A Hidden Semi-Markov State Estimation Method for Continuous Stirred Reactor Systems

Abstract

This invention discloses a hidden semi-Markov state estimation method for a continuous stirred reactor (CSTR) system, relating to the field of industrial process control and state estimation technology. Addressing the problems of low state estimation accuracy, high communication resource consumption, and poor adaptability between modeling and actual reaction characteristics under multimodal operation of CSTRs, this invention constructs a state estimation framework integrating hidden semi-Markov processes based on the core dynamic equations of CSTRs. It designs an adaptive event triggering mechanism, dynamically adjusts the data transmission threshold to reduce communication volume, and constructs a robust estimator based on performance constraints to achieve accurate estimation of reactant concentration and temperature. This invention overcomes the limitations of traditional Markov modeling, reduces estimation errors and communication volume in multimodal switching scenarios, and is suitable for real-time monitoring and optimization control of CSTR systems in chemical production.

Description

Technical Field

[0001] This invention relates to the field of industrial process control and state estimation technology, and in particular to a hidden semi-Markov state estimation method for a continuous stirred reactor system. Background Technology

[0002] CSTRs (Continuous Stirred Tank Reactors) are core equipment in chemical production and are widely used in processes such as polymerization, fermentation, and catalytic reactions. In actual production, CSTR systems often dynamically switch between multiple operating modes due to factors such as changes in feed composition, catalyst activity decay, and cooling system switching, forming a typical switching system. Key state parameters within the reactor, such as reactant concentration and temperature, directly determine product quality and production safety; however, these parameters are often difficult to measure accurately using sensors and must be obtained indirectly through state estimation techniques.

[0003] Existing CSTR system state estimation methods have several limitations: First, traditional methods are mostly based on single-modal model design, which makes it difficult to adapt to multi-modal switching characteristics. When the system jumps between modes such as reaction, cooling, and discharge, the estimation accuracy drops significantly. Second, when using Markov processes to describe mode switching, the assumption that the residence time follows an exponential distribution is inconsistent with the characteristic that the mode duration is affected by the reaction process in actual CSTR operation, resulting in a high degree of model conservatism. Third, the continuous acquisition and transmission of data by sensors leads to excessive communication burden, especially in the scenario of multi-device networking in large-scale chemical industrial parks, which can easily cause network congestion and affect the real-time performance of the estimation. Fourth, the methods do not fully consider issues such as signal transmission attenuation and external disturbances in the industrial environment, resulting in insufficient robustness of the estimation.

[0004] To address the aforementioned issues, there is an urgent need for a state estimation method that can accurately describe CSTR switching characteristics, reduce communication consumption, and possess strong robustness, in order to meet the high precision and high reliability requirements of chemical production for process monitoring. Summary of the Invention

[0005] To address the above technical problems, this invention provides a hidden semi-Markov state estimation method for a continuous stirred reactor system, comprising the following steps:

[0006] S1. Construct the kinetic model and hidden semi-Markov model of the CSTR switching system; based on the laws of material and energy conservation, establish the kinetic equations of the CSTR system to describe the dynamic changes in reactant concentration and reaction temperature; according to the CSTR operating process, divide the system into two modes: reaction heating and isothermal reaction, corresponding to a finite mode space. Mode switching is described by a hidden semi-Markov process {s(k)}, and the transition probability matrix, dwell time probability density function and emission probability matrix are obtained by statistical analysis of historical operating data.

[0007] S2. The trigger threshold is dynamically adjusted and data is transmitted. The sensor collects data according to the sampling period. Data is transmitted to the estimator only when the trigger condition is met; otherwise, the previous data is used.

[0008] S3. Construct an observation mode-dependent hidden semi-Markov state filter; based on the observation mode... With event-triggered data y(k) l An adaptive state estimator is designed; a filtering error system is constructed by combining a periodic event triggering mechanism and time-varying time delay characteristics; and a generalized dissipation performance constraint is introduced.

[0009] S4. Construct a Lyapunov function with a residence time dependency term; by analyzing the Lyapunov function, and combining Schur's complement lemma and linear matrix inequality techniques, derive sufficient conditions for the error system to be mean square stable and satisfy the generalized dissipative performance; introduce a relaxation matrix to handle nonlinear terms when solving for filter parameters, and obtain a set of solvable linear matrix inequality constraints, and obtain the filter parameters after solving.

[0010] S5. Deploy temperature sensors, flow sensors, and edge computing nodes at the CSTR site. After the sensors collect data, they transmit it through industrial Ethernet. The edge nodes run event triggering logic and state estimators; finally, the system runs in real time.

[0011] The technical solution further defined in this invention is:

[0012] Furthermore, in step S1, based on the laws of conservation of material and energy, a kinetic equation for the CSTR system is established to describe the dynamic changes in reactant concentration and reaction temperature, as shown in the following equation:

[0013]

[0014] in, , C A The values ​​represent reactant concentrations in mol / L; subscripts f and a indicate the feed flow index and mode index, respectively; q represents the feed rate in L / min; T represents the reactor temperature in K; V represents the effective reactor volume in L; T c The temperature of the coolant is expressed in Kelvin (K); ρ represents the fluid density, expressed in g / L; C pΔH represents the specific heat capacity of the fluid, in J / (g∙K); ΔH represents the enthalpy change of the reaction, in J / mol; E represents the activation energy, in J / mol; R represents the gas constant, in J / (mol∙K); k0 represents the reaction rate constant, in min. -1 UA represents the heat transfer constant, with units of J / (mol∙K); and These represent the derivatives of reactant concentration and reactor temperature, respectively.

[0015] As described above, in the hidden semi-Markov state estimation method for a continuous stirred reactor system, step S1 divides the system modes into two types based on the CSTR operating process: reaction heating and isothermal reaction, corresponding to a finite mode space. ;make This represents the unstable equilibrium point of reactant concentration, reactor temperature, and coolant temperature; (Definition) , System states x1 and x2 and control inputs ;

[0016] If a state transition exists as shown in the following equation:

[0017]

[0018] The CSTR system is then considered to be linearized with local modal feedback. Based on the dynamic equations, the continuous-time-space state equations are obtained; simultaneously, the continuous system is discretized to obtain the discrete-space state equations.

[0019]

[0020] Where y(k) represents the measured signal; z(k) represents the output signal to be estimated; ω(k) represents the external disturbance in the l2[0,∞) space; s(k) represents the semi-Markov process; μ(k) represents the time-varying delay, 0≤μ(k)≤d, and d represents a known constant; Represents the initial state of the system; for s(k) = a, A a B a C a D a and E a Indicates system parameters.

[0021] As described above, in the hidden semi-Markov state estimation method for a continuous stirred reactor system, step S1 uses a hidden semi-Markov process {s(k)} to describe mode switching, and obtains the transition probability matrix, residence time probability density function, and emission probability matrix through statistical analysis of historical operating data; wherein, the transition probability matrix... , ; Dwell time probability density function ρ ab (τ)=Pr(t n+1 -t n =τ|r n+1 =b,r n =a); Emission probability matrix , Correlate the latent real mode a with the observable mode δ(k)=kt n .

[0022] As described above, in the hidden semi-Markov state estimation method for a continuous stirred reactor system, step S2 defines the trigger error. k l Indicates the previous trigger time. , h represents the sensor's measurement period; construct trigger conditions with dynamic weights:

[0023]

[0024] in, ε represents the weighted matrix for observation mode dependence, and ε represents the triggering mechanism threshold.

[0025] As described above, in the hidden semi-Markov state estimation method for a continuous stirred reactor system, step S3 involves designing an adaptive state estimator:

[0026]

[0027] in, Indicates the estimated state; This represents the output of the estimator; , as well as This represents the estimator parameter matrix, which is updated in real time based on mode switching.

[0028] As described above, in the hidden semi-Markov state estimation method for a continuous stirred reactor system, step S3 defines the augmented state. and estimation error η(k)=k-(k l +mh), 0≤η(k)≤h, combining the periodic event triggering mechanism and time-varying time delay characteristics, a filtering error system is constructed:

[0029]

[0030] in,

[0031] .

[0032] As described above, in the hidden semi-Markov state estimation method for a continuous stirred reactor system, step S3 introduces a generalized dissipative performance constraint to ensure the estimation error... satisfy:

[0033]

[0034] in, .

[0035] As described above, in the hidden semi-Markov state estimation method for a continuous stirred reactor system, step S4 involves constructing a Lyapunov function containing a residence time dependency:

[0036]

[0037] Each independent term is defined as follows:

[0038]

[0039] Where, ∆x(k) = x(k+1) - x(k); R1 and R2 are symmetric positive definite weight matrices.

[0040] As described above, in the hidden semi-Markov state estimation method for a continuous stirred reactor system, in step S4, by analyzing the difference ∆V(k) = V(k+1) - V(k) of the Lyapunov function V(k), and combining Schur's complement lemma and linear matrix inequality techniques, sufficient conditions for the error system to be mean-square stable and satisfying the generalized dissipative performance are derived:

[0041] There exists a positive definite matrix R1, R2 and matrices U1, U2, such that:

[0042]

[0043] Among them, T a This represents the upper bound of the residence time of mode a; Q1, Q2, Q3, and Q4 represent the generalized dissipative performance parameter matrix. If Q4 ≠ 0, then Q1 = 0 and Q2 = 0.

[0044] This represents a partitioned symmetric matrix, whose non-zero elements are:

[0045]

[0046] A relaxation matrix is ​​introduced to handle nonlinear terms during filter parameter solving, resulting in a set of solvable linear matrix inequality constraints. Solving these constraints yields the filter parameters. , , ,in This represents the auxiliary matrix.

[0047] The beneficial effects of this invention are:

[0048] (1) In this invention, a model is constructed based on the CSTR core dynamic equation, combined with the hidden semi-Markov process to describe the switching characteristics. The residence time can be adapted to any distribution such as Weibull, which fits the influence of the reaction process on the mode duration. Compared with traditional Markov modeling, the estimation accuracy is improved by more than 40%, and the modeling accuracy is higher.

[0049] (2) In this invention, through the adaptive event triggering mechanism, data is transmitted only when the state changes suddenly or the estimation error exceeds the limit. In the multi-equipment scenario of chemical industrial parks, the communication volume is reduced by 60%-70%, network congestion is avoided, and the communication burden is significantly reduced.

[0050] (3) In this invention, by setting the values ​​of the generalized dissipation matrices Q1, Q2, Q3, and Q4, L2-L can be obtained. ∞ Performance, H ∞ Performance, passive performance, hybrid H ∞ The filter parameter matrix under common performance indicators such as passive performance and dissipation performance can be selected according to the actual situation and needs, so as to ensure that the concentration estimation error is controlled within a reasonable range and has stronger robustness.

[0051] (4) In this invention, modeling is directly based on CSTR process mode division, which can be seamlessly integrated into the existing DCS control system without large-scale hardware modification. It has low deployment cost and is suitable for various chemical reaction scenarios such as polymerization and fermentation, and has better industrial adaptability. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the overall process of the present invention;

[0053] Figure 2 This is a diagram showing the relationship between the CSTR system modes and the observed modes in an embodiment of the present invention.

[0054] Figure 3 In the embodiments of the present invention, H is mixed ∞ And a graph showing the estimated concentration of products under passive performance;

[0055] Figure 4 This is a data transmission timing diagram of the periodic event triggering mechanism and the continuous event triggering mechanism in an embodiment of the present invention;

[0056] Figure 5 This is an estimation error diagram of the periodic event triggering mechanism and the continuous event triggering mechanism in the embodiments of the present invention. Detailed Implementation

[0057] This embodiment provides a hidden semi-Markov state estimation method for a continuous stirred reactor system, such as... Figure 1 As shown, it includes the following steps:

[0058] S1. Construct the dynamic model and hidden semi-Markov model of the CSTR switching system.

[0059] Based on the laws of conservation of mass and energy, a kinetic equation for the CSTR system is established to describe the dynamic changes in reactant concentration and reaction temperature, as shown in the following equation:

[0060]

[0061] in, , C A The values ​​represent reactant concentrations in mol / L; subscripts f and a indicate the feed flow index and mode index, respectively; q represents the feed rate in L / min; T represents the reactor temperature in K; V represents the effective reactor volume in L; T c The temperature of the coolant is expressed in Kelvin (K); ρ represents the fluid density, expressed in g / L; C p ΔH represents the specific heat capacity of the fluid, in J / (g∙K); ΔH represents the enthalpy change of the reaction, in J / mol; E represents the activation energy, in J / mol; R represents the gas constant, in J / (mol∙K); k0 represents the reaction rate constant, in min. -1 UA represents the heat transfer constant, with units of J / (mol∙K); and These represent the derivatives of reactant concentration and reactor temperature, respectively.

[0062] Based on the CSTR operating process, the system modes are divided into two core modes: "reaction heating" and "isothermal reaction," corresponding to a finite mode space. ;make This represents the unstable equilibrium point corresponding to (reactant concentration, reactor temperature, and coolant temperature); [Definition] , System states x1 and x2 and control inputs .

[0063] If a state transition exists as shown in the following equation:

[0064]

[0065] The CSTR system is considered to be linearized with local modal feedback, and the continuous time-space state equation can be obtained based on the dynamic equation.

[0066] To facilitate computer control, the continuous system is discretized to obtain the discrete-space state equations:

[0067]

[0068] Where y(k) represents the measured signal; z(k) represents the output signal to be estimated; ω(k) represents the external disturbance in the l2[0,∞) space; s(k) represents the semi-Markov process; μ(k) represents the time-varying delay, 0≤μ(k)≤d, and d represents a known constant; Represents the initial state of the system; for s(k) = a, A a B a C a D a and E a Indicates system parameters.

[0069] Mode switching is described by a hidden semi-Markov process {s(k)}, and the transition probability matrix, dwell time probability density function and emission probability matrix are obtained by statistical analysis of historical operating data.

[0070] Transition probability matrix , For example, shifting from the "isothermal reaction" mode to the "cooling and discharging" mode;

[0071] Dwell time probability density function ρ ab (τ)=Pr(t n+1 -t n =τ|r n+1 =b,r n =a), breaking through the memorylessness limitation of traditional Markov processes;

[0072] Emission probability matrix , Correlate the latent real mode a with the observable mode (Sensor signal feature recognition), δ(k)=kt n .

[0073] S2. Design a periodic event triggering mechanism.

[0074] Dynamic adjustment of trigger threshold: defining trigger error k l Indicates the previous trigger time. h represents the sensor's measurement period.

[0075] Construct triggering conditions with dynamic weights:

[0076]

[0077] in, ε represents the weighted matrix for observation mode dependence, and ε represents the triggering mechanism threshold.

[0078] Data transmission logic: The sensor collects data according to the sampling period h, and transmits the data to the estimator only when the trigger condition is met; otherwise, the previous data is used.

[0079] S3. Construct a hidden semi-Markov state filter that depends on the observation mode.

[0080] Estimator architecture design: based on observation modes With event-triggered data y(k) l Design an adaptive state estimator:

[0081]

[0082] in, Indicates the estimated state; This represents the output of the estimator; , as well as This represents the estimator parameter matrix, which is updated in real time based on mode switching.

[0083] Error system construction: defining augmented states and estimation error η(k)=k-(k l +mh), 0≤η(k)≤h, combining the periodic event triggering mechanism and time-varying time delay characteristics, a filtering error system is constructed:

[0084]

[0085] in,

[0086] .

[0087] Robustness Enhancement Design: Introducing generalized dissipative performance constraints to suppress external disturbances and measurement noise, ensuring estimation error... satisfy:

[0088]

[0089] in, .

[0090] S4. Stability and generalized dissipation performance analysis and parameter solution.

[0091] Lyapunov function construction: Constructing Lyapunov functions with residency time dependencies:

[0092]

[0093] Each independent term is defined as follows:

[0094]

[0095] Where, ∆x(k) = x(k+1) - x(k); R1 and R2 are symmetric positive definite weight matrices.

[0096] Derivation of Stability and Performance Criteria: By analyzing the difference ∆V(k) = V(k+1) - V(k) of the Lyapunov function V(k), and combining Schur's complement lemma and linear matrix inequality techniques, we derive the sufficient condition for the error system to be mean-square stable and satisfy the generalized dissipative performance:

[0097] There exists a positive definite matrix R1, R2 and matrices U1, U2, such that:

[0098]

[0099] Among them, T a This represents the upper bound of the residence time of mode a; Q1 represents a semi-Markov kernel; Q2, Q3, and Q4 represent the generalized dissipative performance parameter matrix. If Q4 ≠ 0, then Q1 = 0 and Q2 = 0.

[0100] This represents a partitioned symmetric matrix, whose non-zero elements are:

[0101] .

[0102] A relaxation matrix is ​​introduced to handle nonlinear terms during filter parameter solving, resulting in a set of solvable linear matrix inequality constraints. Solving these constraints yields the filter parameters. , , ,in This represents the auxiliary matrix.

[0103] S5, System Deployment and Real-time Estimation.

[0104] Hardware integration: Temperature and flow sensors and edge computing nodes are deployed in the CSTR field. After the sensors collect data, it is transmitted through industrial Ethernet. The edge nodes run event triggering logic and state estimators.

[0105] Real-time operation process:

[0106] (1) The sensor periodically collects data such as jacket temperature and discharge flow rate;

[0107] (2) The edge node calculates the trigger error, determines whether the transmission conditions are met, and uploads data only when triggered;

[0108] (3) The estimator updates the modal probabilities and estimated states based on the received data and the hidden semi-Markov model;

[0109] (4) Output the concentration and temperature estimation results every 0.05 min for production monitoring.

[0110] In this embodiment, the method is further described in detail in conjunction with the actual application scenario of a CSTR system for polyvinyl chloride production.

[0111] First, set the implementation scenario parameters. The reactant is vinyl chloride monomer, the target product is polyvinyl chloride, and the operating modes include mode one and mode two. Mode one is "reaction heating" (0-60min), and mode two is "isothermal reaction" (60-300min).

[0112] Core dynamic parameter: a1 = -1.506 × 10 13 , a2=2.092, V=100L, ρ=1000g / L, C p =0.239 J / (g∙K), ∆H=-5×10 4 J / mol, E / R=8750K, k0=7.2×10 10 min -1 UA=5×10 4 J / (mol∙K), T f =350K; Parameters of Mode 1: q=50L / min, C Af =1.5mol / L; Parameters for Mode 2: q=200L / min, C Af =0.75mol / L; sensor sampling period 0.05min; communication network adopts industrial Ethernet; transmission delay upper limit d=3.

[0113] Next, we construct a hidden semi-Markov model:

[0114] To facilitate computer control, the discretized modal parameter matrices are as follows:

[0115] .

[0116] The transition probability matrix and the emission probability matrix are defined as follows:

[0117]

[0118] It should be noted that when the emission probability is θ1, the observation mode is synchronized with the system mode; when the emission probability is θ2, the observation mode is asynchronous with the system mode.

[0119] The dwell time probability density function is:

[0120] .

[0121] Next, set the trigger mechanism parameters: set the measurement period h=4; for the periodic event trigger mechanism, the frequency at which the sensor acquires measurement data can be changed by adjusting the measurement period; the smaller the period, the higher the frequency at which the sensor acquires data, and the more data needs to be transmitted; in addition, when the measurement period h=1, the periodic event trigger will become the continuous event trigger.

[0122] Then, the filter parameters are solved, and the filter gain matrix under different performance indicators is obtained by solving the linear matrix inequality constraints.

[0123] Finally, verify the running effect:

[0124] (1) Robust performance: When the emission probability is θ1, the system mode and the observation mode are synchronized; when the emission probability is θ2, the system mode and the observation mode are asynchronous, such as Figure 2 As shown, the designed filter can handle both different situations and complete the estimation of product concentration, exhibiting better universality and a wider range of applications, such as... Figure 3 As shown.

[0125] (2) Communication performance: Within 10 minutes, the periodic event triggering mechanism triggered 18 communications, saving 91.04% of communication resources. The continuous event triggering mechanism triggered 29 communications, saving 85.57% of communication resources. Therefore, the continuous event triggering mechanism proposed in this embodiment can save more communication resources, such as... Figure 4 As shown.

[0126] (3) Estimation accuracy: Under dissipation performance, the estimation error of the periodic event triggering mechanism is lower and the estimation accuracy is higher than that of the continuous event triggering mechanism. The periodic event triggering mechanism filter designed in this embodiment achieves a good balance between estimation accuracy and communication resources, such as... Figure 5 As shown.

[0127] The above implementation results show that the method of this embodiment can accurately estimate the critical state of the CSTR system, significantly reduce the communication burden, and has good industrial application value.

[0128] In addition to the embodiments described above, the present invention may have other implementations. All technical solutions formed by equivalent substitution or equivalent transformation fall within the protection scope claimed by the present invention.

Claims

1. A method for estimating hidden semi-Markov states of a continuous stirred tank reactor system, characterized by: The method comprises the following steps: S1, Constructing the dynamic model and hidden semi-Markov model of CSTR switching system; Based on the law of conservation of mass and energy conservation, the dynamic equation of CSTR system is established to describe the dynamic change of reactant concentration and reaction temperature; According to the operation process of CSTR, the system mode is divided into two modes of reaction temperature rise and constant temperature reaction, corresponding to the limited mode space ; The hidden semi-Markov process {s(k)} is used to describe the mode switching, and the transition probability matrix, residence time probability density function and emission probability matrix are obtained by statistical analysis of historical operation data; S2, triggering threshold dynamic adjustment and data transmission, the sensor collects data according to the sampling period, and only when the triggering condition is met, the data is transmitted to the estimator, otherwise the previous data is used; S3, constructing an observation modal dependent hidden semi-Markov state filter; Based on the observation modal With event-triggered data y(k l ), an adaptive state estimator is designed; combining the periodic event-triggered mechanism with the time-varying time-delay characteristics, a filtering error system is constructed; and a generalized dissipation performance constraint is introduced; S4, constructing a Lyapunov function containing a residence time dependent term; by analyzing the Lyapunov function, combining the Schur complement lemma and the linear matrix inequality technique, the sufficient condition that the error system is mean square stable and satisfies the generalized dissipation performance is derived; a relaxation matrix is introduced to process the nonlinear term when solving the filter parameters, a set of solvable linear matrix inequality constraints are obtained, and the filter parameters are obtained after solving; S5, deploying temperature sensors, flow sensors and edge computing nodes in the CSTR field, the sensors transmit the collected data through industrial Ethernet, and the edge nodes run the event triggered logic and state estimator; Finally, the real-time running system is obtained.

2. The method of claim 1, wherein the method is characterized by: In the step S1, based on the law of conservation of mass and energy conservation, the dynamic equation of the CSTR system is established to describe the dynamic change of the concentration of reactants and reaction temperature, as shown in the following formula: wherein, , , C A represents the reactant concentration in mol / L; the subscripts f and a represent the feed stream index number and the mode index number; q represents the feed flow rate in L / min; T represents the reactor temperature in K; V represents the reactor effective volume in L; T c represents the coolant temperature in K; p represents the fluid density in g / L; C p represents the fluid specific heat capacity in J / (g K); AH represents the reaction enthalpy change in J / mol; E represents the activation energy in J / mol; R represents the gas constant in J / (mol K); k0 represents the reaction rate constant in min -1 ; UA represents the heat transfer constant in J / (mol K); and represent the derivative of the reactant concentration and the reactor temperature, respectively.

3. The method of claim 2, wherein the method is a method of estimating the hidden semi-Markov state of a continuous stirred tank reactor system, characterized by: In the step S1, according to the CSTR operation process, the system mode is divided into two modes of reaction temperature rising and constant temperature reaction, corresponding to the finite mode space ; Let denote the unstable equilibrium point of the concentrations of the reactants, the temperature of the reactor and the temperature of the cooling liquid; define , , the system states x1 and x2 and the control input ; If there is a state transformation as shown in the following formula: The CSTR system is considered to be locally modal feedback linearization, the continuous-time space state equation is obtained based on the dynamic equation; at the same time, the continuous system is discretized to obtain the discrete space state equation: wherein y(k) represents a measurement signal; z(k) represents an output signal to be estimated; ω(k) represents an external disturbance in the space of l2[0,∞); s(k) represents a semi-Markov process; μ(k) represents a time-varying time delay, 0≤μ(k)≤d, d represents a known constant; represents an initial state of the system; for s(k)=a, A a , B a , C a , D a , and E a represent system parameters.

4. The method of claim 3, wherein the method is characterized by: In the step S1, the modal switching is described by using a hidden semi-Markov process {s(k)}, and the transition probability matrix, the residence time probability density function and the emission probability matrix are obtained by statistical analysis of historical operation data; wherein the transition probability matrix , ; the residence time probability density function ρ ab (τ)=Pr(t n+1 -t n =τ|r n+1 =b,r n =a); and the emission probability matrix , associates the hidden true mode a with the observable mode , δ(k)=k-t n .

5. The method of claim 4, wherein: In the step S2, a trigger error is defined , k l denotes the last trigger time, , h denotes the measurement period of the sensor; a trigger condition with dynamic weight is constructed: wherein, represents the observation modality dependent weighting matrix, and ε represents the triggering mechanism threshold.

6. The method of claim 5, wherein the method is characterized by: In the step S3, an adaptive state estimator is designed: wherein represents an estimated state; represents an estimator output; , and represents an estimator parameter matrix, updated in real-time according to the mode switch.

7. The method of claim 6, wherein the method is a method of estimating the hidden semi-Markov state of a continuous stirred tank reactor system, characterized by: In the step S3, the augmented state is defined and the estimation error η(k) = k - (k l + mh), 0 ≤ η(k) ≤ h, combining the periodic event-triggered mechanism with the time-varying time-delay characteristics, a filtering error system is constructed: Wherein, 。 8. The method of claim 7, wherein the method is a method of estimating the hidden semi-Markov state of a continuous stirred tank reactor system, characterized by: In the step S3, the generalized dissipation performance constraint is introduced to ensure the estimation error is satisfied: wherein .

9. The method of claim 8, wherein the method further comprises: In the step S4, a Lyapunov function containing a residence time dependent term is constructed: Each independent term is defined as: where Δx(k) = x(k+1) - x(k); R1and R2are symmetric positive definite weight matrices.

10. The method of claim 9, wherein the method is a method of estimating the hidden semi-Markov state of a continuous stirred tank reactor system, characterized by: In the step S4, by analyzing the difference of the Lyapunov function V(k) ∆V(k)=V(k+1)-V(k), combining the Schur complement lemma and the linear matrix inequality technique, the sufficient condition that the error system is mean square stable and satisfies the generalized dissipation performance is derived: There is a positive definite matrix R1, R2 and matrices U1, U2, such that: where T a denotes the upper bound on the residence time of the modality a; denotes a semi-Markov kernel; Q1, Q2, Q3, Q4denote generalized dissipation property parameter matrices, with Q1= 0 and Q2= 0 if Q4≠ 0; denotes a partitioned symmetric matrix with non-zero elements: A relaxation matrix is introduced to deal with the nonlinear terms in the filter parameter solution, and a set of solvable linear matrix inequality constraints is obtained, and the filter parameters are obtained after solving , , wherein denotes an auxiliary matrix.

Images