Method for controlling furnace temperature based on RBF neural network double-cross amplitude limiting PID

Abstract

The invention relates to the field of blast furnace temperature control, in particular to a method for controlling furnace temperature based on double-cross amplitude limiting PID of an RBF neural network, which comprises the following steps: establishing the RBF neural network, training the RBF neural network by using historical data of a blast furnace, and performing online fine tuning on the RBF neural network by using real-time data of the blast furnace to obtain the RBF neural network capable of reflecting dynamic change of a blast furnace system in real time. The method comprises the following steps: establishing a double-cross amplitude-limiting PID controller, taking the output of an RBF neural network reflecting the dynamic change of a blast furnace system in real time as the input of the double-cross amplitude-limiting PID controller, combining the RBF neural network with the double-cross amplitude-limiting PID controller to form a closed-loop control system, establishing a control strategy, and adjusting the parameters of the double-cross amplitude-limiting PID controller in real time. According to the method, the precision and the stability of a furnace temperature control system are improved by combining the self-learning and self-adaptive capabilities of a radial basis function (RBF) neural network and a double-cross amplitude limiting PID control strategy.

Description

Technical Field

[0001] The invention relates to the field of blast furnace temperature control, in particular to a muffle furnace temperature control method used in stainless steel strip production. Background Art

[0002] In modern industrial production, furnace temperature control is a key link to ensure product quality and production efficiency. Traditional PID control methods are widely used in the field of temperature control due to their simplicity and robustness. However, when faced with nonlinear, time-varying and large hysteresis systems, the control performance of traditional PID control is often unsatisfactory, making it difficult to achieve high-precision temperature control. Summary of the invention

[0003] The purpose of the present invention is to provide a method for controlling furnace temperature based on RBF neural network double cross-limiting PID, which introduces RBF neural network to perform nonlinear compensation on the system and combines double cross-limiting control strategy to achieve high-precision control of furnace temperature and improve the robustness and stability of the system.

[0004] The technical scheme adopted by the present invention is: a method for controlling furnace temperature based on RBF neural network double cross-limiting PID, establishing an RBF neural network, using historical data of a blast furnace to train the RBF neural network, using real-time data of the blast furnace to perform online fine adjustment on the RBF neural network, obtaining an RBF neural network capable of reflecting the dynamic changes of a blast furnace system in real time, establishing a double cross-limiting PID controller, using the output of the RBF neural network capable of reflecting the dynamic changes of the blast furnace system in real time as the input of the double cross-limiting PID controller, combining the RBF neural network with the double cross-limiting PID controller to form a closed-loop control system, establishing a control strategy, and adjusting the parameters of the double cross-limiting PID controller in real time.

[0005] Establishing RBF neural network includes the following contents

[0006] Input layer, the input layer receives the state variables of the control system, including the following variables:

[0007] Temperature error: e(t) = T set -T(t), where T set is the temperature setting value, T(t) is the actual temperature value at time t, and e(t) is the temperature error at time t;

[0008] Temperature error change rate: Δe(t) = e(t) - e(t-1), e(t-1) is the temperature error at time t-1, Δe(t) is the temperature error change rate at time t;

[0009] The input variables form the input vector: x(t) = [e(t), Δe(t)] T, x(t) is the input vector at time t; T is the transpose;

[0010] Hidden layer: The hidden layer performs nonlinear mapping on the input data through radial basis functions. The number of neurons N in the hidden layer is determined by the specific application and experience.

[0011] Definition of radial basis function: Each hidden layer neuron corresponds to a radial basis function, which is in the form of:

[0012] in, is the output of the i-th hidden layer neuron, N ≥ i ≥ 1, c i is the center vector of the ith radial basis function, σ i is the width parameter of the i-th radial basis function;

[0013] Calculate the radial basis function output. For each input vector x(t), calculate the output of all hidden layer neurons: c i1 and c i2 are the two center coordinates of the i-th hidden layer neuron;

[0014] Output layer: The output layer performs weighted summation on the outputs of the hidden layer neurons to obtain the control gain K(t);

[0015] The output vector h(x(t)) of the hidden layer neuron is: h(x(t))=[φ1(x(t)),φ2(x(t)),...,φ N (x(t))] T , where the output K(t) calculation formula of the output layer is:

[0016] K(t)=w T h(x(t))+b,w=[w1,w2,...,w N ] T is the weight vector, b is the bias term, and w i is the weight vector of the i-th neuron in the output layer;

[0017] The parameter that the RBF neural network needs to learn and optimize is c i , σ i 、w i , b;

[0018] Parameter learning and optimization

[0019] The loss function is the mean square error MSE:

[0020] Among them, K target (t) is the target gain;

[0021] Use the gradient descent method to minimize the loss function. For each parameter, calculate the gradient of the loss function and update the parameter value. The following is the specific update formula:

[0022] The weight vector w of the i-th neuron in the output layer i Update: Where η is the learning rate;

[0023] Update of bias term b: b(t) is the bias term at time t, and b(t+1) is the bias term at time t+1;

[0024] The center vector c of the i-th radial basis function i Update:

[0025] Among them, c i (t) is the center vector of the i-th radial basis function at time t, c i+1 (t) is the center vector of the i-th radial basis function at time t+1;

[0026] The width parameter σ of the i-th radial basis function i Update: σ i (t) is the width parameter of the i-th radial basis function at time t, σ i (t+1) is the width parameter of the i-th radial basis function at time t+1; the partial derivative of the loss function with respect to the weight: The partial derivative of the loss function with respect to the bias term b: The loss function is about c i The partial derivative of : in,

[0027]

[0028] The loss function is about σ i The partial derivative of :

[0029] in, The establishment of a dual cross-limited PID controller includes the following contents

[0030] The output of the PID controller is the control signal u(t), which is expressed as: Among them, K p is the proportional gain, K i is the integral gain, K d is the differential gain, K p , K i , K d Dynamically adjusted by the output of the RBF neural network;

[0031] Dynamic adjustment formula, the output of the RBF neural network is K(t), and the parameters of the PID controller are defined as: K p =K(t),K i =αK(t),K d =βK(t), where α and β are constants;

[0032] The control strategy includes a double cross-limited gas furnace temperature control, and the double cross-limited gas furnace temperature control includes the following contents: The heat balance equation of the gas furnace is: Where T(t) is the furnace temperature at time t, C is the heat capacity of the furnace, Q in (t) is the input heat at time t, generated by gas combustion, Q out (t) is the output heat at the moment, including the heat loss in the furnace and the heat transferred to the process medium, Q load (t) is the change in heat demand due to the change in strip thickness and speed at time t;

[0033] The heat generated by gas combustion is expressed as: Q in (t)=∈F gas (t)H gas , where ∈ is the combustion efficiency, which is usually related to the air-fuel ratio λ, and F gas (t) is the gas flow rate at time t, H gas is the lower heating value LHV of the gas;

[0034] The change in heat demand caused by the steel belt load is expressed as: Q load (t) = k·v(t)·h(t), where v(t) is the speed of the steel strip at time t, h(t) is the thickness of the steel strip at time t, and k is a constant representing the heat required for the steel strip per unit thickness and speed. 5. A method for controlling furnace temperature based on RBF neural network double cross-limiting PID according to claim 4, characterized in that: the double cross-limiting gas furnace temperature control also includes the following contents

[0035] Gas flow F gas The setting of (t) is determined by the temperature controller. Using the PI controller, the calculation formula for the gas flow is:

[0036] Among them: F gas,load (t) = k·v(t)·h(t) is the gas flow rate adjusted according to the thickness and speed of the steel strip;

[0037] Air flow rate F air The setting of (t) is determined according to the gas flow rate and the air-fuel ratio λ:

[0038] F air (t) = λ·F gas (t)

[0039] The selection of the air-fuel ratio λ needs to take into account the completeness and economy of combustion, and λ is generally taken between 8 and 11.

[0040] Limiting mechanism

[0041] Gas flow limiter The purpose of gas flow limiter is to ensure that the gas is operated within a safe range to avoid excessive combustion or insufficient gas supply;

[0042] Gas flow limit F gas_max : Determined by safety considerations, or by the maximum allowable air flow,

[0043]

[0044] Gas flow lower limit F gas_min : Determined by the minimum air flow rate, ensuring the minimum air requirement during the combustion process;

[0045]

[0046] Air flow limiter The purpose of air flow limiter is to ensure that the air flow is within a reasonable range, neither too little to cause incomplete combustion nor too much to cause energy loss;

[0047] Air flow upper limit F air_max : Determined by the maximum allowable gas flow rate, F air_max =λ max ·F gas (t);

[0048] Air flow lower limit F air_min : Determined by the minimum allowable gas flow rate, F air_min =λ min ·F gas (t).

[0049] The beneficial effects of the present invention are as follows: the present invention utilizes the self-learning and self-adaptive capabilities of the RBF neural network to optimize the parameters of the PID controller, and avoids overshoot and oscillation in the control process through a double cross-limiting strategy, thereby achieving accurate furnace temperature control. Through the implementation of the present invention, the accuracy and response speed of furnace temperature control can be significantly improved, temperature fluctuations can be reduced, and product quality and production efficiency can be improved. At the same time, the method has strong robustness, can effectively deal with the problems of system nonlinearity, time-varying and large lag, and enhance the stability and reliability of the system. DETAILED DESCRIPTION

[0050] A method of controlling furnace temperature by double cross-limiting PID based on RBF neural network is proposed. RBF neural network is established.

[0051] Establishing RBF neural network includes the following contents

[0052] Input layer, the input layer receives the state variables of the control system, including the following variables:

[0053] Temperature error: e(t) = T set -T(t), where T set is the temperature setting value, T(t) is the actual temperature value at time t, and e(t) is the temperature error at time t;

[0054] Temperature error change rate: Δe(t) = e(t) - e(t-1), e(t-1) is the temperature error at time t-1, Δe(t) is the temperature error change rate at time t;

[0055] The input variables form the input vector: x(t) = [e(t), Δe(t)] T , x(t) is the input vector at time t; T is the transpose;

[0056] Hidden layer: The hidden layer performs nonlinear mapping on the input data through radial basis functions. The number of neurons N in the hidden layer is determined by the specific application and experience.

[0057] Definition of radial basis function: Each hidden layer neuron corresponds to a radial basis function, which is in the form of:

[0058] in, is the output of the i-th hidden layer neuron, N ≥ i ≥ 1, c i is the center vector of the ith radial basis function, σ i is the width parameter of the i-th radial basis function;

[0059] Calculate the radial basis function output. For each input vector x(t), calculate the output of all hidden layer neurons: c i1 and c i2 are the two center coordinates of the i-th hidden layer neuron;

[0060] Output layer: The output layer performs weighted summation on the outputs of the hidden layer neurons to obtain the control gain K(t);

[0061] The output vector h(x(t)) of the hidden layer neuron is: h(x(t))=[φ1(x(t)),φ2(x(t)),...,φ N (x(t))] T , where the output K(t) calculation formula of the output layer is:

[0062] K(t)=w T h(x(t))+b,w=[w1,w2,...,w N ]T is the weight vector, b is the bias term, and w i is the weight vector of the i-th neuron in the output layer;

[0063] The parameter that the RBF neural network needs to learn and optimize is c i , σ i 、w i , b;

[0064] Parameter learning and optimization

[0065] The loss function is the mean square error MSE:

[0066] Among them, K target (t) is the target gain;

[0067] Use the gradient descent method to minimize the loss function. For each parameter, calculate the gradient of the loss function and update the parameter value. The following is the specific update formula:

[0068] The weight vector w of the i-th neuron in the output layer i Update: Where η is the learning rate;

[0069] Update of bias term b: b(t) is the bias term at time t, and b(t+1) is the bias term at time t+1;

[0070] The center vector c of the i-th radial basis function i Update:

[0071] Among them, c i (t) is the center vector of the i-th radial basis function at time t, c i+1 (t) is the center vector of the i-th radial basis function at time t+1;

[0072] The width parameter σ of the i-th radial basis function i Update: σ i (t) is the width parameter of the i-th radial basis function at time t, σ i (t+1) is the width parameter of the i-th radial basis function at time t+1; the partial derivative of the loss function with respect to the weight: The partial derivative of the loss function with respect to the bias term b: The loss function is about c i The partial derivative of : in,

[0073]

[0074] The loss function is about σi The partial derivative of :

[0075] in,

[0076] The RBF neural network is trained using the historical data of the blast furnace (the input and output data of the furnace temperature control system, including the current temperature, target temperature, and heating power, are collected and normalized) to determine the initial parameters. The RBF neural network is fine-tuned online using the real-time data of the blast furnace (real-time training and adjustment during use) to obtain an RBF neural network that can reflect the dynamic changes of the blast furnace system in real time. Ensure that the parameters can reflect the dynamic changes of the system in real time.

[0077] A double cross-limited PID controller is established.

[0078] The establishment of a dual cross-limited PID controller includes the following contents

[0079] The output of the PID controller is the control signal u(t), which is expressed as: Among them, K p is the proportional gain, K i is the integral gain, K d is the differential gain, K p , K i , K d Dynamically adjusted by the output of the RBF neural network;

[0080] Dynamic adjustment formula, the output of the RBF neural network is K(t), and the parameters of the PID controller are defined as: K p =K(t),K i =αK(t),K d =βK(t), where α and β are constants.

[0081] The output of the RBF neural network that reflects the dynamic changes of the blast furnace system in real time is used as the input of the double cross-limiting PID controller. The RBF neural network is combined with the double cross-limiting PID controller to form a closed-loop control system. A control strategy is established to adjust the parameters of the double cross-limiting PID controller in real time.

[0082] The establishment of a dual cross-limited PID controller includes the following contents

[0083] The control strategy includes a double cross-limited gas furnace temperature control, and the double cross-limited gas furnace temperature control includes the following contents: The heat balance equation of the gas furnace is: Where T(t) is the furnace temperature at time t, C is the heat capacity of the furnace, Q in (t) is the input heat at time t, generated by gas combustion, Q out(t) is the output heat at the moment, including the heat loss in the furnace and the heat transferred to the process medium, Q load (t) is the change in heat demand due to the change in strip thickness and speed at time t;

[0084] The heat generated by gas combustion is expressed as: Q in (t)=∈F gas (t)H gas , where ∈ is the combustion efficiency, which is usually related to the air-fuel ratio λ, and F gas (t) is the gas flow rate at time t, H gas is the lower heating value LHV of the gas;

[0085] The change in heat demand caused by the steel belt load is expressed as: Q load (t) = k·v(t)·h(t), where v(t) is the speed of the steel strip at time t, h(t) is the thickness of the steel strip at time t, and k is a constant representing the heat required for the steel strip per unit thickness and speed. The temperature control of the double cross-limited gas furnace also includes the following contents

[0086] Gas flow F gas The setting of (t) is determined by the temperature controller. Using the PI controller, the calculation formula for the gas flow is:

[0087] Among them: F gas,load (t) = k·v(t)·h(t) is the gas flow rate adjusted according to the thickness and speed of the steel strip;

[0088] Air flow rate F air The setting of (t) is determined according to the gas flow rate and the air-fuel ratio λ:

[0089] F air (t) = λ·F gas (t)

[0090] The selection of the air-fuel ratio λ needs to consider the completeness and economy of combustion, and λ is generally between 8 and 11;

[0091] Limiting mechanism

[0092] Gas flow limiter The purpose of gas flow limiter is to ensure that the gas is operated within a safe range to avoid excessive combustion or insufficient gas supply;

[0093] Gas flow limit F gas_max : Determined by safety considerations, or by the maximum allowable air flow,

[0094]

[0095] Gas flow lower limit F gas_min: Determined by the minimum air flow rate, ensuring the minimum air requirement during the combustion process;

[0096]

[0097] Air flow limiter The purpose of air flow limiter is to ensure that the air flow is within a reasonable range, neither too little to cause incomplete combustion nor too much to cause energy loss;

[0098] Air flow upper limit F air_max : Determined by the maximum allowable gas flow rate, F air_max =λ max ·F gas (t);

[0099] Air flow lower limit F air_min : Determined by the minimum allowable gas flow rate, F air_min =λ min ·F gas (t).

[0100] When the temperature measurement value is lower than the set value, the output of the temperature regulator increases accordingly. When the temperature measurement value is higher than the set value, that is, the control process is in a cooling state, the output of the temperature regulator will be significantly reduced.

[0101] The present invention combines the self-learning and adaptive capabilities of radial basis function (RBF) neural network with the double cross-limiting PID control strategy to improve the accuracy and stability of the furnace temperature control system. The RBF neural network is used to train the historical data offline and perform online fine-tuning, design a double cross-limiting PID controller, adjust the parameters of the PID controller in real time, form a closed-loop control system, and verify and optimize it through practical applications. The method can effectively avoid overshoot and oscillation in the control process, adapt to the dynamic changes of the system, and improve the accuracy and robustness of furnace temperature control.

Claims

1. A method for controlling furnace temperature based on RBF neural network double cross-limiting PID, characterized in that: An RBF neural network is established, and the historical data of the blast furnace is used to train the RBF neural network. The real-time data of the blast furnace is used to perform online fine-tuning on the RBF neural network to obtain an RBF neural network that can reflect the dynamic changes of the blast furnace system in real time. A double cross-limiting PID controller is established, and the output of the RBF neural network that reflects the dynamic changes of the blast furnace system in real time is used as the input of the double cross-limiting PID controller. The RBF neural network is combined with the double cross-limiting PID controller to form a closed-loop control system, a control strategy is established, and the parameters of the double cross-limiting PID controller are adjusted in real time.

2. The method for controlling furnace temperature based on RBF neural network double cross-limiting PID according to claim 1 is characterized in that: Establishing RBF neural network includes the following contents Input layer, the input layer receives the state variables of the control system, The following variables are included: Temperature error: e(t) = T set -T(t), where T set is the temperature setting value, T(t) is the actual temperature value at time t, and e(t) is the temperature error at time t; Temperature error change rate: Δe(t) = e(t) - e(t-1), e(t-1) is the temperature error at time t-1, Δe(t) is the temperature error change rate at time t; The input variables form the input vector: x(t) = [e(t), Δe(t)] T , x(t) is the input vector at time t; T is the transpose; Hidden layer: The hidden layer performs nonlinear mapping on the input data through radial basis functions. The number of neurons N in the hidden layer is determined by the specific application and experience. Definition of radial basis function: each hidden layer neuron corresponds to a radial basis function, which is in the form of: in, is the output of the i-th hidden layer neuron, N ≥ i ≥ 1, c i is the center vector of the ith radial basis function, σ i is the width parameter of the i-th radial basis function; Calculate the radial basis function output. For each input vector x(t), calculate the output of all hidden layer neurons: c i1 and c i2 are the two center coordinates of the i-th hidden layer neuron; Output layer: The output layer performs weighted summation on the outputs of the hidden layer neurons to obtain the control gain K(t); The output vector h(x(t)) of the hidden layer neuron is: h(x(t))=[φ1(x(t)),φ2(x(t)),...,φ N (x(t))] T ,in, The output K(t) of the output layer is calculated as: K(t)=w T h(x(t))+b,w=[w1,w2,…,w N ] T is the weight vector, b is the bias term, and w i is the weight vector of the i-th neuron in the output layer; The parameter that the RBF neural network needs to learn and optimize is c i , σ i 、w i , b; Parameter learning and optimization The loss function is the mean square error MSE: Among them, K target (t) is the target gain; Use the gradient descent method to minimize the loss function. For each parameter, calculate the gradient of the loss function and update the parameter value. The following is the specific update formula: The weight vector w of the i-th neuron in the output layer i Update: Where η is the learning rate; Update of bias term b: b(t) is the bias term at time t, and b(t+1) is the bias term at time t+1; The center vector c of the i-th radial basis function i Update: Among them, c i (t) is the center vector of the i-th radial basis function at time t, c i+1 (t) is the center vector of the i-th radial basis function at time t+1; The width parameter σ of the i-th radial basis function i Update: σ i (t) is the width parameter of the i-th radial basis function at time t, σ i (t+1) is the width parameter of the i-th radial basis function at time t+1; The partial derivative of the loss function with respect to the weights: The partial derivative of the loss function with respect to the bias term b: The loss function is about c i The partial derivative of : in, The loss function is about σ i The partial derivative of : in, 3. The method for controlling furnace temperature based on RBF neural network double cross-limiting PID according to claim 2 is characterized in that: The establishment of a dual cross-limited PID controller includes the following contents The output of the PID controller is the control signal u(t), which is expressed as: Among them, K p is the proportional gain, K i is the integral gain, K d is the differential gain, K p , K i , K d Dynamically adjusted by the output of the RBF neural network; Dynamic adjustment formula, the output of the RBF neural network is K(t), and the parameters of the PID controller are defined as: K p =K(t),K i =αK(t),K d =βK(t), where α and β are constants.

4. The method for controlling furnace temperature based on RBF neural network double cross-limiting PID according to claim 3 is characterized in that: The control strategy includes dual cross-limited gas furnace temperature control, and the dual cross-limited gas furnace temperature control includes the following contents The heat balance equation for a gas furnace is: Where T(t) is the furnace temperature at time t, C is the heat capacity of the furnace, Q in (t) is the input heat at time t, generated by gas combustion, Q out (t) is the output heat at the moment, including the heat loss in the furnace and the heat transferred to the process medium, Q load (t) is the change in heat demand due to the change in strip thickness and speed at time t; The heat generated by gas combustion is expressed as: Q in (t)=∈F gas (t)H gas , where ∈ is the combustion efficiency, which is usually related to the air-fuel ratio λ, and F gas (t) is the gas flow rate at time t, H gas is the lower heating value LHV of the gas; The change in heat demand caused by the steel belt load is expressed as: Q load (t) = k·v(t)·h(t), where v(t) is the speed of the steel strip at time t, h(t) is the thickness of the steel strip at time t, and k is a constant representing the heat required for the steel strip per unit thickness and speed.

5. The method for controlling furnace temperature based on RBF neural network double cross-limiting PID according to claim 4 is characterized in that: The double cross-limit gas furnace temperature control also includes the following contents Gas flow F gas The setting of (t) is determined by the temperature controller. Using the PI controller, the calculation formula for the gas flow is: Among them: F gas,load (t) = k·v(t)·h(t) is the gas flow rate adjusted according to the thickness and speed of the steel strip; Air flow rate F air The setting of (t) is determined according to the gas flow rate and the air-fuel ratio λ: F air (t)=λ·F gas (t) The selection of the air-fuel ratio λ needs to consider the completeness and economy of combustion, and λ is generally between 8 and 11; Limiting mechanism Gas flow limit The purpose of gas flow limit is to ensure that the gas runs within a safe range to avoid excessive combustion or insufficient gas supply; Gas flow limit F gas_max : Determined by safety considerations, or by the maximum allowable air flow, Gas flow lower limit F gas_min : Determined by the minimum air flow rate, ensuring the minimum air requirement during the combustion process; Air flow limiter The purpose of air flow limitation is to ensure that the air flow is within a reasonable range, neither too little to cause incomplete combustion nor too much to cause energy loss; Air flow upper limit F air_max : Determined by the maximum allowable gas flow rate, F air_max =λ max ·F gas (t); Air flow lower limit F air_min : Determined by the minimum allowable gas flow rate, F air_min =λ min ·F gas (t).

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