Fuzzy model predictive control method for coal-fired boiler-steam turbine system

Abstract

The invention discloses a fuzzy model predictive control method for a coal-fired boiler-steam turbine system, and mainly relates to the technical field of intelligent environmental protection. Comprising the following steps: S1, constructing a fuzzy prediction model by using Takagi-Sugeno fuzzy logic; s2, constructing a control efficiency evaluation index, and establishing a dual-channel event triggering mechanism; s3, constructing a model prediction controller, constructing an objective function based on the prediction model, and solving an optimal control signal at each sampling moment; s4, performing offline training on the fuzzy prediction model through actual data of the boiler-steam turbine system to obtain a prediction model for a control system; s5, on the basis of a dual-channel event triggering mechanism, updating the prediction model according to real-time data through an online updating strategy; according to the method, the steam drum pressure, the generated power and the steam drum water level can be efficiently and accurately controlled, the calculation overhead can be effectively reduced, and the real-time performance and the stability of a control system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent environmental protection, and specifically to a fuzzy model predictive control method for a coal-fired boiler - steam turbine system. Background Art

[0002] In the traditional control system of a coal-fired boiler - steam turbine (BTS), due to the influence of factors such as coal quality fluctuations, load changes, and external disturbances, the dynamic characteristics of the system are complex and highly nonlinear, resulting in difficulty for conventional control methods (such as PID control, classical MPC, etc.) to balance rapid response and steady-state accuracy.

[0003] Currently, data-driven modeling methods have received extensive attention in the optimal control of boiler combustion. Among them, the T-S fuzzy model, as a piecewise affine model that can effectively describe nonlinear systems, has important application value in the control of the BTS system. Through the predictive control (FMPC) based on the T-S (Takagi-Sugeno) fuzzy model, the control input can be optimized within a limited prediction range, enabling the system state to be maintained near the desired trajectory. However, traditional FMPC methods usually require high-frequency updates of the control strategy, with a large computational burden and difficulty in meeting the online calculation requirements in actual industrial applications. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems existing in the prior art, and provide a dual-channel event-triggered fuzzy model predictive control method for a coal-fired boiler - steam turbine system. This method constructs a T-S fuzzy prediction model and combines a dual-channel event-triggered mechanism to achieve efficient and precise control of the drum pressure, power generation, and drum water level. The core innovation of this method lies in the introduction of a dual-channel event-triggered mechanism for trigger determination during the controller calculation and prediction model update process, and only performing calculations and adjustments at necessary moments, thereby effectively reducing the computational overhead and improving the real-time performance and stability of the control system.

[0005] To achieve the above object, the present invention is realized through the following technical solutions:

[0006] A fuzzy model predictive control method for a coal-fired boiler - steam turbine system, comprising the steps of:

[0007] S1. Construct a fuzzy prediction model using Takagi-Sugeno fuzzy logic;

[0008] S2. Construct a control efficiency evaluation index and establish a dual-channel event-triggered mechanism;

[0009] The control efficiency evaluation index includes: the accuracy of the prediction model and the control effect. Among them, the accuracy of the prediction model is reflected by the model training error, and the control effect is reflected by the tracking error and the response time efficiency;

[0010] The dual-channel event-triggering mechanism is as follows: The prediction model and the control signal are updated only when the accuracy of the prediction model decreases and the control effect deteriorates.

[0011] S3. Construct a model predictive controller, construct an objective function based on the prediction model, and solve for the optimal control signal at each sampling instant.

[0012] S4. Offline train the fuzzy prediction model with the actual data of the boiler-turbine system to obtain the prediction model for the control system.

[0013] S5. Based on the dual-channel event-triggering mechanism, use the online update strategy to update the prediction model according to the real-time data.

[0014] Preferably, in step S1:

[0015] Select the state variables of the system as: x1, x2, x3, where x1 is the drum pressure, with the unit of kg / cm 2 ; x2 is the power generation, with the unit of MW; x3 is the steam density, with the unit of kg / cm3;

[0016] Select the input variables of the system as u1, u2, u3, which are the normalized valve positions for controlling the fuel, the steam flowing to the turbine, and the feedwater flow rate, respectively.

[0017] The control value of the system and its rate of change are also subject to the following constraints:

[0018]

[0019] Select the output of the system as: y1, y2, y3, where y1 is the drum pressure, with the unit of kg / cm 2 ; y2 is the power generation, with the unit of MW; y3 is the drum water level, with the unit of cm;

[0020] Then establish a fuzzy prediction model based on the actual operation data of the above variables.

[0021] Preferably, in step S2, the model training error is expressed as:

[0022]

[0023] where, y i (k) is the actually measured output, is the true output value, and ||·||2 represents the Euclidean distance, which reflects the error between the predicted output and the actual output;

[0024] Then define two variables to reflect the prediction error and its change:

[0025]

[0026] ε(k) = σ(k) - σ(k - 1)

[0027] Among them, σ(k) reflects the magnitude of the model error, and ε(k) reflects the change direction of the model error.

[0028] Preferably, in step S2, the control performance evaluation index is defined as:

[0029] E c (k) = βE te (k) + γE rt (k)

[0030] Among them, β and γ are weight factors used to balance the influence of tracking accuracy and response time on control performance;

[0031] E te (k) is the tracking error, and E te (k) is expressed as:

[0032] E te (k) = ||x(k) - x r (k)||2

[0033] E rt (k) is the response time efficiency, and E rt (k) is expressed as:

[0034]

[0035] Among them, represents the rolling optimization objective function starting from the current moment k within the prediction horizon N, which is usually used to evaluate the comprehensive performance of the system in the next N steps. x and u are the state and control input of the system respectively, indicating the performance of the control strategy within the time interval.

[0036] Preferably, in step S3, the optimization performance index for constructing the model predictive controller is as follows:

[0037]

[0038] Among them, J(k) is the optimization objective function, y(k) is the actual output of the system, is the desired output, representing the reference trajectory predicted by the model, u(k) is the control input, and ||·|| represents the norm operation, where ||u(k)|| 2 represents the energy of the control input to ensure that the control input does not become too large during the optimization process;

[0039] The control input at each sampling moment is:

[0040] Δu(k) = u(k) - u d (k)

[0041] The threshold condition for the tracking error is as follows:

[0042] E te (k) > Λ

[0043] where E te (k) represents the tracking error, Λ > 0 is a constant, serving as the threshold for event-triggered control, ensuring that the controller only executes the control law when the error exceeds a certain limit to reduce the computational burden.

[0044] Preferably, a second trigger condition based on response time efficiency is introduced:

[0045]

[0046] where λ ≥ 1 and ν ≤ 1 are positive constants; e(k) = y r (k) - y(k) represents the tracking error at the current time step $k$.

[0047] where λ ≥ 1 and ν ≤ 1 are positive constants, used to balance the influence of response time efficiency and control input change on the system performance; E rt (k) is the response time efficiency, measuring the dynamic response ability of the system; e(k) = y r (k) - y(k) is the tracking error, y r (k) is the reference output, y(k) is the actual output, and |e(k)| reflects the output error at the current moment; and R Δ u 2 are weight parameters, respectively used to adjust the influence ratio of the error term and the control input change term, ensuring that the trigger condition takes into account the balance between system response and control change.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] To ensure that the drum pressure, power generation, and drum water level of the coal-fired boiler - steam turbine system are stabilized at the target values, the present invention proposes a dual-event-triggered fuzzy model predictive control system, and establishes an online update strategy for the predictive model based on T-S fuzzy logic to improve the prediction accuracy. In order to reduce the consumption of computing resources and communication costs, a dual-channel event-triggered mechanism with a control efficiency evaluation index is innovatively introduced, and the predictive model and control input are dynamically updated according to the control effect, so as to ensure that the system conducts efficient intervention under stable control, and realizes the accurate prediction and control of the drum pressure, power generation, and drum water level of the coal-fired boiler - steam turbine system. Description of the Drawings

[0050] Figure 1 It is the structure diagram of the control system of the present invention;

[0051] Figure 2 It is the schematic diagram of the membership function;

[0052] Figure 3 It is the structure diagram of the boiler combustion system. Specific implementation manners

[0053] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by this application.

[0054] The present invention provides a dual-channel event-triggered fuzzy model predictive control method for a coal-fired boiler-turbine system. First, historical operation data is used for offline training to obtain a fuzzy rule base that can describe the dynamic behavior of the system. Subsequently, during the actual operation process, an online update strategy is adopted to correct the model to cope with external disturbances and operating conditions changes, and improve the model prediction accuracy; based on the constructed T-S fuzzy prediction model, a model predictive control (MPC) framework is designed. The MPC controller solves the optimal control input at each sampling moment to minimize the system deviation and optimize the operating performance of the boiler-turbine system under the condition of meeting the control constraints; based on the real-time monitored system error and prediction error, the accuracy of the T-S fuzzy model is judged. When the prediction error exceeds the set threshold, online model update is triggered to ensure that the prediction model always has a high accuracy. The specific steps of the above method are as follows:

[0055] Step 1: First, the model is offline trained through the actual data of the boiler-turbine system to obtain a prediction model for the control system. Then, an online update strategy is adopted to update the model according to the real-time data, thereby improving the prediction accuracy.

[0056] Step 2: Design an MPC controller, construct an objective function based on the prediction model, and solve the optimal control signal at each sampling moment.

[0057] Step 3: Design a control efficiency evaluation index and establish a dual-channel event-triggered mechanism. Only when the accuracy of the prediction model decreases and the control effect deteriorates will the prediction model and control signal be updated, avoiding unnecessary computational overhead, thereby saving resources and time.

[0058] In the present invention, the event-triggered control (ETC) technology is introduced into the T-S fuzzy predictive control framework to reduce the frequency of control updates while ensuring control performance. The event-triggered mechanism dynamically adjusts the execution time of the controller according to the changes in the system state, and performs calculation updates only when necessary, thereby reducing the computational cost and communication burden and improving the resource utilization efficiency of the system. In the control of the boiler-turbine system, the event-triggered FMPC method can not only improve the control accuracy of the drum pressure, power generation, and drum water level, but also maintain a better combustion efficiency under the condition of large load fluctuations, so as to realize the efficient and low-carbon operation of the coal-fired boiler.

[0059] Example 1: As shown in the attached Figure 1 figure, the present invention relates to a fuzzy model predictive control method for a coal-fired boiler-turbine system, which specifically includes:

[0060] First, establish fuzzy rules. The i-th fuzzy rule is established as follows:

[0061] Rule i: IF and THEN

[0062] y(k + 1) = C i x(k) + D i

[0063] Where represents the number of fuzzy rules, represents the fuzzy set, and are parameter matrices to be identified. The fuzzy set is described by a membership function, and the formats of the three membership functions are unified, as shown in Figure 2 the figure:

[0064] The fuzzy set mainly consists of three elements: smaller, middle, and larger, and their membership functions are respectively expressed as:

[0065]

[0066]

[0067] Where μ represents the membership value.

[0068] h i is the normalized membership function of the i-th fuzzy rule:

[0069]

[0070] The predicted output of the system can be expressed as:

[0071]

[0072] All the parameters to be identified are expressed as:

[0073] Ψ = [A1 B1 C1 D1 … A i B i C i D i T

[0074] Prediction error is inevitable. To reduce the error, the previous prediction error \(e_p(k - 1)\) is used for feedback to minimize the current error:

[0075]

[0076] The goal of the training process is to minimize the cost function:

[0077]

[0078] where T is the total number of training samples, and Ψ represents the parameter vector of the fuzzy system.

[0079] To optimize the cost function, calculate its gradient with respect to the parameter vector Ψ:

[0080]

[0081] The parameter Ψ is iteratively updated using the gradient descent method:

[0082]

[0083] η > 0 is the learning rate, Ψ (k) represents the number of iterations, represents the gradient.

[0084] The stopping conditions for training are expressed as follows:

[0085] 1) The norm of the gradient is less than the preset threshold:

[0086]

[0087] where ∈ is a small value.

[0088] 2) The change in the cost function is negligible:

[0089]

[0090] where δ is the minimum value of the change.

[0091] 3) Reaching the maximum number of iterations t max .

[0092] ​After training is completed, the optimized parameter vector Ψ is obtained, which minimizes the prediction error and provides the trained fuzzy model.

[0093] When the FMPC controller is running, the prediction model can be updated online based on the real-time data of the system to enhance the effectiveness of MPC. First, the model training error is expressed as:

[0094]

[0095] where y i (k) is the actually measured output, is the true output value, ||·||2 represents the Euclidean distance, reflecting the error between the predicted output and the actual output;

[0096] Then two variables are defined to reflect the prediction error and its change:

[0097]

[0098] ε(k) = σ(k) - σ(k - 1)

[0099] where σ(k) and ε(k) reflect the magnitude and the change direction of the model error respectively.

[0100] The tracking error is expressed as:

[0101] E te (k) = ||x(k) - x r (k)||2

[0102] The response rate of the system to the control input is defined as the response time efficiency E rt (k):

[0103]

[0104] The control performance evaluation index is defined as:

[0105] E c (k) = βE te (k) + γE rt (k)

[0106] where β and γ are weight factors, balancing the influence of tracking accuracy and response time on the control performance.

[0107] The event trigger conditions are as follows:

[0108] Event1 = <σ(k)>ξ1, ε(k)>0>

[0109] Event2 = <E c (k)<ξ3, σ(k)>ξ2>

[0110] Event3 = <E c (k)<ξ3, ε(k)>0>

[0111] Event4 = <Other conditions>

[0112] Where ξ1 and ξ2 are prediction error thresholds, satisfying ξ1 > ξ2. In addition, ξ3 is the control efficiency threshold. Specifically, ξ1 represents the maximum error allowed by the model, while ξ2 represents the acceptable error threshold.

[0113] In addition, the choice of ξ2 plays a crucial role in balancing model accuracy and computational cost. A smaller ξ2 will increase the frequency of model updates, thereby improving accuracy, but the computational cost will also be higher. On the contrary, a larger ξ2 will reduce the update frequency, possibly allowing larger prediction errors to persist, but the computational burden is lower.

[0114] Event 1 occurs when the prediction error increases in an undesired direction. Events 2 and 3 indicate that when the control efficiency is below the threshold, online model updates are required. Specifically: Event 2 indicates that the control efficiency is low and the prediction error is large, and an update is needed to improve accuracy. Event 3 occurs when the prediction error increases and the control efficiency is low. Event 4 occurs when the model accuracy is low but the control effect is still satisfactory, or under other specific conditions. In these cases, the model is not updated immediately to save computational resources. The model is only updated when its accuracy drops to affect the control effect. This method minimizes the computational burden while ensuring good control effects.

[0115] The update rules triggered by events are as follows:

[0116]

[0117] Event4 → A3: Ψ(k + 1) = Ψ(k)

[0118] Where 1 > β1 > β2 > 0 are different learning rates for the corresponding parameter update strategies.

[0119] Then design an MPC controller, and construct the optimization performance index as shown below:

[0120]

[0121] Where J(k) is the optimization objective function, y(k) is the actual output of the system, is the desired output, representing the reference trajectory predicted by the model, u(k) is the control input, ||·|| represents the norm operation, where ||u(k)|| 2 represents the energy of the control input, ensuring that the control input does not become too large during the optimization process.

[0122] The control input at each sampling instant can be expressed as the deviation with respect to the desired input:

[0123] Δu(k) = u(k) - u d (k)

[0124] Then, a threshold condition for the tracking error is established:

[0125] E te (k) > Λ

[0126] where Λ > 0 is a constant that allows the control law to be executed based on event triggering.

[0127] To further improve the system performance, a second triggering condition based on response time efficiency is introduced:

[0128]

[0129] where λ ≥ 1 and v ≤ 1 are positive constants. e(k) = y r (k) - y(k) represents the tracking error at the current time step $k$. This condition ensures that the control law is triggered not only based on the tracking error but also takes into account the response rate of the system, enabling the control system to be adjusted more dynamically.

Claims

1. A fuzzy model predictive control method for a coal-fired boiler - steam turbine system, characterized in that, Including the steps: S1. Construct a fuzzy prediction model using Takagi - Sugeno fuzzy logic; S2. Construct an evaluation index for control efficiency and establish a dual - channel event - triggered mechanism; The evaluation index for control efficiency includes: the accuracy of the prediction model and the control effect. Among them, the accuracy of the prediction model is reflected by the model training error, and the control effect is reflected by the tracking error and the response - time efficiency; The dual - channel event - triggered mechanism is: only update the prediction model and the control signal when the accuracy of the prediction model decreases and the control effect deteriorates; S3. Construct a model predictive controller, based on the prediction model, construct an objective function, and solve the optimal control signal at each sampling time; S4. Offline train the fuzzy prediction model with the actual data of the boiler - turbine system to obtain a prediction model for the control system; S5. Based on the dual - channel event - triggered mechanism, use an online update strategy to update the prediction model according to real - time data.

2. The fuzzy model predictive control method for a coal-fired boiler - steam turbine system according to claim 1, characterized in that, In step S1: The state variables of the selected system are: x1, x2, x3, where x1 is the drum pressure, with the unit of kg / cm 2 ; x2 is the power generation, with the unit of MW; x3 is the steam density, with the unit of kg / cm3; Select the input variables of the system as u1, u2, u3, which are the normalized valve positions for controlling fuel, steam flowing to the turbine, and feed - water flow respectively; The control value of the system and its change rate are also subject to the following constraints: The outputs of the selection system are: y1, y2, y3, where y1 is the drum pressure in kg / cm 2 ; y2 is the power generation in MW; y3 is the drum water level in cm; Then establish a fuzzy prediction model based on the actual operation data of the above variables.

3. A fuzzy model predictive control method for a coal-fired boiler - steam turbine system according to claim 1, characterized in that, In step S2, the model training error is expressed as: where y i (k) is the actually measured output, is the true output value, ||·||2 represents the Euclidean distance, reflecting the error between the predicted output and the actual output; Then define two variables to reflect the prediction error and its change: σ(k)=Γ(k)-Γ(k - 1) ε(k)=σ(k)-σ(k - 1) where σ(k) reflects the magnitude of the model error, and ε(k) reflects the change direction of the model error.

4. A fuzzy model predictive control method for a coal-fired boiler - steam turbine system according to claim 1, characterized in that In step S2, the control performance evaluation index is defined as: E c E(k) = βE te + γE(k) rt (k) where β and γ are weight factors used to balance the influence of tracking accuracy and response time on control performance; E te (k) is the tracking error, E te (k) is expressed as: E te (k) = ||x(k) - x r (k)||² E rt (k) is the response time efficiency, E rt (k) is expressed as: Among them, represents the receding horizon optimization objective function starting from the current time k within the prediction horizon N, which is usually used to evaluate the comprehensive performance of the system in the next N steps. x and u are the state and control input of the system respectively, representing the performance of the control strategy within the time interval.

5. A fuzzy model predictive control method for a coal-fired boiler-steam turbine system according to claim 1, characterized in that, In step S3, the optimization performance index for constructing the model predictive controller is as follows: Among them, J(k) is the optimization objective function, y(k) is the actual output of the system, is the desired output, representing the reference trajectory predicted by the model, u(k) is the control input, ||·|| represents the norm operation, where ||u(k)|| 2 represents the energy of the control input to ensure that the control input does not become too large during the optimization process; The control input at each sampling time is: Δu(k) = u(k) - u d (k) The threshold condition for the tracking error is: E te (k)>Λ Among them, E te (k) represents the tracking error, Λ>0 is a constant, serving as the threshold for event-triggered control to ensure that the controller only executes the control law when the error exceeds a certain limit, so as to reduce the computational burden.

6. A fuzzy model predictive control method for a coal-fired boiler-steam turbine system according to claim 5, characterized in that Introduce a second trigger condition based on the response - time efficiency: Among them, λ≥1 and ν≤1 are positive constants used to balance the response time efficiency and the impact of control input changes on system performance; E rt (k) is the response time efficiency, which measures the dynamic response ability of the system; e(k) = y r (k) - y(k) is the tracking error, where y r (k) is the reference output and y(k) is the actual output, and |e(k)| reflects the output error at the current moment; and R Δ u 2 are weight parameters used to adjust the influence proportions of the error term and the control input change term respectively, ensuring that the triggering condition takes into account the balance between system response and control change.

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