Continuous casting control method for isothermal quenching ductile iron production

Abstract

The application relates to the technical field of horizontal continuous casting temperature control, in particular to a continuous casting control method for isothermal quenching nodular cast iron production, which comprises the following steps: collecting the temperature at each preset position in a heating furnace in real time, collecting the heating power of the heating furnace and the temperature of a casting; for the holding stage in the austenitizing process and the isothermal quenching process, adjusting the time constant of a reference model in a Smith predictor used for temperature control, controlling the temperature based on the adjusted Smith predictor, and adjusting the time constant; the process of adjusting the time constant comprises the following steps: obtaining the temperature distribution factor, the thermal response lag time and the power influence factor at each collection time; then obtaining the heat transfer compensation coefficient at each collection time, and adjusting the time constant of the reference model in the Smith predictor. The application aims to improve the accuracy of temperature control and avoid temperature fluctuation in the holding stage.

Description

Technical Field

[0001] This application relates to the field of temperature control technology for horizontal continuous casting, and specifically to a continuous casting control method for the production of isothermal quenched ductile iron. Background Technology

[0002] Isothermal hardened ductile iron is a high-performance ductile iron material that can be obtained by performing a special isothermal hardening process on ductile iron. Since temperature is a key factor affecting the hardness of the profile, it is necessary to strictly control the austenitizing temperature and isothermal hardening temperature during the continuous casting of isothermal hardened ductile iron.

[0003] Because the heating furnace in continuous casting equipment has thermal inertia, the temperature cannot change in time after the control signal is issued, i.e., control delay. Therefore, Smith estimators are often introduced to reduce control delay and avoid overshoot. However, after long-term use, the heating furnace may develop scale due to combustion products, which increases heat transfer resistance and changes the heat transfer coefficient. Therefore, the traditional Smith estimator with a fixed time constant is less effective in reducing control delay, resulting in poor temperature control performance. Summary of the Invention

[0004] In view of the above, it is necessary to provide a continuous casting control method for the production of isothermal quenched ductile iron. Compared with the traditional continuous casting control method for the production of isothermal quenched ductile iron, it improves the accuracy of temperature control and avoids temperature fluctuations during the holding stage.

[0005] The continuous casting control method for isothermal quenched ductile iron production in this application adopts the following technical solution:

[0006] One embodiment of this application provides a continuous casting control method for the production of isothermally quenched ductile iron, the method comprising the following steps:

[0007] The temperature at each preset location inside the heating furnace is collected in real time, as are the heating power of the heating furnace and the temperature of the casting.

[0008] For the holding stage during the austenitizing and isothermal quenching processes, the time constant of the reference model in the Smith predictor used for temperature control is adjusted. The temperature is then controlled based on the adjusted Smith predictor. The process of adjusting the time constant is as follows:

[0009] For the heat preservation stage in the austenitizing process, the temperature distribution at all the preset positions in the heating furnace at each sampling time is analyzed to obtain the temperature distribution factor at each sampling time. Combined with the degree of deviation of the casting temperature from the preset austenitizing temperature at each sampling time, the thermal response hysteresis time at each sampling time is obtained.

[0010] The actual heat preservation time up to each collection moment is obtained. By the difference between the heating power at each collection moment and the preset heating power, and the degree of closeness between the actual heat preservation time and the preset heat preservation time, the power influence factor at each collection moment is obtained.

[0011] By using the temperature distribution factor, thermal response lag time, and power influence factor at each acquisition time, the heat transfer compensation coefficient at each acquisition time is obtained, and the time constant of the reference model in the Smith predictor during the austenitization process is adjusted.

[0012] For the holding stage in the isothermal quenching process, the time constant of the reference model in the Smith predictor is adjusted according to the method of adjusting the time constant of the reference model in the austenitizing process.

[0013] In one embodiment, the process of controlling the temperature based on the adjusted Smith predictor is as follows:

[0014] The feedforward gain matrix and feedback compensation matrix in the Smith predictor are updated in real time using a preset Lyapunov function.

[0015] During the heat preservation stage of the austenitization process, The PID controller in the Smith predictor is input, and the output is a control signal. This control signal controls the heating power of the furnace. This represents the feedforward gain matrix at the current time. This indicates the preset austenitizing temperature; This represents the feedback compensation matrix at the current moment; The current temperature of the casting;

[0016] For the holding stage in the isothermal quenching process, the heating power of the holding stage in the isothermal quenching process is controlled according to the heating power control method of the holding stage in the austenitizing process, wherein the preset austenitizing temperature is replaced by the preset isothermal quenching temperature.

[0017] In one embodiment, the process of determining the temperature distribution factor is as follows:

[0018] Calculate the average temperature at all preset locations inside the heating furnace at each data acquisition time.

[0019] Calculate the difference between the temperature at each preset location inside the heating furnace and the average value at each data collection time;

[0020] The temperature distribution factor is positively correlated with the difference value.

[0021] In one embodiment, the temperature distribution factor is the mean of all the difference values ​​at each acquisition time.

[0022] In one embodiment, the process for determining the thermal response hysteresis time is as follows:

[0023] Calculate the difference between the casting temperature and the preset austenitizing temperature at each data acquisition time.

[0024] The thermal response hysteresis time is positively correlated with the temperature distribution factor and the difference, respectively.

[0025] In one embodiment, the expression for the thermal response hysteresis time is:

[0026] In the formula, This represents the thermal response lag time at the t-th data acquisition moment; represents the positive number obtained by mapping the temperature distribution factor at the t-th acquisition time; ln() represents the logarithmic function with the natural constant as the base; This represents the temperature of the casting at the t-th data collection time. Indicates the preset austenitizing temperature; This indicates a preset value greater than 1.

[0027] In one embodiment, the process for determining the power influence factor is as follows:

[0028] Calculate the difference between the heating power at each data acquisition time and the preset heating power;

[0029] Calculate the ratio of the actual insulation time to the preset insulation time;

[0030] The power influence factor is positively correlated with the ratio and negatively correlated with the difference.

[0031] In one embodiment, the power influence factor is calculated as follows:

[0032] Calculate the reciprocal of the sum of the difference and a preset constant greater than 0;

[0033] The power influence factor is the product of the reciprocal and the ratio.

[0034] In one embodiment, the process of determining the heat transfer compensation coefficient is as follows:

[0035] Calculate the sum of the temperature distribution factor and the thermal response hysteresis time;

[0036] The heat transfer compensation coefficient is the normalized value of the product of the accumulated value and the power influence factor.

[0037] In one embodiment, the adjustment of the time constant of the reference model in the Smith predictor during the austenitization process is expressed as follows:

[0038] In the formula, This represents the time constant at the (t+1)th data acquisition time. This represents the time constant at the t-th acquisition time. This represents the heat transfer compensation coefficient at the t-th data acquisition time.

[0039] This application has at least the following beneficial effects:

[0040] This application takes into account the characteristic that the heat transfer of the heating furnace may be affected by the scaling of combustion products after long-term use. By analyzing the temperature distribution in different areas of the heating furnace, a temperature distribution factor is obtained to characterize the speed of the heat transfer process in the heating furnace. Then, combined with the degree of deviation of the casting temperature from the preset temperature, the thermal response lag time is obtained to characterize the degree of lag caused by heat transfer, so that corresponding compensation measures can be taken according to the severity of the lag.

[0041] Furthermore, considering that even with the same degree of scaling, the required compensation varies depending on the heating power, a power influence factor is obtained by assessing the closeness between the actual and preset holding times, as well as the degree to which the heating power deviates from the preset heating power. This factor reflects the impact of heating power on temperature. Subsequently, by combining the temperature distribution factor, thermal response lag time, and power influence factor, the control lag degree of heat transfer lag is obtained. The time constant is adjusted based on the control lag degree to improve the lag compensation accuracy of the Smith predictor, thereby improving the accuracy of temperature control and preventing temperature fluctuations during the holding period. Attached Figure Description

[0042] To more clearly illustrate the technical solutions and advantages in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 A flowchart of the steps for the continuous casting control method for isothermal quenched ductile iron production provided in this application;

[0044] Figure 2 A simplified schematic diagram of the heating furnace;

[0045] Figure 3 This is a schematic diagram illustrating the process of obtaining the heat transfer compensation coefficient. Detailed Implementation

[0046] In the description of the embodiments in this application, the words "exemplary," "or," and "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design scheme described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design schemes. Specifically, the use of the words "exemplary," "or," and "for example" is intended to present the relevant concepts in a specific manner.

[0047] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. It should be understood that, unless otherwise stated, " / " in this application means "or".

[0048] It should also be noted that the terms "first" and "second" in this application are used to distinguish similar objects, rather than to describe a specific order or sequence.

[0049] The following description, in conjunction with the accompanying drawings, details the specific scheme of the continuous casting control method for isothermal quenching ductile iron production provided in this application.

[0050] This application provides a continuous casting control method for isothermal quenching ductile iron production, specifically, the following continuous casting control method for isothermal quenching ductile iron production is provided. Please refer to [link to relevant documentation]. Figure 1 The method includes the following steps:

[0051] Step S1: Real-time acquisition of the temperature at each preset location inside the heating furnace, and real-time acquisition of the heating power of the heating furnace and the temperature of the casting.

[0052] Temperature sensors are installed inside the heating furnace during the isothermal quenching of ductile iron production. Figure 2 This is a simplified schematic diagram of the heating furnace. Figure 2 The solid rectangles represent the heating furnace, and the dashed rectangles represent the castings. Temperature sensors 1 are installed 10cm above the castings. (Refer to...) Figure 2 At position 1, install temperature sensor 4 50cm below the casting, for reference. Figure 2 At position 4, temperature sensor 2 is installed on the left side of the casting, 50cm from the inner wall of the heating furnace. (Refer to...) Figure 2 Position 2: Install temperature sensor 3 on the right side of the casting, 50cm from the inner wall of the heating furnace, for reference. Figure 2 At position 3, each temperature sensor is used to collect the temperature inside the heating furnace in real time. Simultaneously, a power sensor is used to collect the heating power of the furnace in real time. Furthermore, since position 1 is closest to the casting in this embodiment, the temperature at position 1 is used to represent the temperature of the casting.

[0053] It should be noted that 10cm and 50cm are merely one embodiment of this application, and implementers can set specific values ​​themselves. This application does not impose any special restrictions.

[0054] In this embodiment, the sampling frequency of both the temperature sensor and the power sensor is 10Hz. The sampling frequency value is preset by the user and can be set by the implementer. This application does not impose any special restrictions.

[0055] Data collected from all temperature and power sensors is cleaned to remove outliers, and missing values ​​are filled in using a data filling method. Data cleaning is a well-known technique and will not be described further in this application.

[0056] To avoid the influence of different dimensions on subsequent analysis, the data collected by the temperature sensor is normalized together with the preset austenitizing temperature and the preset isothermal quenching temperature, and the data collected by the power sensor is normalized together with the preset heating power. In this embodiment, the Min-Max normalization method is used for normalization. The Min-Max normalization method is a well-known technique and will not be described in detail here.

[0057] In this embodiment, interpolation is used to fill missing values ​​in the cleaned data. Interpolation is a well-known technique and will not be described in detail here. As other implementation methods, based on the ability to fill missing values ​​in the cleaned data, implementers may use other existing techniques, such as mean filling method, median filling method, etc. This application does not impose any special restrictions.

[0058] Step S2: Adjust the time constant of the reference model in the Smith predictor.

[0059] There are two key processes in isothermal quenching ductile iron continuous casting: the austenitizing process and the isothermal quenching process.

[0060] Austenitizing refers to the process of heating steel to above a critical temperature, causing all or part of the steel's microstructure to transform into austenite. In carbon steel, the microstructure at room temperature is generally ferrite and cementite. When heated to the austenitizing temperature, the carbon content in the ferrite gradually increases, and it begins to transform into austenite. Continued heating and holding for a certain time are necessary to allow the carbon in the austenite to diffuse fully, achieving homogenization. Temperature is a key factor affecting austenitizing; the higher the temperature, the faster the austenitizing rate. However, excessively high temperatures may lead to problems such as coarse grains. In this embodiment, the austenitizing temperature is set to 950℃, and the holding time is set to 1.5 hours. The values ​​of the austenitizing temperature and the holding time are preset by the user and can be set by the implementer; this application does not impose any special restrictions.

[0061] The isothermal quenching process follows the austenitizing process. After austenitizing, the casting is rapidly cooled from the austenitizing temperature to the isothermal quenching temperature. This cooling process must be fast enough to inhibit the formation of other structures such as pearlite and bainite. The casting is held at the isothermal quenching temperature for a certain period of time. At this temperature, over time, carbon in the austenite diffuses into the ferrite, while the ferrite grows in a needle-like form, eventually forming an austenitic structure. In this embodiment, the isothermal quenching temperature is set to 300°C, and the holding time is set to 2 hours. The values ​​of the isothermal quenching temperature and the holding time are preset by the user and can be set by the implementer; this application does not impose any special restrictions.

[0062] For the holding stage in the austenitizing and isothermal quenching processes, the heating power of the furnace can be controlled by the control signal output of a PID (Proportional-Integral-Derivative Controller), thereby controlling the temperature. However, the furnace has thermal inertia; when the temperature needs to be increased, the furnace's internal structure needs to absorb a certain amount of heat to effectively transfer it to the casting. Conversely, when the temperature needs to be decreased, a certain amount of time is required for the heat in the casting to dissipate, leading to control delay and temperature fluctuations, which in turn reduces the performance of the casting. In this case, a Smith predictor can be introduced into the PID control process for compensation, reducing control delay and preventing overshoot.

[0063] The Smith predictor is a control strategy used to compensate for controlled objects with pure time delay characteristics. It consists of a reference model and a conventional controller; in this embodiment, the conventional controller is a PID controller. The reference model is used to simulate the pure time delay of the controlled object. By predicting the pure time delay, the output of the controlled object is adjusted in advance, thereby improving the control performance of the controlled object.

[0064] The time constant is a crucial parameter describing the dynamic response characteristics of a Smith predictor, reflecting its speed of response to input changes. Because traditional Smith predictors do not account for furnace fouling, a fixed time constant cannot accurately reflect the actual heat transfer situation, thus affecting the predictor's performance. Therefore, adaptive adjustment of the time constant is necessary to enable the Smith predictor to better adapt to changes in the heat transfer process.

[0065] A larger time constant results in a slower response of the Smith predictor to temperature changes. When heat transfer efficiency decreases, such as in cases of severe scaling in the furnace, the time constant should be increased to avoid over-adjustment of the heating equipment, which could lead to greater temperature fluctuations and instability in temperature control. Conversely, a smaller time constant results in a faster response of the Smith predictor to temperature changes. However, the time constant should not be too small to avoid over-reacting to normal temperature fluctuations, leading to temperature instability. Take the holding stage in the austenitizing process as an example.

[0066] Step S2.1: By analyzing the temperature distribution at all the preset positions in the heating furnace at each sampling time, the temperature distribution factor at each sampling time is obtained. Combined with the degree to which the casting temperature deviates from the preset austenitizing temperature at each sampling time, the thermal response hysteresis time at each sampling time is obtained.

[0067] After prolonged use, the combustion products of fuel in a heating furnace can lead to scaling. This scaling affects gas flow within the furnace, causing uneven temperature distribution and a decrease in the heat transfer coefficient. This is because scaling occupies space, reducing the cross-sectional area of ​​the gas flow channels. According to fluid mechanics principles, with a constant gas flow rate, a smaller channel cross-sectional area leads to increased gas velocity and flow resistance. Simultaneously, scaling increases the surface roughness of the furnace's internal surfaces. This roughness disrupts the laminar boundary layer, making it easier for the gas flow to transition from laminar to turbulent. In turbulent flow, collisions and mixing between gas molecules are more intense, significantly increasing flow resistance.

[0068] In some complex heating furnace structures, scaling may accumulate more severely in localized areas, even causing blockages in some channels. This alters the gas flow path, resulting in uneven airflow distribution. Uneven airflow leads to uneven temperature distribution in different areas of the heating furnace, affecting heat transfer efficiency.

[0069] Based on the above analysis, by analyzing the temperature distribution at all the preset locations inside the heating furnace at each sampling time, the temperature distribution factor at each sampling time is obtained, and its expression is:

[0070] In the formula, The temperature distribution factor at the t-th sampling time is represented; N represents the number of preset locations; This represents the temperature at the i-th preset position at the t-th data collection time. This represents the average temperature at all the preset locations at the t-th sampling time. Wherein, calculation... and The absolute value of the difference is merely one embodiment of this application. As other implementations, in order to achieve measurement... and Based on the differences between them, implementers may use other calculation methods, such as the square of the difference, the ratio, etc., and this application does not impose any special restrictions.

[0071] It should be noted that for a heating furnace, the greater the temperature difference between different areas, the more uneven the gas flow, that is, the more serious the scaling phenomenon, the more serious the impact on heat transfer during heating, and the greater the compensation deviation of the Smith predictor output.

[0072] The larger the calculated temperature distribution factor, the more severe the scaling in the furnace, meaning the greater the impact on the heat transfer process. This results in a larger compensation deviation in the Smith predictor output, leading to more severe control lag and requiring a larger time delay for compensation. Conversely, the smaller the temperature distribution factor, the less the impact on the heat transfer process, requiring a smaller time constant.

[0073] The temperature distribution factor can only characterize the speed of heat transfer in the furnace. In order to obtain the time that the temperature change lags behind the expected time of the Smith predictor, it is also necessary to consider the temperature change of the casting during the heating process.

[0074] Based on the above analysis, the thermal response hysteresis time at each sampling moment is obtained by using the temperature distribution factor at each sampling moment and the degree to which the casting temperature deviates from the preset austenitizing temperature at each sampling moment. The expression is as follows:

[0075] In the formula, This represents the thermal response lag time at the t-th data acquisition moment; represents the positive number obtained by mapping the temperature distribution factor at the t-th acquisition time; ln() represents the logarithmic function with the natural constant as the base; This represents the temperature of the casting at the t-th data collection time. This indicates the preset austenitizing temperature, which is 950°C in this embodiment; This represents a preset value greater than 1, used to ensure that the calculation result of the logarithmic function is positive. In this embodiment, The value is 1.01. The value is preset by the user, and the implementer can set it according to the actual situation. This application does not impose any special restrictions.

[0076] The purpose of mapping the temperature distribution factor to a positive number is to avoid the situation where the thermal response lag time is forced to 0 when the temperature distribution factor is 0. There are many ways to map data to a positive number, such as calculating the sum of the data and a preset value greater than 0, or using the data as the exponent of an exponential function with the natural constant as the base. In this embodiment, the purpose of mapping the temperature distribution factor to a positive number is achieved by calculating the sum of the temperature distribution factor and a preset value greater than 0. The value of the preset value greater than 0 is preset by the user and can be set by the implementer according to the actual situation. In this embodiment, the value of the preset value greater than 0 is 0.01.

[0077] It should be noted that, for the heat preservation process, the smaller the difference between the casting temperature and the preset austenitizing temperature, the shorter the thermal response lag time; conversely, the greater the difference, the longer the thermal response lag time. During heat transfer, temperature changes over time typically follow an exponential law. The logarithmic function in the formula reflects the nonlinear characteristics of temperature changes during heat transfer. The logarithmic function transforms the exponential temperature change relationship into a form that allows for direct calculation of the thermal response lag time.

[0078] The larger the calculated thermal response lag time, the more severe the control lag caused by heat transfer, and the more the Smith predictor needs to pay attention to the impact of lag on the control effect and take corresponding compensation measures; otherwise, the shorter the control lag time, the more the time constant should be reduced.

[0079] For the holding stage in the isothermal quenching process, the thermal response lag time at each sampling moment during the holding stage is calculated using the same method as in the austenitizing process. The only difference is that the preset austenitizing temperature is replaced with the preset isothermal quenching temperature. In this embodiment, the preset isothermal quenching temperature is 300℃.

[0080] Step S2.2: Obtain the actual heat preservation time up to each collection time. By the difference between the heating power and the preset heating power at each collection time, and the degree of closeness between the actual heat preservation time and the preset heat preservation time, obtain the power influence factor at each collection time.

[0081] Since the required compensation for scaling varies even for the same degree of scaling under different power levels in the heating furnace, the actual holding time up to each sampling moment is obtained. By analyzing the difference between the heating power and the preset heating power at each sampling moment, and the closeness of the actual holding time to the preset holding time, the power influence factor at each sampling moment is derived. The expression is as follows:

[0082] In the formula, This represents the power influence factor at the t-th acquisition time. This represents the heating power of the furnace at the t-th data collection time. This represents the preset heating power during the holding stage of the austenitizing process. In this embodiment, the preset heating power is 50 kW. The moment when the casting temperature first reaches the preset austenitizing temperature is taken as the initial moment. This represents the time interval between the initial time and the t-th acquisition time, i.e., the actual heat preservation time up to the t-th acquisition time; This indicates the preset holding time for the holding stage during the austenitization process; This indicates a preset constant greater than 0, used to avoid a denominator of 0. The value is preset by a person, and the implementer can set it himself. In this embodiment... The value is 0.01. The 50kW value is merely one embodiment of this application; implementers can set its value as they see fit.

[0083] It should be noted that: the greater the difference between the heating power during heat preservation and the target heating power, the smaller the time constant should be to make the Smith predictor's compensation more sensitive and avoid temperature deviations. Conversely, the closer the heat preservation time is to the target heat preservation time, the larger the time constant should be to prevent temperature fluctuations.

[0084] The larger the calculated power influence factor, the greater the influence of the heat preservation time and the heating power of the furnace during the heat preservation process. In this case, the time constant should be increased to avoid excessive compensation and frequent temperature fluctuations. Conversely, the time constant should be decreased to avoid temperature deviations.

[0085] For the holding stage in the isothermal quenching process, the power influence factor at each sampling moment during the holding stage in the austenitizing process is calculated according to the calculation method of the power influence factor at each sampling moment during the holding stage in the isothermal quenching process. Specifically, the preset austenitizing temperature needs to be replaced with the preset isothermal quenching temperature, the preset heating power of the holding stage in the austenitizing process needs to be replaced with the preset heating power of the holding stage in the isothermal quenching process, and the preset holding time of the holding stage in the austenitizing process needs to be replaced with the preset holding time of the holding stage in the isothermal quenching process. In this embodiment, the preset heating power of the holding stage in the isothermal quenching process is 20 kW. 20 kW is merely one embodiment of this application; implementers can set its value as they see fit.

[0086] Step S2.3: By using the temperature distribution factor, thermal response lag time and power influence factor at each acquisition time, the heat transfer compensation coefficient at each acquisition time is obtained, and the time constant of the reference model in the Smith predictor during the austenitization process is adjusted.

[0087] Furthermore, by analyzing the temperature distribution factor, thermal response lag time, and power influence factor at each acquisition moment, the heat transfer compensation coefficient is obtained. This coefficient characterizes the severity of heat transfer lag relative to the response capability of the Smith predictor, as the response capability and speed of the Smith predictor directly determine its ability to make timely and accurate adjustments to temperature deviations. The heat transfer compensation coefficient clarifies the degree of attention and compensation required for heat transfer lag when optimizing the Smith predictor, thus better coordinating the relationship between the heat transfer process and the Smith predictor. The expression for the heat transfer compensation coefficient at each acquisition moment is as follows:

[0088] In the formula, Represents the heat transfer compensation coefficient at the t-th acquisition time; norm() represents the normalization operation; This represents the power influence factor at the t-th acquisition time. This represents the temperature distribution factor at the t-th data acquisition time. This represents the thermal response lag time at the t-th acquisition time. In this embodiment, the hyperbolic tangent function is used to... Normalization is performed.

[0089] It should be noted that the larger the calculated heat transfer compensation coefficient, the more severe the scaling in the heating furnace, which means that the control lag caused by heat transfer lag is more severe. The time constant should be increased to avoid overshoot and temperature fluctuations.

[0090] Furthermore, the time constant of the reference model in the Smith predictor is adjusted using a heat transfer compensation coefficient, expressed as follows:

[0091] In the formula, This represents the time constant at the (t+1)th data acquisition time. This represents the time constant at the t-th acquisition time. This represents the heat transfer compensation coefficient at the t-th acquisition time. It should be noted that in this embodiment, the initial time constant is 10. The value of the initial time constant depends on the actual dynamic characteristics of the controlled object, and the implementer can set it according to the actual situation; this application does not impose any special restrictions. To achieve a better balance between the compensation effect and the stability of the controlled object, the initial heat transfer compensation coefficient is 0.5. The implementer can set the value of the heat transfer compensation coefficient according to the actual situation; this application does not impose any special restrictions. A schematic diagram of the heat transfer compensation coefficient acquisition process is shown below. Figure 3 As shown.

[0092] Step S3: Control the temperature based on the adjusted Smith predictor.

[0093] The reference model is a time-delay-free approximation of the controlled object. Since the controlled object has uncertain parameters, a Lyapunov function is introduced to obtain the adaptive law for each uncertain parameter, and the uncertain parameters are adjusted in real time. The specific process is as follows:

[0094] In this embodiment, the expression for the Lyapunov function is: In the formula, V represents the Lyapunov function; e represents the difference between the casting temperature and the preset austenitizing temperature. This indicates gain uncertainty; Indicates the uncertainty of the time constant; Let F represent the feedforward gain matrix and F represent the feedback compensation matrix.

[0095] In this embodiment, the gain uncertainty, time constant uncertainty, feedforward gain matrix and feedback compensation matrix are all simplified to represent a single value. The initial values ​​of the gain uncertainty, time constant uncertainty, feedforward gain matrix and feedback compensation matrix are 0, 0, 0.1 and 0.2, respectively. The initial values ​​of the gain uncertainty, time constant uncertainty, feedforward gain matrix and feedback compensation matrix are preset by the user. The implementer can set them according to the actual situation. This application does not impose any special restrictions.

[0096] Based on the derivation of the adaptive law using Lyapunov functions, the gain uncertainty, time constant uncertainty, feedforward gain matrix, and feedback compensation matrix are updated. The adaptive law for gain uncertainty is then applied. Adaptive law for time constant uncertainty Adaptive law of feedforward gain matrix Adaptive law of feedback compensation matrix The expressions are as follows: , , , In the formula, e represents the difference between the casting temperature and the preset austenitizing temperature; Z represents the preset austenitizing temperature; Z represents the temperature of the casting. , , , All values ​​represent preset values ​​greater than 0, used to control the speed of parameter updates. If the value is too large, the parameter updates too quickly, potentially causing instability in the controlled object; if the value is too small, the response speed is too slow. Therefore, in this embodiment, to balance the stability and response speed of the controlled object, , , , The values ​​are 0.05, 0.05, 0.001, and 0.001, respectively. , , , The value of is preset by the user and can be set by the implementer; this application does not impose any special restrictions. The derivation of the adaptive law based on the Lyapunov function is a well-known technique and will not be elaborated upon here.

[0097] Furthermore, The error signal at the current moment is input to the PID controller in the Smith predictor. The PID controller outputs a control signal, which is then transmitted to the heating power regulator of the furnace. The heating power regulator adjusts the heating power of the furnace to maintain a stable temperature. This represents the feedforward gain matrix at the current time. This indicates the preset austenitizing temperature; This represents the feedback compensation matrix at the current moment; The temperature of the casting at the current moment.

[0098] For the holding stage in the isothermal quenching process, the heating power of the holding stage in the isothermal quenching process is controlled according to the heating power control method of the holding stage in the austenitizing process, wherein the preset austenitizing temperature is replaced by the preset isothermal quenching temperature.

[0099] In summary, this application takes into account the characteristic that the heat transfer of the heating furnace may be affected by the scaling of combustion products after long-term use. By analyzing the temperature distribution in different areas of the heating furnace, a temperature distribution factor is obtained to characterize the speed of the heat transfer process in the heating furnace. Then, combined with the degree of deviation of the casting temperature from the preset temperature, the thermal response lag time is obtained to characterize the degree of lag caused by heat transfer, so that corresponding compensation measures can be taken according to the severity of the lag.

[0100] Furthermore, considering that even with the same degree of scaling, the required compensation varies depending on the heating power, a power influence factor is obtained by assessing the closeness between the actual and preset holding times, as well as the degree to which the heating power deviates from the preset heating power. This factor reflects the impact of heating power on temperature. Subsequently, by combining the temperature distribution factor, thermal response lag time, and power influence factor, the control lag degree of heat transfer lag is obtained. The time constant is adjusted based on the control lag degree to improve the lag compensation accuracy of the Smith predictor, thereby improving the accuracy of temperature control and avoiding temperature fluctuations.

[0101] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than that shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. In the descriptions corresponding to the flowcharts and block diagrams in the accompanying drawings, the operations or steps corresponding to different blocks may also occur in a different order than disclosed in the description, and sometimes there is no specific order between different operations or steps. For example, two consecutive operations or steps may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. Each block in a block diagram and / or flowchart, and combinations of blocks in a block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0102] It will be apparent to those skilled in the art that this application is not limited to the details of the exemplary embodiments described above, and that this application can be implemented in other specific forms without departing from its essential characteristics. Therefore, the embodiments described above should be considered exemplary and non-limiting in all respects.

Claims

1. A continuous casting control method for the production of isothermally quenched ductile iron, characterized in that, The method includes the following steps: The temperature at each preset location inside the heating furnace is collected in real time, as are the heating power of the heating furnace and the temperature of the casting. For the holding stage during the austenitizing and isothermal quenching processes, the time constant of the reference model in the Smith predictor used for temperature control is adjusted. The temperature is then controlled based on the adjusted Smith predictor. The process of adjusting the time constant is as follows: For the heat preservation stage in the austenitizing process, the temperature distribution at all the preset positions in the heating furnace at each sampling time is analyzed to obtain the temperature distribution factor at each sampling time. Combined with the degree of deviation of the casting temperature from the preset austenitizing temperature at each sampling time, the thermal response hysteresis time at each sampling time is obtained. The actual heat preservation time up to each collection moment is obtained. By the difference between the heating power at each collection moment and the preset heating power, and the degree of closeness between the actual heat preservation time and the preset heat preservation time, the power influence factor at each collection moment is obtained. By using the temperature distribution factor, thermal response lag time, and power influence factor at each acquisition time, the heat transfer compensation coefficient at each acquisition time is obtained, and the time constant of the reference model in the Smith predictor during the austenitization process is adjusted. For the holding stage in the isothermal quenching process, the time constant of the reference model in the Smith predictor is adjusted according to the method of adjusting the time constant of the reference model in the austenitizing process. The process of controlling the temperature based on the adjusted Smith predictor is as follows: The feedforward gain matrix and feedback compensation matrix in the Smith predictor are updated in real time using a preset Lyapunov function. During the heat preservation stage of the austenitization process, The PID controller in the Smith predictor is input, and the output is a control signal. This control signal controls the heating power of the furnace. This represents the feedforward gain matrix at the current time. This indicates the preset austenitizing temperature; This represents the feedback compensation matrix at the current moment; The current temperature of the casting; For the holding stage in the isothermal quenching process, the heating power of the holding stage in the isothermal quenching process is controlled according to the heating power control method of the holding stage in the austenitizing process, wherein the preset austenitizing temperature is replaced with the preset isothermal quenching temperature. The process for determining the thermal response hysteresis time is as follows: Calculate the difference between the casting temperature and the preset austenitizing temperature at each data acquisition time. The thermal response hysteresis time is positively correlated with the temperature distribution factor and the difference, respectively. The process for determining the heat transfer compensation coefficient is as follows: Calculate the sum of the temperature distribution factor and the thermal response hysteresis time; The heat transfer compensation coefficient is the normalized value of the product of the accumulated value and the power influence factor; The time constant of the reference model in the Smith predictor during the austenitization process is adjusted as follows: In the formula, This represents the time constant at the (t+1)th data acquisition time. This represents the time constant at the t-th acquisition time. This represents the heat transfer compensation coefficient at the t-th data acquisition time.

2. The continuous casting control method for isothermal quenching ductile iron production as described in claim 1, characterized in that, The process for determining the temperature distribution factor is as follows: Calculate the average temperature at all preset locations inside the heating furnace at each data acquisition time. Calculate the difference between the temperature at each preset location inside the heating furnace and the average value at each data collection time; The temperature distribution factor is positively correlated with the difference value.

3. The continuous casting control method for isothermal quenching ductile iron production as described in claim 2, characterized in that, The temperature distribution factor is the mean of all the differences at each acquisition time.

4. The continuous casting control method for isothermal quenching ductile iron production as described in claim 1, characterized in that, The expression for the thermal response hysteresis time is: In the formula, This represents the thermal response lag time at the t-th data acquisition moment; represents the positive number obtained by mapping the temperature distribution factor at the t-th acquisition time; ln() represents the logarithmic function with the natural constant as the base; This represents the temperature of the casting at the t-th data collection time. Indicates the preset austenitizing temperature; This indicates a preset value greater than 1.

5. The continuous casting control method for isothermal quenching ductile iron production as described in claim 1, characterized in that, The process for determining the power influence factor is as follows: Calculate the difference between the heating power at each data acquisition time and the preset heating power; Calculate the ratio of the actual insulation time to the preset insulation time; The power influence factor is positively correlated with the ratio and negatively correlated with the difference.

6. The continuous casting control method for isothermal quenching ductile iron production as described in claim 5, characterized in that, The calculation method for the power influence factor is as follows: Calculate the reciprocal of the sum of the difference and a preset constant greater than 0; The power influence factor is the product of the reciprocal and the ratio.

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