CN113110049B - Reliable estimation method for monitoring temperature of celadon biscuit firing kiln - Google Patents
Reliable estimation method for monitoring temperature of celadon biscuit firing kiln Download PDFInfo
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- CN113110049B CN113110049B CN202110396018.8A CN202110396018A CN113110049B CN 113110049 B CN113110049 B CN 113110049B CN 202110396018 A CN202110396018 A CN 202110396018A CN 113110049 B CN113110049 B CN 113110049B
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract
The invention discloses a reliable estimation method for monitoring the temperature of a celadon biscuit firing kiln. The temperature change and measurement of the celadon biscuit firing kiln have obvious time lag, the kiln temperature is influenced by random and deterministic disturbance of gas, air and celadon blank materials, the kiln temperature cannot be monitored accurately in real time, and the celadon biscuit firing quality is difficult to guarantee. The invention designs a reliable estimator for monitoring the temperature of the celadon biscuit firing kiln, and considers the uncertain change of estimator parameters caused by the change of the external environment and the aging of estimator elements. An effective solving method of the estimator gain is established through robust asymptotic mean square stability analysis and interference suppression performance analysis of an estimation error augmentation system for monitoring the temperature of the furnace. The method provided by the invention can realize real-time, accurate and reliable estimation of the kiln temperature in the celadon biscuit firing process, accurately master the kiln temperature state and provide guarantee for improving biscuit firing quality.
Description
Technical Field
The invention belongs to the technical field of automation, and provides a reliable method for real-time and accurate monitoring of celadon biscuit firing kiln temperature by designing a reliable state estimator, wherein the method relates to modeling of a celadon biscuit firing process temperature monitoring system, stability analysis and interference suppression performance analysis of an estimation error augmentation system and a design method of a corresponding reliable estimator. The method can be used in the existing Longquan celadon processing and manufacturing industries.
Background
Longquan celadon began in the period of two jin's of three kingdoms, and has been in history for more than 1600 years to the present. The Longquan celadon which is pale in glaze and warm and moist like jade is a treasure in China porcelain on history, is a treasure for people all over the world since ancient times, has high popularity in China, and is popular in many countries and regions of Asia, Africa, Europe, America and Australia. As a bright representative in the porcelain history, the Longquan celadon is the only ceramic project which is currently selected in the United nations textbook organization 'human non-material cultural heritage'.
Porcelain bisque firing refers to the firing process of unglazed porcelain blanks, and is an important process in the porcelain processing and manufacturing process. The Longquan celadon also adopts a biscuit firing process, and the celadon blank is biscuit fired and then glazed. The celadon biscuit firing mainly aims to improve the strength of a celadon blank, facilitate subsequent processing procedures of decoration, carving and glazing, reduce the breakage rate in the manufacturing process, reduce the glazing breakage rate and improve the yield. Through the biscuit firing link, the strength of the celadon blank is increased, a thin-wall product can be manufactured, meanwhile, the water absorption is strong, the glazing is fast, the glaze absorption is uniform, the glaze surface is smooth and smooth, and an important foundation is laid for the final successful manufacture of the celadon.
The modern Longquan celadon production and processing mostly uses a liquefied gas furnace kiln, and compared with the traditional dragon kiln for burning firewood, the modern liquefied gas furnace kiln is convenient for controlling the temperature and firing atmosphere of the kiln. In order to grasp the temperature in the celadon liquefied gas furnace, a thermocouple is generally installed in the furnace for measuring the temperature in the furnace. However, because the furnace temperature changes and measurement have a significant hysteresis effect, and the furnace temperature is influenced by the change factors of gas, air and celadon blank materials, the real-time performance and accuracy of the furnace temperature measured by the thermocouple are greatly influenced, so that the temperature rise process of celadon biscuit firing is not stable, the temperature field distribution difference is large, and the requirement of celadon processing on the furnace temperature cannot be met. In addition, the designed estimator is easy to generate uncertainty change of the estimator parameters under the influence of external environment change and aging of estimator elements, and can generate obvious influence on estimation precision and reliability. Therefore, a reliable estimation method for monitoring the temperature of the biscuit firing kiln automatically is urgently needed, the uncertain change of the gain of an estimator is considered, the real-time, accurate and reliable estimation of the kiln temperature in the biscuit firing process of the celadon is realized, the breakage rate is reduced, the glaze firing yield is improved, and a foundation is laid for the automatic control of the temperature of the follow-up biscuit firing kiln of the celadon.
Disclosure of Invention
The invention aims to provide a reliable estimation method for monitoring the temperature of a celadon biscuit firing kiln, aiming at the defect that the real-time property, the accuracy and the reliability of the kiln temperature detection in the current celadon biscuit firing process cannot meet the production and processing requirements.
The method comprises the steps of establishing a state space model of a celadon biscuit firing kiln temperature monitoring system by using a mixed random modeling method combining a combustion science principle, a fluid mechanics principle and experimental data, taking the hysteresis effect of kiln temperature detection and the influence of various random variation factors into consideration by an obtained random time-lag differential equation, introducing uncertainty parameter variation of estimator gain by using an uncertainty analysis and modeling method, obtaining a robust asymptotic mean square stability criterion of an estimation error augmentation system for celadon biscuit firing kiln temperature monitoring by using a Lyapunov stability principle and a random analysis method, analyzing the anti-interference inhibition performance of the estimation error augmentation system on the basis, and finally establishing a solving method of a reliable estimator based on a linear matrix inequality. The invention can provide a real-time, accurate and reliable estimation method for the celadon biscuit firing kiln temperature detection, simultaneously considers the complex factors of various time lags, random disturbance, disturbance input with bounded energy and uncertain change of the parameters of an estimator gain matrix, thereby having strong practicability, laying a foundation for the automatic control of the celadon biscuit firing kiln temperature and being used for the production and the processing of the modern Longquan celadon.
The method comprises the following specific steps:
step one, establishing a state space model of a celadon biscuit firing kiln temperature monitoring system;
firstly, according to the principle of combustion of liquefied gas, the principle of fluid mechanics and data measured by experiments, in combination with the structure of a celadon biscuit firing kiln, a mixed random modeling method and a state space representation method are utilized to establish the following random time-lag differential equation:
wherein x (t) ═ x1(t) x2(t) x3(t) x4(t) x5(t)]TRepresenting the state vector of the celadon biscuit firing kiln at time T, where the superscript T represents the transpose of the matrix, x1(t) is the temperature in the kiln, which is the monitoring quantity, x, required by the invention2(t) is the pressure in the kiln, x3(t) is the oxygen concentration in the kiln, x4(t) is the gas flow velocity in the kiln, x5(t) is the calorific value of the fuel gas; y (t) ═ y1(t) y2(t)]TIs an output measured value of a celadon biscuit firing kiln monitoring system at the time t, wherein y1(t) is the temperature measurement value in the kiln of the roasting furnace measured by a thermocouple, y2(t) is the heat value of the flue gas at the outlet of the biscuiting furnace, which represents the sufficient degree of combustion of the liquefied petroleum gas in the biscuiting process, and is measured by a flue gas analyzer arranged at the outlet of the biscuiting furnace; v (t) is tThe 1-dimensional disturbance input with bounded time energy is the disturbance of the biscuit firing process caused by decomposition of water and organic matters discharged in the drying process of the celadon blank in the biscuit firing process and the distribution of a gas flow field in a kiln; omega (t) is 1-dimensional Brownian motion of zero mean value at the time t, and represents random influence factors in celadon biscuit firing detection, including gas heat value, air oxygen content, air moisture and random fluctuation of gas moisture and air temperature; z (t) is the adjusted output vector of 1 dimension at time t; d is a differential sign; a positive scalar τ is the time delay, representing the lag in the furnace temperature variation and the dependence on the initial state; the initial condition of the kiln temperature monitoring system is that x (mu) is x0And- τ. ltoreq. mu. ltoreq.0, where x0The system initial value measured at time t-0.
A∈R5×5,M∈R5×5,B∈R5×1,A1∈R5×5,M1∈R5×5,C∈R2×5，D∈R5×1,N∈R1×5All are known real matrices obtained by system modeling, wherein
Represents n1×n2And (5) maintaining a real matrix.
Designing a reliable estimator of a celadon biscuit firing kiln temperature monitoring system;
the present invention designs a reliable estimator of the type described below
In the formula (I), the compound is shown in the specification,
is the state variable of the estimator at the time t,
represents n3A dimension real vector;
Af∈R5×5,Bf∈R5×2,Nf∈R1×5to needA gain matrix of a reliable estimator to be designed;
ΔAf∈R5×5,ΔNf∈R1×5the following relationship is satisfied for the gain uncertainty of the estimator, representing the uncertainty change of the estimator gain value due to the environment change and the aging of the estimator
Wherein HA∈R5×2,HN∈R1×2,G∈R2×5A matrix of constants of appropriate dimensions, F (t) e R2×2I represents an identity matrix having an appropriate dimension for the time-varying disturbance matrix at time t, and I in the above equation (3) is a 2 × 2-dimensional identity matrix. Wherein the matrix HA,HNThe specific form and parameter values of G, F (t) can be obtained by uncertainty analysis and modeling methods.
Step three, establishing an error model for reliable estimation of the temperature monitoring system;
selecting augmented State variables
And error vector
The following estimation error augmentation system equation can be obtained
In the formula (I), the compound is shown in the specification,
where 0 represents a matrix of 0 with appropriate dimensions.
It is an object of the invention to design a gain matrix a of a reliable estimatorf,Bf,NfSo that the estimation error augmentation system (4) corresponding to the furnace temperature monitoring in the celadon biscuit firing process is robust mean square asymptotically stable when v (t) is 0 and is in a zero initial condition
The time performance index J is less than 0, wherein
Then (2) is a reliable estimator for the system (1) designed by the present invention, where the positive scalar γ represents a given disturbance rejection level, γ >0, and E {. cndot. } represents the mathematical expectation operation.
Solving a reliable estimator for monitoring the temperature of the celadon biscuit firing kiln;
step 1: random stability analysis of the estimation error augmentation system;
selecting Lyapunov functional
In the formula, P is more than 0, Q is more than 0 and is a positive definite symmetric matrix to be solved with 10 multiplied by 10 dimensions.
When the perturbation v (t) is 0, the random analysis of Ito lemma is used
In the formula (I), the compound is shown in the specification,
and is
The notation LV (ξ (t)) denotes the infinitesimal operator of V (ξ (t)), the asterisk denotes the symmetry term in the symmetry matrix, i.e. in the above formula #denotesΦ12Is transferred to
If phi is less than 0, then ensure that
Namely, the estimation error augmentation system (4) is stable in the asymptotic robust mean square when v (t) is 0.
Step 2: estimating interference suppression performance analysis of the error augmentation system;
giving a disturbance rejection degree gamma >0, gamma is a scalar quantity and is defined by a performance index J in the third step and a zero initial condition
And robust mean square asymptotic stability, known
And is provided with
In the formula (I), the compound is shown in the specification,
obviously, if xi <0, J <0 is present, and it is easy to understand the complement of Shu (Schur), xi <0 is equivalent to the following inequality
Therefore, if inequality (6) holds, the estimation error augmentation system (4) is robust mean-square asymptotically stable with a given disturbance rejection performance γ > 0.
And 3, step 3: solving a gain matrix of the reliable estimator;
let the matrix P be
In the formula, X and V are positive definite symmetric matrices of 5 × 5 dimensions.
Substituting the expression and matrix P of each matrix in the formula (4) into the inequality (6) to obtain
In the formula
Ω13＝XA1-VBfD，Ω23＝VA1-VBfD，
H1＝[0 0 HA HA 0 0 0]T，G1＝[0 0 0 G 0 0 0]
H2＝[0 HN 0 0 0 0 0]T，G2＝[0 0 0 0 G 0 0]
From the basic inequality relationship, Σ <0 is equivalent to the presence of two positive numbers ε1And ε2So that the following equation holds
In the formula, superscript-1 denotes inverting the matrix or inverting the scalar.
Performing matrix variable substitution, selecting
Substitution inequality sigma0Less than 0, as can be seen by matrix operation and Schur complement theorem0<0 is equivalent to the linear matrix inequality pi <0 holds, wherein
In the formula (I), the compound is shown in the specification,
from selected matrix variables
It is easy to know that the matrix parameters of the estimator (2) are
Thus, for a given interference suppression degree γ >0, the linear matrix inequality in MATLAB is used (a)LMI) tool box solves inequality (8), can obtain matrix V,
Bf，
the gain matrix of the reliable estimator of the celadon bisque firing temperature monitoring system designed by the invention can be calculated by the formula (9).
The invention provides a reliable estimation method for celadon biscuit firing kiln temperature monitoring, aiming at the problems of poor real-time performance, accuracy and reliability in the current Longquan celadon biscuit firing kiln temperature monitoring. Because the change of the temperature in the kiln and the measurement have time lag and are influenced by various deterministic and random factors, a state space model of the celadon biscuit firing kiln temperature monitoring system is established by using a mixed modeling method of combustion science, hydromechanics and experimental data. The parameter uncertainty of the estimator gain is considered in the design of the furnace temperature estimator, so that the furnace temperature monitoring system designed by the invention is reliable to various random and deterministic interferences and estimator gain variation. The invention utilizes the Lyapunov stability principle and the random analysis method to analyze the stability and the interference suppression performance of the estimation error augmentation system, and can conveniently solve the reliable estimator gain of the celadon biscuit firing kiln temperature monitoring system through matrix analysis and a linear matrix inequality technology. The method can be used for monitoring the celadon biscuit firing kiln temperature in real time, accurately and reliably, thereby providing guarantee for improving the celadon biscuit firing quality and the yield.
Detailed Description
The method comprises the following specific steps:
step one, establishing a state space model of a celadon biscuit firing kiln temperature monitoring system;
firstly, according to the principle of combustion of liquefied gas, the principle of fluid mechanics and data measured by experiments, in combination with the structure of a celadon biscuit firing kiln, a mixed random modeling method and a state space representation method are utilized to establish the following random time-lag differential equation:
wherein x (t) ═ x1(t) x2(t) x3(t) x4(t) x5(t)]TRepresenting the state vector of the celadon biscuit firing kiln at time T, where the superscript T represents the transpose of the matrix, x1(t) is the temperature in the kiln, which is the monitoring quantity, x, required by the invention2(t) is the pressure in the kiln, x3(t) is the oxygen concentration in the kiln, x4(t) is the gas flow velocity in the kiln, x5(t) is the calorific value of the fuel gas; y (t) ═ y1(t) y2(t)]TIs an output measured value of a celadon biscuit firing kiln monitoring system at the time t, wherein y1(t) is the temperature measurement value in the kiln of the roasting furnace measured by a thermocouple, y2(t) is the heat value of the flue gas at the outlet of the biscuiting furnace, which represents the sufficient degree of combustion of the liquefied petroleum gas in the biscuiting process, and is measured by a flue gas analyzer arranged at the outlet of the biscuiting furnace; v (t) is 1-dimensional disturbance input with bounded energy at the time t, which is disturbance generated on the biscuit firing process by decomposition of water and organic matters discharged in the drying process of the celadon biscuit and distribution of a gas flow field in a kiln; omega (t) is 1-dimensional Brownian motion of zero mean value at the time t, and represents random influence factors in celadon biscuit firing detection, including gas heat value, air oxygen content, air moisture and random fluctuation of gas moisture and air temperature; z (t) is the adjusted output vector of 1 dimension at time t; d is a differential sign; a positive scalar τ is the time delay, representing the lag in the furnace temperature variation and the dependence on the initial state; the initial condition of the kiln temperature monitoring system is that x (mu) is x0And- τ. ltoreq. mu. ltoreq.0, where x0The system initial value measured at time t-0.
A∈R5×5,M∈R5×5,B∈R5×1,A1∈R5×5,M1∈R5×5,C∈R2×5，D∈R5×1,N∈R1×5All are known real matrices obtained by system modeling, wherein
Represents n1×n2And (5) maintaining a real matrix.
Designing a reliable estimator of a celadon biscuit firing kiln temperature monitoring system;
the present invention designs a reliable estimator of the type described below
In the formula (I), the compound is shown in the specification,
is the state variable of the estimator at the time t,
represents n3A dimension real vector;
Af∈R5×5,Bf∈R5×2,Nf∈R1×5a gain matrix for a reliable estimator to be designed;
ΔAf∈R5×5,ΔNf∈R1×5the following relationship is satisfied for the gain uncertainty of the estimator, representing the uncertainty change of the estimator gain value due to the environment change and the aging of the estimator
Wherein HA∈R5×2,HN∈R1×2,G∈R2×5A matrix of constants of appropriate dimensions, F (t) e R2×2I represents an identity matrix having an appropriate dimension for the time-varying disturbance matrix at time t, and I in the above equation (3) is a 2 × 2-dimensional identity matrix. Wherein the matrix HA,HNThe specific form and parameter values of G, F (t) can be obtained by uncertainty analysis and modeling methods.
Step three, establishing an error model for reliable estimation of the temperature monitoring system;
selecting augmented State variables
And error vector
The following estimation error augmentation system equation can be obtained
In the formula (I), the compound is shown in the specification,
where 0 represents a matrix of 0 with appropriate dimensions.
It is an object of the invention to design a gain matrix a of a reliable estimatorf,Bf,NfSo that the estimation error augmentation system (4) corresponding to the furnace temperature monitoring in the celadon biscuit firing process is robust mean square asymptotically stable when v (t) is 0 and is in a zero initial condition
The time performance index J is less than 0, wherein
Then (2) is a reliable estimator for the system (1) designed by the present invention, where the positive scalar γ represents a given disturbance rejection level, γ >0, and E {. cndot. } represents the mathematical expectation operation.
Solving a reliable estimator for monitoring the temperature of the celadon biscuit firing kiln;
step 1: random stability analysis of the estimation error augmentation system;
selecting Lyapunov functional
In the formula, P is more than 0, Q is more than 0 and is a positive definite symmetric matrix to be solved with 10 multiplied by 10 dimensions.
When the perturbation v (t) is 0, the random analysis of Ito lemma is used
In the formula (I), the compound is shown in the specification,
and is
The notation LV (ξ (t)) denotes the infinitesimal operator of V (ξ (t)), the asterisk denotes the symmetry term in the symmetry matrix, i.e. in the above formula #denotesΦ12Is transferred to
If phi is less than 0, then ensure that
Namely, the estimation error augmentation system (4) is stable in the asymptotic robust mean square when v (t) is 0.
Step 2: estimating interference suppression performance analysis of the error augmentation system;
given a perturbation suppression degree gamma >0, gamma is a scalar,by the definition of performance index J in step three, and zero initial condition
And robust mean square asymptotic stability, known
And is provided with
In the formula (I), the compound is shown in the specification,
obviously, if xi <0, J <0 is present, and it is easy to understand the complement of Shu (Schur), xi <0 is equivalent to the following inequality
Therefore, if inequality (6) holds, the estimation error augmentation system (4) is robust mean-square asymptotically stable with a given disturbance rejection performance γ > 0.
And 3, step 3: solving a gain matrix of the reliable estimator;
let the matrix P be
In the formula, X and V are positive definite symmetric matrices of 5 × 5 dimensions.
Substituting the expression and matrix P of each matrix in the formula (4) into the inequality (6) to obtain
In the formula
Ω13＝XA1-VBfD，Ω23＝VA1-VBfD，
H1＝[0 0 HA HA 0 0 0]T，G1＝[0 0 0 G 0 0 0]
H2＝[0 HN 0 0 0 0 0]T，G2＝[0 0 0 0 G 0 0]
From the basic inequality relationship, Σ <0 is equivalent to the presence of two positive numbers ε1And ε2So that the following equation holds
In the formula, superscript-1 denotes inverting the matrix or inverting the scalar.
Performing matrix variable substitution, selecting
Substitution inequality sigma0Less than 0, as can be seen by matrix operation and Schur complement theorem0<0 is equivalent to the linear matrix inequality pi <0 holds, wherein
In the formula (I), the compound is shown in the specification,
from selected matrix variables
It is easy to know that the matrix parameters of the estimator (2) are
Thus, for a given interference suppression degree γ >0, the matrix can be obtained by solving the inequality (8) using the Linear Matrix Inequality (LMI) toolkit in MATLAB
The gain matrix of the reliable estimator of the celadon bisque firing temperature monitoring system designed by the invention can be calculated by the formula (9).
Claims (1)
1. A reliable estimation method for monitoring the temperature of a celadon biscuit firing kiln is characterized by comprising the following steps:
step one, establishing a state space model of a celadon biscuit firing kiln temperature monitoring system;
firstly, according to the principle of combustion of liquefied gas, the principle of fluid mechanics and data measured by experiments, in combination with the structure of a celadon biscuit firing kiln, a mixed random modeling method and a state space representation method are utilized to establish the following random time-lag differential equation:
wherein x (t) ═ x1(t) x2(t) x3(t) x4(t) x5(t)]TRepresenting the state vector of the celadon biscuit firing kiln at time T, where the superscript T represents the transpose of the matrix, x1(t) is the temperature in the furnace, i.e. the monitoring quantity to be obtained, x2(t) is the pressure in the kiln, x3(t) is the oxygen concentration in the kiln, x4(t) is the gas flow velocity in the kiln, x5(t) is the calorific value of the fuel gas; y (t) ═ y1(t) y2(t)]TIs an output measured value of a celadon biscuit firing kiln monitoring system at the time t, wherein y1(t) is the temperature measurement value in the kiln of the roasting furnace measured by a thermocouple, y2(t) is the heat value of the flue gas at the outlet of the biscuiting furnace, which represents the sufficient degree of combustion of the liquefied petroleum gas in the biscuiting process, and is measured by a flue gas analyzer arranged at the outlet of the biscuiting furnace; v (t) is 1-dimensional disturbance input with bounded energy at the time t, which is disturbance generated on the biscuit firing process by decomposition of water and organic matters discharged in the drying process of the celadon biscuit and distribution of a gas flow field in a kiln; omega (t) is 1-dimensional Brownian motion of zero mean value at the time t, and represents random influence factors in celadon biscuit firing detection, including gas heat value, air oxygen content, air moisture and random fluctuation of gas moisture and air temperature; z (t) is the adjusted output vector of 1 dimension at time t; d is a differential sign; a positive scalar τ is the time delay, representing the lag in the furnace temperature variation and the dependence on the initial state; the initial condition of the kiln temperature monitoring system is that x (mu) is x0And- τ. ltoreq. mu. ltoreq.0, where x0The system initial value measured at the moment when t is 0; a is an element of R5×5,M∈R5×5,B∈R5×1,A1∈R5×5,M1∈R5×5,C∈R2×5，D∈R5×1,N∈R1×5All are known real matrices obtained by system modeling, wherein
Represents n1×n2Moment of truth of dimensionArraying;
designing a reliable estimator of a celadon biscuit firing kiln temperature monitoring system;
the following types of reliable estimators are designed
In the formula (I), the compound is shown in the specification,
is the state variable of the estimator at the time t,
represents n3A dimension real vector; a. thef∈R5×5,Bf∈R5×2,Nf∈R1×5A gain matrix for a reliable estimator to be designed; delta Af∈R5×5,△Nf∈R1×5The following relationship is satisfied for the gain uncertainty of the estimator, representing the uncertainty change of the estimator gain value due to the environment change and the aging of the estimator
Wherein HA∈R5×2,HN∈R1×2,G∈R2×5A matrix of constants of appropriate dimensions, F (t) e R2×2I is a time-varying disturbance matrix at time t, I represents an identity matrix having a suitable dimension, and I in the above formula (3) is a 2 × 2-dimensional identity matrix; wherein the matrix HA,HNThe specific form and parameter values of G, F (t) can be obtained by uncertainty analysis and modeling methods;
step three, establishing an error model for reliable estimation of the temperature monitoring system;
selecting augmented State variables
And error vector
The following estimation error augmentation system equation can be obtained
In the formula (I), the compound is shown in the specification,
where 0 represents a matrix of 0 with appropriate dimensions;
designing the gain matrix A of a reliable estimatorf,Bf,NfSo that the estimation error augmentation system (4) corresponding to the furnace temperature monitoring in the celadon biscuit firing process is robust mean square asymptotically stable when v (t) is 0 and is in a zero initial condition
Time performance index J<0, wherein
Then (2) is a reliable estimator for the system (1), the positive scalar γ represents a given disturbance suppression degree, γ >0, and E {. cndot. } represents the mathematical expectation operation;
solving a reliable estimator for monitoring the temperature of the celadon biscuit firing kiln;
step 1: random stability analysis of the estimation error augmentation system;
selecting Lyapunov functional
In the formula, P >0 and Q >0 are positive definite symmetric matrixes to be solved with 10 multiplied by 10 dimensions;
when the perturbation v (t) is 0, the random analysis of Ito lemma is used
In the formula (I), the compound is shown in the specification,
and is
The notation LV (ξ (t)) denotes the infinitesimal operator of V (ξ (t)), the asterisk denotes the symmetry term in the symmetry matrix, i.e. in the above formula #denotesΦ12Is transferred to
If phi<0, then ensure that
Namely, the robust mean square asymptotically stabilizes when v (t) is 0 by the estimation error augmentation system (4);
step 2: estimating interference suppression performance analysis of the error augmentation system;
given disturbance rejection degree gamma>0, gamma is scalar quantity, derived from performance index J in step threeDefinition, and zero initial conditions
And robust mean square asymptotic stability, known
And is provided with
In the formula (I), the compound is shown in the specification,
obviously, if xi <0, then J <0, and is clear from Schur complement, xi <0 is equivalent to the following inequality
Therefore, if the inequality (6) is true, the estimation error augmentation system (4) is robust mean-square asymptotically stable with a given disturbance rejection performance γ > 0;
and 3, step 3: solving a gain matrix of the reliable estimator;
let the matrix P be
Wherein X and V are positive definite symmetric matrixes of 5X 5 dimensions;
substituting the expression and matrix P of each matrix in the formula (4) into the inequality (6) to obtain
In the formula
Ω13＝XA1-VBfD，Ω23＝VA1-VBfD，
H1＝[0 0 HA HA 0 0 0]T，G1＝[0 0 0 G 0 0 0]
H2＝[0 HN 0 0 0 0 0]T，G2＝[0 0 0 0 G 0 0]
According to the basic inequality relationship, sigma<0 is equivalent to the presence of two positive numbers epsilon1And ε2So that the following equation holds
In the formula, the superscript-1 represents the inversion of a matrix or the reciprocal of a scalar;
performing matrix variable substitution, selecting
Substitution inequality sigma0<0, known by matrix operation and Schur complement theory0<0, etcPi equivalent to linear matrix inequality<0 is established, wherein
In the formula (I), the compound is shown in the specification,
from selected matrix variables
It is easy to know that the matrix parameters of the estimator (2) are
Thus, for a given interference suppression degree γ>0, solving an inequality (8) by utilizing a linear matrix inequality tool box in MATLAB to obtain a matrix V,
the gain matrix of the reliable estimator of the celadon bisque firing temperature monitoring system can be calculated by the formula (9).
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