CN111382499A - Joint estimation method for system fault and disturbance of chemical circulation reactor - Google Patents

Joint estimation method for system fault and disturbance of chemical circulation reactor Download PDF

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CN111382499A
CN111382499A CN202010062834.0A CN202010062834A CN111382499A CN 111382499 A CN111382499 A CN 111382499A CN 202010062834 A CN202010062834 A CN 202010062834A CN 111382499 A CN111382499 A CN 111382499A
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CN111382499B (en
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姜顺
张青杭
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Jiangnan University
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Abstract

A joint estimation method for system fault and disturbance of a chemical circulation reactor belongs to the field of networked systems; firstly, establishing a chemical circulation reactor system model under the conditions of random packet loss, sensor saturation, disturbance and fault, and then designing an intermediate observer to realize the estimation of state variables, faults and disturbance signals by introducing intermediate variables; then, a Lyapunov stability theory and a linear matrix inequality analysis method are applied to obtain a consistent bounded condition of a state estimation error system and a sufficient condition that an intermediate observer has a solution; and finally, solving parameters of the intermediate observer by using a Matlab YALMIP toolbox, thereby realizing the joint estimation of the disturbance and the fault. The method considers random packet loss, sensor saturation, external disturbance and system faults which may occur under the actual condition, can effectively estimate the accurate value of the fault in time, is suitable for fault estimation of a general chemical circulation reactor system, and has better universality.

Description

Joint estimation method for system fault and disturbance of chemical circulation reactor
Technical Field
The invention belongs to the field of networked systems, and relates to a chemical loop reactor system fault and disturbance joint estimation method based on an intermediate observer
Background
In recent years, with rapid development and cross-integration of network communication and automatic control technologies, networked systems are gradually applied to various fields of industrial automation. The networked system is a spatially distributed system in which sensors, actuators, controllers, and estimators are connected via a shared communications network. Compared with the traditional point-to-point system connection, the network-based control scheme can reduce the wiring of the system, increase the reliability of the system and facilitate the installation and maintenance of the system. However, due to the limited bandwidth and channel interference, delay, loss and timing disorder may occur during the transmission of the data packet through the network channel, and these adverse factors may deteriorate the system performance and may induce system instability.
For many reaction processes, such as ammonia synthesis and methanol synthesis, the conversion per pass is not high due to the limitation of chemical equilibrium, and in order to improve the utilization rate of raw materials, the outlet materials containing a large amount of reactants are recycled technically. Chemical circulation reactors are reaction equipment widely used in such chemical production. The number of sensors and controllers connected to the network in the cyclic reaction process is increased, the sensors and controllers are more easily influenced by the non-ideal network environment, meanwhile, due to physical or technical reasons and the like, the sensors cannot provide signals with overlarge amplitudes generally, and sensor saturation is a very common phenomenon in engineering application. Therefore, under the conditions of random packet loss and sensor saturation constraint, the method has important significance in accurately and effectively estimating the faults occurring in the system.
Disclosure of Invention
In view of the problems in the prior art, the present invention provides a method for joint estimation of faults and disturbances of a chemical loop reactor system based on an intermediate observer. The external disturbance, the process fault and the sensor saturation suffered by the chemical circulation reactor system are considered, and the intermediate observer is designed to accurately and effectively estimate the fault of the system by introducing the intermediate variable.
The technical scheme of the invention is as follows:
a joint estimation method for fault and disturbance of a chemical loop reactor system comprises the following steps:
1) establishing a controlled object model of the chemical loop reactor networked system with sensor saturation constraint and fault:
Figure BDA0002375062180000011
wherein:
Figure BDA0002375062180000012
is the state vector of the system and,
Figure BDA0002375062180000013
is the output vector of the system and is,
Figure BDA0002375062180000014
is the input disturbance of the system and,
Figure BDA0002375062180000015
is a fault signal to be estimated and,
Figure BDA0002375062180000016
is the initial value of the state vector, τ (k) represents the discrete time delay and satisfies τm≤τ(k)≤τM，τmAnd τMRespectively representing the upper limit and the lower limit of the time delay; f (k) satisfies | | f (k +1) -f (k) | | ≦ θ1And | | f (k) | | is less than or equal to theta3D (k) satisfies | | d (k +1) -d (k) | | | ≦ θ2And | | | d (k) | | is less than or equal to theta4(ii) a System parameter matrix
Figure BDA0002375062180000017
Figure BDA0002375062180000018
And
Figure BDA0002375062180000019
is a known constant matrix; theta1，θ2，θ3，θ4Is a known constant, the saturation function σ (·):
Figure BDA00023750621800000110
is defined as
Figure BDA00023750621800000111
Saturation function σ for each sensori(vi)＝sign(vi)·min{vi，max，|vi|}，k＝1，2，...，i，...，m，vi，maxIs the maximum value of the ith element of the saturation vector, σi(. h) is the i-th component of the saturation function σ (-), viIs an unknown scalar quantity, representing the saturation function σi(. g), m represents the number of elements, sign is a sign function. For a given diagonal matrix M2＞M1Not less than 0, sigma (·) satisfies the following inequality:
[σ(y(k))-M1y(k)]T[σ(y(k))-M2y(k)]≤0 (2)
divides σ (cx (k)) into a linear part and a non-linear part,
Figure BDA0002375062180000021
Figure BDA0002375062180000022
wherein
Figure BDA0002375062180000023
Is a non-linear function of the vector,
Figure BDA0002375062180000024
is a known symmetric positive definite matrix and,
Figure BDA0002375062180000025
considering random packet loss possibly occurring in a network channel between the sensor and the fault estimator, a measurement signal finally received by the estimator end can be expressed as
Figure BDA0002375062180000026
Wherein βkSatisfies Bernoulli random sequence for describing the packet loss in the system, when βkWhen 1, no packet is lost in the system, when βkWhen the value is 0, the data packet in the system is completely lost; the probability of occurrence of packet loss is
Figure BDA0002375062180000027
Figure BDA0002375062180000028
Figure BDA0002375062180000029
Here, the
Figure BDA00023750621800000210
Is a known constant.
2) Designing an intermediate observer:
introducing intermediate variables
ξ(k)＝f(k)-Kx(k) (4)
φ(k)＝d(k)-Rx(k) (5)
According to formulae (1), (4) and (5) then
ξ(k+1)＝f(k+1)-K(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D1φ(k)+D1Rx(k))
φ(k+1)＝d(k+1)-R(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D1φ(k)+D1Rx(k))
The intermediate observer was designed as follows:
Figure BDA00023750621800000211
Figure BDA00023750621800000212
Figure BDA00023750621800000213
Figure BDA00023750621800000214
Figure BDA00023750621800000215
Figure BDA00023750621800000216
where ξ (k), φ (k) is an intermediate state variable,
Figure BDA00023750621800000217
x (K), ξ (K), phi (K), y (K), f (K), d (K), K, where K is wFT，
Figure BDA00023750621800000218
w, μ are variables to be designed; l is the gain of the observer.
Definition of
Figure BDA00023750621800000219
Figure BDA00023750621800000220
The state estimation error system is as follows:
Figure BDA0002375062180000031
Figure BDA0002375062180000032
Figure BDA0002375062180000033
ef(k)＝eξ(k)+wFTex(k) (7)
ed(k)＝eφ(k)+μD1 Tex(k) (8)
wherein:
Figure BDA0002375062180000034
the formulae (7), (8) and
Figure BDA0002375062180000035
substituting into formula (9) to obtain
Figure BDA0002375062180000036
Definition of
Figure BDA0002375062180000037
An error system for the following augmented state is obtained
Figure BDA0002375062180000038
Figure BDA0002375062180000039
Figure BDA00023750621800000310
E1＝[0 0 I 0]T，E2＝[0 0 0 I]T，∏＝A+wFFT+μD1D1 T，∏1＝-wFT∏，∏2＝-μD1 T∏；
3) The state estimation error system is consistently bounded and the intermediate observer has sufficient conditions as follows:
Figure BDA0002375062180000041
in formula (9) according to symmetrySymmetric terms with omitted matrix properties, 0 is a zero matrix;
Figure BDA0002375062180000042
Figure BDA0002375062180000043
is a symmetrical positive definite matrix and is characterized in that,
Figure BDA0002375062180000044
is an unknown non-singular matrix, δ1，δ2，δ3，δ4Is an unknown positive scalar quantity, gamma > 0, mu > 0, w > 0 is a given known scalar quantity, I is a unit matrix; i isn×nIs an n × n-dimensional identity matrix.
Figure BDA0002375062180000045
Ξ11＝-P+(τM-τm+1)Q，
Figure BDA0002375062180000046
T＝[0 I n×n0 0]。
Given constant
Figure BDA0002375062180000047
And gamma, mu, w, solving the formula (9) by using a YALMIP tool box in MATLAB, and if positive definite matrixes P, Q and a matrix H exist to ensure that the formula (9) is established, the state estimation error system is uniformly bounded, and the parameter of an intermediate observer is L-TP-1H, i.e. step 4) can be performed; when the unknown variables have no feasible solution, the system is not consistently bounded, the intermediate observer parameters cannot be obtained, and the step 4) cannot be carried out;
4) fault estimation for chemical looping reactor networked systems
According to the actuator fault occurring in the actual operation of the networked system of the chemical loop reactor, the intermediate observer parameter L is obtained by the formula (10), and then the intermediate observer parameter L is obtained by calculation
Figure BDA0002375062180000048
Thereby yielding an estimate of the fault.
The invention has the beneficial effects that: the invention simultaneously considers the random packet loss, system fault and sensor saturation external disturbance condition which may occur in the networked system, realizes the joint estimation of the system state, fault and disturbance by designing the intermediate observer, and estimates the fault of the system under the conditions of the random packet loss and the sensor saturation.
Drawings
FIG. 1 is a flow chart of a method for joint estimation of faults and disturbances in a networked system of a chemical loop reactor.
FIG. 2 is a schematic diagram of a chemical looping reactor.
FIG. 3 is
Figure BDA0002375062180000049
A state estimation diagram of a time system, wherein (a) is a system state component x1(ii) a change in (b) a state component x and an estimated map thereof2And its estimated map.
FIG. 4 is
Figure BDA00023750621800000410
An estimated map of system failures.
FIG. 5 is
Figure BDA00023750621800000411
And (4) estimating the external disturbance of the time.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
Referring to fig. 1, a method for joint estimation of chemical loop reactor system faults and disturbances based on an intermediate observer includes the steps of:
step 1: establishing a controlled object model of the chemical loop reactor system with sensor saturation constraints and faults:
the state space equation of the chemical circulation reactor system with time delay is shown as the formula (10):
Figure BDA0002375062180000051
wherein:
Figure BDA0002375062180000052
is the state vector of the system and,
Figure BDA0002375062180000053
is the output vector of the system and is,
Figure BDA0002375062180000054
is the input disturbance of the system and,
Figure BDA0002375062180000055
is a fault signal to be estimated and,
Figure BDA0002375062180000056
is the initial value of the state vector, τ (k) represents the discrete time delay and satisfies τm≤τ(k)≤τM，τmAnd τMRespectively representing the upper limit and the lower limit of the time delay; f (k) satisfies | | f (k +1) -f (k) | | ≦ θ1And | | f (k) | | is less than or equal to theta3D (k) satisfies | | d (k +1) -d (k) | | | ≦ θ2And | | | d (k) | | is less than or equal to theta4(ii) a System parameter matrix
Figure BDA0002375062180000057
Figure BDA0002375062180000058
And
Figure BDA0002375062180000059
is a known constant matrix; theta1，θ2，θ3，θ4Is a known constant, E {. cndot } represents a mathematical expectation; saturation function σ (·):
Figure BDA00023750621800000510
is defined as
Figure BDA00023750621800000511
Saturation function σ for each sensori(vi)＝sign(vi)·min{vi，max，|vi|}，k＝1，2，...，i，...，m，vi，maxIs the maximum value of the ith element of the saturation vector, σi(. h) is the i-th component of the saturation function σ (-), viIs an unknown scalar quantity, representing a function sigmai(. g), m represents the number of elements, sign is a sign function. For a given diagonal matrix M2＞M1Not less than 0, sigma (·) satisfies the following inequality:
[σ(y(k))-M1y(k)]T[σ(y(k))-M2y(k)]≤0 (11)
divides σ (cx (k)) into a linear part and a non-linear part,
Figure BDA00023750621800000512
Figure BDA00023750621800000513
wherein
Figure BDA00023750621800000514
Is a non-linear function of the vector,
Figure BDA00023750621800000515
is a known symmetric positive definite matrix and,
Figure BDA00023750621800000516
considering random packet loss possibly occurring in a network channel between the sensor and the fault estimator, a measurement signal finally received by the estimator end can be expressed as
Figure BDA00023750621800000517
Wherein βkSatisfies Bernoulli random sequence for describing the packet loss in the system, when βkWhen 1, no packet is lost in the system, when βkWhen the value is 0, the data packet in the system is completely lost; the probability of occurrence of packet loss is
Figure BDA00023750621800000518
Figure BDA00023750621800000519
Figure BDA00023750621800000520
Here, the
Figure BDA00023750621800000521
Is a known constant.
Step 2: designing an intermediate observer:
by introducing intermediate variables
ξ(k)＝f(k)-Kx(k) (12)
φ(k)＝d(k)-Rx(k) (13)
According to formulae (10), (12) and (13) there are
ξ(k+1)＝f(k+1)-K(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D1φ(k)+D1Rx(k))
φ(k+1)＝d(k+1)-R(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D1φ(k)+D1Rx(k))
The intermediate observer was designed as follows:
Figure BDA0002375062180000061
Figure BDA0002375062180000062
Figure BDA0002375062180000063
Figure BDA0002375062180000064
Figure BDA0002375062180000065
Figure BDA0002375062180000066
where ξ (k), φ (k) is an intermediate state variable,
Figure BDA0002375062180000067
x (K), ξ (K), phi (K), y (K), f (K), d (K), K, where K is wFT，
Figure BDA00023750621800000616
w, μ are variables to be designed; l is the gain of the observer.
Definition of
Figure BDA0002375062180000068
Figure BDA0002375062180000069
The state estimation error system is as follows:
Figure BDA00023750621800000610
Figure BDA00023750621800000611
Figure BDA00023750621800000612
ef(k)＝eξ(k)+wFTex(k) (15)
ed(k)＝eφ(k)+μD1 Tex(k) (16)
wherein:
Figure BDA00023750621800000613
the formulae (15), (16) and
Figure BDA00023750621800000614
substituted into (14) to obtain
Figure BDA00023750621800000615
Definition of
Figure BDA0002375062180000071
An error system for the following augmented state is obtained
Figure BDA0002375062180000072
Figure BDA0002375062180000073
Figure BDA0002375062180000074
E1＝[0 0 I 0]T，E2＝[0 0 0 I]T，∏＝A+wFFT+μD1D1 T，∏1＝-wFT∏，∏2＝-μD1 T∏；
And step 3: the state estimation error system is consistently bounded and sufficient conditions exist in the intermediate observer
Step 3.1: sufficient condition that state estimation error system is consistently bounded
Constructing a Lyapunov function:
V(k)＝V1(k)+V2(k)+V3(k)
V1(k)＝ηT(k)Pη(k)，
Figure BDA0002375062180000075
note that | | f (k +1) -f (k) | | ≦ θ1，||d(k+1)-d(k)||≤θ2，||f(k)||≤θ3，||d(k)||≤θ4，
To V1(k) Difference is obtained
Figure BDA0002375062180000076
E {. represents a mathematical expectation;
like
Figure BDA0002375062180000077
Figure BDA0002375062180000078
By adding the formulae (10), (11) and (12) and substituting the formula (13)
E{ΔV(k)}＝E{ΔV1(k)}+E{ΔV2(k)}+E{ΔV3(k)}＝ζT(k)Λζ(k)+θ
In the formula,
Figure BDA0002375062180000081
Figure BDA0002375062180000082
Figure BDA0002375062180000083
Figure BDA0002375062180000084
Figure BDA0002375062180000085
according to the theory of the stability of Lyapunov,for a given constant
Figure BDA0002375062180000086
If there is a positive definite matrix P > 0, Q > 0, and matrix H such that Λ < 0 in equation (17), then equation (18) holds, and the state error system is consistently bounded.
E{ΔV(k)}≤-λmin(-Λ)E{||η(k)||2}+θ2(18)
When the state error system obtained in the step 3.1 is consistent and bounded, executing the step 3.2; if the state error system obtained at step 3.1 is not consistently bounded, then the state estimation error system is not consistently bounded and step 3.2 cannot be performed.
Step 3.2: sufficient condition for the existence of the intermediate observer
Writing formula (17) to
Figure BDA0002375062180000087
Wherein,
Figure BDA0002375062180000088
applying Schur complementary theory to formula (19), and multiplying right-hand times diag { I, I, I, I, I, I, P, P }, and making
Figure BDA0002375062180000089
A linear matrix inequality (9) can be obtained. Given constant
Figure BDA00023750621800000810
And γ, μ, w, solving equation (9) using the yalmipip toolbox in MATLAB, where if positive definite matrices P, Q and H exist such that equation (17) holds true, the state estimation error system is consistently bounded, and the intermediate observer parameter is L ═ TP-1H, i.e. step 4) can be performed; when the unknown variables have no feasible solution, the system is not consistently bounded, the intermediate observer parameters cannot be obtained, and the step 4) cannot be carried out;
and 4, step 4: fault estimation for chemical looping reactor networked systems
And (3) calculating to obtain an estimated value of the fault according to the parameters of the intermediate observer obtained in the step (3.2), thereby realizing the estimation of the fault of the chemical circulation reactor system.
Example (b):
by adopting the method for jointly estimating the faults and the disturbances of the chemical circulating reactor system based on the intermediate observer, the state estimation error system is consistently bounded under the condition of considering the saturation constraint and the faults of the sensor. The specific implementation method comprises the following steps:
the material balance equation of the chemical circulation reactor system is
Figure BDA0002375062180000091
Wherein, C1And C2Is the reactor discharge. C2fIs the feed composition to reactor 2, R1And R2Is the circulation flow rate, F2Is the feed flow rate, α1And α2Is the reaction time constant, V1And V2Is the reactor volume, omega1And ω2Is the residence time of the reactants in the reactor, Fp1Is the discharge flow rate of the reactor.
Order to
Figure BDA0002375062180000092
C1＝x1，C2＝x2Considering faults and disturbances in the reaction, equation (20) is written as follows
Figure BDA0002375062180000093
The equation of state space is
Figure BDA0002375062180000094
Wherein,
Figure BDA0002375062180000095
let omega1＝ω2＝4，α1＝α2＝0.15，R1＝R2＝0.4，V1＝V2＝1，F2＝0.5，Fp1＝1，τM＝3，τm＝2，
Obtain a system parameter matrix of
Figure BDA0002375062180000096
The disturbance matrix, the output matrix and the fault matrix are
Figure BDA0002375062180000097
The sensor saturation nonlinear function is
Figure BDA0002375062180000101
Input disturbance is
Figure BDA0002375062180000102
The actuator is out of order
Figure BDA0002375062180000103
Assume an initial state x (0) [ -10) of the system]TObserver initial state
Figure BDA0002375062180000104
Selecting gamma is 1, w is 0.5, mu is 0.1, network channel parameter
Figure BDA0002375062180000105
Using the YALMIP toolbox to solve for equation (9) with observer gain of
Figure BDA0002375062180000106
FIG. 3 is
Figure BDA0002375062180000107
The state of the time system and the state estimation diagram, FIG. 4 is
Figure BDA0002375062180000108
FIG. 5 is a diagram of actuator failure estimation
Figure BDA0002375062180000109
Temporal input and output disturbances and disturbance estimation maps.
In a word, from the simulation result, the designed intermediate observer is effective, can estimate the fault of the reactor and the external disturbance signal thereof in real time, and can successfully realize the fault on-line estimation of the reactor system under the saturation constraint of the sensor.

Claims (1)

1. A joint estimation method for fault and disturbance of a chemical circulation reactor system is characterized by comprising the following steps:
1) establishing a controlled object model of the chemical loop reactor system with sensor saturation constraints and faults:
Figure FDA0002375062170000011
wherein:
Figure FDA0002375062170000012
is the state vector of the system and,
Figure FDA0002375062170000013
is the output vector of the system and is,
Figure FDA0002375062170000014
is the input disturbance of the system and,
Figure FDA0002375062170000015
is a fault signal to be estimated and,
Figure FDA0002375062170000016
is the initial value of the state vector, τ (k) represents the discrete time delay and satisfies τm≤τ(k)≤τM，τmAnd τMRespectively representing the upper limit and the lower limit of the time delay; f (k) satisfies | | f (k +1) -f (k) | | ≦ θ1And | | f (k) | | is less than or equal to theta3D (k) satisfies | | d (k +1) -d (k) | | | ≦ θ2And | | | d (k) | | is less than or equal to theta4(ii) a System parameter matrix
Figure FDA0002375062170000017
Figure FDA0002375062170000018
And
Figure FDA0002375062170000019
is a known constant matrix; theta1，θ2，θ3，θ4Is a known constant, a saturation function
Figure FDA00023750621700000110
Is defined as
Figure FDA00023750621700000111
Saturation function σ for each sensori(vi)＝sign(vi)·min{vi，max，|vi|}，k＝1，2，...，i，...，m，vi，maxIs the maximum value of the ith element of the saturation vector, σi(. h) is the i-th component of the saturation function σ (-), viIs an unknown scalar quantity, representing a function sigmai(v), m represents the number of elements, sign is a sign function; for a given diagonal matrix M2＞M1Not less than 0, sigma (·) satisfies the following inequality:
[σ(y(k))-M1y(k)]T[σ(y(k))-M2y(k)]≤0 (2)
divides σ (cx (k)) into a linear part and a non-linear part,
Figure FDA00023750621700000112
Figure FDA00023750621700000113
wherein
Figure FDA00023750621700000114
Is a non-linear function of the vector,
Figure FDA00023750621700000115
is a known symmetric positive definite matrix and,
Figure FDA00023750621700000116
considering the random packet loss possibly occurring in the network channel between the sensor and the fault estimator, the measurement signal finally received by the estimator end is expressed as
Figure FDA00023750621700000117
Wherein βkSatisfies Bernoulli random sequence for describing the packet loss in the system, when βkWhen 1, no packet is lost in the system, when βkWhen the value is 0, the data packet in the system is completely lost; the probability of occurrence of packet loss is
Figure FDA00023750621700000118
Figure FDA00023750621700000119
Figure FDA00023750621700000120
Here, the
Figure FDA00023750621700000121
Is a known constant;
2) designing an intermediate observer:
introducing intermediate variables
ξ(k)＝f(k)-Kx(k) (4)
φ(k)＝d(k)-Rx(k) (5)
According to formulae (1), (4) and (5) then
ξ(k+1)＝f(k+1)-K(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D1φ(k)+D1Rx(k))
φ(k+1)＝d(k+1)-R(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D1φ(k)+D1Rx(k))
The intermediate observer was designed as follows:
Figure FDA0002375062170000021
Figure FDA0002375062170000022
Figure FDA0002375062170000023
Figure FDA0002375062170000024
Figure FDA0002375062170000025
Figure FDA0002375062170000026
where ξ (k), φ (k) is an intermediate state variable,
Figure FDA0002375062170000027
x (K), ξ (K), phi (K), y (K), f (K), d (K), K, where K is wFT，
Figure FDA0002375062170000028
w, μ are variables to be designed; l is the gain of the observer;
definition of
Figure FDA0002375062170000029
Figure FDA00023750621700000210
The state estimation error system is as follows:
Figure FDA00023750621700000211
Figure FDA00023750621700000212
Figure FDA00023750621700000213
ef(k)＝eξ(k)+wFTex(k) (7)
ed(k)＝eφ(k)+μD1 Tex(k) (8)
wherein:
Figure FDA00023750621700000214
the formulae (7), (8) and
Figure FDA00023750621700000215
substituting into formula (6) to obtain
Figure FDA0002375062170000031
Definition of
Figure FDA0002375062170000032
An error system for the following augmented state is obtained
Figure FDA0002375062170000033
Figure FDA0002375062170000034
Figure FDA0002375062170000035
E1＝[0 0 I 0]T，E2＝[0 0 0 I]T，∏＝A+wFFT+μD1D1 T，∏1＝-wFT∏，∏2＝-μD1 T∏；
3) The state estimation error system is consistently bounded and the solvable sufficient conditions of the intermediate observer parameters are:
Figure FDA0002375062170000036
in formula (9), denotes a symmetric term omitted according to the properties of the symmetric matrix, and 0 is a zero matrix;
Figure FDA0002375062170000037
Figure FDA0002375062170000038
is a symmetrical positive definite matrix and is characterized in that,
Figure FDA0002375062170000039
is an unknown non-singular matrix, δ1，δ2，δ3，δ4Is an unknown positive scalar quantity, gamma > 0, mu > 0, w > 0 is a given known scalar quantity, I is a unit matrix; i isn×nIs an n × n-dimensional identity matrix;
Figure FDA00023750621700000310
Ξ11＝-P+(τM-τm+1)Q，
Figure FDA00023750621700000311
T＝[0 In×n0 0]；
given constant
Figure FDA00023750621700000312
And gamma, mu, w, solving the formula (9) by using a YALMIP tool box in MATLAB, and if positive definite matrixes P, Q and a matrix H exist to ensure that the formula (9) is established, the state estimation error system is uniformly bounded, and the parameter of an intermediate observer is L-TP-1H, i.e. step 4) can be performed; when the unknown variables have no feasible solution, the system is not consistently bounded, the intermediate observer parameters cannot be obtained, and the step 4) cannot be carried out;
4) fault estimation for chemical looping reactor networked systems
According to the actuator fault occurring in the actual operation of the chemical circulation reactor networked system, the intermediate observer parameter L is obtained by the formula (9), and then the intermediate observer parameter L is obtained by calculation
Figure FDA00023750621700000313
Thereby obtaining an estimate of the fault signal.
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