Disclosure of Invention
The invention aims to provide a fan control system fault-tolerant control method considering random time delay, and provides a state feedback controller, so that the system is stable when a fault occurs and obtains smaller conservatism and good robustness.
In order to achieve the purpose, the invention adopts the following technical scheme:
a fan control system fault-tolerant control method considering random time delay is characterized by comprising the following steps:
state space equation control step S110:
considering the influence of external disturbance, establishing a state space equation of the fan torque control system:
Figure BDA0002803896050000021
wherein
Figure BDA0002803896050000022
A state variable representing the state of the system,
Figure BDA0002803896050000023
which represents the controlled output of the system and,
Figure BDA0002803896050000024
a control input is represented that is a control input,
Figure BDA0002803896050000025
represents an external disturbance, wherein
Figure BDA0002803896050000026
Respectively representing Euclidean spaces with dimensions of n, l, p and Q, wherein A, B, C, Q and D are known parameter matrixes with proper dimensions;
sample H∞The controller configuring step S120:
taking into account actuator faults in a network control system, a control signal u is introducedF(t) applying discrete sampling instants t with an in-control input time lagmThe Bernoulli distribution is used to describe the random time lag, an improved system state equation is obtained,
Figure BDA0002803896050000027
constraint condition matrix design step S130:
integrating related theories, and adopting a Lyapunov stability analysis method according to a model with random time lag and actuator fault to obtain the asymptotic stability of a network control system and meet the requirement of H∞A constraint condition matrix of a controller with robust stability performance of the fault tolerant controller;
state feedback controller gain matrix
Figure BDA0002803896050000031
Calculation step S140:
obtaining state feedback controller gain matrix by matrix inequality calculation
Figure BDA0002803896050000032
The invention further discloses a storage medium for storing computer executable instructions, which is characterized in that:
the computer executable instructions, when executed by a processor, perform the fault tolerant sampling control method of a fan torque control system described above that takes into account random time delays and actuator failures.
The invention has the following advantages:
1) the invention aims to consider a fan torque control system with actuator faults and random time lag, and also considers the influence of external disturbance in the system. A closed-loop control system model is established, and a solution for asymptotic stability and fault-tolerant control of a closed-loop system is provided;
2) in the invention, the condition of random time lag existing in a fan torque control system is considered, a Lyapunov-Classofsky function containing random time lag information is established, the time lag is analyzed and processed based on an extended complementary convex optimization matrix method, sufficient conditions for stabilizing the system are obtained, and the conservatism of the system is obviously reduced;
3) the invention is applied to a typical fan torque control system, can obtain good performance characteristics, and proves the effective application prospect of the invention in the actual fan torque control system.
Drawings
FIG. 1 is a flow chart of a method for fault tolerant control of a wind turbine control system that accounts for random time delays according to an embodiment of the present invention;
FIG. 2 is a schematic illustration of a Bernoulli probability distribution of ζ (t) in accordance with a specific embodiment of the present invention;
FIG. 3 is a schematic diagram of system control performance according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some of the structures related to the present invention are shown in the drawings, not all of the structures.
The invention provides a fan control system fault-tolerant control method considering random time delay, fully considers the problems of random time delay, actuator faults and external disturbance in a fan torque control system, and provides a state feedback controller design method through a Lyapunov stability theory and an expanded complementary convex matrix inequality technology, so that the system is stable when faults occur and obtains smaller conservatism and good robustness.
Specifically, referring to fig. 1, a flowchart of a random time delay considered fault-tolerant control method of a wind turbine control system according to an embodiment of the present invention is shown, where the method includes the following steps:
state space equation control step S110:
considering the influence of external disturbance, establishing a state space equation of the fan torque control system:
Figure BDA0002803896050000041
wherein
Figure BDA0002803896050000042
A state variable representing the state of the system,
Figure BDA0002803896050000043
which represents the controlled output of the system and,
Figure BDA0002803896050000044
a control input is represented that is a control input,
Figure BDA0002803896050000045
represents an external disturbance, wherein
Figure BDA0002803896050000046
Respectively representing Euclidean spaces with dimensions of n, l, p and Q, wherein A, B, C, Q and D are known parameter matrixes with proper dimensions;
sample H∞The controller configuring step S120:
taking into account actuator faults in a network control system, a control signal u is introducedF(t) applying the input while adopting the controlHysteresis processing discrete sampling time tmBernoulli distribution is applied to describe random time lags, resulting in an improved system equation of state.
Specifically, the step includes the following substeps:
introducing a control signal uF(t) substep S121:
because of control signal faults in the fan torque control system, conventional state feedback control designs are not suitable for fan torque control systems. The sub-step considers the actuator fault in the fan torque control system and introduces uF(t) to describe a control signal for characterizing a fault condition in the system model:
uF(t)＝Gu(t) (34)
wherein G is actuator fault matrix and is represented by G1,g2,...,gmA diagonal matrix is formed, and g is more than or equal to 0r≤1，g r1 indicates that the r-th actuator is normal, if 0 < gr< 1 indicates that the r-th actuator has a partial failure, and grA value of 0 indicates that the r-th actuator is completely damaged.
Handling discrete sampling instants tmSubstep S122:
assume that controller u (t) is sampled based on a zero-order hold circuit and sampling program before entering the network, tm(m ≦ 0, 1. -) denotes a sampling time, and satisfies 0 ≦ t0＜t1＜…＜tm< … and
Figure BDA0002803896050000051
the state feedback controller is then described as:
Figure BDA0002803896050000055
Figure BDA0002803896050000054
to state feedback gain matrix, the system dynamics equation can therefore be described as:
Figure BDA0002803896050000052
the closed loop system contains continuous signals and discrete signals at the same time, and the situation is processed by introducing an input time-lag method by using sampling data transformation, wherein the sampling time tmIs defined as:
tm＝t-(t-tm)＝t-h(t) (37)
the controller is now described as u (t)m)＝u(t-h(t)),tm≤t≤tm+1Wherein u (t)m) H (t) is time-varying time lag for discrete time control input, satisfying h0≤h(t)≤h2，h0And h2Given a constant.
Applying bernoulli distribution to improve the system state equation substep S123:
due to various external random factors or communication disturbances in the fan torque control system, the skew typically occurs in a random fashion. Random skew signals can cause system instability, ringing, and some other poor performance problems. Therefore, it is very valuable to consider the effect of random skew in a network control system.
In this sub-step the random time lag is described by a bernoulli distribution, introducing two sets describing the probability distribution of h (t):
Figure BDA0002803896050000053
wherein h is1∈[h0,h2]，
Figure BDA0002803896050000061
Denotes h (t) e [ h0,h1) The situation of (1) occurs;
Figure BDA0002803896050000062
denotes h (t) e [ h1,h2]The situation of (a) occurs that,
Figure BDA0002803896050000063
suppose that the probabilities of the two cases occurring are respectively
Figure BDA0002803896050000064
And
Figure BDA0002803896050000065
followed by the introduction of the bernoulli distribution sequence ξ (t):
Figure BDA0002803896050000066
i.e. ξ (t) satisfies the probability
Figure BDA0002803896050000067
Figure BDA0002803896050000068
Wherein
Figure BDA0002803896050000069
Mathematical expectation representing ξ (t), ξ0Is within the interval [0,1]Can see the constant of
Figure BDA00028038960500000610
Figure BDA00028038960500000611
Representing the probability of an event occurring;
introducing two time-lag variables
Figure BDA00028038960500000612
And
Figure BDA00028038960500000613
satisfy h0≤h1(t)≤h1And h is1≤h2(t)≤h2By considering random time lags, the system state equation can be expressed as:
Figure BDA00028038960500000614
the equivalent forms can be expressed as:
Figure BDA00028038960500000615
constraint condition matrix design step S130:
integrating related theories, and adopting a Lyapunov stability analysis method according to a model with random time lag and actuator fault to obtain the asymptotic stability of a network control system and meet the requirement of H∞A constraint matrix for a controller with robust stability performance for a fault tolerant controller.
Specifically, the method comprises the following substeps:
a guiding sorting substep S131:
the following three arguments are collated as necessary to demonstrate the main conclusions,
introduction 1: for any given matrix R > 0, given scalars m and n and m < n, let vector x [ m, n ] be a derivable function, the inequality holds:
Figure BDA0002803896050000071
wherein tau is1＝x(n)-x(m)，
Figure BDA0002803896050000072
2, leading: for any given matrix R > 0, given scalars m and n and m < n, for any integrable function x: [ m, n ], the following inequality holds:
Figure BDA0002803896050000073
and 3, introduction: for a positive scalar β, λ ∈ (0,1), when β + λ ═ 1, for any matrix W1、W2And a matrix R1> 0 and R2When > 0, the inequality holds:
Figure BDA0002803896050000074
wherein
Figure BDA0002803896050000075
And
Figure BDA0002803896050000076
the lyapunov stability analysis method introduces substep S132:
study has a robust H∞The method comprises the following steps of (1) setting a disturbance attenuation coefficient sigma and designing a state feedback controller to enable a network control system to meet the following two requirements:
c) when the external disturbance input d (t) is 0, the closed loop system is asymptotically stable;
d) under the zero initial condition, for any non-zero disturbance d (t) ≠ 0, the controller output L (t) satisfies
Figure BDA0002803896050000077
Construction of the Lyapunov-Classofsky function:
V(x(t))＝V1(x(t))+V2(x(t))+V3(x(t))+V4(x(t)) (45)
wherein
Figure BDA0002803896050000078
Figure BDA0002803896050000079
Figure BDA00028038960500000710
Figure BDA00028038960500000711
Wherein h is10＝h1-h0And h is21＝h2-h1Symmetric matrix
Figure BDA00028038960500000712
Figure BDA0002803896050000081
By scaling the integral term after derivative of the lyapunov function by combining the theorems 1, 2 and 3, the derivative of the lyapunov function can be estimated as:
Figure BDA0002803896050000082
wherein the content of the first and second substances,
Figure BDA0002803896050000083
by the introduction of the general formula 3,
Figure BDA0002803896050000084
the expectation of (c) can be estimated as:
Figure BDA0002803896050000085
wherein the content of the first and second substances,
Figure BDA0002803896050000086
Figure BDA0002803896050000087
Figure BDA0002803896050000088
Figure BDA0002803896050000089
adding a zero matrix inequality condition:
Figure BDA0002803896050000091
when in use
Figure BDA0002803896050000092
When the temperature of the water is higher than the set temperature,
Figure BDA0002803896050000093
the condition is satisfied, namely the system is asymptotically stable, namely:
Figure BDA0002803896050000094
Figure BDA0002803896050000095
finding H∞Fault tolerant controller gain matrix according to H∞Performance constraints, defined at zero initial conditions:
Figure BDA0002803896050000096
by the aid of the supplementary theory of Schur,
Figure BDA0002803896050000097
the condition is satisfied,
integration of the above equation from 0 to + ∞ yields:
Figure BDA0002803896050000098
i.e. L (t) | non-woven2＜σ2‖d(t)‖2This means that the closed-loop fault-tolerant control system satisfies H for all non-zero disturbance inputs d (t)∞The performance index sigma, and the closed loop system is asymptotically stable.
Where V (0), V (+ ∞) represent the states of the lyapunov function x (t) ═ 0 and x (t) + ∞.
The constraint condition matrix is derived in sub-step S133:
by utilizing the Lyapunov stability theory and the extended complementary convex optimization matrix inequality analysis method, the network control system is obtained to be asymptotically stable and meet the requirement of H∞Sufficient condition of the fault-tolerant controller:
for a given positive scalar ε1,ε2,ξ0And 0 is not less than h0＜h1＜h2When there is a symmetric positive definite matrix
Figure BDA0002803896050000099
Real matrix
Figure BDA00028038960500000910
And a suitable dimensional matrix
Figure BDA00028038960500000911
If the matrix inequalities (54) to (57) are satisfied, the closed-loop fault-tolerant control system of the network control system with random time-varying delay time is gradually stabilized when the actuator fails, and H is realized∞And (5) fault-tolerant control.
Figure BDA0002803896050000101
Figure BDA0002803896050000102
Figure BDA0002803896050000103
Figure BDA0002803896050000104
Wherein denotes the transposition of the matrix of symmetrical positions,
Figure BDA0002803896050000105
Figure BDA0002803896050000106
Figure BDA0002803896050000107
Figure BDA0002803896050000111
Figure BDA0002803896050000112
Figure BDA0002803896050000113
Figure BDA0002803896050000114
Figure BDA0002803896050000115
Figure BDA0002803896050000116
Figure BDA00028038960500001117
Figure BDA0002803896050000117
Figure BDA0002803896050000118
Figure BDA0002803896050000119
Figure BDA00028038960500001110
Figure BDA00028038960500001111
Figure BDA00028038960500001112
Figure BDA00028038960500001113
Figure BDA00028038960500001114
Figure BDA00028038960500001115
Figure BDA00028038960500001116
Figure BDA0002803896050000121
it is worth noting that the controller gain
Figure BDA0002803896050000128
Coupled with F, and therefore require further processing to compute the matrix using the LMI toolkit
Figure BDA0002803896050000129
State feedback controller gain matrix
Figure BDA00028038960500001210
Calculation step S140:
obtaining state feedback controller gain matrix by matrix inequality calculation
Figure BDA00028038960500001211
Specifically, order
Figure BDA0002803896050000122
When the matrix inequalities (58) to (61) are satisfied, the LMI toolbox can be used to obtain the gain matrix of the state feedback controller
Figure BDA00028038960500001212
Figure BDA0002803896050000123
Figure BDA0002803896050000124
Figure BDA0002803896050000125
Figure BDA0002803896050000126
Wherein:
Figure BDA0002803896050000127
Figure BDA0002803896050000131
Figure BDA0002803896050000132
Figure BDA0002803896050000133
Figure BDA0002803896050000134
Figure BDA0002803896050000135
Figure BDA0002803896050000136
Figure BDA0002803896050000137
by solving the matrix inequality, the closed-loop network control system conforming to H can be obtained∞State feedback controller gain matrix under fault tolerant control conditions
Figure BDA00028038960500001310
Further, the present invention also discloses a storage medium for storing computer executable instructions, which is characterized in that:
the computer executable instructions, when executed by a processor, perform the fault tolerant sampling control method of a fan torque control system described above that takes into account random time delays and actuator failures.
Example (b):
taking a typical fan torque control system as an example:
Figure BDA0002803896050000138
wherein:
Figure BDA0002803896050000139
Q＝[0 0 0.542]
selecting the fault rate G of the actuator to be 0.5, the maximum controlled output torque to be 5 N.m and the maximum control input umaxAnother parameter ε 101＝1,ε20.2 for xi0＝0.1,h0＝0.01s,h1＝0.02s，h20.04 s. The upper bound h with the product is indicated in the table below2Is decreased, H∞The performance index sigma increases.
To further evaluate the performance of the system, the presence of external disturbances was considered:
Figure BDA0002803896050000141
minimum H by applying the invention to a typical fan torque control system∞Performance index σ 11.7782, allowable controller gain matrix
Figure BDA0002803896050000142
The calculation is as follows:
Figure BDA0002803896050000143
the bernoulli probability distribution of ξ (t) is reflected in fig. 2, and the system control performance is reflected in fig. 3. As can be seen, the fan torque control system is still able to operate stably when the actuator fails, and performance requirements | L (t) | < 1 and | uF(t)|＜|umaxL is satisfied. Compared with the traditional fault-tolerant control method of the fan torque control system, the method has the advantages that the control system has less conservatism and better constraint performance. The fault-tolerant controller designed by the invention can ensure that the fan torque control system considering random time lag has good robustness integrity when an actuator fails.
The invention has the following advantages:
1) the invention aims to consider a fan torque control system with actuator faults and random time lag, and also considers the influence of external disturbance in the system. A closed-loop control system model is established, and a solution for asymptotic stability and fault-tolerant control of a closed-loop system is provided;
2) in the invention, the condition of random time lag existing in a fan torque control system is considered, a Lyapunov-Classofsky function containing random time lag information is established, the time lag is analyzed and processed based on an extended complementary convex optimization matrix method, sufficient conditions for stabilizing the system are obtained, and the conservatism of the system is obviously reduced;
3) the invention is applied to a typical fan torque control system, can obtain good performance characteristics, and proves the effective application prospect of the invention in the actual fan torque control system.
It will be apparent to those skilled in the art that the various elements or steps of the invention described above may be implemented using a general purpose computing device, they may be centralized on a single computing device, or alternatively, they may be implemented using program code that is executable by a computing device, such that they may be stored in a memory device and executed by a computing device, or they may be separately fabricated into various integrated circuit modules, or multiple ones of them may be fabricated into a single integrated circuit module. Thus, the present invention is not limited to any specific combination of hardware and software.
While the invention has been described in further detail with reference to specific preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. A fan control system fault-tolerant control method considering random time delay is characterized by comprising the following steps:
state space equation control step S110:
considering the influence of external disturbance, establishing a state space equation of the fan torque control system:
Figure FDA0002803896040000011
wherein
Figure FDA0002803896040000012
A state variable representing the state of the system,
Figure FDA0002803896040000013
which represents the controlled output of the system and,
Figure FDA0002803896040000014
a control input is represented that is a control input,
Figure FDA0002803896040000015
represents an external disturbance, wherein
Figure FDA0002803896040000016
Respectively representing Euclidean spaces with dimensions of n, l, p and q; a, B, C, Q and D are known parameter matrixes with proper dimensions;
sample H∞The controller configuring step S120:
taking into account actuator faults in a network control system, a control signal u is introducedF(t) applying discrete sampling instants t with an in-control input time lagmThe Bernoulli distribution is used to describe the random time lag, an improved system state equation is obtained,
Figure FDA0002803896040000017
L(t)＝Qx(t)
constraint condition matrix design step S130:
integrating related theories, and adopting a Lyapunov stability analysis method according to a model with random time lag and actuator fault to obtain the asymptotic stability of a network control system and meet the requirement of H∞A constraint condition matrix of a controller with robust stability performance of the fault tolerant controller;
state feedback controller gain matrix κ calculation step S140:
and calculating a state feedback controller gain matrix kappa through a matrix inequality.
2. The fault-tolerant control method of a wind turbine control system according to claim 1,
the sample H∞The controller constructing step S120 is specifically:
introducing a control signal uF(t) substep S121:
considering actuator faults in a fan torque control system, introducing uF(t) to describe a control signal for characterizing a fault condition in the system model:
uF(t)＝Gu(t) (3)
wherein G is actuator fault matrix and is represented by G1,g2,...,gmA diagonal matrix is formed, and g is more than or equal to 0r≤1，gr1 indicates that the r-th actuator is normal, if 0 < gr< 1 indicates that the r-th actuator has a partial failure, and gr0 indicates the firstr actuators are damaged completely;
handling discrete sampling instants tmSubstep S122:
assume that controller u (t) is sampled based on a zero-order hold circuit and sampling program before entering the network, tm(m ≦ 0, 1. -) denotes a sampling time, and satisfies 0 ≦ t0＜t1＜…＜tm< … and
Figure FDA0002803896040000021
the state feedback controller is then described as:
Figure FDA0002803896040000023
κ is the state feedback gain matrix, so the system dynamics equation can be described as:
Figure FDA0002803896040000022
the closed loop system contains continuous signals and discrete signals at the same time, and the situation is processed by introducing an input time-lag method by using sampling data transformation, wherein the sampling time tmIs defined as:
tm＝t-(t-tm)＝t-h(t) (6)
the controller is now described as u (t)m)＝u(t-h(t)),tm≤t≤tm+1Wherein u (t)m) H (t) is time-varying time lag for discrete time control input, satisfying h0≤h(t)≤h2，h0And h2Is a given constant;
applying bernoulli distribution to improve the system state equation substep S123:
in this sub-step the random time lag is described by a bernoulli distribution, introducing two sets describing the probability distribution of h (t):
Figure FDA0002803896040000031
wherein h is1∈[h0,h2]，
Figure FDA0002803896040000032
Denotes h (t) e [ h0,h1) The situation of (1) occurs;
Figure FDA0002803896040000033
denotes h (t) e [ h1,h2]The situation of (a) occurs that,
Figure FDA0002803896040000034
suppose that the probabilities of the two cases occurring are respectively
Figure FDA0002803896040000035
And
Figure FDA0002803896040000036
followed by the introduction of the bernoulli distribution sequence ξ (t):
Figure FDA0002803896040000037
i.e. ξ (t) satisfies the probability
Figure FDA0002803896040000038
Figure FDA0002803896040000039
Wherein
Figure FDA00028038960400000310
Mathematical expectation representing ξ (t), ξ0Is within the interval [0,1]Is constant in the direction of the normal axis of the pipe,
Figure FDA00028038960400000311
indicates the probability of the occurrence of an event, and can be seen
Figure FDA00028038960400000312
Introducing two time-lag variables
Figure FDA00028038960400000313
And
Figure FDA00028038960400000314
satisfy h0≤h1(t)≤h1And h is1≤h2(t)≤h2By considering random time lags, the system state equation can be expressed as:
Figure FDA00028038960400000315
the equivalent forms can be expressed as:
Figure FDA00028038960400000316
L(t)＝Qx(t)
3. the fault tolerant control method of a wind turbine control system according to claim 1 or 2,
the constraint condition matrix designing step S130 specifically includes:
a guiding sorting substep S131:
the following three arguments are collated as necessary to demonstrate the main conclusions,
introduction 1: for any given matrix R > 0, given scalars m and n and m < n, let vector x [ m, n ] be a derivable function, the inequality holds:
Figure FDA0002803896040000041
wherein tau is1＝x(n)-x(m)，
Figure FDA0002803896040000042
2, leading: for any given matrix R > 0, given scalars m and n and m < n, for any integrable function x: [ m, n ], the following inequality holds:
Figure FDA0002803896040000043
and 3, introduction: for a positive scalar β, λ ∈ (0,1), when β + λ ═ 1, for any matrix W1、W2And a matrix R1> 0 and R2When > 0, the inequality holds:
Figure FDA0002803896040000044
wherein
Figure FDA0002803896040000045
And
Figure FDA0002803896040000046
the lyapunov stability analysis method introduces substep S132:
study has a robust H∞The method comprises the following steps of (1) setting a disturbance attenuation coefficient sigma and designing a state feedback controller to enable a network control system to meet the following two requirements:
a) when the external disturbance input d (t) is 0, the closed loop system is asymptotically stable;
b) under the zero initial condition, for any non-zero disturbance d (t) ≠ 0, the controller output L (t) satisfies
Figure FDA0002803896040000047
Construction of the Lyapunov-Classofsky function:
V(x(t))＝V1(x(t))+V2(x(t))+V3(x(t))+V4(x(t)) (14)
wherein
Figure FDA0002803896040000048
Figure FDA0002803896040000049
Figure FDA00028038960400000410
Figure FDA00028038960400000411
Wherein h is10＝h1-h0And h is21＝h2-h1Symmetric matrix
Figure FDA00028038960400000412
Figure FDA0002803896040000051
By scaling the integral term after derivative of the lyapunov function by combining the theorems 1, 2 and 3, the derivative of the lyapunov function can be estimated as:
Figure FDA0002803896040000052
wherein the content of the first and second substances,
Figure FDA0002803896040000053
by passingIn the introduction of 3, the method comprises the following steps of,
Figure FDA0002803896040000054
the expectation of (c) is estimated as:
Figure FDA0002803896040000055
wherein the content of the first and second substances,
Figure FDA0002803896040000056
Figure FDA0002803896040000057
Figure FDA0002803896040000058
Figure FDA0002803896040000059
adding a zero matrix inequality condition:
Figure FDA0002803896040000061
when in use
Figure FDA0002803896040000062
When the temperature of the water is higher than the set temperature,
Figure FDA0002803896040000063
the condition is satisfied, namely the system is asymptotically stable, namely:
Figure FDA0002803896040000064
Figure FDA0002803896040000065
finding H∞Fault tolerant controller gain matrix according to H∞Performance constraints, defined at zero initial conditions:
Figure FDA0002803896040000066
by the aid of the supplementary theory of Schur,
Figure FDA0002803896040000067
the condition is satisfied,
integration of the above equation from 0 to + ∞ yields:
Figure FDA0002803896040000068
i.e. L (t) | non-woven2＜σ2||d(t)||2This means that the closed-loop fault-tolerant control system satisfies H for all non-zero disturbance inputs d (t)∞Performance index sigma, and the closed loop system is asymptotically stable;
wherein V (0) and V (+ ∞) represent states of the Lyapunov function x (t) ═ 0 and x (t) + ∞,
the constraint condition matrix is derived in sub-step S133:
by utilizing the Lyapunov stability theory and the extended complementary convex optimization matrix inequality analysis method, the network control system is obtained to be asymptotically stable and meet the requirement of H∞Sufficient condition of the fault-tolerant controller:
for a given positive scalar ε1,ε2,ξ0And 0 is not less than h0＜h1＜h2When there is a symmetric positive definite matrix
Figure FDA0002803896040000069
Real matrix
Figure FDA00028038960400000610
And a suitable dimensional matrix
Figure FDA00028038960400000611
If the matrix inequalities (54) to (57) are satisfied, the closed-loop fault-tolerant control system of the network control system with random time-varying delay time is gradually stabilized when the actuator fails, and H is realized∞And (5) fault-tolerant control.
Figure FDA0002803896040000071
Figure FDA0002803896040000072
Figure FDA0002803896040000073
Figure FDA0002803896040000074
Wherein denotes the transposition of the matrix of symmetrical positions,
Figure FDA0002803896040000075
Figure FDA0002803896040000076
Figure FDA0002803896040000077
Figure FDA0002803896040000081
Figure FDA0002803896040000082
Figure FDA0002803896040000083
Figure FDA0002803896040000084
Figure FDA0002803896040000085
Figure FDA0002803896040000086
Y10＝Qm1
Figure FDA0002803896040000087
Figure FDA0002803896040000088
Γ1＝col{m1,(h1(t)-h0)m8+(h1-h1(t))m9,(h2(t)-h1)m10+(h2-h2(t))m11}
Γ2＝col{m13,m2-m4,m4-m6}
mj＝[0n×(j-1)n,In×n,0n×(12-j)n+1],j＝1,2,...,11
m12＝[01×11n,I1×1,01×n]
m13＝[0n×11n+1,In×n]
Figure FDA0002803896040000089
Figure FDA00028038960400000810
Figure FDA00028038960400000811
Figure FDA0002803896040000091
4. the fault-tolerant control method of a wind turbine control system according to claim 3,
the state feedback controller gain matrix
Figure FDA0002803896040000092
The calculating step S140 specifically includes:
specifically, order
Figure FDA0002803896040000093
When the matrix inequalities (58) to (61) are satisfied, calculating and obtaining a gain matrix of the state feedback controller
Figure FDA0002803896040000094
Figure FDA0002803896040000095
Figure FDA0002803896040000096
Figure FDA0002803896040000097
Figure FDA0002803896040000098
Wherein:
Figure FDA0002803896040000099
Figure FDA00028038960400000910
Figure FDA0002803896040000101
Figure FDA0002803896040000102
Figure FDA0002803896040000103
Figure FDA0002803896040000104
Figure FDA0002803896040000105
Figure FDA0002803896040000106
by solving the matrix inequality, the closed-loop network control system conforming to H can be obtained∞State feedback controller gain matrix under fault tolerant control conditions
Figure FDA0002803896040000107
5. A storage medium for storing computer-executable instructions, characterized in that:
the computer executable instructions, when executed by a processor, perform the method of fault tolerant sampling control of a wind turbine torque control system taking into account random time delays and actuator faults as claimed in any one of claims 1 to 4.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114909312A (en) * 2021-12-23 2022-08-16 国网宁夏电力有限公司超高压公司 Fan control method and system of air cooling system and electronic equipment
CN114909312B (en) * 2021-12-23 2023-09-15 国网宁夏电力有限公司超高压公司 Fan control method and system of air cooling system and electronic equipment

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