CN110362060B - Diagnosis method for simultaneous failure of control system actuator and sensor - Google Patents

Diagnosis method for simultaneous failure of control system actuator and sensor Download PDF

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CN110362060B
CN110362060B CN201910583157.4A CN201910583157A CN110362060B CN 110362060 B CN110362060 B CN 110362060B CN 201910583157 A CN201910583157 A CN 201910583157A CN 110362060 B CN110362060 B CN 110362060B
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万怡仕
肖玲斐
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • 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
    • G05B23/0259—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterized by the response to fault detection
    • G05B23/0275—Fault isolation and identification, e.g. classify fault; estimate cause or root of failure
    • 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

Abstract

The invention discloses a method for diagnosing faults of an actuator and a sensor of a control system at the same time, which comprises the steps of firstly, converting a fault model of the sensor into a fault model of the actuator, and modifying a fault diagnosis scheme of the actuator to solve the problem of diagnosing faults of a false actuator; and then, when the faults of the actuator and the sensor exist in the system at the same time, combining the sliding mode observer of the fault diagnosis scheme of the pseudo actuator with the sliding mode observer suitable for the faults of the common actuator to act on the system, and completing fault diagnosis by analyzing the residual error.

Description

Diagnosis method for simultaneous failure of control system actuator and sensor
Technical Field
The invention relates to an actuator diagnosis technology, in particular to a diagnosis method for controlling system actuators and sensors to simultaneously fail, which is mainly used for failure analysis of a common automatic control system under the condition that the actuators and the sensors simultaneously fail.
Background
The two background technologies mainly related to the technology are an actuator diagnosis technology based on a sliding-mode observer (reference document: Liu Jing. fault diagnosis technology based on the sliding-mode observer and application research thereof in a flight control system [ D ]. Nanjing: Nanjing aerospace university Automation institute, 2008), and a scheme for converting sensor faults into an actuator fault model (reference document: Huang Yishan, Zhang Chang Van, Severe.
The fault diagnosis scheme is designed for solving the fault diagnosis of the control system actuator, and mainly comprises the steps of designing a sliding mode fault observer group, obtaining a residual error value between a system and an observer through SIMULINK simulation software, obtaining the residual error group through the sliding mode observer group, analyzing and comparing the residual error group to judge a fault source, and estimating the size of the fault value through the sliding mode observer. The method has the defect that when the system is in sensor failure, the failure diagnosis mode is interfered by the sensor failure value and is further influenced by collecting system data and then using the technology to simulate in SIMULINK software.
The second technique is designed for simplifying the sensor fault diagnosis process, and skillfully converts a system model with sensor faults into a system model similar to the faults of an actuator by constructing a system state variable, so that the problem of sensor fault diagnosis can be solved by a fault diagnosis method of the actuator. At present, the fault diagnosis method of the sensor is relatively complex, and the diagnosis process of the system only when the sensor fault occurs can be greatly simplified by the method. However, the technology has no solution to the problem that the system simultaneously has actuator faults and sensor faults.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a method for diagnosing when the actuator and the sensor of the control system are simultaneously in failure, aiming at the defects involved in the background technology.
The invention adopts the following technical scheme for solving the technical problems:
a method for diagnosing the simultaneous failure of an actuator and a sensor of a control system comprises the following steps:
step 1), establishing a system fault model containing m sensors:
Figure GDA0003121083010000011
y＝Cx+Gfs
wherein: x belongs to Rn and is an unmeasured system state vector, y belongs to Rn and is a measurable system output vector, and u belongs to Rn and is a measurable system input vector; A. b, C, G are all dimensional matrices obtained when the control system is linearized and converted to a state space model, and (A, C) is considerable; f. ofsIs a sensor fault vector, which is a bounded linear function; Δ (t) represents the system uncertainty disturbance;
by adding the state variable z, the fault model of the system sensor with m sensors is written into the following form:
Figure GDA0003121083010000021
Figure GDA0003121083010000022
wherein
Figure GDA0003121083010000023
Step 2), establishing a system fault model containing n actuators:
Figure GDA0003121083010000024
y＝Cx
wherein f isaThe fault vector of the actuator is a bounded linear function;
putting the fault models of the n actuators into the fault models of the m sensors to obtain a comprehensive fault model:
Figure GDA0003121083010000025
Figure GDA0003121083010000026
wherein
Figure GDA0003121083010000027
Step 3), designing a fault observer for the faults of the actuator and the false actuator, namely the faults of the sensor, and then combining the fault observers into an observer group;
order to
Figure GDA0003121083010000028
Is a matrix
Figure GDA0003121083010000029
The effect is equal to the proper dimension matrix A in the original system, so that
Figure GDA00031210830100000210
Is a matrix
Figure GDA00031210830100000211
Is a matrix
Figure GDA00031210830100000212
[0I]Is a matrix
Figure GDA00031210830100000213
Step 3.1), for actuator failure, in case the following assumptions are satisfied:
assume that 1: the matrix B is full rank;
assume 2: there is an adaptive matrix L1、F1And a positive definite matrix P1、Q1Satisfies the following conditions:
Figure GDA00031210830100000214
Figure GDA00031210830100000215
assume that 3: the norm of external disturbance delta (t) is bounded, | | delta (t) | | is less than or equal to W1，W1Is a positive number; actuator failure faBounded, | | fa||≤M1，M1Is positive and the external disturbance is much smaller than the actuator failure, i.e. W1<<M1；
Setting n executor fault observers:
Figure GDA00031210830100000216
Figure GDA0003121083010000031
in the formula (I), the compound is shown in the specification,
Figure GDA0003121083010000032
is the state variable in the fault observer corresponding to the ith actuator,
Figure GDA0003121083010000033
Figure GDA0003121083010000034
is the system output vector in the fault observer corresponding to the ith actuator,
Figure GDA0003121083010000035
biis a matrix
Figure GDA0003121083010000036
Column vector of the ith column, δ1Is a preset small positive number; fiRefers to the matrix F1The number of the ith row of (a),
Figure GDA0003121083010000037
switching gain rho of actuator fault observer1Satisfy rho1≥M1And is and
Figure GDA0003121083010000038
is a Hurwitz matrix;
step 3.2), under the condition that the following assumptions are met:
assume that 1: matrix array
Figure GDA0003121083010000039
Column full rank;
assume 2: there is an adaptive matrix L2、F2And a positive definite matrix P2、Q2Satisfies the following conditions:
Figure GDA00031210830100000310
Figure GDA00031210830100000311
assume that 3: the norm of external disturbance delta (t) is bounded, | | delta (t) | | is less than or equal to W2，W2Is a positive number; sensor failure fsBounded, | | fs||≤M2，W2<<M2；
Setting m false executor fault observers, namely sensor fault observers:
Figure GDA00031210830100000312
Figure GDA00031210830100000313
in the formula (I), the compound is shown in the specification,
Figure GDA00031210830100000314
is the state variable in the fault observer corresponding to the jth sensor,
Figure GDA00031210830100000315
Figure GDA00031210830100000316
is the system output vector in the fault observer corresponding to the jth sensor,
Figure GDA00031210830100000317
δ2is a preset small positive number;
Figure GDA00031210830100000318
is a matrix
Figure GDA00031210830100000319
Column vector of j-th column, FjRefers to the matrix F2The (c) th row of (a),
Figure GDA00031210830100000320
switched gain ρ of sensor fault observer2Satisfy rho2≥M2And is and
Figure GDA00031210830100000321
is a Hurwitz matrix;
step 3.3), combining the n actuator fault observers and the m sensor fault observers into an observer group;
step 4), enabling the observer group to act on the comprehensive fault model, namely enabling n actuator fault observers and m sensor fault observers in the observer group to act on the system fault models of n actuators and m sensors in the comprehensive fault model in a one-to-one correspondence mode, and obtaining residual error images between m + n system state variables and observer state variables;
and 5) screening the same residual images from the m + n residual images, marking the residual images as r, comparing each residual image r left after screening from the m + n residual images with the residual image r, and if the residual value of the residual image r is smaller than that of the residual image r at any time, determining that the residual image r corresponds to a sensor or an actuator corresponding to an observer, namely a fault source, wherein mu in the observer is a fault sourceiOr mujThe value is an estimate of the fault size.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the theoretical derivation shows that the sensor fault is converted into the actuator fault, and the method for diagnosing the fault by using the actuator fault observer can well complete the detection and isolation of the fault and greatly simplify the process of diagnosing the fault of the sensor.
2. When an actuator fault and a sensor fault occur simultaneously, the interference between fault signals can be greatly reduced by converting the sensor fault into the actuator fault (see the following example specifically).
Drawings
FIG. 1 is a flow chart of a fault diagnosis method;
FIG. 2 is a diagram of a linear full-dimensional observer fault diagnosis architecture;
FIG. 3(a) and FIG. 3(b) are the original actuator fault values in the system and the fault estimation values obtained by the observer corresponding to the fault actuator, respectively;
fig. 4(a) and 4(b) are respectively a system state variable residual error image obtained by an observer acting on a system with an actuator fault, and a system state variable residual error image obtained by a common full-dimensional observer when the system is in an actuator fault state;
FIG. 5(a) and FIG. 5(b) are the original sensor fault values in the system, and the fault estimation values obtained by the observer corresponding to the faulty sensor, respectively;
fig. 6(a) is a system state variable residual image obtained by a fault observer corresponding to a faulty sensor, and fig. 6(b), 6(c), and 6(d) are system state variable residual images obtained by fault observers corresponding to three types of non-faulty sensors, respectively;
fig. 7(a) and 7(b) are estimated failure values obtained by an observer corresponding to a failed actuator in a system in which actuator and sensor failures occur simultaneously, and original actuator failure values in a system in which actuator and sensor failures occur simultaneously, respectively;
fig. 8(a) and 8(b) are estimated failure values obtained by an observer corresponding to a failed sensor in a system in which failures of an actuator and a sensor occur simultaneously, and raw sensor failure values in a system in which failures of an actuator and a sensor occur simultaneously, respectively;
fig. 9(a) and 9(b) are respectively residual images obtained by observers corresponding to a failed actuator in a system in which a failure occurs in the actuator and a failure in the sensor at the same time, and residual images obtained by observers corresponding to the sensor in a system in which a failure occurs in the actuator and the sensor at the same time; fig. 9(c), 9(d), and 9(e) are system state variable residual images obtained by observers corresponding to actuators and sensors that do not fail in three systems in which the actuators and the sensors fail at the same time, respectively.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, components are exaggerated for clarity.
The core idea of the fault diagnosis method researched by the invention is that the system output is estimated by constructing an observer, and then the system output is compared with the output measured value to obtain residual error information. Therefore, the method focuses on the residual error acquisition process, and simultaneously considers that the residual error has the directionality corresponding to the fault during the design so as to carry out fault isolation and evaluation. A flow chart of a fault diagnosis method based on the sliding-mode observer is shown in fig. 1.
In general, a common full-dimensional observer can be used to reconstruct the original system state by estimating the system state, and then a residual error is generated to realize fault diagnosis. The structure diagram of the fault diagnosis of a general linear full-dimensional observer is shown in fig. 2.
Where u, d, f are the known input, unknown input and fault vector of the system, y and
Figure GDA0003121083010000054
respectively, the actual output of the system and the output of the state observer, and L is the state feedback matrix of the state observer. The system residual r can be obtained by a full-dimensional state observer. As long as the state observer is designed, the main content of the fault diagnosis is finished, and the fault diagnosis can be finished only by analyzing the residual error signal. However, in order to isolate a fault, it is necessary to obtain residuals with a certain structure, or make the residuals have directivity corresponding to each fault.
Taking a certain engine model as an example, the state space model of the linear disturbance system obtained by linearizing the system model is as follows:
Figure GDA0003121083010000051
y＝Cx
wherein: x e Rn is the system state vector, y e Rn is the system output vector, and u e Rn is the system input vector. A, B and C are all dimension-adaptive matrixes. Δ (t) represents the system uncertainty disturbance. And (A, C) is considerable.
The actuator fault types can be divided into: actuatorFault stuck, actuator constant gain variation, and actuator bias failure. The actuator snap-through failure (i.e., snap-through failure) is analyzed as a failure model. If the actuator fault function is set to faWe assume that there are n actuators in the system, and only one actuator fails at a time in the n actuators, so we have n failure models in total, and a sliding-mode observer is designed for each actuator for failure diagnosis of the actuator.
When the ith actuator fails, the original system model should be described as:
Figure GDA0003121083010000052
y＝Cx
wherein B is (B1 … bn),
Figure GDA0003121083010000053
is the fault of the first actuator, ujIt is the control amount expected when the jth actuator is operating normally without a failure. u. oflCorresponds to the ith actuator control amount.
Sensor failure types can be divided into: sensor failure, stuck sensor constant gain variation, and sensor bias failure. The study is carried out by taking the dead sensor fault as a fault model. If the sensor fault function vector is set as fsThen the sensor fault model can be described as:
Figure GDA0003121083010000061
y＝Cx+Gfs
wherein: x is the non-measurable system state vector, y is the measurable system output vector, and u is the measurable system input vector. A, B, C and G are all dimension-adaptive matrixes. f. ofsIs a sensor failure and is a bounded linear function. Δ (t) represents the system uncertainty disturbance.
Assume that 1: no fault of jth sensorWhen f is presentsj0; in the event of a fault, fsjIs a non-zero function. Wherein f issjIs fsThe row vector for row j, represents the jth sensor fault.
Assume 2: g is a column full rank matrix. The practical engineering significance of the method is that when one sensor breaks down, the normal work of other sensors is not influenced, namely, each sensor works independently and does not influence each other.
Assume that 3: (A, C) is considerable.
Assume 4: sensor failure is a bounded function.
As mentioned above, the sensor fault observer based on the sliding mode principle is complicated to design, and the main way of converting the sensor fault is described herein (according to the prior art).
The main idea in this section is to convert a sensor failure into a false actuator failure by introducing new state variables.
The following definitions are made:
definition 1: g ═ G1 … Gj … Gr ], where Gj is the column vector of the j-th column of G.
Definition 2: f. ofs＝[fs1…fsj…fsr]', wherein fsjIs fsRow vector for row j.
Definition 3: let rjIndicating the jth fault when a (a ≦ r) sensor faults occur simultaneously.
Based on the assumption that a is the most simultaneous sensor fault at any moment, the fault situation is modeled as
Figure GDA0003121083010000062
Figure GDA0003121083010000063
First order low pass filter defining as output signal a state variable z
Figure GDA0003121083010000064
In the formula AsThe matrix can be arbitrary, BsThe matrix is full rank, where A is selectedsThe matrix is a zero matrix, BsThe matrix is an identity matrix.
Substituting the above equation into the system state equation to obtain:
Figure GDA0003121083010000065
the new system equation is thus obtained as:
Figure GDA0003121083010000071
Figure GDA0003121083010000072
if defined, are
Figure GDA0003121083010000073
Substituting the formula to obtain:
Figure GDA0003121083010000074
Figure GDA0003121083010000075
as can be seen from the above equation, a sensor fault is converted into an actuator fault by the introduction of the state variable z. Thus, actuator failure can be detected by using the method of actuator failure.
We first introduced a sliding mode observer designed for actuator failure with the aid of previous research efforts. For the actuator fault model introduced previously:
Figure GDA0003121083010000076
y＝Cx
wherein B is (B1 … bn),
Figure GDA0003121083010000077
is the fault of the first actuator, ujIt is the control amount expected when the jth actuator is operating normally without a failure. u. oflCorresponds to the ith actuator control amount. We assume that only one actuator fails at a time, and the finally designed fault observer can be directly applied to a multi-actuator fault structure, which will be mentioned later.
In order to design a sliding-mode observer with desired characteristics, the system needs to satisfy the following assumptions:
assume that 1: matrix B column full rank.
Assume 2: there is an adaptive matrix L1，F1And a positive definite matrix P1，Q1Satisfies the following conditions:
(A-L1C)TP1+P1(A-L1C)＝-Q1
P1B＝CTF1 T
assume that 3: the norm of external disturbance delta (t) is bounded, | | delta (t) | | is less than or equal to W1，W1Is a positive number; actuator failure faBounded, | | fa||≤M1，M1Is a positive number and the external disturbance is much smaller than the actuator failure, i.e. W1<<M1。
Since only one actuator fault occurs at a time, there are n possible fault models, and for the n fault models, a set of sliding-mode observers is designed:
Figure GDA0003121083010000078
Figure GDA0003121083010000079
in the formula: delta1Is a very small positive number. FiRefers to the matrix F1The number of the ith row of (a),
Figure GDA0003121083010000081
designed switching gain rho of sliding mode observer1Need to satisfy rho1M and A-LC is a Hurwitz matrix. Based on the above assumptions, we can select the positive definite matrix P1，Q1Obtaining the matrix F1Thereby completing the design of the sliding mode observer. Note that F here1The parameters of the matrix we solve according to hypothesis 2, but not the optimal solution, because the solution of the optimal solution is too complex, here a little simplified. The above observer designs are background art
We define the residual of the sliding-mode observer as:
Figure GDA0003121083010000082
when the ith actuator fails, the residual error of the observer
Figure GDA0003121083010000083
Should be quite small and when i ≠ l, it is generally the case
Figure GDA0003121083010000084
Is not equal to zero in any time period and is far larger than
Figure GDA0003121083010000085
Thus, the residual signal can be monitored
Figure GDA0003121083010000086
To detect an actuator fault corresponding to isolating the residual.
Once it is identified as the ith actuatorIf a fault occurs, then
Figure GDA0003121083010000087
Should be sufficiently small. Further suppose that
Figure GDA0003121083010000088
Also small enough, we can implement fault estimation s of actuator faults in the following way, thus implementing actuator fault reconstruction:
Figure GDA0003121083010000089
to summarize, it is this sliding mode observer that passes μ in the observeriThe variable simulates a fault value in an actual system, so that a residual value between an output value generated by an observer corresponding to a faulted actuator and the actual system is very small, only the faulted actuator fault observer can simulate the fault value of the original system due to the existence of the matrix F, so that the final residual value is very small, other observers simulate fault values corresponding to other actuators, other actuators do not have faults, and therefore the fault variable cannot counteract the fault of the original system, the final residual value is very large, and therefore fault diagnosis and isolation are achieved.
From the foregoing we can convert the fault model of a sensor into the following form:
Figure GDA00031210830100000810
Figure GDA00031210830100000811
it is stated that this is a sensor failure model similar to actuator failure, and in this context, we will refer to
Figure GDA00031210830100000812
This term is considered to be the actuator failure component, which of course is translated from a sensor failure. However, this is exactly the same as the actuator failure, and we need to make corresponding changes by applying the previous sliding-mode observer designed for the actuator failure:
assume that 1: matrix array
Figure GDA0003121083010000091
Column full rank;
assume 2: there is an adaptive matrix L2、F2And a positive definite matrix P2、Q2Satisfies the following conditions:
Figure GDA0003121083010000092
Figure GDA0003121083010000093
assume that 3: the norm of external disturbance delta (t) is bounded, | | delta (t) | | is less than or equal to W2，W2Is a positive number; sensor failure fsBounded, | | fs||≤M2，W2<<M2；
Setting m-r pseudo-actuator fault observers, namely sensor fault observers:
Figure GDA0003121083010000094
Figure GDA0003121083010000095
in the formula: delta2Is a preset small positive number.
Figure GDA0003121083010000096
Is the state variable in the fault observer corresponding to the jth sensor,
Figure GDA0003121083010000097
Figure GDA0003121083010000098
is the system output vector in the fault observer corresponding to the jth sensor,
Figure GDA0003121083010000099
Figure GDA00031210830100000910
is a matrix
Figure GDA00031210830100000911
Column vector of j-th column, FjRefers to the matrix F2The (c) th row of (a),
Figure GDA00031210830100000912
switched gain ρ of sensor fault observer2Satisfy rho2≥M2And is and
Figure GDA00031210830100000913
is a Hurwitz matrix; the principle is the same as for the previous actuator failure.
For the case that the actuator and the sensor simultaneously have faults, we can solve the problem by using a sliding mode observer obtained before, because we convert the fault of the sensor into the fault form of the actuator, which is only equivalent to the fault problem of one multi-actuator in principle. Then we can directly apply the above actuator fault observer and sensor fault observer group to solve the fault diagnosis problem.
Next, we take the example of one actuator failure and one sensor failure occurring at the same time for principle analysis, and the conclusion can be generalized to the case of multiple failures occurring at the same time.
Principle analysis:
(1) let us assume that an actuator fault occurs on actuator a1, and the corresponding actuator fault observer is denoted as a1, and let us assume that a sensor fault occurs on sensor S1, and the corresponding sensor fault observer is denoted as S1. We use the failure observer group of actuator and failure observer group of sensor to observe the behavior of the system with failure, although we name differently, these two observers belong to the same type.
(2) The basis for fault diagnosis is still residual signals, and since the two faults are converted into actuator faults in form, and since the two actuators act on different state variables and have small mutual interference, the independence of corresponding fault signals can be ensured.
(3) When the actuator fault observer A1 is used for observing a system, since the observer is not interfered by another actuator fault, and is equivalent to act on the system with only the actuator having the fault, the observer can simulate the fault value of the original actuator a1, so that the residual value is smaller than that of other observers acting on the system, and the fault detection and isolation are realized.
(4) Similarly, when the sensor fault observer S1 acts on the system, it can also simulate the sensor fault value of the original system, so that the residual value is smaller than that when other observers act on the system, thereby realizing the detection and isolation of the fault.
(5) Based on the above conclusions, we only need to find two groups of residual values smaller than other residual values in the residual signal, and can determine the fault occurrence position and fault value of the system according to their corresponding fault observers.
The simulation example adopts a state space model after linearization of an engine control system, and meanwhile, a disturbance term delta (t) is added to simulate a real situation:
Figure GDA0003121083010000101
y＝Cx
the model parameters are as follows:
Figure GDA0003121083010000102
D＝0；
the system has two state variables, a system input and four system outputs, an actuator and four sensors. And (A, C) is considerable. In the simulation, the simplest situation, namely the situation that the input quantity is zero and the initial state variable is zero, is used for carrying out simulation, and the performance of a fault observer for detecting and isolating faults is mainly verified. For better illustration in this example, separate actuator fault and sensor fault diagnostic processes are also performed. The method comprises the following specific steps:
actuator fault simulation verification
As mentioned before, for this simulation we set a fault in only one actuator, then for the fault model mentioned before:
Figure GDA0003121083010000103
y＝Cx
we set a fault in an actuator of the system, and the specific form of the fault of the actuator can be expressed as follows:
Figure GDA0003121083010000104
in the formula: we set the actuator fault faFor early latent fault, and | | | faAnd | | is less than or equal to M, and M is equal to 1. At the same time M>>W holds.
According to the following:
Figure GDA0003121083010000111
Figure GDA0003121083010000112
a modified sliding mode observer group is provided corresponding to a potentially malfunctioning actuator.
L＝(A-A0)C-1。
Switching gain ρ of observer1The selection is as follows: ρ 300.
Normal number delta for damping buffeting1And delta2Are all taken as 1
The positive definite matrices P and Q are selected as follows: p ═ I2，Q＝2I2. Matrix a0 ═ I2。
The system disturbance term is chosen to be Δ (t) ═ 0.01sin (t).
The matrix F is calculated from the previous assumption [ 00.213600.0244 ]
Residual signal:
Figure GDA0003121083010000113
because the system model only has one actuator, the system fault can be judged by the following steps: if the residual signal
Figure GDA0003121083010000114
Is very small, and the residual error obtained by the full-dimensional observer after the fault observer is removed is not equal to 0 in any period and is far larger than the residual error
Figure GDA0003121083010000115
It can be judged that the actuator has failed and μ can be passed1A corresponding actuator fault is estimated.
Sensor fault simulation verification
For the sensor fault model:
Figure GDA0003121083010000116
Figure GDA0003121083010000117
also taking the example of only one sensor failing, we set a failure in the first sensor, and the specific form of the failure of the sensor can be expressed as follows:
Figure GDA0003121083010000118
in this system model, four sensors are used, so that four modified sliding mode observer groups corresponding to the four sensors which may fail are needed.
L＝(A-A0)C^(-1)。
Switching gain ρ of observer2The selection is as follows: ρ 120.
Normal number delta for damping buffeting1And delta2All take 1.
The positive definite matrices P and Q are selected as follows: p ═ I6，Q＝2I6. Matrix A0＝-I6。
The system disturbance term is chosen to be Δ (t) ═ 0.01sin (t).
Matrix G ═ I4，
Also, the former assumption uses the calculation of F matrix (note that the values of the system adaptive matrix a, B, C have changed at this time), and thus obtains all observer parameters.
Residual signal:
Figure GDA0003121083010000121
if the residual signal
Figure GDA0003121083010000122
Is very small, and
Figure GDA0003121083010000123
is not equal to 0 at any time interval and is far greater than
Figure GDA0003121083010000124
It can be judged that the first sensor has failed, and the first sensor is failedCan pass through mu1A corresponding actuator fault is estimated.
Simulation of simultaneous failure of actuator and sensor
In the project of the invention, the previous aero-engine model is taken as an example to perform the simulation of the double faults, and in order to verify that the fault signals of the two faults do not interfere with each other, the fault value of the sudden change is increased to be different from the fault signal of the actuator. We change the sensor failure to:
Figure GDA0003121083010000125
meanwhile, the fault value of the actuator is changed into:
Figure GDA0003121083010000126
the actuator failure above is then imposed in the sensor failure system. Since the parameters of the system are parameters of the sensor fault model, the parameters of the actuator fault observer need to be adjusted correspondingly, the system parameters in the sensor fault model are used for calculation, a new matrix F is obtained according to assumed conditions [ 00.02000.0255 ], and then the actuator fault observer and the sensor fault observer are used as fault observer groups to observe the system respectively to obtain residual errors so as to perform fault analysis.
Then, the simulation result is analyzed, and the fault value can be better simulated by the actuator fault observer as shown in fig. 3(a) and fig. 3(b)
As can be seen from fig. 4(a) and 4(b), the fault amount given above is an abrupt change with a value of 1, and the abrupt change in our present residual signal graph r1 is only 0.03, which is much smaller than the initial fault value, and satisfies the first condition of fault diagnosis: residual signal
Figure GDA0003121083010000127
Is very small.
In contrast, after the fault observer is removed, the mutation amount of the residual error obtained by the full-dimensional observer reaches 0.4 which is far greater than that of the residual error obtained by the full-dimensional observer
Figure GDA0003121083010000128
According to the previous conclusion, the fault of the actuator can be judged, and the effectiveness of the sliding mode observer is verified.
FIGS. 5(a) and 5(b) are graphs comparing the simulated fault values of the first sensor fault observer
It should be noted that, since the solution method of the F matrix used herein is calculated completely according to the design method of the actuator fault observer before, and is also not optimized, the obtained simulation result may not be perfect, but has no great relation, and we can see the residual value.
From fig. 6(a), fig. 6(b), fig. 6(c) and fig. 6(d), we can see that the error rate is significantly much smaller than the other three residual signals in the abrupt change section r1, which proves that the first sensor has a fault, and further verifies the effectiveness of the fault detection and fault isolation method. This sensor fault observer is valid.
When the actuator failure and the sensor failure occur simultaneously, as shown in fig. 7(a) and 7(b), a failure simulation value can be obtained when the actuator failure observer a1 acts on the system.
Fig. 8(a) shows estimated values of faults obtained by observers corresponding to faulty sensors in a system in which faults of actuators and sensors occur simultaneously, fig. 8(b) shows simulated values of faults obtained when the first sensor fault observer S1 acts on the system, and similarly, since the design F does not adopt an optimal solution, the simulated values of faults obtained by us can only approximately restore the fault values of the original system, but the fault detection and the fault isolation are not affected.
The residual errors obtained by the actuator fault observer are recorded as r1, the residual errors obtained by the sensor fault observer are respectively recorded as r2, r3, r4 and r5, and the residual error signal diagrams are shown in fig. 9(a), 9(b), 9(c), 9(d) and 9(e), and the observed residual errors r1 and r2 are all smaller than the other three residual error values, so that the first actuator and the first sensor can be judged to be in fault, and the effectiveness of the method on fault detection and fault isolation is verified.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only illustrative of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A method for diagnosing when a control system actuator and a sensor are simultaneously faulty, comprising the steps of:
step 1), establishing a system fault model containing m sensors:
Figure FDA0003435713680000011
y＝Cx+Gfs
wherein: x belongs to Rn and is an unmeasured system state vector, y belongs to Rn and is a measurable system output vector, and u belongs to Rn and is a measurable system input vector; A. b, C, G are all dimensional matrices obtained when the control system is linearized and converted to a state space model, and (A, C) is considerable; f. ofsIs a sensor fault vector, which is a bounded linear function; Δ (t) represents the system uncertainty disturbance;
by adding the state variable z, the fault model of the system sensor with m sensors is written into the following form:
Figure FDA0003435713680000012
Figure FDA0003435713680000013
wherein z is [0I ═]
Figure FDA0003435713680000014
Step 2), establishing a system fault model containing n actuators:
Figure FDA0003435713680000015
y＝Cx
wherein f isaThe fault vector of the actuator is a bounded linear function;
putting the fault models of the n actuators into the fault models of the m sensors to obtain a comprehensive fault model:
Figure FDA0003435713680000016
Figure FDA0003435713680000017
wherein z is [0I ═]
Figure FDA0003435713680000018
Step 3), designing a fault observer for the faults of the actuator and the false actuator, namely the faults of the sensor, and then combining the fault observers into an observer group;
order to
Figure FDA0003435713680000019
Is a matrix
Figure FDA00034357136800000110
The effect is equal to the proper dimension matrix A in the original system, so that
Figure FDA00034357136800000111
Is a matrix
Figure FDA00034357136800000112
Is a matrix
Figure FDA00034357136800000113
[0I]Is a matrix
Figure FDA00034357136800000114
Step 3.1), for actuator failure, in case the following assumptions are satisfied:
assume that 1: the matrix B is full rank;
assume 2: there is an adaptive matrix L1、F1And a positive definite matrix P1、Q1Satisfies the following conditions:
Figure FDA00034357136800000115
Figure FDA00034357136800000116
assume that 3: the norm of external disturbance delta (t) is bounded, | | delta (t) | | is less than or equal to W1，W1Is a positive number; actuator failure faBounded, | | fa||≤M1，M1Is positive and the external disturbance is much smaller than the actuator failure, i.e. W1<<M1；
Setting n executor fault observers:
Figure FDA0003435713680000021
Figure FDA0003435713680000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003435713680000023
is the state variable in the fault observer corresponding to the ith actuator,
Figure FDA0003435713680000024
Figure FDA0003435713680000025
is the system output vector in the fault observer corresponding to the ith actuator,
Figure FDA0003435713680000026
biis a matrix
Figure FDA0003435713680000027
Column vector of the ith column, δ1Is a preset small positive number; fiRefers to the matrix F1The number of the ith row of (a),
Figure FDA0003435713680000028
switching gain rho of actuator fault observer1Satisfy rho1≥M1And is and
Figure FDA0003435713680000029
is a Hurwitz matrix;
step 3.2), under the condition that the following assumptions are met:
assume that 1: matrix array
Figure FDA00034357136800000210
Column full rank;
assume 2: there is an adaptive matrix L2、F2And a positive definite matrix P2、Q2Satisfies the following conditions:
Figure FDA00034357136800000211
Figure FDA00034357136800000212
assume that 3: the norm of external disturbance delta (t) is bounded, | | delta (t) | | is less than or equal to W2，W2Is a positive number; sensor failure fsBounded, | | fs||≤M2，W2<<M2；
Setting m false executor fault observers, namely sensor fault observers:
Figure FDA00034357136800000213
Figure FDA00034357136800000214
in the formula (I), the compound is shown in the specification,
Figure FDA00034357136800000215
is the state variable in the fault observer corresponding to the jth sensor,
Figure FDA00034357136800000216
Figure FDA00034357136800000217
is toThe system output vector in the fault observer corresponding to the jth sensor,
Figure FDA00034357136800000218
δ2is a preset small positive number;
Figure FDA00034357136800000219
is a matrix
Figure FDA00034357136800000220
Column vector of j-th column, FjRefers to the matrix F2The (c) th row of (a),
Figure FDA00034357136800000221
switched gain ρ of sensor fault observer2Satisfy rho2≥M2And is and
Figure FDA00034357136800000222
is a Hurwitz matrix;
step 3.3), combining the n actuator fault observers and the m sensor fault observers into an observer group;
step 4), enabling the observer group to act on the comprehensive fault model, namely enabling n actuator fault observers and m sensor fault observers in the observer group to act on the system fault models of n actuators and m sensors in the comprehensive fault model in a one-to-one correspondence mode, and obtaining residual error images between m + n system state variables and observer state variables;
and 5) screening the same residual images from the m + n residual images, marking the residual images as r, comparing each residual image r left after screening from the m + n residual images with the residual image r, and if the residual value of the residual image r is smaller than that of the residual image r at any time, determining that the residual image r corresponds to a sensor or an actuator corresponding to an observer, namely a fault source, wherein mu in the observer is a fault sourceiOr mujThe value is an estimate of the fault size.
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