A self-disturbance decoupling control method for main steam temperature of a gas-fired boiler

Abstract

The application discloses a kind of gas boiler main steam temperature self-disturbance decoupling control methods, comprising: signal detection device measures various signal data involved in the present application, then data is processed;Using the data after processing, the system model of double-input double-output is established, and the system model is identified;The system model after identification is decoupled, and the system is decoupled into two single-input single-output systems;For system, design linear self-disturbance controller to realize boiler main steam temperature stable control;Firefly algorithm is used to optimize linear self-disturbance controller parameter, and the control quality of main steam temperature control system is improved, the present application is aimed at the problems, such as nonlinearity, multiple disturbance and the like existing in the process of gas power generation boiler main steam temperature control, adopts the control strategy that linear self-disturbance control and decoupling control are combined, and the mutual coupling action between furnace gas flow and low-temperature superheater, desuperheating water flow and high-temperature superheater outlet temperature is decoupled and eliminated using Gauss elimination method.

Description

Technical Field

[0001] This invention belongs to the field of thermal power generation and intelligent optimization control technology, and more specifically, relates to a method for self-disturbance rejection and decoupling control of main steam temperature in a gas-fired boiler. Background Technology

[0002] Main steam temperature is a crucial controlled parameter for gas-fired power plant boilers, and its stability directly impacts the economic efficiency and reliability of the generator unit. Typically, the main steam temperature control deviation is required to be within ±5℃ of the setpoint. This controlled object exhibits characteristics such as high time delay, large inertia, and strong coupling. As thermal power units gradually develop towards larger capacity and higher parameters, conventional PID control algorithms are insufficient to meet on-site control requirements, often necessitating manual intervention. Therefore, seeking a reasonable intelligent optimization control method for main steam temperature is of great significance. Currently, the control method for main steam temperature in gas-fired power plant boilers primarily relies on water spray desuperheating. Water spray valves are installed symmetrically on both sides of the steam pipeline, and the water spray volume is controlled by adjusting the valve opening, thereby achieving control of the main steam temperature.

[0003] However, the on-site operating environment for gas-fired boilers is complex and variable. For example, the calorific value of the gas, pressure changes, and temperature of the desuperheating water all directly interfere with the regulation of the main steam temperature of the boiler. In addition, the equipment conditions of the generator set are constantly changing over time, the thermal model is uncertain, and the operating conditions deviate from the optimal conditions. This makes the actual control effect of the main steam temperature of the boiler unsatisfactory, with large steam temperature fluctuations. The main steam temperature system of the gas-fired boiler in the power plant has problems such as nonlinearity, multiple disturbances, and strong coupling. Summary of the Invention

[0004] The purpose of this invention is to provide an active disturbance rejection and decoupling control method for the main steam temperature of a gas-fired boiler. Addressing the problems of nonlinearity, multiple disturbances, and strong coupling in the main steam temperature system of a gas-fired boiler in a power plant, and to solve the issue that PID control cannot meet the quality requirements of main steam temperature control, advanced control algorithms such as adaptive PID, genetic algorithms, neural networks, and active disturbance rejection control have been successively applied to the steam superheating system of gas-fired boilers. Among them, active disturbance rejection control technology absorbs the advantages of PID control while improving its disadvantages, enabling the prediction and compensation of disturbances to the controlled object and model mismatch. It has good control effects on many nonlinear, large-time-lag complex systems. Applying active disturbance rejection control technology to the steam superheating system of a gas-fired boiler not only plays an important role in improving the robustness and anti-interference ability of the system, but also helps to stabilize the boiler combustion process, ensure the safe operation of the turbine equipment, and improve the operating economy of the generator set. This scheme adopts a control strategy combining linear active disturbance rejection control and decoupling control, and designs an active disturbance rejection and decoupling control system for the main steam temperature. To improve the control performance and accuracy of the system, the firefly algorithm is used, with the ITAE integral performance index as the objective function of the firefly algorithm. The firefly algorithm is used to adjust the active disturbance rejection controller parameter ω. c b0 is optimized to improve the controller's control effect, enabling the system to respond quickly to disturbances and track the set value, thus maintaining the stability of the main steam temperature.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for self-disturbance rejection and decoupling control of main steam temperature in a gas-fired boiler, comprising the following steps:

[0006] Step S1: The signal detection device measures the furnace gas flow signal, desuperheating water flow signal, desuperheater inlet temperature signal, and high-temperature superheater outlet temperature signal, and normalizes the measured data.

[0007] Step S2: Based on the normalized data, establish a dual-input dual-output system model with furnace gas flow rate and desuperheating water flow rate as inputs and desuperheater inlet temperature and high-temperature superheater outlet temperature as outputs. Use the least squares method to identify the model parameters.

[0008] Step S3: Use the Gaussian elimination variable decoupling method to decouple the identified system model, so that the dual-input dual-output system is decoupled into two single-input single-output systems;

[0009] Step S4: Design a linear active disturbance rejection controller to control the furnace gas flow and desuperheating water flow, so as to achieve stable control of the boiler main steam temperature;

[0010] Step S5: Introduce the Firefly Algorithm and use it to optimize the parameters of the linear active disturbance rejection controller, thereby improving the control quality of the main steam temperature control system.

[0011] In a preferred embodiment of the present invention, in step 1, the signal detection device is a temperature measuring device installed at the desuperheater inlet and the high-temperature superheater outlet of the gas-fired boiler steam-water system to measure the steam temperature at the desuperheater inlet and the steam temperature at the high-temperature superheater outlet, respectively. Flow measuring devices are installed at the furnace gas regulating valve and the desuperheating water regulating valve to measure the gas flow rate and the desuperheating water flow rate, respectively. When there are variable load disturbances in the desuperheater inlet temperature, high-temperature superheater outlet temperature, gas flow rate, and desuperheating water flow rate, the signal detection device collects data every 5 minutes, for a total of 2000 sets of data. The normalized data is processed using the following formula:

[0012]

[0013] Where, x i For the measured signal sample data, x min x is the minimum value of the sample data. max x is the maximum value of the sample data. inorm For sample data x i The normalized value.

[0014] As a preferred embodiment of the present invention, the expression for the dual-input dual-output system model in step 2 is as follows:

[0015]

[0016] Where y1(k) is the desuperheater inlet temperature output, u1(k-τ) is the desuperheater inlet temperature input, y2(k) is the high-temperature superheater outlet temperature output, u2(k-τ) is the high-temperature superheater outlet temperature input, τ is the time delay coefficient, ξ1(k) and ξ2(k) are unmeasurable noise, and A(z) -1 ) and B(z) -1 The shift operator constant coefficient polynomial is expanded as follows:

[0017]

[0018] Since the system noise is unmeasurable, the above system model expression is transformed into matrix form:

[0019]

[0020] In step 2, the least squares method is used to identify the model parameters. First, the above system model matrix expression is converted into a least squares form:

[0021]

[0022] in, θ1(k), θ2(k) and The expansion is as follows:

[0023]

[0024] The optimal estimates of y1(k), y2(k), θ1(k), and θ2(k) are defined as follows: and The optimal estimate of the system output is expressed as:

[0025]

[0026] The error between the optimal estimate and the actual output is defined in the formula as:

[0027]

[0028] The error matrix is ​​expressed in the form of:

[0029]

[0030] To achieve the optimal estimate, the sum of squared residuals needs to be minimized. The objective function is designed as follows:

[0031]

[0032] Finding the minimum variance, the objective function is the optimal estimate. and Find the partial derivative and make it equal to 0, then:

[0033]

[0034] Get parameters Least squares estimate:

[0035]

[0036] The optimal estimate of the system output is expressed as:

[0037]

[0038] In a preferred embodiment of the present invention, step 3 involves decoupling the identified system model. The coupling matrix of the known dual-input dual-output system is:

[0039]

[0040] The system control input is Constructing virtual control variables Substituting the dummy variables back into the system model expression yields:

[0041]

[0042] Verify whether the virtual control quantity U can be completely decoupled based on the inverse matrix of B. Solve for the inverse matrix of B using Gaussian elimination. Let the singular matrix B = R1L2 be as follows:

[0043]

[0044] The inverse matrix R1 can be solved. -1 The inverse matrix L2 -1 Then, through matrix operations Solve for B -1 This achieves system decoupling, ensuring a one-to-one correspondence between inputs and outputs, as shown in the following equation:

[0045]

[0046] At this point, the control input u can achieve the desired effect through the virtual control input U, expressed as u = B. -1 U, the decoupling principle diagram is attached. Figure 2 As shown, by examining the relationship between the control input and the virtual control input, it can be seen that, under the same output value setting, the control input and the virtual control input exhibit the same trend of change.

[0047] As a preferred embodiment of the present invention, the process of designing a linear active disturbance rejection controller to control the furnace gas flow rate u1 and the desuperheating water flow rate u2 in step 4 is as follows:

[0048] LESO stands for Linear Extended Observer, LSEF for Linear State Error Feedback, r is the given value, y is the actual system output, u is the control signal, z1 and z2 are the estimated values ​​of state variables x1 and x2, z3 is the observed estimated value of the unknown total disturbance f, and b0 is the estimated value of the gain b. The mathematical model of the second-order linear active disturbance rejection control system can be described as follows:

[0049]

[0050] Where ω is the unknown external disturbance of the system, g is the unknown total disturbance of the system, and b is the parameter of the controlled object. The second-order model can also be written as:

[0051]

[0052] Let x1 = y, Define x3 = f = g + (b - b0)u as the system's extended state. The state-space expression of the system is:

[0053]

[0054] y is obtained through LESO. The estimated value of f is as follows:

[0055]

[0056] Where β1, β2, and β3 are observer parameters, derived from the attached... Figure 1 It can be seen that,

[0057]

[0058] When LESO is accurately tuned, z1, z2, and z3 will track y respectively. f, Substitute the above equation into have to:

[0059] y = f - z³ + u₀ ≈ u₀

[0060] At this point, the system is equivalent to a standard form with two integral cascaded elements, and the system can be controlled by a PI controller, i.e.:

[0061]

[0062] Combining the above two equations and simplifying, we obtain the differential equation of the closed-loop system as shown in the following equation:

[0063]

[0064] The corresponding closed-loop transfer function of the system is as follows:

[0065]

[0066] LADRC block diagram, k p k d β1, β2, and β3 are respectively converted into controller bandwidth ω. c The functions of ω0 and the observer bandwidth ω0 are as follows:

[0067]

[0068] The expected equation will become as follows:

[0069]

[0070] Further simplifying the parameters, we get ω0 = 4ω c In summary, linear active disturbance rejection control only requires tuning ω. c Two controller parameters, b0 and b0, are sufficient to give the system good control performance. To obtain the optimal LADRC control performance, this paper uses the firefly algorithm parameter ω. c b0 is optimized to achieve stable control of the boiler main steam temperature.

[0071] As a preferred embodiment of the present invention, step 5 uses the firefly algorithm to optimize the linear active disturbance rejection controller parameter ω. cThe b0 process is as follows:

[0072] The two parameters of the linear active disturbance rejection controller are considered as a set of feasible solutions (ω) in space. c First, define the relative fluorescence brightness of the algorithm as: (b0)

[0073]

[0074] Where I0 represents the brightness value of an individual in the population, and j represents the spatial distance between individuals i and j.

[0075]

[0076] d represents the spatial dimension of the individual, i.e., the number of parameters to be optimized. γ is the light intensity absorption coefficient. As the light intensity decreases, the distance that a firefly can perceive each time becomes limited, so it is necessary to continuously iterate and gradually approach the optimal value. Relative brightness is defined as follows:

[0077]

[0078] Where β0 is the maximum attraction, which is usually set to 1, the firefly position update formula is defined as follows:

[0079]

[0080] in, Let be the spatial coordinates of fireflies i and j, ρ represent the current iteration number of the population, α∈[0,1] is the step size factor when updating the individual position, and rand is a random number in [0,1]. The ITAE index is selected as the objective function value of the firefly algorithm.

[0081]

[0082] A smaller ITAE metric indicates a better result.

[0083]

[0084] It can be seen that the better the objective function value, the brighter the firefly.

[0085] Beneficial effects

[0086] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0087] 1. This invention addresses the nonlinearity and multiple disturbances in the main steam temperature control process of gas-fired power generation boilers. It adopts a control strategy combining linear active disturbance rejection control and decoupling control. The Gaussian elimination method is used to decouple and eliminate the mutual coupling between furnace gas flow and low-temperature superheater, desuperheating water flow and high-temperature superheater outlet temperature. When the main steam temperature exhibits nonlinearity and large lag, linear active disturbance rejection control is used to improve the system's control performance and accuracy, thereby achieving stable control of the main steam temperature.

[0088] 2. This invention addresses the common practice of using traditional PID cascade control for main steam temperature control in thermal power boilers. While PID cascade control is simple to debug on-site, it has limited margin for good dynamic quality and cannot adapt to the nonlinear, multi-disturbance, and large time-delay characteristics of the main steam temperature control system. To address this issue, this solution effectively addresses the nonlinear, multi-disturbance, and large time-delay characteristics of the main steam temperature, saving labor costs and improving economic efficiency.

[0089] 3. While there are many advanced control technologies for main steam temperature in the prior art, such as prediction technology and neural network technology, they are more theoretical and mainly rely on simulation verification, with poor application in engineering fields. In contrast, this solution has the characteristics of strong popularization, easy on-site debugging, and good application in engineering fields. Attached Figure Description

[0090] Appendix Figure 1 Block diagram of main steam temperature control principle;

[0091] Appendix Figure 2 Control diagram for decoupling principle;

[0092] Appendix Figure 3 This is a flowchart of the Firefly algorithm. Detailed Implementation

[0093] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0094] Please see Figure 1-3 This invention provides a technical solution: a method for self-disturbing decoupling control of main steam temperature in a gas-fired boiler, comprising the following steps:

[0095] Step S1: The signal detection device measures the furnace gas flow signal, desuperheating water flow signal, desuperheater inlet temperature signal, and high-temperature superheater outlet temperature signal, and normalizes the measured data.

[0096] Step S2: Based on the normalized data, establish a dual-input dual-output system model with furnace gas flow rate and desuperheating water flow rate as inputs and desuperheater inlet temperature and high-temperature superheater outlet temperature as outputs. Use the least squares method to identify the model parameters.

[0097] Step S3: Use the Gaussian elimination variable decoupling method to decouple the identified system model, so that the dual-input dual-output system is decoupled into two single-input single-output systems;

[0098] Step S4: Design a linear active disturbance rejection controller to control the furnace gas flow and desuperheating water flow, so as to achieve stable control of the boiler main steam temperature;

[0099] Step S5: Introduce the Firefly Algorithm and use it to optimize the parameters of the linear active disturbance rejection controller, thereby improving the control quality of the main steam temperature control system.

[0100] In a further improvement, the signal detection device in step 1 is a temperature measuring device installed at the desuperheater inlet and the high-temperature superheater outlet of the gas-fired boiler steam-water system to measure the steam temperature at the desuperheater inlet and the steam temperature at the high-temperature superheater outlet, respectively. Flow measuring devices are installed at the furnace gas regulating valve and the desuperheating water regulating valve to measure the gas flow rate and the desuperheating water flow rate, respectively. Under conditions of variable load disturbances in the desuperheater inlet temperature, high-temperature superheater outlet temperature, gas flow rate, and desuperheating water flow rate, the signal detection device collects data every 5 minutes, for a total of 2000 sets of data. The normalized data is processed using the following formula:

[0101]

[0102] Where, x i For the measured signal sample data, x min x is the minimum value of the sample data. max x is the maximum value of the sample data. inorm For sample data x i The normalized value.

[0103] Further improved, the model expression for the dual-input dual-output system in step 2 is as follows:

[0104]

[0105] Where y1(k) is the desuperheater inlet temperature output, u1(k-τ) is the desuperheater inlet temperature input, y2(k) is the high-temperature superheater outlet temperature output, u2(k-τ) is the high-temperature superheater outlet temperature input, τ is the time delay coefficient, ξ1(k) and ξ2(k) are unmeasurable noise, and A(z) -1 ) and B(z) -1The shift operator constant coefficient polynomial is expanded as follows:

[0106]

[0107] Since the system noise is unmeasurable, the above system model expression is transformed into matrix form:

[0108]

[0109] In step 2, the least squares method is used to identify the model parameters. First, the above system model matrix expression is converted into a least squares form:

[0110]

[0111] in, θ1(k), θ2(k) and The expansion is as follows:

[0112]

[0113]

[0114] The optimal estimates of y1(k), y2(k), θ1(k), and θ2(k) are defined as follows: and The optimal estimate of the system output is expressed as:

[0115]

[0116] The error between the optimal estimate and the actual output is defined in the formula as:

[0117]

[0118] The error matrix is ​​expressed in the form of:

[0119]

[0120] To achieve the optimal estimate, the sum of squared residuals needs to be minimized. The objective function is designed as follows:

[0121]

[0122] Finding the minimum variance, the objective function is the optimal estimate. and Find the partial derivative and make it equal to 0, then:

[0123]

[0124] Get parameters Least squares estimate:

[0125]

[0126] The optimal estimate of the system output is expressed as:

[0127]

[0128] In a further improvement, step 3 decouples the identified system model, and the coupling matrix of the known dual-input dual-output system is:

[0129]

[0130] The system control input is Constructing virtual control variables Substituting the dummy variables back into the system model expression yields:

[0131]

[0132] Verify whether the virtual control quantity U can be completely decoupled based on the inverse matrix of B. Solve for the inverse matrix of B using Gaussian elimination. Let the singular matrix B = R1L2 be as follows:

[0133]

[0134] The inverse matrix R1 can be solved. -1 The inverse matrix L2 -1 Then, through matrix operations Solve for B -1 This achieves system decoupling, ensuring a one-to-one correspondence between inputs and outputs, as shown in the following equation:

[0135]

[0136] At this point, the control input u can achieve the desired effect through the virtual control input U, expressed as u = B. -1 U, the decoupling principle diagram is attached. Figure 2 As shown, by examining the relationship between the control input and the virtual control input, it can be seen that, under the same output value setting, the control input and the virtual control input exhibit the same trend of change.

[0137] In a further improvement, the process of designing a linear active disturbance rejection controller to control the furnace gas flow rate u1 and the desuperheating water flow rate u2 in step 4 is as follows:

[0138] LESO stands for Linear Extended Observer, LSEF for Linear State Error Feedback, r is the given value, y is the actual system output, u is the control signal, z1 and z2 are the estimated values ​​of state variables x1 and x2, z3 is the observed estimated value of the unknown total disturbance f, and b0 is the estimated value of the gain b. The mathematical model of the second-order linear active disturbance rejection control system can be described as follows:

[0139]

[0140] Where ω is the unknown external disturbance of the system, g is the unknown total disturbance of the system, and b is the parameter of the controlled object. The second-order model can also be written as:

[0141]

[0142] Let x1 = y, Define x3 = f = g + (b - b0)u as the system's extended state. The state-space expression of the system is:

[0143]

[0144] y is obtained through LESO. The estimated value of f is as follows:

[0145]

[0146] Where β1, β2, and β3 are observer parameters, derived from the attached... Figure 1 It can be seen that,

[0147]

[0148] When LESO is accurately tuned, z1, z2, and z3 will track y respectively. f, Substitute the above equation into have to:

[0149] y = f - z³ + u₀ ≈ u₀

[0150] At this point, the system is equivalent to a standard form with two integral cascaded elements, and the system can be controlled by a PI controller, i.e.:

[0151]

[0152] Combining the above two equations and simplifying, we obtain the differential equation of the closed-loop system as shown in the following equation:

[0153]

[0154] The corresponding closed-loop transfer function of the system is as follows:

[0155]

[0156] Regarding the appendix Figure 1 The LADRC block diagram, with k p k d β1, β2, and β3 are respectively converted into controller bandwidth ω. c The functions of ω0 and the observer bandwidth ω0 are as follows:

[0157]

[0158] The expected equation will become as follows:

[0159]

[0160] Further simplifying the parameters, we get ω0 = 4ω c In summary, linear active disturbance rejection control only requires tuning ω. c Two controller parameters, b0 and b0, are sufficient to give the system good control performance. To obtain the optimal LADRC control performance, this paper uses the firefly algorithm parameter ω. c b0 is optimized to achieve stable control of the boiler main steam temperature.

[0161] In a further improvement, step 5 uses the firefly algorithm to optimize the linear active disturbance rejection controller parameters ω. c The b0 process is as follows:

[0162] The two parameters of the linear active disturbance rejection controller are considered as a set of feasible solutions (ω) in space. c First, define the relative fluorescence brightness of the algorithm as: (b0)

[0163]

[0164] Where I0 represents the brightness value of an individual in the population, and j represents the spatial distance between individuals i and j.

[0165]

[0166] d represents the spatial dimension of the individual, i.e., the number of parameters to be optimized. γ is the light intensity absorption coefficient. As the light intensity decreases, the distance that a firefly can perceive each time becomes limited, so it is necessary to continuously iterate and gradually approach the optimal value. Relative brightness is defined as follows:

[0167]

[0168] Where β0 is the maximum attraction, which is usually set to 1, the firefly position update formula is defined as follows:

[0169]

[0170] in, Let be the spatial coordinates of fireflies i and j, ρ represent the current iteration number of the population, α∈[0,1] is the step size factor when updating the individual position, and rand is a random number in [0,1]. The ITAE index is selected as the objective function value of the firefly algorithm.

[0171]

[0172] A smaller ITAE metric indicates a better result.

[0173]

[0174] It can be seen that the better the objective function value, the brighter the firefly. The specific optimization process is shown in the attached figure. Figure 3 As shown.

[0175] The present invention and its embodiments have been described above illustratively. This description is not restrictive, and the figures shown are only one embodiment of the present invention; the actual structure is not limited thereto. Therefore, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for self-disturbing decoupling control of main steam temperature in a gas-fired boiler, characterized in that, Includes the following steps: Step S1: The signal detection device measures the furnace gas flow signal, desuperheating water flow signal, desuperheater inlet temperature signal, and high-temperature superheater outlet temperature signal, and normalizes the measured data. Step S2: Based on the normalized data, establish a dual-input dual-output system model with furnace gas flow rate and desuperheating water flow rate as inputs and desuperheater inlet temperature and high-temperature superheater outlet temperature as outputs. Use the least squares method to identify the model parameters. Step S3: Use the Gaussian elimination variable decoupling method to decouple the identified system model, so that the dual-input dual-output system is decoupled into two single-input single-output systems; Step S4: Design a linear active disturbance rejection controller to control the furnace gas flow and desuperheating water flow, so as to achieve stable control of the boiler main steam temperature; Step S5: Introduce the Firefly Algorithm and use it to optimize the parameters of the linear active disturbance rejection controller, thereby improving the control quality of the main steam temperature control system.

2. The method for self-disturbing decoupling control of main steam temperature in a gas-fired boiler according to claim 1, characterized in that: In step 1, the signal detection device is a temperature measuring device installed at the desuperheater inlet and high-temperature superheater outlet of the gas-fired boiler steam-water system to measure the steam temperature at the desuperheater inlet and the steam temperature at the high-temperature superheater outlet, respectively. Flow measuring devices are installed at the furnace gas regulating valve and the desuperheating water regulating valve to measure the gas flow rate and the desuperheating water flow rate, respectively. Under conditions of variable load disturbances in the desuperheater inlet temperature, high-temperature superheater outlet temperature, gas flow rate, and desuperheating water flow rate, the signal detection device collects data every 5 minutes, for a total of 2000 sets of data. Normalization is performed on the data using the following formula: ； in, For the measured signal sample data, The minimum value of the sample data. The maximum value of the sample data. For sample data The normalized value.

3. The method for self-disturbing decoupling control of main steam temperature in a gas-fired boiler according to claim 2, characterized in that: The expression for the dual-input dual-output system model in step 2 is as follows: ； in, The output temperature is the inlet temperature of the desuperheater. Input temperature for the desuperheater inlet. Output temperature at the outlet of the high-temperature superheater. Input for the high-temperature superheater outlet temperature. The time delay coefficient, and Unmeasurable noise and The constant-coefficient polynomial for the shift operator is expanded as follows: ； Since the system noise is unmeasurable, the above dual-input dual-output system model expression is transformed into matrix form: ； In step 2, the least squares method is used to identify the model parameters. First, the matrix expression above is converted into a least squares form: ； in, , , , , and The expansion is as follows: ； ； ； ； ； ； definition , , and The optimal estimate is , , and The optimal estimate of the system output is expressed as: ； The error between the optimal estimate and the actual output is defined in the formula as: ； The error matrix is ​​expressed in the form of: ； To achieve the optimal estimate, the sum of squared residuals needs to be minimized. The objective function is designed as follows: ； Finding the minimum variance, the objective function is the optimal estimate. and Find the partial derivative and make it equal to 0, then: ； Get parameters Least squares estimate: ； The optimal estimate of the system output is expressed as: 。 4. The method for self-disturbing decoupling control of main steam temperature in a gas-fired boiler according to claim 3, characterized in that: In step 3, the identified system model is decoupled. The coupling matrix of the known dual-input dual-output system is: ； The system control input is Constructing virtual control variables Substituting the dummy variables back into the system model expression yields: ； according to Verification of virtual control quantity using inverse matrix Can complete decoupling be achieved? This can be solved using Gaussian elimination. Let the inverse matrix be the singular matrix. as follows: ； It can be solved inverse matrix and inverse matrix Then, through matrix operations Solve This achieves system decoupling, ensuring a one-to-one correspondence between inputs and outputs, as shown in the following equation: ； At this time, control input It can be controlled via virtual input To achieve the desired effect, the expression is: The decoupling principle works by understanding the relationship between the control input and the virtual control input. When the same output value is set, the control input and the virtual control input will have the same trend of change.

5. The method for self-disturbing decoupling control of main steam temperature in a gas-fired boiler according to claim 4, characterized in that: In step 4, a linear active disturbance rejection controller is designed to control the furnace gas flow rate. and desuperheating water flow rate The process is as follows: LESO stands for Linear Extended Observer, and LSEF stands for Linear State Error Feedback. For a given value, This is the actual output of the system. For control signals, , State variables , The estimated value, Total Unknown Disturbance The observed estimates, Gain The estimated value, the mathematical model of the second-order linear active disturbance rejection control system can be described as: ； in, For unknown external disturbances to the system, The total disturbance of the system is unknown. For the parameters of the controlled object, the second-order model can also be written as: ； make , ,definition This is a system expansion state. The state-space expression of the system is: ； Obtained through LESO , , The estimated values ​​are as follows: ； in , , For observer parameters, ； When LESO is accurately tuned , , Will track separately , , Substitute the above formula into have to: ； At this point, the system is equivalent to a standard form with two integral cascaded elements, and the system can be controlled by a PI controller, i.e.: ； Combining the above two equations and simplifying, we obtain the differential equation of the closed-loop system as shown in the following equation: ； The corresponding closed-loop transfer function of the system is as follows: ； LADRC block diagram, , and , , These are respectively converted into controller bandwidth. The function and observer bandwidth The function is as follows: ； The expected equation will become as follows: ； Further simplification of the parameters, namely In summary, linear active disturbance rejection control only requires tuning. , Two controller parameters are sufficient to achieve good system control performance. To obtain optimal LADRC control performance, this paper uses the Firefly algorithm parameters. , Optimization was carried out to achieve stable control of the boiler's main steam temperature.

6. The method for self-disturbing decoupling control of main steam temperature in a gas-fired boiler according to claim 5, characterized in that: In step 5, the firefly algorithm is used to optimize the parameters of the linear active disturbance rejection controller. , The process is as follows: The two parameters of the linear active disturbance rejection controller are considered as a set of feasible solutions in space. First, define the relative fluorescence intensity of the algorithm as: ； in, This represents the brightness value of an individual within the population. and Spatial distance: ； This represents the spatial dimension of an individual, i.e., the number of parameters to be optimized. Let be the light intensity absorption coefficient. As the light intensity decreases, the distance that a firefly can perceive each time becomes limited. Therefore, iterative processes are needed to gradually approach the optimal value. The relative brightness is defined as follows: ； in, To maximize attraction, it is generally set to 1. The firefly position update formula is defined as follows: ； in, , Let i and j be the spatial coordinates of fireflies. This indicates the current iteration number of the population. The step size factor for individual position updates. For random numbers in the range [0,1], the ITAE index is chosen as the objective function value for the firefly algorithm. ； A smaller ITAE metric indicates a better result. ； It can be seen that the better the objective function value, the brighter the firefly.

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