CN111382499B - Combined estimation method for system faults and disturbances of chemical cycle reactor - Google Patents
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- QGZKDVFQNNGYKY-UHFFFAOYSA-N Ammonia Chemical compound N QGZKDVFQNNGYKY-UHFFFAOYSA-N 0.000 description 2
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Abstract
A joint estimation method for system faults and disturbances of a chemical loop reactor belongs to the field of networked systems; firstly, establishing a chemical loop reactor system model under the conditions of random packet loss, sensor saturation, disturbance and fault, and then designing an intermediate observer by introducing intermediate variables to realize estimation of state variables, faults and disturbance signals; then, a Lyapunov stability theory and a linear matrix inequality analysis method are used to obtain a sufficient condition that a state estimation error system is consistent and bounded and a middle observer is solved; and finally, solving by using a Matlab YALMIP tool box to obtain parameters of the intermediate observer, thereby realizing joint estimation of disturbance and faults. The method considers random packet loss, sensor saturation, external disturbance and system faults which possibly occur under the actual condition, can effectively estimate the accurate value of the faults in time, is suitable for fault estimation of a general chemical circulation reactor system, and has better universality.
Description
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 increasingly applied to various fields of industrial automation. The networked system is a spatially distributed system in which the components of the sensor, actuator, controller, and estimator are connected by a shared communication network. Compared with the traditional point-to-point system connection, the network-based control scheme can reduce wiring of the system, increase reliability of the system and enable the system to be easily installed and maintained. However, due to the influence of bandwidth limitation, channel interference and other factors, delay, loss, timing disorder and other phenomena may occur in the process of data packet transmission in the network channel, and these adverse factors may deteriorate the system performance and may induce instability of the system.
For many reaction processes, such as ammonia synthesis, methanol synthesis, etc., the single pass conversion is not high due to chemical equilibrium limitations, and the process is performed with the outlet materials containing a large amount of reactants recycled in order to increase the utilization of the raw materials. Chemical looping reactors are widely used in such chemical production reaction equipment. The sensors and controllers of the reaction process access network with circulation are increased, the sensors and controllers are more easily influenced by non-ideal network environments, meanwhile, the sensors cannot normally provide signals with excessive amplitude due to physical or technical reasons, and the sensors are saturated in engineering application. Therefore, under the conditions of random packet loss and sensor saturation constraint, accurate and effective estimation of faults in a system is of great significance.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a combined estimation method for the faults and the disturbance of a chemical loop reactor system based on an intermediate observer. Taking external disturbance, process faults and sensor saturation suffered by a chemical loop reactor system into consideration, an intermediate observer is designed to accurately and effectively estimate faults of the system by introducing intermediate variables.
The technical scheme of the invention is as follows:
a method for joint estimation of faults and disturbances in a chemical looping reactor system, comprising the steps of:
1) Establishing a controlled object model of a chemical looping reactor networked system with sensor saturation constraints and faults:
wherein:is a state vector of the system,/>Is the output vector of the system,/>Is the input disturbance of the system,/->Is a fault signal to be estimated, < >>Is the initial value of the state vector, τ (k) represents the discrete delay and satisfies τ m ≤τ(k)≤τ M ，τ m And τ M Respectively representing an upper limit and a lower limit of time delay; f (k) satisfies the condition of f (k+1) -f (k) is less than or equal to theta 1 And f (k) is less than or equal to theta 3 D (k) satisfies the condition of d (k+1) -d (k) is less than or equal to theta 2 And d (k) is less than or equal to theta 4 The method comprises the steps of carrying out a first treatment on the surface of the System parameter matrix And->Is a known constant matrix; θ 1 ，θ 2 ，θ 3 ，θ 4 Is a known constant, the saturation function σ (): />Is defined as
For each sensor saturation function sigma i (v i )＝sign(v i )·min{v i，max ，|v i |}，k＝1，2，...，i，...，m，v i，max Is the maximum value of the ith element of the saturation vector, sigma i (. Cndot.) is the ith component of the saturation function σ (. Cndot.), v i Is an unknown scalar representing the saturation function sigma i (. Cndot.) the variable, m, represents the number of elements and sign is a sign function. For a given diagonal matrix M 2 ＞M 1 0, σ (-) satisfies the following inequality:
[σ(y(k))-M 1 y(k)] T [σ(y(k))-M 2 y(k)]≤0 (2)
sigma (Cx (k)) is divided into a linear part and a nonlinear part,
wherein the method comprises the steps ofNonlinear vector function, ++>Is a known symmetric positive definite matrix,considering random packet loss which may occur in a network channel between a sensor and a fault estimator, a measurement signal finally received by the estimator side can be expressed as
Wherein: beta k Satisfies Bernoulli random sequence, which is used for describing possible packet loss in the system, when beta k When=1, it indicates that no packet is lost in the system, when β k When the value is=0, the data packet in the system is completely lost; the probability of packet loss is
Here, theIs a known constant.
2) Designing a middle 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)
ξ(k+1)＝f(k+1)-K(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D 1 φ(k)+D 1 Rx(k))
φ(k+1)＝d(k+1)-R(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D 1 φ(k)+D 1 Rx(k))
The intermediate observer is designed as follows:
wherein: ζ (k), φ (k) is the middleThe state variable(s),estimated values of x (K), ζ (K), φ (K), y (K), f (K), d (K), k=wf, respectively T ，/>w, μ is the variable to be designed; l is the gain of the observer.
Definition of the definition The state estimation error system is as follows:
e f (k)＝e ξ (k)+wF T e x (k) (7)
e d (k)＝e φ (k)+μD 1 T e x (k) (8)
wherein:
formula (7) and formula (8)Substituting (9) to obtain
Definition of the definitionThe following augmented state error system is obtained
E 1 ＝[0 0 I 0] T ，E 2 ＝[0 0 0 I] T ，∏＝A+wFF T +μD 1 D 1 T ，∏ 1 ＝-wF T ∏，∏ 2 ＝-μD 1 T ∏；
3) The state estimation error system is consistent with the sufficient conditions of the boundary and intermediate observers that:
in formula (9), the symmetry term omitted according to the symmetry matrix property, 0 is zero matrix; is a symmetric positive definite matrix, < >>Is unknown non-singular momentArray, delta 1 ，δ 2 ，δ 3 ，δ 4 Is an unknown positive scalar, γ > 0, μ > 0,w > 0 is a given known scalar, and I is an identity matrix; i n×n Is an n x n dimensional identity matrix.Ξ 11 ＝-P+(τ M -τ m +1)Q，/>T＝[0 I n×n 0 0]。
Given constantAnd γ, μ, w, solving equation (9) using yalminip toolkit in MATLAB, when there is a positive definite matrix P, Q and matrix H such that equation (9) holds, the state estimation error system is consistently bounded, with an intermediate observer parameter of l=tp -1 H, i.e. step 4) can be performed; when the above unknown variables have no feasible solution, the system is not consistently bounded and cannot obtain intermediate observer parameters, step 4) cannot be performed;
4) Fault estimation for chemical loop reactor networked systems
Obtaining an intermediate observer parameter L from the equation (10) according to the actuator failure occurring during the actual operation of the networked system of continuous chemical looping reactors, and then calculating to obtainThereby obtaining an estimate of the fault.
The invention has the beneficial effects that: the invention considers the random packet loss, system fault and sensor saturation external disturbance situation possibly happening in the networked system, and realizes the joint estimation of the system state, fault and disturbance by designing the intermediate observer, and the estimation of the fault happening in the system is still accurate and effective under the condition of random packet loss and sensor saturation.
Drawings
FIG. 1 is a flow chart of a method for joint estimation of faults and disturbances in a networked system of chemical looping reactors.
FIG. 2 is a schematic diagram of a chemical looping reactor.
FIG. 3 is a schematic diagram of a preferred embodiment of the present inventionState estimation diagram of time system, wherein (a) is system state component x 1 (b) state component x 2 Is a variation of (1) and its estimated map.
FIG. 4 is a schematic diagram of a preferred embodiment of the present inventionAn estimated map of system faults.
FIG. 5 is a schematic diagram of a preferred embodiment of the present inventionAn external disturbance estimation map.
Detailed Description
The following describes the embodiments of the present invention further with reference to the drawings.
Referring to fig. 1, a joint estimation method of a chemical looping reactor system fault and disturbance based on an intermediate observer includes the following steps:
step 1: establishing a controlled object model of the chemical looping reactor system in which sensor saturation constraints and faults exist:
the state space equation of the delayed chemical looping reactor system is formula (10):
wherein:is a state vector of the system,/>Is the output vector of the system,/>Is the input disturbance of the system,/->Is a fault signal to be estimated, < >>Is the initial value of the state vector, τ (k) represents the discrete delay and satisfies τ m ≤τ(k)≤τ M ，τ m And τ M Respectively representing an upper limit and a lower limit of time delay; f (k) satisfies the condition of f (k+1) -f (k) is less than or equal to theta 1 And f (k) is less than or equal to theta 3 D (k) satisfies the condition of d (k+1) -d (k) is less than or equal to theta 2 And d (k) is less than or equal to theta 4 The method comprises the steps of carrying out a first treatment on the surface of the System parameter matrix And->Is a known constant matrix; θ 1 ，θ 2 ，θ 3 ，θ 4 Is a known constant, E { · } represents a mathematical expectation; saturation function σ (·): />Is defined as
For each sensor saturation function sigma i (v i )＝sign(v i )·min{v i，max ，|v i |}，k＝1，2，...，i，...，m，v i，max Is the maximum value of the ith element of the saturation vector, sigma i (. Cndot.) is the ith component of the saturation function σ (. Cndot.), v i Is an unknown scalar representing the function sigma i (. Cndot.) the variable, m, represents the number of elements and sign is a sign function. For a given diagonal matrix M 2 ＞M 1 0, σ (-) satisfies the following inequality:
[σ(y(k))-M 1 y(k)] T [σ(y(k))-M 2 y(k)]≤0 (11)
sigma (Cx (k)) is divided into a linear part and a nonlinear part,
wherein the method comprises the steps ofNonlinear vector function, ++>Is a known symmetric positive definite matrix,considering random packet loss which may occur in a network channel between a sensor and a fault estimator, a measurement signal finally received by the estimator side can be expressed as
Wherein: beta k Satisfies Bernoulli random sequence, which is used for describing possible packet loss in the system, when beta k When=1, it indicates that no packet is lost in the system, when β k When the value is=0, the data packet in the system is completely lost; the probability of packet loss is
Here, theIs a known constant.
Step 2: designing a middle 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)
ξ(k+1)＝f(k+1)-K(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D 1 φ(k)+D 1 Rx(k))
φ(k+1)＝d(k+1)-R(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D 1 φ(k)+D 1 Rx(k))
The intermediate observer is designed as follows:
wherein: ζ (k), φ (k) is an intermediate state variable,estimated values of x (K), ζ (K), φ (K), y (K), f (K), d (K), k=wf, respectively T ，/>w, μ is the variable to be designed; l is the gain of the observer.
Definition of the definition The state estimation error system is as follows:
e f (k)＝e ξ (k)+wF T e x (k) (15)
e d (k)＝e φ (k)+μD 1 T e x (k) (16)
wherein:
formula (15) and formula (16) are given as followsSubstituting (14) to obtain
Definition of the definitionThe following augmented state error system is obtained
E 1 ＝[0 0 I 0] T ，E 2 ＝[0 0 0 I] T ，∏＝A+wFF T +μD 1 D 1 T ，∏ 1 ＝-wF T ∏，∏ 2 ＝-μD 1 T ∏；
Step 3: state estimation error system consistent with sufficient conditions for existence of intermediate observers
Step 3.1: condition for consistent and bounded state estimation error system
Constructing a Lyapunov function:
V(k)＝V 1 (k)+V 2 (k)+V 3 (k)
V 1 (k)＝η T (k)Pη(k)，
note that ||f (k+1) -f (k) is less than or equal to theta 1 ，||d(k+1)-d(k)||≤θ 2 ，||f(k)||≤θ 3 ，||d(k)||≤θ 4 ，
For V 1 (k) Difference is obtained
E {. Cndot. } represents mathematical expectation;
similarly, the
Adding the formulas (10), (11) and (12), and substituting the formula (13) into the mixture to obtain
E{ΔV(k)}＝E{ΔV 1 (k)}+E{ΔV 2 (k)}+E{ΔV 3 (k)}＝ζ T (k)Λζ(k)+θ
In the method, in the process of the invention,
according to Lyapunov stability theory, for a given constantIf there is a positive definite matrix P > 0, Q > 0, and matrix H is such that Λ < 0 in equation (17), then equation (18) holds and the state error system is consistently bounded.
E{ΔV(k)}≤-λ min (-Λ)E{||η(k)|| 2 }+θ 2 (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 in 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: adequate conditions for the presence of intermediate observers
Formula (17) is written as follows
Wherein,applying Schur's complement to formula (19) and multiplying left and right diag { I, I, I, I, I, I, I, P, P }, let->A linear matrix inequality (9) can be obtained. Given constant->And γ, μ, w, solving equation (9) using yalminip toolkit in MATLAB, when positive definite matrices P, Q and H exist such that equation (17) holds, the state estimation error system is consistently bounded, with intermediate observer parameters of l=tp -1 H, i.e. capable of enteringLine step 4); when the above unknown variables have no feasible solution, the system is not consistently bounded and cannot obtain intermediate observer parameters, step 4) cannot be performed;
step 4: fault estimation for chemical loop reactor networked systems
And (3) calculating to obtain an estimated value of the fault according to the intermediate observer parameters obtained in the step (3.2), thereby realizing the estimation of the fault of the chemical loop reactor system.
Examples:
by adopting the joint estimation method of the faults and the disturbance of the chemical loop reactor system based on the intermediate observer, the state estimation error system is consistent and bounded under the condition of considering the sensor saturation constraint and the faults. The specific implementation method is as follows:
the material balance equation of the chemical loop reactor system is that
Wherein C is 1 And C 2 Is the reactor discharge. C (C) 2f Is the feed composition of reactor 2, R 1 And R is 2 Is the circulation flow rate, F 2 Is the feed flow rate, alpha 1 And alpha 2 Is the reaction time constant, V 1 And V 2 Is the reactor volume, ω 1 And omega 2 Is the residence time of the reactants in the reactor, F p1 Is the discharge flow rate of the reactor.
Order theC 1 ＝x 1 ，C 2 ＝x 2 Considering faults and disturbances in the reaction, equation (20) is written as follows
The equation of state space is
Wherein,
let omega 1 ＝ω 2 ＝4，α 1 ＝α 2 ＝0.15，R 1 ＝R 2 ＝0.4，V 1 ＝V 2 ＝1，F 2 ＝0.5，F p1 ＝1，τ M ＝3，τ m ＝2，
Obtaining a system parameter matrix as
Disturbance matrix, output matrix and fault matrix are
The sensor saturation nonlinear function is
Input disturbance is
The failure of the actuator is
Assume that the initial state of the system x (0) = [ -1 0] T Observer initial stateSelecting γ=1, w=0.5, μ=0.1, network channel parameter +.>Solving (9) using the yalminip toolbox with observer gain of
FIG. 3 is a schematic diagram of a preferred embodiment of the present inventionState of time system and state estimation diagram, FIG. 4 is +.>Actuator failure estimation at time, FIG. 5 is +.>Input and output disturbance and disturbance estimation diagram.
In a word, from the simulation result, the designed intermediate observer is effective, can estimate faults and external disturbance signals of the reactor in real time, and can successfully realize the on-line fault estimation of the reactor system under the saturation constraint of the sensor.
Claims (1)
1. A method for joint estimation of faults and disturbances in a chemical looping reactor system, comprising the steps of:
1) Establishing a controlled object model of the chemical looping reactor system in which sensor saturation constraints and faults exist:
wherein:is a state vector of the system,/>Is the output vector of the system,/>Is the input disturbance of the system,/->Is a fault signal to be estimated, < >>Is the initial value of the state vector, τ (k) represents the discrete delay and satisfies τ m ≤τ(k)≤τ M ，τ m And τ M Respectively representing an upper limit and a lower limit of time delay; f (k) satisfies the condition of f (k+1) -f (k) is less than or equal to theta 1 And f (k) is less than or equal to theta 3 D (k) satisfies the condition of d (k+1) -d (k) is less than or equal to theta 2 And d (k) is less than or equal to theta 4 The method comprises the steps of carrying out a first treatment on the surface of the System parameter matrix And->Is a known constant matrix; θ 1 ，θ 2 ，θ 3 ，θ 4 Is a known constant, saturation function sigma (.:): is>Is defined as
For each sensor saturation function sigma i (ν i )＝sign(ν i )·min{ν i,max ,|v i |},k＝1,2,...,i,...,m，v i，max Is the maximum value of the ith element of the saturation vector, sigma i (. Cndot.) is the ith component of the saturation function σ (. Cndot.), v i Is an unknown scalar representing the function sigma i The variable of (-), m represents the number of elements and sign is a sign function; for a given diagonal matrix M 2 ＞M 1 0, σ (-) satisfies the following inequality:
[σ(y(k))-M 1 y(k)] T [σ(y(k))-M 2 y(k)]≤0 (2)
sigma (Cx (k)) is divided into a linear part and a nonlinear part,
wherein the method comprises the steps ofNonlinear vector function, ++>Is a known symmetric positive definite matrix,
considering random packet loss possibly occurring in a network channel between a sensor and a fault estimator, a measurement signal finally received by the estimator is expressed as
Wherein: beta k Satisfies Bernoulli random sequence, which is used for describing possible packet loss in the system, when beta k When=1, it indicates that no packet is lost in the system, when β k When the value is=0, the data packet in the system is completely lost; the probability of packet loss is
Here, theIs a known constant;
2) Designing a middle 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)
ξ(k+1)＝f(k+1)-K(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D 1 φ(k)+D 1 Rx(k))
φ(k+1)＝d(k+1)-R(Ax(k)+Bx(k-τ(k))+Fξ(k)+FKx(k)+D 1 φ(k)+D 1 Rx(k))
The intermediate observer is designed as follows:
wherein: ζ (k), φ (k) is an intermediate state variable,estimated values of x (K), ζ (K), φ (K), y (K), f (K), d (K), k=wf, respectively T ，/>w, μ is the variable to be designed; l is the intermediate observer parameter;
definition of the definition The state estimation error system is as follows:
e f (k)＝e ξ (k)+wF T e x (k) (7)
e d (k)＝e φ (k)+μD 1 T e x (k) (8)
wherein:
formula (7) and formula (8)Substituting (6) to obtain
Definition of the definitionThe following augmented state error system is obtained
E 1 ＝[0 0 I 0] T ，E 2 ＝[0 0 0 I] T ，Π＝A+wFF T +μD 1 D 1 T ，Π 1 ＝-wF T Π，Π 2 ＝-μD 1 T Π；
3) The state estimation error system is consistent with the full conditions that the boundary and intermediate observer parameters can be solved for:
in formula (9), the symmetry term omitted according to the symmetry matrix properties, 0 is zero matrix; is a symmetric positive definite matrix, < >>Is an unknown non-singular matrix, delta 1 ，δ 2 ，δ 3 ，δ 4 Is an unknown positive scalar, γ > 0, μ > 0,w > 0 is a given known scalar, and I is an identity matrix; i n×n Is an n x n dimensional identity matrix;Ξ 11 ＝-P+(τ M -τ m +1)Q，/>T＝[0 I n×n 0 0]；
given constantAnd γ, μ, w, solving equation (9) using yalminip toolkit in MATLAB, when there is a positive definite matrix P, Q and matrix H such that equation (9) holds, the state estimation error system is consistently bounded, with an intermediate observer parameter of l=tp -1 H, i.e. step 4) can be performed; when the above unknown variables have no feasible solution, the system is not consistently bounded and cannot obtain intermediate observer parameters, step 4) cannot be performed;
4) Fault estimation for chemical loop reactor networked systems
Obtaining an intermediate observer parameter L according to the formula (9) according to the actuator fault generated when the chemical circulation reactor networking system actually operates, and then calculating to obtainThereby obtaining an estimate of the fault signal.
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