A nonlinear model prediction temperature control method for a semiconductor temperature-controlled synthesis reactor

Abstract

The present invention belongs to the fields of fine chemical reaction safety testing and automated chemistry technology, and specifically discloses a nonlinear model predictive temperature control method for a semiconductor temperature-controlled synthesis reactor. The method comprises the following steps: constructing a dynamic heat transfer model of the system based on the semiconductor temperature-controlled synthesis reactor; designing a nonlinear model predictive controller based on the heat transfer model of the synthesis reactor; constructing a multi-constraint objective function for nonlinear predictive control based on the characteristics of the controlled object; and solving the optimal control sequence for the nonlinear model predictive controller using the projected gradient method. Compared to traditional PID temperature control algorithms, the nonlinear model predictive temperature control algorithm designed by the present invention can achieve accurate prediction and control of the reactor temperature, ensuring that the chemical reaction proceeds at the optimal temperature and improving the robustness and adaptability of the control system.

Description

Technical Field

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

[0002] As core equipment in chemical production systems, synthesis reactors operate through complex multiphase physicochemical changes, interfacial mass and heat transfer, and dynamic energy balance processes, forming highly nonlinear, time-varying systems. Traditional processes often utilize a dynamic oil bath system coupled to the reactor's temperature control architecture, regulating the reactor's temperature through external heat exchange. Semiconductor-controlled synthesis reactors utilize Peltier elements for temperature control, offering advantages over dynamic oil bath systems in terms of faster response and greater anti-interference capabilities.

[0003] The semiconductor temperature-controlled synthesis reactor involved in this application is an intelligent instrument that can accurately simulate kettle-type semi-batch reaction processes in a laboratory environment. Equipped with a high-precision sensing system and advanced control algorithms, the device can monitor key parameters such as temperature, pressure, and feed quality within the reactor 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 capabilities, it provides a scientific basis for reaction safety risk assessment, process development, and optimization, and is an important scientific research instrument used in the field of fine chemicals for reaction safety assessment and automated chemistry research.

[0004] The semiconductor temperature-controlled and 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 uniform heating 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 reactor cover, a reactor, a metal uniform heating jacket, a Peltier current controller, and pipelines connecting the Peltier cooling element and the circulating water bath system.

[0005] The reactor is embedded in a metal heat-regulating jacket. Peltier elements and Peltier cooling elements are secured to the jacket's periphery via fasteners. A compensating heater and a stirring mechanism (consisting of a stirring paddle and a stirring driver) are secured to the jacket's upper end via the reactor lid. A circulating water bath is connected to the Peltier cooling element. Temperature sensors measure the circulating water bath, the sample temperature within the reactor, and the jacket's temperature. Temperature control in semiconductor-controlled synthesis reactors relies on the compensating heater and its power driver. Sample temperature is controlled by the Peltier elements, which transfer heat through the jacket.

[0006] In semiconductor temperature-controlled synthesis reactors, Peltier elements are often used to achieve rapid heating or cooling, thereby controlling the sample temperature within the reactor. However, the relationship between the Peltier element's input (usually current I) and its output (heat flow or temperature change at the hot and cold ends) is typically nonlinear. This nonlinearity stems primarily from the following factors: First, the coupling of the thermoelectric effect and the Joule heating effect. The Peltier element not only generates direct heat transfer due to current, but also generates Joule heating due to resistance, resulting in a complex nonlinear relationship between the actual temperature response and the input current. Second, the temperature dependence of the element's internal materials and changes in the operating environment can also cause nonlinear output response.

[0007] Furthermore, if the system structure and hardware performance remain unchanged, temperature control performance depends solely 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 nonlinear systems, the PID control algorithm may be unable to capture and compensate for the system's nonlinear behavior, resulting in suboptimal control results. Furthermore, the PID controller adjusts the control input only based on current and past error information, lacking the ability to predict future system behavior. Nonlinear systems often exhibit complex behavior, and insufficient predictive capabilities can easily lead to a slow response to future disturbances or nonlinear changes. Summary of the Invention

[0008] The present invention addresses the above-mentioned challenges by providing a nonlinear model-based predictive temperature control method for a semiconductor temperature-controlled synthesis reactor. By establishing a dynamic heat transfer model for the reactor, constructing a nonlinear predictive control problem with multiple constraints, and employing the projected gradient descent method to solve the optimal control input online, the method achieves precise control and real-time adjustment of the reactor temperature. This method exhibits high precision, real-time performance, the ability to satisfy multiple constraints, and robustness, making it suitable for demanding chemical reaction safety testing and automated chemical process control.

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

[0010] 1. Construction of 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 to consider the heat exchange between the sample temperature and the structure temperature, as well as the nonlinear effect of current on temperature. Its continuous-time dynamic model can be expressed as:

[0011]

[0012]

[0013]

[0014] Wherein, formula (1) is the heat balance equation of the sample in the reactor, which represents the heat exchange between the sample and the metal uniform heating jacket. Formula (2) is the heat balance equation of the metal uniform heating jacket, which represents the heat loss from the metal uniform heating jacket to the external environment, the heat transferred from the Peltier to the metal uniform heating jacket, and the heat exchange with the sample temperature in the reactor. Formula (3) is the power output expression of the Peltier element. represents the specific heat capacity and mass of the sample in the synthesis reactor, Indicates the rate of change of the sample temperature in the reactor, 、 Indicates the sample temperature and the metal uniform heating jacket temperature, represents the heat transfer coefficient between the sample and the inner wall of the reactor, represents the specific heat capacity and mass of the metal uniform heating jacket of the synthesis reactor, Indicates the temperature change rate of the metal uniform heating jacket, represents the cooling power of the Peltier element, represents the heat dissipation coefficient, Indicates the ambient temperature, represents the Peltier coefficient of the Peltier element, represents the current loaded on the Peltier element, represents the internal resistance of the Peltier element, represents the heat flow coefficient of the Peltier element itself, Indicates the hot-end temperature of the Peltier element.

[0015] 2. Model prediction output: The continuous dynamic heat transfer model is discretized using the Euler method, and the prediction output of the discrete heat transfer model is obtained:

[0016]

[0017]

[0018] in represents the sample temperature at the kth step in the future, represents the temperature of the metal uniform heating jacket in the kth step in the future, Indicates the future The sample temperature at the time, Indicates the future The temperature of the metal uniform heating jacket at the moment, Indicates the Input current at the moment.

[0019] 3. Construction of 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 and limit the drastic change of input current; and predict the temperature The penalty function is constructed for the part that exceeds the safety range to obtain the total objective function :

[0020]

[0021] in, is the error tracking term, making the predicted sample temperature Tracking preset target temperature ; To control the input change rate and limit the drastic changes in input current; and are the weight coefficients of tracking error and control input smoothness, respectively, which are used to balance the control proportions of the two control targets of input and output; For the prediction time domain, To control the time domain; The reference trajectory gives the state value that the system is expected to reach at each sampling moment in the future; is the state constraint penalty function. Its 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 the finite difference method to calculate the objective function About controlling input current Gradient:

[0023]

[0024] in is a small positive number, For the standard basis vectors, for Input at the moment.

[0025] The input update is given by:

[0026]

[0027] in, For the The solution at the iteration, Indicates The objective function gradient at is the step length, It is a projection operator, which is used to transform the input vector Mapped to a set of constraints.

[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, it is input into the heat transfer system and the system state is updated according to the discrete model:

[0029]

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

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

[0032] Based on dynamic models and nonlinear predictive control, the system behavior of semiconductor temperature-controlled synthesis reactors can be more accurately described, while simultaneously considering input and output state constraints to ensure that current and temperature remain within safe and reasonable ranges, effectively preventing the temperature from exceeding the safe range. Real-time solutions are achieved through rolling optimization and projected gradient descent. Furthermore, the use of online feedback and optimization makes the system highly adaptable to model uncertainties and external disturbances, improving the overall robustness of the control system, enabling precise tracking of the target temperature and enhancing the system's temperature control accuracy and performance. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0035] Figure 3 This is the temperature control curve of the nonlinear model predictive control algorithm. DETAILED DESCRIPTION

[0036] The present invention is described in detail below with reference to the accompanying drawings and specific implementation cases. 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 disclosure of the present invention more thorough and comprehensive.

[0037] The embodiment of the present application provides a nonlinear model prediction temperature control method for a semiconductor temperature-controlled synthesis reactor, comprising the following steps:

[0038] Dynamic heat transfer model construction:

[0039] First, the heat transfer mechanism of the semiconductor temperature-controlled synthesis reactor is modeled. The heat release of the compensating heating rod and the heat release of the chemical reaction are not considered. Only the heat exchange between the Peltier element and the sample through the metal uniform heating jacket is focused on. The heat loss from the sample through the reactor cover is ignored. Only the heat transfer from the metal uniform heating jacket to the sample in the reactor is considered. For the sample in the reactor, the following heat balance equation is obtained:

[0040]

[0041] For the outer metal uniform heating jacket, considering the heat loss to the external environment, the heat transferred from the Peltier to the metal uniform heating jacket, and the heat transferred from the sample temperature in the reactor to the metal uniform heating jacket, the following heat balance equation is obtained for the metal uniform heating jacket:

[0042]

[0043] in, represents the specific heat capacity and mass of the sample in the synthesis reactor, 、 Indicates the sample temperature and the metal uniform heating jacket temperature, represents the heat transfer coefficient between the sample and the inner wall of the reactor, represents the specific heat capacity and mass of the metal uniform heating jacket of the synthesis reactor, β represents the heat loss coefficient, represents the ambient temperature, α represents the Peltier coefficient of the Peltier element, I represents the current loaded on the Peltier element, R represents the internal resistance of the Peltier element, K represents the heat flow coefficient of the Peltier element itself, Indicates the hot-end temperature of the Peltier element.

[0044] Discretization of dynamic heat transfer model:

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

[0046]

[0047] in, is the system state vector, is the control input, is a function that describes the dynamics of the system.

[0048] Nonlinear model predictive control requires predictive control based on the state trajectory of N future sampling points of the model at the current moment. Therefore, the Euler method is used to discretize the continuous time differential equation, and the sampling period is set to , discrete moments ,in =0,1,2,…Define the state variables at discrete moments as:

[0049]

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

[0051]

[0052] Using Euler's method There are approximately:

[0053]

[0054]

[0055] Arrange to get the kth step in the future The temperature expression is:

[0056]

[0057] Similarly, we can get the kth step in the future The temperature expression is:

[0058]

[0059] Multi-constraint objective function construction:

[0060] For the current input and sample temperature output of the semiconductor temperature-controlled synthesis reactor, it is necessary to consider imposing boundary constraints on the input current I to prevent excessive current from damaging the Peltier element. At the same time, state constraints on the sample temperature Tr are required to prevent thermal runaway.

[0061]

[0062]

[0063] in is the minimum value of the input current, is the maximum value of the input current, To predict temperature The output lower limit, To predict temperature The output limit of .

[0064] Furthermore, in order to make the system work within a safe range, when constructing the objective function, it is necessary to add a penalty to the part of the predicted temperature Tr that exceeds the safe range, as shown in the following formula:

[0065]

[0066] in is the penalty coefficient.

[0067] Construct the tracking error term at the same time , so that the predicted sample temperature Tracks preset target temperature .

[0068]

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

[0070]

[0071] in For the prediction time domain, To control the time domain.

[0072] In summary, the overall objective function :

[0073]

[0074] Solve for the optimal control sequence:

[0075] After obtaining the objective function, the projected gradient descent method is used to solve the optimal control sequence, and the finite difference method is used to calculate the objective function About control input Gradient:

[0076]

[0077] in is a small positive number, For the standard basis vectors, for Input at the moment.

[0078] The input update is given by:

[0079]

[0080] in, is the update step size, Represents the objective function exist The gradient at is the projection operator.

[0081] Next, we will update the input Projecting into the feasible region limits the input to a safe range:

[0082]

[0083] Control input and system status update:

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

[0085]

[0086] like Figure 1 As shown in the figure, after the nonlinear prediction model is introduced, the temperature control of the semiconductor temperature-controlled synthesis reactor is as follows: by setting the target temperature Generate smooth reference trajectory , impose constraints at each sampling stage and output the optimal control quantity through rolling optimization , optimal control quantity Drive the controlled object to produce temperature response At the same time, the nonlinear prediction model outputs the predicted temperature response , and calculate the error between the two Feedback is sent back for correction.

[0087] The control effect of the present invention is described below with reference to a simulated temperature control process curve of a semiconductor temperature-controlled synthesis reactor.

[0088] For example, the isothermal control of raising the sample temperature from room temperature (25°C) to 80°C is as follows: Figure 2 and Figure 3 is the process output curve of the sample temperature obtained by using different temperature control algorithms, where Figure 2 The sample temperature output curve using the PID temperature control algorithm, the sample temperature in the reactor The temperature starts to rise from 25°C, and the output current is first output at the maximum value of -12A (the negative sign represents the current input direction). When the sample temperature reaches the target temperature of 80°C, the PID control adjusts the input current to keep the sample temperature around 80°C. Figure 3In this example, the sample temperature output curve obtained using the nonlinear model predictive temperature control algorithm described in this invention is shown. The sample temperature in the reactor begins to rise from 25°C, with the output current initially reaching a maximum value of -12A (the negative sign represents the direction of the current input). When the sample temperature reaches near the target temperature of 80°C, the nonlinear model predictive control (NMPC) adjusts the input current to maintain a stable sample temperature of 80°C. In terms of overshoot, stabilization time, and temperature control performance, the temperature control smoothness and convergence speed of the nonlinear model predictive temperature control algorithm described in this invention are significantly superior to those of PID. Furthermore, compared to the input current calculated by PID, the nonlinear model predictive control algorithm exhibits smaller current oscillations and faster stabilization time, resulting in a shorter time for the system to reach a stable state.

[0089] In summary, the present invention proposes a temperature control method for a semiconductor temperature-controlled synthesis reactor based on nonlinear model predictive control. This method establishes an accurate dynamic heat transfer model, designs a nonlinear model predictive optimization problem with multiple constraints, and utilizes projected gradient descent to solve for the optimal control input. This method achieves real-time online control of the reactor temperature and significantly improves the stability of the temperature control process.

[0090] The above description is merely one embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will appreciate that the present invention may be modified and altered in various ways based on practical circumstances. Any modifications, substitutions, and improvements within the scope of the present invention are intended to be included within the scope of the present invention.

Claims

1. A nonlinear model prediction temperature control method for a semiconductor temperature-controlled synthesis reactor, characterized in that: The following steps are involved: Constructing a dynamic heat transfer model: Based on the structure and thermal characteristics of the semiconductor temperature-controlled synthesis reactor, a continuous-time dynamic heat transfer model was established that took into account the nonlinear effects of sample temperature, metal uniform heating jacket temperature, and current on temperature. Model prediction output: Discretizing 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 the metal uniform heating jacket 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 predicted temperatures exceeding a safe range; Solving the optimal control sequence: using 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, the first control input in the optimal control input sequence is applied to the heat transfer system as the current control signal, and the system state is updated according to the discrete heat transfer model; The continuous-time dynamic heat transfer model is expressed as: (1) (2) (3) Wherein, formula (1) is the heat balance equation of the sample in the reactor, formula (2) is the heat balance equation of the metal uniform heating jacket, and formula (3) is the power output expression of the Peltier element. represents the specific heat capacity and mass of the sample in the synthesis reactor, The rate of change of sample temperature in the epicyclic reactor, 、 Indicates the sample temperature and the metal uniform heating jacket temperature, represents the heat transfer coefficient between the sample and the inner wall of the reactor, represents the specific heat capacity and mass of the metal uniform heating jacket of the synthesis reactor, Indicates the temperature change rate of the metal uniform heating jacket, represents the cooling power of the Peltier element, represents the heat dissipation coefficient, Indicates the ambient temperature, represents the Peltier coefficient of the Peltier element, represents the current loaded on the Peltier element, represents the internal resistance of the Peltier element, represents the heat flow coefficient of the Peltier element itself, Indicates the hot-end temperature of the Peltier element.

2. The nonlinear model prediction temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 1, 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 uniform heating jacket temperature at multiple sampling points in the future.

3. The nonlinear model prediction temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 2, characterized in that: The optimization algorithm adopts the projected gradient descent method to solve the optimal control input sequence by calculating the gradient of the objective function with respect to the control input and performing iterative updates.

4. The nonlinear model prediction temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 1, characterized in that: In the dynamic heat transfer model, there is a nonlinear relationship between the power output of the Peltier element and the current loaded thereon, and the relationship takes into account the coupling of the thermoelectric effect and the Joule heating effect.

5. The nonlinear model prediction 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 to ensure that the sample temperature can accurately track the preset target temperature trajectory.

6. The nonlinear model prediction 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 rate of change of the control input current, avoid severe fluctuations in the current, and thus improve the stability and reliability of the control process.

7. The nonlinear model prediction 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 portion of the predicted temperature that exceeds a set safety range, thereby preventing temperature runaway and ensuring that the reactor operates within a safe temperature range.

8. The nonlinear model prediction temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 1 or 3, 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.

9. The nonlinear model prediction temperature control method for a semiconductor temperature-controlled synthesis reactor according to claim 8, 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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