Nonlinear model predictive temperature control method for semiconductor temperature control type synthesis reactor

Abstract

The invention belongs to the technical field of fine chemical reaction safety testing and automatic chemistry, and particularly discloses a nonlinear model predictive temperature control method of a semiconductor temperature control type synthesis reactor. The method comprises the following steps: constructing a dynamic heat transfer model of the system based on the semiconductor temperature control type synthesis reactor; designing a nonlinear model prediction controller according to the heat transfer model of the synthesis reactor; constructing a multi-constraint objective function for nonlinear predictive control according to the characteristics of the controlled object; and solving an optimal control sequence for the nonlinear model prediction controller by adopting a projection gradient method. Compared with a traditional PID temperature control algorithm, the temperature of the reactor can be accurately predicted and controlled through the designed nonlinear model prediction temperature control algorithm, it is ensured that the chemical reaction is conducted at the optimal temperature, and the robustness and adaptability of a control system are improved.

Description

Technical Field

[0001] The present invention belongs to the field of fine chemical reaction safety testing and automated chemistry research, and relates to a non-linear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor. Background Art

[0002] As the core equipment of the chemical production system, the synthesis reactor undergoes complex multiphase physical and chemical changes, phase interface mass and heat transfer, and energy dynamic balance processes during its operation, forming a highly non-linear time-varying system. Traditional processes mostly adopt a temperature control architecture that couples a dynamic oil bath system with a reaction kettle, and adjusts the temperature inside the kettle through external circulation heat exchange. The semiconductor temperature-controlled synthesis reactor uses Peltier elements as the temperature control object, and has the advantages of fast response speed and strong anti-interference ability compared with the temperature control using a dynamic oil bath system.

[0003] The semiconductor temperature-controlled synthesis reactor involved in this application is an intelligent instrument that can accurately simulate the semi-batch reaction process of a kettle in a laboratory environment. The device is equipped with a high-precision sensing system and advanced control algorithms, and can monitor key parameters such as the temperature, pressure, and feeding quality inside the reaction kettle in real time, and automatically calculate core reaction kinetic indicators such as reaction heat release and conversion rate based on real-time data. Through its comprehensive data acquisition and analysis functions, it provides a scientific basis for reaction safety risk assessment, process development and optimization, and is an important scientific research instrument for reaction safety assessment and automated chemistry research in the field of fine chemicals.

[0004] The semiconductor temperature-controlled synthesis reactor includes: a stirring paddle, a stirring driver, a compensating heating rod, a Peltier cooling element, a circulating water bath system, a Peltier element, a sample temperature sensor, a metal heat homogenizing jacket temperature sensor, a circulating water bath temperature sensor, a compensating heating rod power driver, a signal communication server, a host computer monitoring system, a reaction kettle cover, a reaction kettle, a metal heat homogenizing jacket, a Peltier current controller, and a pipeline connecting the Peltier cooling element and the circulating water bath system.

[0005] The reaction kettle is embedded in the metal heat homogenizing jacket. The Peltier element and the Peltier cooling element are fixed around the metal heat homogenizing jacket through fasteners. The compensating heating rod and the stirring device (composed of a stirring paddle and a stirring driver) are fixed to the upper end of the metal heat homogenizing jacket through the reaction kettle cover. The circulating water bath system is connected to the Peltier cooling element, and the temperature sensors measure the temperature of the circulating water bath system, the sample temperature inside the reaction kettle, and the temperature of the metal heat homogenizing jacket respectively. The temperature control of the semiconductor temperature-controlled synthesis reactor relies on the compensating heating rod and the compensating heating rod power driver; and the Peltier element transfers heat through the metal heat homogenizing jacket to achieve sample temperature control.

[0006] For semiconductor temperature-controlled synthesis reactors, Peltier elements are often used to achieve rapid heating or cooling, thereby controlling the temperature of the samples inside the reactor. However, the relationship between the input of the Peltier element (usually current I) and its output (heat flow or temperature change at the hot and cold ends) is usually non-linear. This non-linearity is mainly due to the following factors: First, the coupling of the thermoelectric effect and the Joule heating effect. The Peltier element not only generates direct heat transfer based on the current but also generates Joule heat due to resistance, resulting in a complex non-linear relationship between the actual temperature response and the input current. Second, the temperature dependence of the internal materials of the element and the changes in the working environment will also cause non-linear output responses.

[0007] In addition, under the condition that the system structure principle and hardware performance remain unchanged, the temperature control performance only depends on the temperature control algorithm in the monitoring system. The traditional PID control algorithm is essentially a linear control method based on the assumption that the system is linear or approximately linear. For non-linear systems, the PID control algorithm may not be able to capture and compensate for the non-linear behavior of the system, resulting in unsatisfactory control effects. Moreover, the PID controller only adjusts the control input based on the current and past error information and lacks the ability to predict future system behavior. The behavior of non-linear systems is often relatively complex, and the lack of prediction ability easily leads to slow responses to future disturbances or non-linear changes. Summary of the Invention

[0008] The object of the present invention is: In view of the above situation, the present invention provides a non-linear model predictive temperature control method for semiconductor temperature-controlled synthesis reactors. By establishing a dynamic heat transfer model of the reactor, constructing a non-linear predictive control problem with multiple constraints, and using the projected gradient descent method to solve the optimal control input online, the present invention can achieve precise control and real-time adjustment of the reactor temperature. This method has high precision, real-time performance, the ability to satisfy multiple constraints, and high robustness, and is applicable to high-demand chemical reaction safety tests and automated chemical process control.

[0009] The method of the present invention includes the following steps:

[0010] 1. Construction of the dynamic heat transfer model: Based on the structure and thermal characteristics of the semiconductor temperature-controlled synthesis reactor, the heat transfer model of the reactor is constructed considering the heat exchange between the sample temperature and the structural temperature, as well as the non-linear influence of the current on the temperature. Its continuous-time dynamic model can be expressed as:

[0011]

[0012]

[0013]

[0014] Among them, Equation (1) is the thermal equilibrium equation of the sample in the reaction kettle, which represents the heat exchange between the sample and the metal heat - uniforming jacket. Equation (2) is the thermal equilibrium equation of the metal heat - uniforming jacket, which represents the heat loss from the metal heat - uniforming jacket to the external environment, the heat transferred to the metal heat - uniforming jacket by the Peltier element, and the heat exchange with the temperature of the sample in the reaction kettle. Equation (3) is the power output expression of the Peltier element. represents the specific heat capacity and mass of the sample in the synthesis reactor. represents the rate of change of the temperature of the sample in the reaction kettle. 、 represents the sample temperature and the temperature of the metal heat - uniforming jacket. represents the heat transfer coefficient between the sample and the inner wall of the reaction kettle. represents the specific heat capacity and mass of the metal heat - uniforming jacket of the synthesis reactor. represents the rate of change of the temperature of the metal heat - uniforming jacket. represents the refrigeration power of the Peltier element. represents the heat dissipation coefficient. represents the ambient temperature. represents the Peltier coefficient of the Peltier element. represents the current applied to the Peltier element. represents the internal resistance of the Peltier element. represents the heat flow coefficient of the Peltier element itself. represents the hot - end temperature of the Peltier element.

[0015] 2. Model prediction output: Taking as the sampling time, the continuous dynamic heat transfer model is discretized by the Euler method to obtain the predicted output of the discrete heat transfer model:

[0016]

[0017]

[0018] Among them represents the sample temperature at the k - th future step. represents the temperature of the metal heat - uniforming jacket at the k - th future step. represents the sample temperature at the moment in the future. represents the temperature of the metal heat - uniforming jacket at the moment in the future. represents the input current at the moment.

[0019] 3. Construction of the multi - constraint objective function: Construct a tracking error term to make the sample temperature Tr track the preset target temperature ; At the same time, control the input smoothness to limit the drastic change of the input current; and construct a penalty function for the part of the predicted temperature that exceeds the safe range to obtain the total objective function :

[0020]

[0021] where is the error tracking term, which makes the predicted sample temperature track the preset target temperature ; is the control input change rate term, which limits the drastic change of the input current; and are the weight coefficients of the tracking error and the control input smoothness respectively, which are used to balance the control ratios of the two control objectives of the input and output; is the prediction time domain, is the control time domain; is the reference trajectory, and the reference trajectory gives the expected state values that the system should reach at each future sampling moment; is the state constraint penalty function. The purpose is to prevent the output from exceeding the limit value.

[0022] 4. Solve the optimal control sequence: Use the projected gradient descent method to calculate the optimal control input, and use the finite difference method to calculate the gradient of the objective function with respect to the control input current :

[0023]

[0024] where is a small positive number, is the th standard basis vector, is the input at time

[0025] The input update is given by the following formula:

[0026]

[0027] where is the solution at the th iteration, represents the gradient of the objective function at , is the step size, is the projection operator, and its role is to map the input vector into the constraint set.

[0028] 5. Control Input Application and System State Update: In each control cycle, the first control input in the optimal input sequence is used as the current control signal and input into the heat transfer system, and the system state is updated according to the discrete model:

[0029]

[0030] where is the functional relationship between the input and the output.

[0031] The beneficial effects of the present invention are:

[0032] Based on the dynamic model and nonlinear predictive control, it can more accurately describe the system behavior of the semiconductor temperature-controlled synthesis reactor. At the same time, considering the input and output state constraints, it ensures that both the current and the temperature are within a safe and reasonable range, effectively preventing the temperature from exceeding the safe interval. And through rolling optimization and the projection gradient descent method, real-time solution is achieved. In addition, by using online feedback and optimization, the system has strong adaptability to model uncertainties and external disturbances, improving the overall robustness of the control system, achieving precise tracking of the target temperature and improving the temperature control accuracy and performance of the system. Description of the Drawings

[0033] Figure 1 is the block diagram of the temperature control system for the semiconductor temperature-controlled synthesis reactor;

[0034] Figure 2 is the temperature control curve of the PID control algorithm;

[0035] Figure 3 is the temperature control curve of the nonlinear model predictive control algorithm. Detailed Embodiments

[0036] The following will describe the present invention in detail with reference to the drawings and specific embodiments. It should be noted that the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosed content of the present invention more thorough and comprehensive.

[0037] A nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor provided by an embodiment of the present application includes the following steps:

[0038] Construction of the Dynamic Heat Transfer Model:

[0039] First, a heat transfer mechanism model of the semiconductor temperature-controlled synthesis reactor is established. Without considering the heat release of the compensation heating rod, the heat release of the chemical reaction, etc., only focusing on the heat exchange between the Peltier element and the sample through the metal heat uniform jacket; ignoring the heat dissipated by the sample through the kettle cover; only considering the heat transfer from the metal heat uniform jacket to the sample in the reaction kettle, then for the sample in the reaction kettle, there is the following heat balance equation:

[0040]

[0041] For the outer metal heat uniform jacket, considering its heat loss to the external environment, the heat transferred from the Peltier to the metal heat uniform jacket, and the heat transferred from the sample temperature in the reaction kettle to it, then for the metal heat uniform jacket, there is the following heat balance equation:

[0042]

[0043] Among them, represents the specific heat capacity and mass of the sample in the synthesis reactor, 、 represent the sample temperature and the temperature of the metal heat uniform jacket, represents the heat transfer coefficient between the sample and the inner wall of the reaction kettle, represent the specific heat capacity and mass of the metal heat uniform jacket of the synthesis reactor, β represents the heat dissipation coefficient, represents the environmental temperature, α represents the Peltier coefficient of the Peltier element, I represents the current applied to the Peltier element, R represents the internal resistance of the Peltier element, K represents the heat flow coefficient of the Peltier element itself, represents the hot end temperature of the Peltier element.

[0044] Discretization of the dynamic heat transfer model:

[0045] The heat dynamics of the synthesis reactor is essentially a continuous-time system, and the continuous-time dynamics of the semiconductor temperature-controlled synthesis reactor system can be described by the following differential equation:

[0046]

[0047] Among them, is the system state vector, is the control input, is the function describing the system dynamics.

[0048] Nonlinear model predictive control needs to perform predictive control based on the state trajectory of the model at the next N sampling points at the current moment. Therefore, the Euler method is used to discretize the continuous-time differential equation. Let the sampling period be , the discrete time , where For \(n = 0, 1, 2, \cdots\), the state variables at discrete times are defined as:

[0049]

[0050] The continuous-time differential equation (1) is:

[0051]

[0052] Using Euler's method, at we approximately have:

[0053]

[0054]

[0055] After rearrangement, the temperature expression at the \(k\)-th future step is obtained as:

[0056]

[0057] Similarly, the temperature expression at the \(k\)-th future step is obtained as:

[0058]

[0059] Construction of the multi-constraint objective function:

[0060] For the current input and sample temperature output of the semiconductor temperature-controlled synthesis reactor, boundary constraints need to be considered for the input current \(I\) to prevent excessive current from damaging the Peltier element. At the same time, state constraints need to be imposed on the sample temperature \(T_r\) to prevent thermal runaway.

[0061]

[0062]

[0063] where is the minimum value of the input current, is the maximum value of the input current, is the lower limit of the predicted temperature , is the upper limit of the predicted temperature .

[0064] Furthermore, to make the system operate within a safe range, when constructing the objective function, a penalty needs to be added to the part where the predicted temperature \(T_r\) exceeds the safe interval, as shown in the following equation:

[0065]

[0066] where is the penalty coefficient.

[0067] Meanwhile, construct the tracking error term , so that the predicted sample temperature tracks the preset target temperature .

[0068]

[0069] And in order to limit the drastic change of the input current, add the control input change rate term , to control the smoothness of the input, which is given by:

[0070]

[0071] where is the prediction horizon, is the control horizon.

[0072] To sum up, construct the total objective function :

[0073]

[0074] Solve the optimal control sequence:

[0075] After obtaining the objective function, use the projected gradient descent method to solve the optimal control sequence, and use the finite difference method to calculate the gradient of the objective function with respect to the control input :

[0076]

[0077] where is a small positive number, is the th standard basis vector, is the input at time

[0078] The input update is given by:

[0079]

[0080] where, is the update step size, represents the gradient of the objective function at , is the projection operator.

[0081] Next, project the updated input into the feasible region, that is, limit the input within the safe range:

[0082]

[0083] Control input and system state update:

[0084] After solving the optimal control sequence, the first control input in the optimal input sequence is used as the current control signal and input into the discrete model, and the Euler method is used to update the system state. At the same time, the updated system state is fed back into the next optimization:

[0085]

[0086] As Figure 1 shown, after introducing the nonlinear prediction model, the temperature control of the semiconductor temperature-controlled synthesis reactor is as follows: By setting the target temperature a smooth reference trajectory is generated , and constraint conditions are applied at each sampling stage and the optimal control quantity is obtained by rolling optimization , the optimal control quantity drives the controlled object to generate a temperature response , and at the same time, the nonlinear prediction model outputs the predicted temperature response , and the error between the two is calculated and fed back to the feedback correction.

[0087] The control effect of the present invention is described below in conjunction with the simulation temperature control process curve of the semiconductor temperature-controlled synthesis reactor.

[0088] Taking the isothermal control of raising the sample temperature from room temperature 25°C to 80°C as an example, Figure 2 and Figure 3 are the process output curves of the sample temperature obtained by using different temperature control algorithms, where Figure 2 is the sample temperature output curve obtained by using the PID temperature control algorithm. The sample temperature in the reaction kettle starts to rise from 25°C, and the output current first outputs at the maximum value of -12 A (the negative sign represents the current input direction). When the sample temperature reaches near the target temperature of 80°C, the PID control adjusts the input current magnitude to keep the sample temperature maintained near 80°C; Figure 3The sample temperature output curve obtained by using the non-linear model predictive temperature control algorithm mentioned in the present invention. The sample temperature in the reactor starts to rise from 25°C, and the output current first outputs at the maximum value of -12 A (the negative sign represents the current input direction). When the sample temperature reaches near the target temperature of 80°C, the non-linear model predictive control (NMPC) adjusts the input current magnitude to keep the sample temperature stable at 80°C. In terms of overshoot, settling time, and temperature control performance, the temperature control smoothness and convergence speed of the non-linear model predictive temperature control algorithm mentioned in the present invention are significantly better than those of PID. Moreover, compared with the input current calculated by PID, the current oscillation amplitude of the non-linear model predictive control algorithm is small and the settling time is fast, making the time for the system to reach the stable state shorter.

[0089] In summary, the present invention proposes a temperature control method for a semiconductor temperature-controlled synthesis reactor based on non-linear model predictive control. By establishing an accurate heat transfer dynamic model, designing a non-linear model predictive optimization problem with multiple constraints, and using the projected gradient descent method to solve the optimal control input, the real-time online control of the reactor temperature is achieved, significantly improving the stability of the temperature control process.

[0090] The above is only one embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention can be modified and changed according to actual situations. Any modifications, equivalent replacements, and improvements made within the principle of the present invention should be included within the scope of the present invention.

Claims

1. A nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor, characterized in that, It includes the following steps: Construct a dynamic heat transfer model: Based on the structure and thermal characteristics of a semiconductor temperature-controlled synthesis reactor, establish a dynamic heat transfer model that takes into account the sample temperature, structural temperature, and the non-linear influence of current on temperature; Model prediction output: Discretize the dynamic heat transfer model to obtain the prediction output of the discrete heat transfer model, which is used to predict the sample temperature and structural temperature at future times; Construct a multi-constraint objective function: Construct a multi-constraint objective function that includes a tracking error term, a control input smoothness term, and a penalty term for the predicted temperature exceeding the safe range; Solve the optimal control sequence: Use an optimization algorithm to calculate the optimal control input sequence to minimize the multi-constraint objective function; Control input application and system state update: In each control cycle, apply the first control input in the optimal control input sequence as the current control signal to the heat transfer system, and update the system state according to the discrete heat transfer model.

2. The nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 1, characterized in that, The dynamic heat transfer model takes into account the heat exchange between the sample and the metal heat jacket, the power of the Peltier element, and the influence of the ambient temperature on the system.

3. The nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 1 or 2, characterized in that, The discrete heat transfer model is obtained by discretizing the continuous-time dynamic heat transfer model based on the Euler method and is used to predict the sample temperature and the metal heat jacket temperature at multiple future sampling points.

4. The nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 3, characterized in that, The optimization algorithm uses the projected gradient descent method to calculate the gradient of the objective function with respect to the control input and performs iterative updates to solve the optimal control input sequence.

5. The nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 2, characterized in that, In the dynamic heat transfer model, there is a non-linear relationship between the power output of the Peltier element and the current applied to it, which takes into account the coupling of the thermoelectric effect and the Joule heat effect.

6. The nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 1, characterized in that, The tracking error term in the multi-constraint objective function is used to measure the deviation between the predicted temperature and the target temperature.

7. The nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 1, characterized in that, The control input smoothness term in the multi-constraint objective function is used to limit the change rate of the control input current, avoid drastic fluctuations in the current, and thus improve the stability and reliability of the control process.

8. The nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 1, characterized in that, The penalty term in the multi-constraint objective function penalizes the part of the predicted temperature that exceeds the set safe range to prevent temperature runaway and ensure that the reactor operates within the safe temperature range.

9. The nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 1 or 4, characterized in that, When solving the optimal control input sequence, the optimization algorithm uses the finite difference method to calculate the gradient of the objective function with respect to the control input to improve the efficiency and accuracy of the optimization process.

10. The nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 9, characterized in that, In the control input application and system state update step, the updated system state is used for the next optimization calculation through a feedback mechanism to achieve closed-loop control of the reactor temperature.

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