CN112987683B - Fault positioning method for dead zone non-smooth sandwich system - Google Patents

Fault positioning method for dead zone non-smooth sandwich system Download PDF

Info

Publication number
CN112987683B
CN112987683B CN202110025922.8A CN202110025922A CN112987683B CN 112987683 B CN112987683 B CN 112987683B CN 202110025922 A CN202110025922 A CN 202110025922A CN 112987683 B CN112987683 B CN 112987683B
Authority
CN
China
Prior art keywords
state
fault
dead zone
estimation error
converges
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110025922.8A
Other languages
Chinese (zh)
Other versions
CN112987683A (en
Inventor
周祖鹏
刘旭锋
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guilin University of Electronic Technology
Original Assignee
Guilin University of Electronic Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Guilin University of Electronic Technology filed Critical Guilin University of Electronic Technology
Priority to CN202110025922.8A priority Critical patent/CN112987683B/en
Publication of CN112987683A publication Critical patent/CN112987683A/en
Application granted granted Critical
Publication of CN112987683B publication Critical patent/CN112987683B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
    • G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/20—Pc systems
    • G05B2219/24—Pc safety
    • G05B2219/24065—Real time diagnostics

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Testing And Monitoring For Control Systems (AREA)

Abstract

The invention discloses a fault positioning method of a dead zone non-smooth sandwich system, which constructs a non-smooth observer capable of automatically switching along with the change of a system working interval according to a state space equation of the dead zone non-smooth sandwich system and the state space equation of the constructed dead zone non-smooth sandwich system and gives the existence condition of the observer; high-precision optical digital encoders are respectively arranged at the input end and the output end of the sandwich system, input and output data of the system are obtained through the high-precision optical digital encoders, the state of the system is estimated by using a constructed observer, and the state estimation error are calculated and drawn; and finally, analyzing the corresponding relation between the fault and the state estimation error, and determining the occurrence position and the type of the system fault. The method only needs the input and output numbers of the known system, has few types of sampling data, is simple to use and has high positioning reliability.

Description

Fault positioning method for dead zone non-smooth sandwich system
Technical Field
The invention relates to the field of nonlinear system fault positioning, in particular to a fault positioning method for a dead zone non-smooth sandwich system.
Background
There is a class of system dead zone sandwich systems in the industry. By a linear subsystem L1Non-smooth link N, linear subsystem L2The three subsystems are connected in series. There is a possibility of failure of all three subsystems of the system. Mechanical devices with gear transmission or belt transmission can be regarded as sandwich systems, such as automobile gearboxes, transmission systems of lathes, production lines, steering systems of gun towers, angle adjusting systems of large astronomical telescopes and the like. When the system is in fault, the first condition for removing the fault is to find the position after the fault occurs. The current fault location technology is mainly applied to fault location in systems such as high-voltage transmission lines or power grids. For example, the invention patent with chinese patent publication No. CN110531222A discloses a fault location method for a high-voltage transmission line based on Matlab, which uses a symmetric component method to locate the distance of fault points on the high-voltage transmission line by analyzing the simulation results of Matlab and Simulink software for the possible short circuit and ground fault on the high-voltage transmission line. The invention patent with Chinese patent publication number CN111965490A discloses a simulation-based micro-grid fault positioning method in a micro-gridAnd each node is provided with a fault detection device for detecting the state signal of the node, the state characteristic of the node is provided through a microprocessor, and the fault type and the corresponding fault detection device are obtained through experimental simulation analysis, namely the fault node is determined. Very little research has been done on the localization of faults in sandwich systems. Aiming at the defects of the prior art, the invention discloses a fault of a state estimation error method positioning system.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a fault positioning method of a dead zone non-smooth sandwich system, which can accurately position three faults in the dead zone non-smooth sandwich system.
The technical scheme for realizing the purpose of the invention is as follows:
a fault locating method for a dead zone non-smooth sandwich system comprises the following steps:
1) constructing a non-smooth state space equation capable of accurately describing a dead zone sandwich system with faults by using a key item separation principle and a switching function, wherein the dead zone nonlinear characteristic is characterized in that the size of output is only related to the size of input at the current moment and is not related to the input and the output at the previous moment, u (k) and y (k) are respectively measurable input and output variables in the dead zone sandwich system with faults, v (k) is a measurable variable, and v (k) is a measurable variable1(k) And v2(k) Is an unmeasurable intermediate variable, L1Representing the front-end linear subsystem, L2Representing the back-end linear subsystem, D1And D2Is the width of the dead zone, m1And m2Is the slope of the linear region, f (k) represents the fault of the system, and the state space equation of the system is established when the dead zone sandwich system containing the fault is provided, which is as follows:
1-1) establishing a state space equation of the linear subsystem: according to the linear system theory, the linear subsystem L1The state space equation of (a) is as follows:
Figure GDA0003342726260000021
according to the linear system theory, the linear subsystem L2The state space equation of (a) is as follows:
Figure GDA0003342726260000022
wherein
Figure GDA0003342726260000023
u∈R1 ×1，y∈R1×1，f∈R1×1，uf∈R1×1，af∈R1×1，bf∈R1×1，
Figure GDA0003342726260000024
Are respectively L1、L2The state transition matrix of (a) is,
Figure GDA0003342726260000025
are respectively L1、L2The input matrix of (a) is selected,
Figure GDA0003342726260000026
are respectively L1、L2The output matrix of (a) is obtained,
Figure GDA0003342726260000027
for the failure matrix, u ∈ R1×1As input, y ∈ R1×1For output, f ∈ R1×1Is a failure of the system, afAs a factor of a failed link, bfInput coefficients for unknown fault links; u. off∈R1×1The input for the failed link is unknown; a isfAnd bfObtained from a priori knowledge of system faults, known; suppose ufIs bounded, afIs less than 1, i.e. | af|<1, so that the fault system is stable according to the linear system stability condition, niFor the dimension of the i-th linear system, let
Figure GDA0003342726260000028
And is
Figure GDA0003342726260000029
1-2) establishing a state space equation of the dead zone subsystem: defining intermediate variables m (k), w1(k) Comprises the following steps:
m(k)＝m1+(m2-m1)h(k)
w1(k)＝m(k)(x(k)-D1h1(k)+D2h2(k))
wherein
Figure GDA00033427262600000210
In order to be a function of the switching,
obtaining the following according to the input-output relation of the dead zone:
v2(k)＝w1(k)-h3(k)w1(k)＝(1-h3(k))w1(k)，
wherein
Figure GDA0003342726260000031
Also as a switching function, when h3(k) When 0, the system operates in the linear region, and v2(k)＝w1(k) (ii) a When h is generated3(k) When 1, the system operates in the dead zone, and v2(k)＝w1(k)-w1(k) 0, according to the input-output characteristics of the dead zone:
Figure GDA00033427262600000311
due to the fact that
Figure GDA0003342726260000032
Substituting the formula (2) into the formula (3) to obtain:
Figure GDA0003342726260000033
1-3) establishing an integral state space equation of the dead zone sandwich system: according to formula (1), formula (2), formula (4) and
Figure GDA0003342726260000034
the state space equation of the linear motor drive system is as follows:
Figure GDA0003342726260000035
wherein
Figure GDA0003342726260000036
Figure GDA0003342726260000037
According to the characteristics of the sandwich system, only the output y (k) of the system can be directly measured, so that
Figure GDA0003342726260000038
Wherein
Figure GDA0003342726260000039
0 is a zero matrix of the corresponding order
Figure GDA00033427262600000310
Equation (5) is written as follows:
Figure GDA0003342726260000041
wherein etaiSwitching vectors introduced for considering the existence of dead zone non-linear characteristics of the system;
2) constructing a non-smooth observer capable of automatically switching along with the change of the working interval of the dead zone sandwich system with the fault according to the non-smooth state space equation of the dead zone sandwich system with the fault, which is constructed in the step 1), and giving the existence condition of the observer, wherein the method comprises the following steps:
Figure GDA0003342726260000042
wherein Kpj、kijRespectively the proportional gain and the integral gain of the ith working interval,
Figure GDA0003342726260000043
Figure GDA0003342726260000044
x (k), y (k), f (k), eta, respectivelyiWhen j is 1, 2, or 3, i is j, then
Figure GDA0003342726260000045
The convergence condition of the switching proportional-integral observer is Aj-KpjThe characteristic value of C is within the unit circle.
3) According to the characteristics of a practical second-order system, i.e. n1＝n2X is 21∈R2×1，x2∈R2×1Let x be1＝[X12，X12]、x2＝[X21，X22]X12 and X12 each represent L1X21 and X22 represent L, respectively2First and second state variables of; respectively arranging high-precision optical digital encoders at the input end and the output end of the sandwich system, acquiring input and output data of the system through the high-precision optical digital encoders, estimating the state of the system by adopting the observer constructed in the step 1), calculating and drawing a state and state estimation error diagram, and specifically, respectively aiming at the existence of L in the system by utilizing a Simulink module and an m editor in Matlab1Fault, or dead zone increasing fault, or L2When the fault occurs, estimating the state of the system, and calculating to obtain the state and a state estimation error;
the Simulink module comprises an ideal input module, a summation module, a controller and an L1Subsystem, dead zone link, L2Subsystem, feedback gain and connecting line, and also includes L1Fault signal, or L2A fault signal, or dead zone increasing module; when the system contains only L1In case of failure, will L2Fault signal f of2Setting the dead zone width to be zero, wherein the dead zone width is a normal width; when the system contains only L2In case of failure, will L1Fault signal f of1Setting the dead zone width to be zero, wherein the dead zone width is a normal width; when the system increases only the dead zone width, L is set1Fault signal f of1And L2Fault signal f of2Set to zero;
the m editor executes the following operations:
3-1) initializing the estimated values of the state variables:
order:
Figure GDA0003342726260000051
and calculate
Figure GDA0003342726260000052
Determining sampling frequency, simulation time and cycle number N according to the characteristics of an actual system, and collecting an input signal u and an output signal y;
3-2) let k be 3;
3-3) judging whether k is less than or equal to N, if k is less than or equal to N, executing the step 3-4), and if k is greater than N, finishing the operation;
3-4) if
Figure GDA0003342726260000053
The following operations are performed:
Figure GDA0003342726260000054
Figure GDA0003342726260000055
Figure GDA0003342726260000056
if it is
Figure GDA0003342726260000057
The following operations are performed:
Figure GDA0003342726260000058
Figure GDA0003342726260000059
Figure GDA00033427262600000510
if it is
Figure GDA00033427262600000511
The following operations are performed:
Figure GDA00033427262600000512
Figure GDA00033427262600000513
Figure GDA00033427262600000514
3-5) adding 1 to the value of k, and repeating the step 3-3);
4) the estimation errors of the 4 states of X12, X12, X21 and X22 are obtained through analysis and simulation, and the occurrence position and the type of the system fault are determined, specifically as follows:
4-1) if the estimation error of the state X11 converges to zero, the estimation error of the state X12 converges to zero, the estimation error of the state X21 converges to zero, and the estimation error of the state X22 converges to zero, no fault occurs;
4-2) if the state X11 estimation error converges to a fixed value, the state X12 estimation error converges to zero, the state X21 estimation error converges to zero, and the state X22 estimation error converges to zero, then a fault occurs at L1Subsystem, and step fault;
4-3) converging an interval if the estimation error of the state X11 changes according to a sine rule; the estimation error of the state X12 changes according to a sine rule and converges an interval; state X21 estimates error convergence to zero; state X22 estimates error convergence to zero; the fault occurs at L1Subsystem, and is sinusoidal fault with attenuated amplitude;
4-4) if the estimation error of the state X11 converges to zero, the estimation error of the state X12 converges to zero, the estimation error of the state X21 converges to a constant range, and the estimation error of the state X22 converges to zero, the fault is that the dead zone width is too large;
4-5) if the state X11 estimation error converges to a fixed value, the state X12 estimation error converges to a fixed value, the state X21 estimation error converges to a fixed value, and the state X22 estimation error converges to a fixed value, a fault occurs at L2Subsystem, and step fault;
4-6) converging an interval if the estimation error of the state X11 changes according to a sine rule; the estimation error of the state X12 changes according to a sine rule and converges an interval; the estimation error of the state X21 changes according to a sine rule and converges an interval; the estimation error of the state X22 changes according to a sine rule and converges an interval; the fault occurs at L2Subsystem, and is a sinusoidal fault with attenuated amplitude.
The method adopts a state estimation error method to position the fault of the dead zone non-smooth sandwich system, only needs the input and output numbers of the known system, has less types of sampling data, is simple to use and has high positioning reliability.
Drawings
FIG. 1 is a block diagram of a dead zone sandwich system with a fault;
FIG. 2 is a Simulink model diagram of three faults of a dead zone sandwich system;
FIG. 3 is the estimated error for 4 states of the system without failure;
FIG. 4 is an error of 4 states of the system with a step fault at L1;
FIG. 5 is an error of 4 states of the system with a sinusoidal fault at L1;
FIG. 6 is an error for 4 states of the system as the dead band width increases;
FIG. 7 is the error for 4 states of the system with a step fault at L2;
fig. 8 shows the error of 4 states of the system when L2 has a sinusoidal fault.
Detailed Description
The invention will be further elucidated with reference to the drawings and examples, without however being limited thereto.
Example (b):
a fault locating method for a dead zone non-smooth sandwich system comprises the following steps:
1) constructing a non-smooth state space equation capable of accurately describing a dead zone sandwich system with faults by using a key item separation principle and a switching function, wherein the dead zone nonlinear characteristic is characterized in that the size of output is only related to the size of input at the current moment and is not related to the input and the output at the previous moment, u (k) and y (k) are respectively measurable input and output variables in the dead zone sandwich system with faults, v (k) is a measurable variable, and v (k) is a measurable variable1(k) And v2(k) Is an unmeasurable intermediate variable, L1Representing the front-end linear subsystem, L2Representing the back-end linear subsystem, D1And D2Is the width of the dead zone, m1And m2Is the slope of the linear region, f (k) represents the fault of the system, and the state space equation of the system is established for the dead zone sandwich system with the fault as shown in fig. 1, which is as follows:
1-1) establishing a state space equation of the linear subsystem: according to the linear system theory, the linear subsystem L1The state space equation of (a) is as follows:
Figure GDA0003342726260000071
according to the linear system theory, the linear subsystem L2The state space equation of (a) is as follows:
Figure GDA0003342726260000072
wherein
Figure GDA0003342726260000073
u∈R1 ×1，y∈R1×1，f∈R1×1，uf∈R1×1，af∈R1×1，bf∈R1×1，x11And x12Each represents L1First and second state variables, x21And x22Each represents L2The first and second state variables of (a),
Figure GDA0003342726260000074
are respectively L1、L2The state transition matrix of (a) is,
Figure GDA0003342726260000075
are respectively L1、L2The input matrix of (a) is selected,
Figure GDA0003342726260000076
are respectively L1、L2The output matrix of (a) is obtained,
Figure GDA0003342726260000077
for the failure matrix, u ∈ R1×1As input, y ∈ R1×1For output, f ∈ R1×1Is a failure of the system, afAs a factor of a failed link, bfInput coefficients for unknown fault links; u. off∈R1×1The input for the failed link is unknown; a isfAnd bfObtained from a priori knowledge of system faults, known; suppose ufIs bounded, afIs less than 1, i.e. | af|<1, so that the fault system is stable according to the linear system stability condition, niFor the dimension of the i-th linear system, let
Figure GDA0003342726260000078
And is
Figure GDA0003342726260000079
1-2) establishing a state space equation of the dead zone subsystem: defining intermediate variables m (k), w1(k) Comprises the following steps:
m(k)＝m1+(m2-m1)h(k)
w1(k)＝m(k)(x(k)-D1h1(k)+D2h2(k))
wherein
Figure GDA0003342726260000081
In order to be a function of the switching,
obtaining the following according to the input-output relation of the dead zone:
v2(k)＝w1(k)-h3(k)w1(k)＝(1-h3(k))w1(k)，
wherein
Figure GDA0003342726260000082
Also as a switching function, when h3(k) When 0, the system operates in the linear region, and v2(k)＝w1(k) (ii) a When h is generated3(k) When 1, the system operates in the dead zone, and v2(k)＝w1(k)-w1(k) 0, according to the input-output characteristics of the dead zone:
Figure GDA00033427262600000811
due to the fact that
Figure GDA0003342726260000083
Substituting the formula (2) into the formula (3) to obtain:
Figure GDA0003342726260000084
1-3) establishing an integral state space equation of the dead zone sandwich system: according to formula (1), formula (2), formula (4) and
Figure GDA0003342726260000085
then:
Figure GDA0003342726260000086
wherein
Figure GDA0003342726260000087
Figure GDA0003342726260000088
According to the characteristics of the sandwich system, only the output y (k) of the system can be directly measured, so that
Figure GDA0003342726260000089
Wherein
Figure GDA00033427262600000810
0 is a zero matrix of the corresponding order
Figure GDA0003342726260000091
Equation (5) is written as follows:
Figure GDA0003342726260000092
wherein etaiSwitching vectors introduced for considering the existence of dead zone non-linear characteristics of the system;
2) constructing a non-smooth observer capable of automatically switching along with the change of the working interval of the dead zone sandwich system with the fault according to the non-smooth state space equation of the dead zone sandwich system with the fault, which is constructed in the step 1), and giving the existence condition of the observer, wherein the method comprises the following steps:
Figure GDA0003342726260000093
wherein Kpj、kijThe ith working interval is proportional gain and integral gain,
Figure GDA0003342726260000094
Figure GDA0003342726260000095
x (k), y (k), f (k), eta, respectivelyiWhen j is 1, 2, or 3, i is j, then
Figure GDA0003342726260000096
The non-smooth observer has a convergence condition of Aj-KpjThe characteristic value of C is within the unit circle.
3) According to the characteristics of the actual second-order system, then n1＝n2＝2，x1∈R2×1,x2∈R2×1Let x be1＝[X11，X12]T,x2＝[X21，X22]T. X11 and X12 each represent L1X21 and X22 represent L, respectively2First and second state variables. Arranging high-precision optical digital encoders at the input end and the output end of the sandwich system respectively, acquiring input and output data of the system through the high-precision optical digital encoders, estimating the state of the system by adopting the observer constructed in the step 1), calculating and drawing the state and the state estimation errorSpecifically, the method utilizes a Simulink module and an m editor in Matlab to respectively aim at the existence of L in the system1Fault, dead zone increasing fault, L2When the fault occurs, estimating the state of the system, and calculating to obtain the state and a state estimation error;
the Simulink module comprises an ideal input module, a summation module, a controller and an L1Subsystem, dead zone link, L2Subsystem, feedback gain and connecting line, and also includes L1Fault signal, or L2A fault signal, or dead zone increasing module; when the system contains only L1In case of failure, will L2Fault signal f of2Setting the dead zone width to be zero, wherein the dead zone width is 0.02 of the normal width; when the system contains only L2In case of failure, will L1Fault signal f of1Setting the dead zone width to be zero, wherein the dead zone width is 0.02 of the normal width; when the dead zone width of the system is increased, L is adjusted1Fault signal f of1And L2Fault signal f of2Set to zero;
the m editor executes the following operations:
3-1) initializing the estimated value of the state variable and the estimated value of the fault:
order:
Figure GDA0003342726260000101
and calculate
Figure GDA0003342726260000102
Order:
Figure GDA0003342726260000103
determining sampling frequency, state estimation time and defined cycle number N according to the characteristics of an actual system, and acquiring an input signal u and an output signal y;
3-2) let k be 3;
3-3) judging whether k is less than or equal to N, if k is less than or equal to N, executing the step 3-4), and if k is greater than N, finishing the operation;
3-4) if
Figure GDA0003342726260000104
The following operations are performed:
Figure GDA0003342726260000105
Figure GDA0003342726260000106
Figure GDA0003342726260000107
if it is
Figure GDA0003342726260000108
The following operations are performed:
Figure GDA0003342726260000109
Figure GDA00033427262600001010
Figure GDA00033427262600001011
if it is
Figure GDA00033427262600001012
The following operations are performed:
Figure GDA00033427262600001013
Figure GDA00033427262600001014
Figure GDA00033427262600001015
3-5) adding 1 to the value of k, and repeating the step 3-3);
4) the estimation errors of the 4 states of X12, X12, X21 and X22 are obtained through analysis and simulation, and the occurrence position and the type of the system fault are determined, specifically as follows:
4-1) if the estimation error of the state X11 converges to zero, the estimation error of the state X12 converges to zero, the estimation error of the state X21 converges to zero, and the estimation error of the state X22 converges to zero, no fault occurs;
4-2) if the state X11 estimation error converges to a fixed value, the state X12 estimation error converges to zero, the state X21 estimation error converges to zero, and the state X22 estimation error converges to zero, then a fault occurs at L1Subsystem, and step fault;
4-3) converging an interval if the estimation error of the state X11 changes according to a sine rule; the estimation error of the state X12 changes according to a sine rule and converges an interval; state X21 estimates error convergence to zero; state X22 estimates error convergence to zero; the fault occurs at L1Subsystem, and is sinusoidal fault with attenuated amplitude;
4-4) if the estimation error of the state X11 converges to zero, the estimation error of the state X12 converges to zero, the estimation error of the state X21 converges to a constant range, and the estimation error of the state X22 converges to zero, the fault is that the dead zone width is too large;
4-5) if the state X11 estimation error converges to a fixed value, the state X12 estimation error converges to a fixed value, the state X21 estimation error converges to a fixed value, and the state X22 estimation error converges to a fixed value, a fault occurs at L2Subsystem, and step fault;
4-6) converging an interval if the estimation error of the state X11 changes according to a sine rule; the estimation error of the state X12 changes according to a sine rule and converges an interval; the estimation error of the state X21 changes according to a sine rule and converges an interval; the estimation error of the state X22 changes according to a sine rule and converges an interval; the fault occurs at L2Subsystem, and is a sinusoidal fault with attenuated amplitude.
Example (b):
(1) without failure
When there is no fault, the estimation errors for the 4 states (x11, x12, x21, x22) all eventually converge to zero, as shown in fig. 3.
(2) L1 step fault
Ideal input signal u is 0.5sin (5t), dead zone width is normal width 0.02, L2The fault signal f2 is zero and is given to L at 1s (100 th sampling point), respectively1And adding a step fault with the amplitude of 0v (no fault), a step fault with the amplitude of 1v and a step fault with the amplitude of 10v, and estimating the state of the system by adopting a non-smooth observer.
As shown in fig. 4, in the three cases, the estimation error of the state x11 converges to a fixed value after the occurrence of a failure (after 1 s) through 20 sampling points (0.2s), and the shape of the estimation error also coincides with the shape of the failure signal, but the estimation error convergence value of the state x11 also increases in proportion to the increase in the failure amplitude. The estimation errors for the remaining three states (states x12, x21, x22) eventually converge to "zero" (within 0.05% of the fault signal amplitude).
Further, as shown in fig. 5, when the fault frequency increases, the amplitude of the estimation error convergence value of the state x11 changes little, and the estimation errors of the remaining three states (states x12, x21, x22) eventually converge to "zero" (within 0.05% of the fault signal amplitude).
(3) Increase of dead zone width
Ideal input signal u is 0.5sin (5t), L1Fault signal f1 is zero, L2The fault signal f2 is zero. When the dead zone widths are 0.02 (normal width), 0.1, 0.2, 2, respectively, the state of the system is estimated using a non-smooth observer.
As shown in fig. 6, when the dead zone width is increased from 0.02 to 0.1, 0.2, 2, the estimation error of the state x21 converges to a certain range. As the dead band width increases to 0.2 and above, the estimated error curves for state x21 coincide, converging to a constant range. When the dead zone width is 0.2 or less, the estimation error of the state x21 converges to zero. The estimated error for the remaining 3 states (x11, x12, x22) converges to "zero" to within 0.1% of the input.
(4) L2 step fault
Ideal input signal u is 0.5sin (5t), dead zone width is normal width 0.02, L1The fault signal f1 is zero.
As shown in fig. 7, at 1s (100 th sampling point), a step fault (no fault) with an amplitude of 0v, a step fault with an amplitude of 1v, and a step fault with an amplitude of 2v are added, respectively. A non-smooth observer is used to estimate the state of the system. In the three cases, the estimation errors of 4 states (x11, x12, x21, and x22) converge to a fixed value after the occurrence of a fault (after 1 s) through 20 sampling points (0.2s), and the shape of the estimation error also matches the shape of the fault signal. As the magnitude of the fault increases, the convergence of the estimation error for state x11 also increases.
Further, the magnitude of the estimation error convergence value range of the 4 states (x11, x12, x21, x22) changes little when the failure frequency increases.

Claims (3)

1. A fault positioning method for a dead zone non-smooth sandwich system is characterized by comprising the following steps:
1) constructing a non-smooth state space equation capable of accurately describing a dead zone sandwich system with faults by using a key item separation principle and a switching function, wherein the dead zone nonlinear characteristic is characterized in that the size of output is only related to the size of input at the current moment and is not related to the input and the output at the previous moment, u (k) and y (k) are respectively measurable input and output variables in the dead zone sandwich system with faults, v (k) is a measurable variable, and v (k) is a measurable variable1(k) And v2(k) Is an unmeasurable intermediate variable, L1Representing the front-end linear subsystem, L2Representing the back-end linear subsystem, D1And D2Is the width of the dead zone, m1And m2Is the slope of the linear region, f (k) represents the fault of the system, and the state space equation of the system is established when the dead zone sandwich system containing the fault is provided, which is as follows:
1-1) establishing a state space equation of the linear subsystem: according to the linear system theory, the linear subsystem L1The state space equation of (a) is as follows:
Figure FDA0003342726250000011
according to the linear system theory, the linear subsystem L2The state space equation of (a) is as follows:
Figure FDA0003342726250000012
wherein
Figure FDA0003342726250000013
u∈R1×1，y∈R1×1，f∈R1×1，uf∈R1×1，af∈R1×1，bf∈R1×1，
Figure FDA0003342726250000014
Are respectively L1、L2The state transition matrix of (a) is,
Figure FDA0003342726250000015
are respectively L1、L2The input matrix of (a) is selected,
Figure FDA0003342726250000016
are respectively L1、L2The output matrix of (a) is obtained,
Figure FDA0003342726250000017
for the failure matrix, u ∈ R1×1As input, y ∈ R1×1For output, f ∈ R1×1Is a failure of the system, afAs a factor of a failed link, bfInput coefficients for unknown fault links; u. off∈R1×1The input for the failed link is unknown; a isfAnd bfObtained from a priori knowledge of system faults, known; suppose ufIs bounded, afIs less than 1, i.e. | af|<1, so that the fault system is stable according to the linear system stability condition, niFor the dimension of the i-th linear system, let
Figure FDA0003342726250000018
And is
Figure FDA0003342726250000019
1-2) establishing a state space equation of the dead zone subsystem: defining intermediate variables m (k), w1(k) Comprises the following steps:
m(k)＝m1+(m2-m1)h(k)
w1(k)＝m(k)(x(k)-D1h1(k)+D2h2(k))
wherein
Figure FDA0003342726250000021
In order to be a function of the switching,
obtaining the following according to the input-output relation of the dead zone:
v2(k)＝w1(k)-h3(k)w1(k)＝(1-h3(k))w1(k)，
wherein
Figure FDA0003342726250000022
Also as a switching function, when h3(k) When 0, the system operates in the linear region, and v2(k)＝w1(k) (ii) a When h is generated3(k) When 1, the system operates in the dead zone, and v2(k)＝w1(k)-w1(k) 0, according to the input-output characteristics of the dead zone:
Figure FDA0003342726250000023
due to the fact that
Figure FDA0003342726250000024
Substituting the formula (2) into the formula (3) to obtain:
Figure FDA0003342726250000025
1-3) establishing an integral state space equation of the dead zone sandwich system: according to formula (1), formula (2), formula (4) and
Figure FDA0003342726250000026
then there is
Figure FDA0003342726250000027
Wherein
Figure FDA0003342726250000028
Figure FDA0003342726250000031
According to the characteristics of the sandwich system, only the output y (k) of the system can be directly measured, so that
Figure FDA0003342726250000032
Wherein
Figure FDA0003342726250000033
0 is a zero matrix of the corresponding order
Figure FDA0003342726250000034
Then the formula (5) writesIn the following form:
Figure FDA0003342726250000035
wherein etaiSwitching vectors introduced for considering the existence of dead zone non-linear characteristics of the system;
2) constructing a non-smooth observer capable of automatically switching along with the change of the working interval of the dead zone sandwich system with the fault according to the non-smooth state space equation of the dead zone sandwich system with the fault, which is constructed in the step 1), and giving the existence condition of the observer, wherein the method comprises the following steps:
Figure FDA0003342726250000036
wherein Kpj、kijRespectively the proportional gain and the integral gain of the ith working interval,
Figure FDA0003342726250000037
Figure FDA0003342726250000038
x (k), y (k), f (k), eta, respectivelyiWhen j is 1, 2, or 3, i is j, then
Figure FDA0003342726250000039
The non-smooth observer has a convergence condition of Aj-KpjThe eigenvalues of C are within the unit circle;
3) according to the characteristics of a practical second-order system, i.e. n1＝n2X is 21∈R2×1，x2∈R2×1Let x be1＝[X12，X12]T、x2＝[X21，X22]TX12 and X12 each represent L1X21 and X22 represent L, respectively2First and second state variables of; input in a Sandwich SystemArranging high-precision optical digital encoders at the end and the output end respectively, acquiring input and output data of the dead zone sandwich system through the high-precision optical digital encoders, estimating the state of the system by adopting the observer constructed in the step 1), calculating and drawing a state and state estimation error diagram, specifically, respectively aiming at the existence of L in the system by utilizing a Simulink module and an m editor in Matlab1Fault, dead zone increasing fault, L2When the fault occurs, estimating the state of the system, and calculating to obtain the error of a state meter;
4) the estimation errors of the 4 states of X12, X12, X21 and X22 are obtained through analysis and simulation, and the occurrence position and the type of the system fault are determined, specifically as follows:
4-1) if the estimation error of the state X11 converges to zero, the estimation error of the state X12 converges to zero, the estimation error of the state X21 converges to zero, and the estimation error of the state X22 converges to zero, no fault occurs;
4-2) if the state X11 estimation error converges to a fixed value, the state X12 estimation error converges to zero, the state X21 estimation error converges to zero, and the state X22 estimation error converges to zero, then a fault occurs at L1Subsystem, and step fault;
4-3) converging an interval if the estimation error of the state X11 changes according to a sine rule; the estimation error of the state X12 changes according to a sine rule and converges an interval; state X21 estimates error convergence to zero; state X22 estimates error convergence to zero; the fault occurs at L1Subsystem, and is sinusoidal fault with attenuated amplitude;
4-4) if the estimation error of the state X11 converges to zero, the estimation error of the state X12 converges to zero, the estimation error of the state X21 converges to a constant range, and the estimation error of the state X22 converges to zero, the fault is that the dead zone width is too large;
4-5) if the state X11 estimation error converges to a fixed value, the state X12 estimation error converges to a fixed value, the state X21 estimation error converges to a fixed value, and the state X22 estimation error converges to a fixed value, a fault occurs at L2Subsystem, and step fault;
4-6) converging an interval if the estimation error of the state X11 changes according to a sine rule; state X12 estimationThe error changes according to the sine rule and converges into an interval; the estimation error of the state X21 changes according to a sine rule and converges an interval; the estimation error of the state X22 changes according to a sine rule and converges an interval; the fault occurs at L2Subsystem, and is a sinusoidal fault with attenuated amplitude.
2. The method of claim 1, wherein the Simulink module comprises an ideal input, a summation module, a controller, and L1Subsystem, dead zone link, L2Subsystem, feedback gain and connecting line, and also includes L1Fault signal, or L2A fault signal, or dead zone increasing module; when only L is present1In case of failure, will L2Fault signal f of2Setting the dead zone width to be zero, wherein the dead zone width is a normal width; when the system contains only L2In case of failure, will L1Fault signal f of1Setting the dead zone width to be zero, wherein the dead zone width is a normal width; when the system increases only the dead zone width, L is set1Fault signal f of1And L2Fault signal f of2Is set to zero.
3. The method of claim 1, wherein the m editor performs the following operations:
3-1) initializing the estimated values of the state variables:
order:
Figure FDA0003342726250000051
and calculate
Figure FDA0003342726250000052
Determining sampling frequency, sampling time and cycle number N according to the characteristics of an actual system, and acquiring an input signal u and an output signal y of the system;
3-2) let k be 3;
3-3) judging whether k is less than or equal to N, if k is less than or equal to N, executing the step 3-4), and if k is greater than N, finishing the operation;
3-4) if
Figure FDA0003342726250000053
The following operations are performed:
Figure FDA0003342726250000054
Figure FDA0003342726250000055
Figure FDA0003342726250000056
if it is
Figure FDA0003342726250000057
The following operations are performed:
Figure FDA0003342726250000058
Figure FDA0003342726250000059
Figure FDA00033427262500000510
if it is
Figure FDA00033427262500000511
The following operations are performed:
Figure FDA00033427262500000512
Figure FDA00033427262500000513
Figure FDA00033427262500000514
3-5) adding 1 to the value of k, repeating steps 3-3).
CN202110025922.8A 2021-01-08 2021-01-08 Fault positioning method for dead zone non-smooth sandwich system Active CN112987683B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110025922.8A CN112987683B (en) 2021-01-08 2021-01-08 Fault positioning method for dead zone non-smooth sandwich system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110025922.8A CN112987683B (en) 2021-01-08 2021-01-08 Fault positioning method for dead zone non-smooth sandwich system

Publications (2)

Publication Number Publication Date
CN112987683A CN112987683A (en) 2021-06-18
CN112987683B true CN112987683B (en) 2022-02-18

Family

ID=76345315

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110025922.8A Active CN112987683B (en) 2021-01-08 2021-01-08 Fault positioning method for dead zone non-smooth sandwich system

Country Status (1)

Country Link
CN (1) CN112987683B (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105204332A (en) * 2015-08-10 2015-12-30 桂林电子科技大学 State estimation method for composite sandwich system with dead zone and hysteresis on the basis of non-smooth observer
CN108227679A (en) * 2018-01-12 2018-06-29 桂林电子科技大学 A kind of method for estimating state containing faulty gap Sandwich system
CN108279569A (en) * 2018-01-12 2018-07-13 桂林电子科技大学 A kind of method for estimating state containing faulty sluggish Sandwich system

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7398259B2 (en) * 2002-03-12 2008-07-08 Knowmtech, Llc Training of a physical neural network
US7036559B2 (en) * 2003-07-08 2006-05-02 Daniel Stanimirovic Fully articulated and comprehensive air and fluid distribution, metering, and control method and apparatus for primary movers, heat exchangers, and terminal flow devices
CN102131383B (en) * 2008-06-26 2014-07-23 Solix生物燃料公司 Model based controls for use with bioreactors
TW201135165A (en) * 2010-04-06 2011-10-16 Donald S Stern Solar panel with lens and reflector
CN111714975B (en) * 2020-06-10 2021-11-23 浙江工业大学 Plate type air inlet purifier, air inlet system and method of vehicle-mounted fuel cell

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105204332A (en) * 2015-08-10 2015-12-30 桂林电子科技大学 State estimation method for composite sandwich system with dead zone and hysteresis on the basis of non-smooth observer
CN108227679A (en) * 2018-01-12 2018-06-29 桂林电子科技大学 A kind of method for estimating state containing faulty gap Sandwich system
CN108279569A (en) * 2018-01-12 2018-07-13 桂林电子科技大学 A kind of method for estimating state containing faulty sluggish Sandwich system

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
《Fault detection of mechanical systems with inherent backlash》;Yonghong Tan;《2013 10th IEEE INTERNATIONAL CONFERENCE ON NETWORKING, SENSING AND CONTROL (ICNSC)》;20130412;第77页-第82页 *
《基于鲁棒观测器的带间隙三明治系统故障预报》;周祖鹏;《控制理论与应用》;20150615(第6期);第753页-第761页 *

Also Published As

Publication number Publication date
CN112987683A (en) 2021-06-18

Similar Documents

Publication Publication Date Title
CN110908364B (en) Fault detection method based on robust interval estimation
CN101635457B (en) Electric network parameter estimation method based on parameter sensitivity of state estimation residual error
CN103245881B (en) Power distribution network fault analyzing method and device based on tidal current distribution characteristics
CN105978725A (en) Non-fragile distributed fault estimation method based on sensor network
CN102377180A (en) Power system load modeling method based on electric energy quality monitoring system
CN103996073A (en) Photometric-network real-time-correction self-learning ARMA model photovoltaic power prediction method
CN107192961A (en) Novel power battery SOC estimation method
CN103116136A (en) Lithium battery charge state assessment method based on finite difference expansion Kalman algorithm
CN113075585A (en) NPC three-level inverter composite open-circuit fault diagnosis method
CN111752262A (en) Actuator fault observer and fault-tolerant controller integrated design method
CN113325708A (en) Fault estimation method of multi-unmanned aerial vehicle system based on heterogeneous multi-agent
CN103984988A (en) Method for correcting super-short-term prediction of photovoltaic power of ARMA module in real time through light metering network
CN112987683B (en) Fault positioning method for dead zone non-smooth sandwich system
CN103646013A (en) Multiple fault reconstruction method based on covariance matrix norm approximation
US20210103263A1 (en) Systems and methods for hybrid dynamic state estimation
CN112731193B (en) NPC inverter multi-class fault diagnosis method based on sliding-mode observer
CN103984987A (en) Ultrashort-term prediction method for wind electricity power of ARMA model with anemometer network real-time correction
CN103513160B (en) A kind of same-tower double-circuit direct-current transmission line fault line selection
CN113033077A (en) Direct-current transmission line fault distance measurement method based on neural network algorithm
CN107069710B (en) Power system state estimation method considering new energy space-time correlation
CN109193639A (en) A kind of electric system Robust filter method
CN104200002A (en) Method for extracting modal parameter from viscous damping vibration signals
CN110768628B (en) Photovoltaic array fault detection method
Wang et al. Advances in fault detection and diagnosis using filtering analysis
Ji et al. A graph-theoretic method for identification of electric power distribution system topology

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant