Distributed control method and system for multi-temperature-zone quartz tube furnace
By employing a distributed control architecture and Nash optimal strategy, the single-point failure risk and thermal coupling problem of multi-temperature zone quartz tube furnaces were solved, achieving highly reliable and high-precision temperature control.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- WENZHOU UNIV
- Filing Date
- 2026-06-05
- Publication Date
- 2026-07-03
Smart Images
Figure CN122329035A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of furnace temperature control technology, and in particular to a distributed control method and system for a multi-temperature zone quartz tube furnace. Background Technology
[0002] Quartz tube furnaces are widely used high-temperature reaction equipment in chemical, metallurgical, electronic, and new energy fields. Multi-temperature zone quartz tube furnaces have multiple independent temperature control zones arranged axially within the same furnace body. Significant heat conduction and radiation coupling effects exist between these zones, causing temperature changes to affect each other. Furthermore, the furnace body has high thermal inertia and significant response lag, forming a typical nonlinear, strongly coupled, and large-hysteresis complex system. Ensuring temperature stability in each zone and accurately tracking the setpoint is crucial for the reaction process and product quality within the tube.
[0003] Currently, temperature control in multi-zone quartz tube furnaces mostly employs dynamic matrix control methods based on finite step response models. This method does not require precise system identification; it directly establishes a predictive model using step response data, and can adapt to the dynamic characteristics of the furnace temperature system to a certain extent. However, existing dynamic matrix control schemes generally adopt a centralized control architecture, where a single central controller collects data from all temperature zones, performs global optimization calculations, and then sends commands to the actuators in each temperature zone.
[0004] Centralized architectures have inherent technical drawbacks: a failure in the central controller immediately paralyzes the entire control system, resulting in extremely low fault tolerance; real-time data from all temperature zones must be aggregated to the central controller for processing, leading to heavy communication loads and significant latency, impacting the real-time performance of temperature regulation; furthermore, while the thermal coupling effects between temperature zones can be handled uniformly in centralized optimization, the computational complexity increases exponentially with the number of temperature zones, making it difficult to meet rapid response requirements. Therefore, how to improve system reliability and real-time performance while ensuring control quality, and effectively handle strong coupling and model uncertainties between temperature zones, is a pressing issue in this field. Summary of the Invention
[0005] The technical problem this invention aims to solve is to address the shortcomings of the aforementioned technologies by providing a distributed control method for multi-temperature zone quartz tube furnaces. This method overcomes the limitations of existing centralized dynamic matrix control systems, which rely on a single central controller, suffer from single-point-of-failure risks and communication delays, and fail to consider control quantity coordination under multi-temperature zone thermal coupling, making it difficult to balance real-time performance and robustness. To achieve the above objective, this invention provides a distributed control method for multi-temperature zone quartz tube furnaces, executed by a controller, comprising: S 1. Obtain real-time step response data of the quartz tube furnace temperature system, establish a predictive model of the controlled object, and calculate... Time of the first The model predicts the output temperature value of each temperature zone subsystem, among which... This refers to the temperature zone number. This is the current sampling time; S 2: Collection The time measured at the first The actual output temperature value of each temperature zone subsystem is compared with the model predicted output temperature value to construct the model prediction error. The model prediction error is used to correct the prediction output. The corrected prediction output sequence is obtained through error weighting. Based on the corrected prediction output sequence, the initial prediction output sequence is obtained, and the first prediction output sequence is calculated based on the initial prediction output sequence. Each temperature zone subsystem in Predicted output value under continuous control increments To control the time domain; S 3: Establish the first The quadratic performance index function of each temperature zone subsystem is subjected to rolling optimization with the goal of minimizing prediction error and minimizing input control quantity; S 4: The first Each temperature zone subsystem in Substituting the predicted output value under continuous control increments into the quadratic performance index function, a step-wise dynamic matrix control is adopted. Combined with the step-wise control increment sequence, the performance index is solved based on Nash optimality to obtain the Nash optimal control increment sequence for each temperature zone subsystem. The first term is taken as the instantaneous control increment and applied to the corresponding temperature zone subsystem.
[0006] Preferably, the S 1 includes: Multi-temperature zone quartz tube furnace has Each temperature zone is a subsystem of a temperature zone. The uncertainty of the input control quantity is measured using Euclidean space to characterize the system uncertainty and constrain the range of variation of the input control quantity, thereby establishing the allowable control set for each temperature subsystem. as follows:
[0007] in, , This represents the uncertainty of a norm-bounded input control quantity. Represents European-style space. and These are known and measurable real parameters. It has Lebesgue The uncertainty of measurable elements satisfies ; In the allowable control set Within the range, with the first The control input for the temperature zone subsystem is the input to the first temperature zone subsystem. A step response experiment was conducted on the output of the subsystem in each temperature region, and the results were recorded. The input pair of the th _th The step response curves of the outputs, where , ; The step response curve is fitted to a smooth curve using filtering, and each sampling time is recorded. The step response data is used to construct the first... The input pair of the th _ ... The step response model vector of each output :
[0008] in, for Step response sample value at time, For the number of samples, For the first The input pair of the th _th The modeling time domain of each output; Based on step response model vector Establish the dynamic matrix of the controlled object and its uncertain parameter matrix , and All 1-th order matrix To optimize the time domain, To control the time domain, and The forms are as follows:
[0009]
[0010] in For the first The input pair of the th _th The data of the output step response. For the corresponding uncertain parameters; According to the dynamic matrix and uncertain parameter matrix , combined The control increments of each temperature zone subsystem at each time point are calculated. Time of the first The model predicts the output temperature value of each temperature zone subsystem.
[0011] Preferably, the calculation yields Time of the first The model predicts the output temperature values for each temperature zone subsystem, including: exist Constantly add control increments to each temperature zone subsystem , obtained the The model predicts the output temperature value of the individual temperature zone subsystem. :
[0012] in:
[0013]
[0014]
[0015]
[0016] in To model the time domain, to They represent the first Each temperature zone subsystem in Always The model predicts the output temperature value after adding control increments at each step. to express Always The initial predicted output temperature value at time [time]. and The first The temperature zone subsystem and the first The temperature zone subsystem for the first A vector is constructed from the step response data of the subsystem in each temperature range. and These are the corresponding uncertain parameter vectors. for Control increments for each temperature zone subsystem at all times.
[0017] Preferably, the S 2 includes: Compare the actual output temperature value with the model's predicted output temperature value to construct the model prediction error. :
[0018] in, express The time measured at the first The actual output temperature value of each temperature zone subsystem; By weighting the errors, the prediction of future output is corrected, resulting in the corrected predicted output sequence. :
[0019] in:
[0020] They represent the first Each temperature zone subsystem in Correction values for the time-matter model. The weight matrix is for error compensation. For error correction coefficients, For modeling the time domain.
[0021] Preferably, the S 2 also includes: get Time of the first Initial predicted output sequence of each temperature zone subsystem :
[0022] in for The state transition matrix of order n is of the following form:
[0023] Calculate the first Each temperature zone subsystem in Continuous control increment Predicted output value :
[0024] in:
[0025]
[0026]
[0027] in For the first Individual temperature zone subsystem Always The initial predicted output value at time 1. To optimize the time domain, Is calculating the first The Nash optimal solution obtained for other temperature subsystems when considering only one temperature subsystem.
[0028] Preferably, the S3 includes: Establish the quadratic performance index function :
[0029] Rolling optimization is performed with the objectives of minimizing prediction error and minimizing input control quantity; whereby For the first The predicted output sequence of each temperature zone subsystem For the first Reference trajectory sequence of temperatures for each temperature subsystem. This is the error weighting coefficient matrix. To control the weighting coefficient matrix, and These are the weighting coefficients; The reference trajectory sequence satisfy:
[0030] in The smoothing coefficient is the reference trajectory. for Time of the first The actual process output of the temperature zone subsystem For the first The desired temperature of each temperature zone subsystem.
[0031] Preferably, the S 4 includes: Predict the output value Substituting into the quadratic performance index function and expanding, we get:
[0032] Based on the step-by-step control concept, the control increment sequence is... and The constraints are:
[0033] in for Time of the first Control increments for each temperature zone subsystem It is a step factor; calculate ,in The dynamic matrix vector after step factor transformation is expressed as follows:
[0034] Let the control quantity weighting matrix Then we have:
[0035] Based on the idea of Nash optimality, with To minimize the objective function for the control variables, solve... Substituting these values into the ladder-like constraint relationship, the optimal control increment is obtained. :
[0036] Calculated That is, the first The optimal control increment in the furnace temperature control of the individual temperature zone subsystem.
[0037] Preferred, in At that moment, the The optimal control increment for the new iteration of the temperature zone subsystem is:
[0038] The control increment for the entire furnace temperature system is:
[0039] The first Individual temperature zone subsystem The first term of the Nash optimal solution at time step 1 is used as the instantaneous control increment. , obtained the The actual control quantity of the temperature zone subsystem , acting on the Each temperature zone subsystem; In the next time step, repeat the above steps to continue solving the problem. Real-time control increment of each temperature zone subsystem This leads to the optimal control increment sequence for the entire system. And so on, in a loop.
[0040] Preferably, the uncertain parameter is determined. The upper and lower bounds are defined, including the following steps: a In the allowable control set Within the range, calculate the uncertain parameters. The upper and lower bounds are taken. Substitute the upper bound into the solution formula ; b Calculate the prediction error ,if If the result is positive, stop the calculation; otherwise, according to the binary search principle, take half of the upper bound and repeat the steps. a ), until an uncertain parameter is found. The lower bound; cIn the obtained uncertain parameters Within the range defined by the upper and lower bounds, for Take values and determine the uncertain parameter matrix. .
[0041] A distributed control system for the temperature of a multi-temperature zone quartz tube furnace, comprising: The prediction model building module is used to acquire real-time step response data of the quartz tube furnace temperature system, build a prediction model of the controlled object, and calculate... Time of the first The model predicts the output temperature value of each temperature zone subsystem, among which... This refers to the temperature zone number. This is the current sampling time; Feedback correction module, used for data acquisition The time measured at the first The actual output temperature value of each temperature zone subsystem is compared with the model predicted output temperature value to construct the model prediction error. The model prediction error is used to correct the prediction output. The corrected prediction output sequence is obtained through error weighting. Based on the corrected prediction output sequence, the initial prediction output sequence is obtained, and the first prediction output sequence is calculated based on the initial prediction output sequence. Each temperature zone subsystem in Predicted output value under continuous control increments To control the time domain; The rolling optimization module is used to establish the first The quadratic performance index function of each temperature zone subsystem is subjected to rolling optimization with the goal of minimizing prediction error and minimizing input control quantity; The optimal control incremental sequence solver module is used to solve the th... Each temperature zone subsystem in Substituting the predicted output value under continuous control increments into the quadratic performance index function, a step-wise dynamic matrix control is adopted. Combined with the step-wise control increment sequence, the performance index is solved according to Nash optimality to obtain the Nash optimal control increment sequence of each temperature zone subsystem, and the first term is taken as the instantaneous control increment.
[0042] Compared with the prior art, the beneficial effects of the present invention are: This invention uses a distributed control architecture to operate each temperature zone as an independent subsystem in parallel. Each controller only needs to interact to control the incremental sequence, avoiding the single point of failure risk caused by centralized control relying on a single central controller and the communication delay caused by the convergence of all data. This significantly improves the system's fault tolerance and real-time response speed. An uncertain parameter matrix is explicitly introduced into the prediction model, and the upper and lower bounds of the parameters are determined by binary search, enabling the controller to accommodate model mismatch and parameter perturbation, thereby enhancing the system's robustness.
[0043] This invention employs a stepped control increment sequence constraint, ensuring that the control increment changes smoothly and proportionally according to a step factor. This effectively suppresses drastic fluctuations in the control action of each temperature zone and reduces temperature overshoot and oscillations caused by thermal coupling between temperature zones. Based on a distributed iterative solution mechanism using a Nash optimal strategy, each temperature zone collaboratively optimizes under the assumption that other temperature zones adopt optimal responses, achieving coordinated control of a strongly coupled multi-temperature zone system while balancing global control quality and local computational efficiency.
[0044] The feedback correction stage of this invention utilizes real-time temperature measurement error to correct the predicted output sequence, eliminating the influence of model steady-state error and external disturbances, and ensuring steady-state temperature tracking accuracy. Simulation and experimental results show that the method of this invention enables each temperature zone to quickly and smoothly reach the set temperature, with small steady-state error and strong anti-interference ability, providing a highly reliable, high-precision, and robust temperature control scheme for multi-temperature zone quartz tube furnaces. Attached Figure Description
[0045] Figure 1 This is a schematic diagram of the step-type dynamic matrix control method of the present invention. Detailed Implementation
[0046] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0047] This embodiment provides a distributed control method for the furnace temperature of a multi-temperature zone quartz tube furnace. The method is executed by a controller, and the multi-temperature zone quartz tube furnace has… Each temperature zone is a subsystem of its own. The value is an integer greater than 1. Each temperature zone subsystem is equipped with an actuator and a sensor. The actuator is used to adjust the heating power or gas flow rate of that temperature zone, and the sensor is used to monitor the furnace temperature of that temperature zone in real time. Each temperature zone subsystem corresponds to a distributed controller, and the distributed controllers are connected through a communication network to exchange information such as control increment sequences.
[0048] like Figure 1 As shown, the method includes the following steps: S 1. Obtain real-time step response data of the quartz tube furnace temperature system, establish a predictive model of the controlled object, and calculate... Time of the first The model predicts the output temperature value of each temperature zone subsystem, among which... This refers to the temperature zone number. This represents the current sampling time.
[0049] The specific process is as follows: Multi-temperature zone quartz tube furnace has There are several temperature zones, each of which is considered a temperature zone subsystem.
[0050] First, the uncertainty of the input control quantity is measured using Euclidean space, and the allowable control set for each temperature zone subsystem is established. as follows:
[0051] in, , This represents the uncertainty of a norm-bounded input control quantity. Represents European-style space. and These are known and measurable real parameters. It has Lebesgue The uncertainty of measurable elements satisfies Allow control set The establishment of this is to ensure the success of subsequent steps. S There is a solution when solving for the optimal control increment in step 4.
[0052] In the allowable control set Within the range, with the first The control quantity of the temperature zone subsystem is the input, and for the first temperature zone subsystem... A step response experiment was conducted on the output of the subsystem in each temperature region, and the results were recorded. The input pair of the th _th The step response curves of the outputs, where , .
[0053] The obtained step response curve is fitted into a smooth curve by filtering, and the curve is recorded at each sampling time. The corresponding step response data is then obtained, which is the real-time step response data in step S1. The sampling time is defined as... , , The model's step response will at some point... It then tended to stabilize, when and The error tends to When, it can be approximated as It equals the steady-state value of the step response. Establish the first... The input pair of the th _th Step response model vector between outputs :
[0054] in, for Step response sample value at time, This represents the current number of samples. For the first The input pair of the th _th The modeling time domain of each output.
[0055] Using the obtained step response model vector Establish the dynamic matrix of the controlled object and its uncertain parameter matrix Its form is as follows:
[0056]
[0057] in For the first The input of the temperature zone subsystem to the first Each temperature zone subsystem Order dynamic matrix, For the first The input of the temperature zone subsystem to the first The uncertainty parameter matrix of a temperature range subsystem For the first The input pair of the th _th The data of the output step response. For the corresponding uncertain parameters, , These represent the optimization time domain and control time domain of the distributed dynamic matrix control algorithm, respectively. Dynamic matrix With the uncertain parameter matrix Together they constitute the controlled object prediction model in step S1.
[0058] Get the The current temperature zone subsystem Initial prediction output sequence at time step .exist Constantly add control increments to each temperature zone subsystem , obtained the The model predicts the output temperature value of the individual temperature zone subsystem. :
[0059] in:
[0060]
[0061] in To model the time domain, to They represent the first Each temperature zone subsystem in Always The model predicts the output temperature value after adding control increments at each step. to express Always The initial predicted output temperature value at time [time]. and The first The temperature zone subsystem and the first The temperature zone subsystem for the first A vector is constructed from the step response data of the subsystem in each temperature range. and These are the corresponding uncertain parameter vectors. for Control increments for each temperature zone subsystem at all times.
[0062] S 2: Collection The time measured at the first The actual output temperature value of each temperature zone subsystem is compared with the model predicted output temperature value to construct the model prediction error. The model prediction error is used to correct the prediction output. The corrected prediction output sequence is obtained through error weighting. Based on the corrected prediction output sequence, the initial prediction output sequence is obtained, and the first prediction output sequence is calculated based on the initial prediction output sequence. Each temperature zone subsystem in Predicted output value under continuous control increments To control the time domain.
[0063] The specific process is as follows: The controller collects data through sensors configured in each temperature zone subsystem. Time of the first The actual output temperature value of each temperature zone subsystem .
[0064] Compare the actual output with the model's predicted output to construct the model prediction error. :
[0065] in, express The time measured at the first The actual temperature output value of each temperature zone subsystem. for Always The model predicts the output temperature value at any given time.
[0066] By weighting the errors, the prediction of future output is corrected, resulting in the corrected predicted output sequence. :
[0067] in:
[0068] They represent the first Each temperature zone subsystem in Correction values for the time-matter model. The weight matrix is for error compensation. For error correction coefficients, For modeling the time domain.
[0069] get Time of the first Initial predicted output sequence of each temperature zone subsystem :
[0070] in for The state transition matrix of order n is of the following form:
[0071] Calculate the first Each temperature zone subsystem in A series of control increments Predicted output value :
[0072] in:
[0073]
[0074] in For the first Individual temperature zone subsystem Always The initial predicted output value at time 1. To optimize the time domain, Is calculating the first The Nash optimal solution obtained for other temperature subsystems when considering only one temperature subsystem.
[0075] S 3: Establish the first The quadratic performance index function of each temperature zone subsystem is subjected to rolling optimization with the goal of minimizing prediction error and input control quantity.
[0076] The specific process is as follows: Regarding the first For each temperature zone subsystem, with the objectives of minimizing prediction error and minimizing input control quantity, a quadratic performance index function weighted by output prediction error and control quantity is established. :
[0077] in, For the first The predicted output sequence of each temperature zone subsystem For the first Reference trajectory sequence of each temperature subsystem This is the error weighting coefficient matrix. To control the weighting coefficient matrix, and These are the weighting coefficients.
[0078] The reference trajectory sequence satisfy:
[0079] in The smoothing coefficient is the reference trajectory. for Time of the first The actual process output of the temperature zone subsystem For the first The desired temperature of each temperature zone subsystem.
[0080] S 4: The first Each temperature zone subsystem in Substituting the predicted output value under continuous control increments into the quadratic performance index function, a step-wise dynamic matrix control is adopted. Combined with the step-wise control increment sequence, the performance index is solved according to Nash optimality to obtain the Nash optimal control increment sequence of each temperature zone subsystem, and the first term is taken as the instantaneous control increment.
[0081] The specific process is as follows: Predict the output value Substituting into the quadratic performance index function and expanding, we get:
[0082] Based on the step-by-step control concept, the control increment sequence is... and The constraints are:
[0083] in for Time of the first Control increments for each temperature zone subsystem It is the step factor.
[0084] calculate ,in The dynamic matrix vector after step factor transformation is expressed as follows:
[0085]
[0086] For ease of calculation, let the control quantity weighting matrix be... Then we have:
[0087] Based on the idea of Nash optimality, with Minimize the objective function while controlling for variables. Solve. By substituting the values into the step-wise constraint relationship, the optimal control increment can be obtained. :
[0088] Calculated This refers to the optimal control increment in the furnace temperature control of each temperature zone subsystem.
[0089] exist At that moment, the The optimal control increment for the new iteration of the temperature zone subsystem is:
[0090] The control increment for the entire furnace temperature system is:
[0091] The first Individual temperature zone subsystem The first term of the Nash optimal solution at time step 1 is used as the instantaneous control increment. , obtained the The actual control quantity of the temperature zone subsystem , acting on the By identifying each temperature zone subsystem, the optimal control quantity for furnace temperature control in each temperature zone subsystem can be obtained.
[0092] In the next moment Repeat the above steps S 1 to S 4. Continue solving the problem. Real-time control increment of each temperature zone subsystem This leads to the optimal control increment sequence for the entire system. And so on, in a loop. When the temperature error of each temperature zone is within a preset threshold (e.g., ... When the temperature is within a certain range, it is considered to have reached a steady state, and the obtained optimal control increment and temperature value are saved.
[0093] Methods for determining the upper and lower bounds of uncertain parameters: In the above steps S 1 to S During the implementation of step 4, uncertain parameters The upper and lower bounds are determined by the following steps: a In the allowable control set Within the range, calculate the uncertain parameters. The upper and lower bounds are taken. Substitute the upper bound into the solution formula ; b Calculate the prediction error ,if If the result is positive, stop the calculation; otherwise, according to the binary search principle, take half of the upper bound and repeat the steps. a ), until an uncertain parameter is found. The lower bound; c In the obtained uncertain parameters Within the range defined by the upper and lower bounds, for Take values, and then determine the uncertain parameter matrix. .
[0094] The optimal control increment sequence obtained by the above method is the optimal control input for the multi-temperature zone quartz tube furnace.
[0095] This embodiment uses the temperature control of a vacuum atmosphere quartz tube furnace as an example for illustration. The vacuum atmosphere quartz tube furnace is a typical multi-temperature zone quartz tube furnace, and its furnace body is divided along the axial direction into... Each temperature zone is equipped with an independent gas flow valve as an actuator to regulate the flow of protective gas entering that zone; each temperature zone is also equipped with a thermocouple as a sensor to monitor the furnace temperature in real time. The gas flow valve and thermocouple corresponding to each temperature zone are communicatively connected to the controller.
[0096] In this embodiment, the input control quantity is the gas flow rate, and the output quantity is the furnace temperature measured by the thermocouple. The steps are as described in Embodiment 1. S 1 to S 4. Implement distributed control, with the following specific parameters selected: sampling period. Modeling in the time domain Optimize the time domain Control time domain Error correction coefficient Step factor Softening coefficient .
[0097] The controller will calculate the instantaneous control increment. The control signal is sent to the gas flow valve, which adjusts its opening based on the received control increment, thereby changing the gas flow rate entering the temperature zone and regulating the furnace temperature.
[0098] Using the above method, the temperature of each temperature zone can quickly and stably reach the set temperature, with small steady-state error and strong anti-interference ability. It effectively avoids thermal coupling oscillation between temperature zones and improves the robustness and reliability of the system.
[0099] This embodiment provides a distributed control system for the temperature of a multi-temperature zone quartz tube furnace. The system includes multiple temperature zones and at least one controller. Each temperature zone is equipped with an actuator and a sensor. The actuator is a gas flow valve or a heater, and the sensor is a thermocouple. The controller is communicatively connected to the sensor and actuator of each temperature zone. The controller includes one or more processors and a memory storing program instructions. When the program instructions are executed by the one or more processors, the controller performs the method described in Embodiment 1 or Embodiment 2.
[0100] Specifically, the controller includes: The prediction model building module is used to acquire real-time step response data of the quartz tube furnace temperature system, build a prediction model of the controlled object, and calculate... Time of the first The model predicts the output temperature value of the individual temperature zone subsystem. Feedback correction module, used for data acquisition The time measured at the first The actual output temperature value of each temperature zone subsystem is compared with the model predicted output temperature value to construct the model prediction error. The model prediction error is used to correct the prediction output. The corrected prediction output sequence is obtained through error weighting. Based on the corrected prediction output sequence, the initial prediction output sequence is obtained, and the first prediction output sequence is calculated based on the initial prediction output sequence. Each temperature zone subsystem in Predicted output value under continuous control increments; The rolling optimization module is used to establish the first The quadratic performance index function of each temperature zone subsystem is subjected to rolling optimization with the goal of minimizing prediction error and minimizing input control quantity; The optimal control incremental sequence solver module is used to solve the th... Each temperature zone subsystem in Substituting the predicted output value under continuous control increments into the quadratic performance index function, a step-wise dynamic matrix control is adopted. Combined with the step-wise control increment sequence, the performance index is solved according to Nash optimality to obtain the Nash optimal control increment sequence of each temperature zone subsystem, and the first term is taken as the instantaneous control increment.
[0101] The distributed control method and system for a multi-temperature zone quartz tube furnace provided by this invention treats each temperature zone as an independent subsystem and adopts a distributed control architecture. The controllers of each temperature zone operate in parallel and optimize collaboratively, effectively avoiding the risk of system paralysis due to a single central controller failure in traditional centralized control schemes, significantly improving system reliability and fault tolerance. Simultaneously, an uncertain parameter matrix is introduced into the predictive model, and the upper and lower bounds of the uncertain parameters are accurately determined using a binary search method. This enables the controller to effectively cope with uncertainties such as parameter perturbations and model mismatches present in actual industrial processes, significantly enhancing system robustness. A step factor is introduced through step-type control constraints, allowing the control increment to change smoothly according to a preset ratio, avoiding temperature overshoot and system oscillations caused by sudden changes in control quantity. A multi-temperature zone collaborative optimization mechanism is constructed based on a Nash optimal strategy, realizing coordinated control of a strongly coupled multi-temperature zone system and solving the problem of handling thermal coupling effects between temperature zones.
[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A distributed control method for the furnace temperature of a multi-temperature zone quartz tube furnace, characterized in that, The method, executed by the controller, includes: S 1. Obtain real-time step response data of the quartz tube furnace temperature system, establish a predictive model of the controlled object, and calculate... Time of the first The model predicts the output temperature value of each temperature zone subsystem, among which... This refers to the temperature zone number. This is the current sampling time; Multi-temperature zone quartz tube furnace has Each temperature zone is a subsystem of a temperature zone. The uncertainty of the input control quantity is measured using Euclidean space to characterize the system uncertainty and constrain the range of variation of the input control quantity, thereby establishing the allowable control set for each temperature subsystem. as follows: in, , This represents the uncertainty of a norm-bounded input control quantity. Represents European-style space. and These are known and measurable real parameters. It has Lebesgue The uncertainty of measurable elements satisfies ; In the allowable control set Within the range, with the first The control input for the temperature zone subsystem is the input to the first temperature zone subsystem. A step response experiment was conducted on the output of the subsystem in each temperature region, and the results were recorded. The input pair of the th _th The step response curves of the outputs, where , ; The step response curve is fitted to a smooth curve using filtering, and each sampling time is recorded. The step response data is used to construct the first... The input pair of the th _th The step response model vector of each output : in, for Step response sample value at time, For the number of samples, For the first The input pair of the th _th The modeling time domain of each output; Based on step response model vector Establish the dynamic matrix of the controlled object and its uncertain parameter matrix , and All 1-th order matrix, To optimize the time domain, To control the time domain, and The forms are as follows: in For the first The input pair of the th _th The data of the output step response. For the corresponding uncertain parameters; According to the dynamic matrix and uncertain parameter matrix , combined The control increments of each temperature zone subsystem at each time point are calculated. Time of the first The model predicts the output temperature value of the individual temperature zone subsystem. S 2: Collection The time measured at the first The actual output temperature value of each temperature zone subsystem is compared with the model predicted output temperature value to construct the model prediction error. The model prediction error is used to correct the prediction output. The corrected prediction output sequence is obtained through error weighting. Based on the corrected prediction output sequence, the initial prediction output sequence is obtained, and the first prediction output sequence is calculated based on the initial prediction output sequence. Each temperature zone subsystem in Predicted output value under continuous control increments To control the time domain; S 3: Establish the first The quadratic performance index function of each temperature zone subsystem is subjected to rolling optimization with the goal of minimizing prediction error and minimizing input control quantity; S 4: The first Each temperature zone subsystem in Substituting the predicted output value under continuous control increments into the quadratic performance index function, a step-wise dynamic matrix control is adopted. Combined with the step-wise control increment sequence, the performance index is solved based on Nash optimality to obtain the Nash optimal control increment sequence for each temperature zone subsystem. The first term is taken as the instantaneous control increment and applied to the corresponding temperature zone subsystem.
2. The method according to claim 1, characterized in that, The calculation yielded Time of the first The model predicts the output temperature values for each temperature zone subsystem, including: exist Constantly add control increments to each temperature zone subsystem , obtained the The model predicts the output temperature value of the individual temperature zone subsystem. : in: in To model the time domain, to They represent the first Each temperature zone subsystem in Always The model predicts the output temperature value after adding control increments at each step. to express Always The initial predicted output temperature value at time [time]. and The first The temperature zone subsystem and the first The temperature zone subsystem for the first A vector is constructed from the step response data of the subsystem in each temperature range. and These are the corresponding uncertain parameter vectors. for Control increments for each temperature zone subsystem at all times.
3. The method according to claim 1, characterized in that, The S 2 includes: Compare the actual output temperature value with the model's predicted output temperature value to construct the model prediction error. : in, express The time measured at the first The actual output temperature value of each temperature zone subsystem; By weighting the errors, the prediction of future output is corrected, resulting in the corrected predicted output sequence. : in: They represent the first Each temperature zone subsystem in Correction values for the time-matter model, The weight matrix is for error compensation. For error correction coefficients, For modeling the time domain.
4. The method according to claim 3, characterized in that, The S 2 also includes: get Time of the first Initial predicted output sequence of each temperature zone subsystem : in for The state transition matrix of order n is of the following form: Calculate the first Each temperature zone subsystem in Continuous control increment Predicted output value : in: in For the first Individual temperature zone subsystem Always The initial predicted output value at time 1. To optimize the time domain, Is calculating the first The Nash optimal solution obtained for other temperature subsystems when considering only one temperature subsystem.
5. The method according to claim 1, characterized in that, The S 3 includes: Establish the quadratic performance index function : Rolling optimization is performed with the objectives of minimizing prediction error and minimizing input control quantity; whereby For the first The predicted output sequence of each temperature zone subsystem For the first Reference trajectory sequence of temperatures for each temperature subsystem. This is the error weighting coefficient matrix. To control the weighting coefficient matrix, and These are the weighting coefficients; The reference trajectory sequence satisfy: in The smoothing coefficient is the reference trajectory. for Time of the first The actual process output of the temperature zone subsystem For the first The desired temperature of each temperature zone subsystem.
6. The method according to claim 1, characterized in that, The S 4 includes: Predict the output value Substituting into the quadratic performance index function and expanding, we get: Based on the step-by-step control concept, the control increment sequence is... and The constraints are: in for Time of the first Control increments for each temperature zone subsystem It is a step factor; calculate ,in The dynamic matrix vector after step factor transformation is expressed as follows: Let the control quantity weighting matrix Then we have: Based on the idea of Nash optimality, with To minimize the objective function for the control variables, solve... Substituting these values into the ladder-like constraint relationship, the optimal control increment is obtained. : Calculated That is, the first The optimal control increment in the furnace temperature control of the individual temperature zone subsystem.
7. The method according to claim 6, characterized in that, exist At that moment, the The optimal control increment for the new iteration of the temperature zone subsystem is: The control increment for the entire furnace temperature system is: The first Individual temperature zone subsystem The first term of the Nash optimal solution at time step 1 is used as the instantaneous control increment. , obtained the The actual control quantity of the temperature zone subsystem , acting on the Each temperature zone subsystem; In the next time step, repeat the above steps to continue solving the problem. Real-time control increment of each temperature zone subsystem This leads to the optimal control increment sequence for the entire system. And so on, in a loop.
8. The method according to claim 1, characterized in that, Determine the uncertain parameters The upper and lower bounds are defined, including the following steps: a In the allowable control set Within the range, calculate the uncertain parameters The upper and lower bounds are taken. Substitute the upper bound into the solution formula ; b Calculate the prediction error ,if If the result is positive, stop the calculation; otherwise, according to the binary search principle, take half of the upper bound and repeat the steps. a ), until an uncertain parameter is found. The lower bound; c In the obtained uncertain parameters Within the range defined by the upper and lower bounds, for Take values and determine the uncertain parameter matrix. .
9. A distributed control system for the furnace temperature of a multi-temperature zone quartz tube furnace, characterized in that, include: The prediction model building module is used to acquire real-time step response data of the quartz tube furnace temperature system, build a prediction model of the controlled object, and calculate... Time of the first The model predicts the output temperature value of each temperature zone subsystem, among which... This refers to the temperature zone number. This is the current sampling time; Feedback correction module, used for data acquisition The time measured at the first The actual output temperature value of each temperature zone subsystem is compared with the model predicted output temperature value to construct the model prediction error. The model prediction error is used to correct the prediction output. The corrected prediction output sequence is obtained through error weighting. Based on the corrected prediction output sequence, the initial prediction output sequence is obtained, and the first prediction output sequence is calculated based on the initial prediction output sequence. Each temperature zone subsystem in Predicted output value under continuous control increments To control the time domain; The rolling optimization module is used to establish the first The quadratic performance index function of each temperature zone subsystem is subjected to rolling optimization with the goal of minimizing prediction error and minimizing input control quantity; The optimal control incremental sequence solver module is used to solve the th... Each temperature zone subsystem in Substituting the predicted output value under continuous control increments into the quadratic performance index function, a step-wise dynamic matrix control is adopted. Combined with the step-wise control increment sequence, the performance index is solved according to Nash optimality to obtain the Nash optimal control increment sequence of each temperature zone subsystem, and the first term is taken as the instantaneous control increment.