Micro-bubble precipitation type flotation system

Abstract

The invention discloses a microbubble precipitation type flotation system, which relates to the technical field of mineral processing, and comprises a data acquisition module for collecting flotation data of a historical microbubble precipitation type flotation system and generating a bubble generation data array and a mineral particle data set; the feature extraction module is used for screening out features related to bubble generation and mineral particle flotation efficiency in the data set; the flotation parameter generation module is used for establishing an automatic control model of the microbubble precipitation type flotation system based on the bubble generation rate and the mineral particle flotation rate, adjusting bubbles and mineral particles of the flotation system and generating flotation regulation and control parameters; and the parameter adjusting module is used for inputting the flotation regulation and control parameters into the microbubble precipitation type flotation system for parameter adjustment according to the flotation regulation and control parameters. Through automatic adjustment, the flotation process is accurately optimized on the basis of real-time feedback of the bubble generation rate and the mineral particle flotation rate, and the flotation efficiency and the mineral recovery rate are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of mineral processing, in particular to a microbubble precipitation flotation system. Background Art

[0002] Microbubble precipitation flotation systems are a solid-liquid separation technology widely used in mineral processing and metal smelting. The flotation process separates mineral particles by generating bubbles and leveraging their buoyancy. It is a core process in processing ores containing useful minerals. Traditional flotation technology relies primarily on manual adjustment of operating parameters. However, due to the high complexity and dynamic nature of the flotation process, traditional methods are unable to effectively address the nonlinearity, time-varying nature, and uncertainty inherent in the process. In particular, there is often a complex interaction between the bubble generation rate and the flotation rate of the mineral particles, leading to fluctuations in flotation efficiency. Therefore, the research and development of more intelligent and automated microbubble precipitation flotation systems is crucial for improving flotation efficiency, reducing manual intervention, and increasing resource utilization.

[0003] With advancements in sensor technology, data acquisition, and computer technology, automated control methods based on real-time data feedback are becoming a research hotspot in the flotation field. By collecting and analyzing real-time data from the flotation process, combined with feature extraction and control algorithms, it is possible to adjust the bubble generation rate and mineral particle flotation efficiency in real time, further optimizing the flotation process and improving mineral recovery and flotation performance. Summary of the Invention

[0004] In order to solve the above technical problems, a microbubble precipitation flotation system is provided. This technical solution solves the above problems.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0006] A microbubble precipitation flotation system, comprising:

[0007] The data acquisition module is used to collect the flotation data of the historical micro-bubble precipitation flotation system, including bubble generation data and mineral particle data, and generate a bubble generation data array and a mineral particle data set;

[0008] a feature extraction module, the feature extraction module being electrically connected to the historical data acquisition module, and configured to screen out features related to bubble generation in the data set based on the bubble generation data set, and determine the bubble generation rate; and to screen out features related to mineral particle flotation efficiency in the data set based on the mineral particle data set, and determine the mineral particle flotation rate;

[0009] The flotation parameter generation module and the flotation control module are electrically connected to the feature extraction module. The flotation control module is used to establish an automatic control model of the microbubble precipitation flotation system based on the bubble generation rate and the mineral particle flotation rate, adjust the bubbles and mineral particles in the flotation system, and generate flotation control parameters;

[0010] The parameter adjustment module is electrically connected to the flotation parameter generation module, and is used to input the flotation control parameters into the microbubble precipitation flotation system for parameter adjustment according to the flotation control parameters.

[0011] Preferably, the data acquisition module specifically includes:

[0012] The acquisition unit, based on sensors in the flotation system, collects bubble generation data and mineral particle data during the flotation process;

[0013] The data integration unit packages the bubble generation data and mineral particle data within the specified time window into a bubble generation data array and a mineral particle data set according to the start time to the end time of the flotation process and each minute as a time window;

[0014] The data preprocessing unit preprocesses the data set based on the bubble generation data array and the mineral particle data set, wherein the preprocessing includes denoising and format unification.

[0015] Preferably, the feature extraction module includes:

[0016] The bubble feature extraction unit is used to screen out features related to the bubble generation rate based on the bubble generation data set and determine the bubble generation rate;

[0017] The mineral particle feature extraction unit is electrically connected to the bubble feature extraction unit. The mineral particle feature extraction unit is used to screen out features related to the mineral particle flotation efficiency based on the mineral particle data set and determine the mineral particle flotation rate.

[0018] Preferably, the bubble feature extraction unit and the mineral particle feature extraction unit specifically include: calculating and determining the bubble generation rate based on the bubble generation characteristics in the bubble generation data set, and calculating and determining the mineral particle flotation rate based on the mineral particle characteristics in the mineral particle data set.

[0019] Preferably, the step of screening out features related to the bubble generation rate based on the bubble generation data set and determining the bubble generation rate specifically includes:

[0020] The bubble rate calculation formula is:

[0021]

[0022] Where, is the bubble change rate, Generate the value of the bubble corresponding to the t-th time node For the The bubble generation value corresponding to the time node, and is the time difference between two time nodes.

[0023] Preferably, the flotation parameter generation module specifically includes:

[0024] The bubble change rate array unit is used to generate a bubble change rate array based on the bubble generation rate;

[0025] The mineral particle flotation efficiency array unit is used to generate a mineral particle flotation efficiency array based on the mineral particle flotation rate;

[0026] A flotation parameter combination unit, used to combine the bubble generation rate and the mineral particle flotation rate to generate a flotation control parameter;

[0027] The bubble regulating unit is used to adjust the bubble generation process in the flotation system based on the flotation control parameters to optimize the flotation effect;

[0028] The mineral particle adjustment unit is used to adjust the distribution and sedimentation of mineral particles during the flotation process based on the flotation control parameters to improve the flotation efficiency.

[0029] Preferably, the flotation control parameters generated by combining the bubble generation rate and the mineral particle flotation rate specifically include:

[0030] According to the bubble generation rate and mineral particle flotation rate, an automatic control model of the flotation system is established based on regression analysis, and the optimized flotation control parameters are generated according to the control model;

[0031] Among them, the automatic control model formula is:

[0032]

[0033] Where, represents the flotation control parameter, is the bubble generation rate, is the mineral particle flotation rate, is the regression analysis function.

[0034] Preferably, adjusting the distribution and sedimentation of mineral particles during the flotation process based on flotation control parameters includes:

[0035] receiving a flotation control parameter, a data set derived from a combination of a bubble generation rate and a mineral particle flotation rate, including the bubble generation rate and the mineral particle flotation rate;

[0036] Based on the flotation control parameters, the bubble generation rate is adjusted to ensure that the bubble generation matches the flotation rate of the mineral particles;

[0037] Based on the flotation control parameters, the bubble size is adjusted. The distribution of bubbles affects the interaction between bubbles and mineral particles. The bubble generation rate and bubble size are adjusted to achieve the optimization of bubble distribution.

[0038] The bubble generation rate, size and distribution are continuously adjusted based on the real-time measured flotation effect.

[0039] Preferably, the parameter adjustment module specifically includes:

[0040] Flotation control parameter reception and decoding: Receives, decodes and analyzes the flotation control parameters generated by the flotation parameter generation module. The flotation control parameters include bubble generation rate and mineral particle flotation rate.

[0041] Mapping flotation control parameters to specific system parameters, including bubble generation rate, mineral particle distribution, and reactor operating conditions;

[0042] Generate corresponding adjustment plans based on flotation control parameters, calculate the optimal combination between bubble generation rate and mineral particle flotation rate, and formulate adjustment plans to ensure the optimal ratio of bubbles to mineral particles and achieve the best flotation efficiency;

[0043] The control system issues corresponding instructions to adaptively adjust the bubble generator and mineral particle distribution equipment, monitor the changes of bubbles and mineral particles in the flotation system in real time, and ensure that the adjustments reach the expected goals;

[0044] Collect real-time bubble generation and mineral particle flotation data in the flotation system, compare the flotation effects before and after adjustment, and analyze whether the target flotation efficiency has been achieved.

[0045] Preferably, the adaptively adjusting the bubble generator and the mineral particle distribution device by issuing corresponding instructions through the control system specifically includes:

[0046] Among them, the adaptive adjustment formula is:

[0047]

[0048] Where, is the control signal, Proportional gain constant, Integral gain constant, Differential gain constant, is the error at the current moment, is the integral term of the error, The derivative of the error.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] The present invention proposes to optimize the flotation process accurately and improve flotation efficiency and mineral recovery rate through automated regulation based on real-time feedback of bubble generation rate and mineral particle flotation rate. The system reduces manual intervention, improves stability and reliability, and uses real-time monitoring and adaptive control algorithms to ensure continuous optimization of the flotation process, reduce energy consumption and costs. The intelligent control model enables the system to adapt to the needs of different ores, accurately adjusts the matching of bubbles and minerals, improves resource recovery rate, promotes continuous improvement of flotation technology, and ensures optimal flotation effect and resource utilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a system framework diagram of the present invention;

[0052] Figure 2 This is the internal system framework diagram of the feature extraction module in the present invention. DETAILED DESCRIPTION

[0053] The following description is intended to disclose the present invention so that those skilled in the art can implement the present invention. The preferred embodiments described below are merely examples, and those skilled in the art may conceive of other obvious variations.

[0054] Reference Figure 1 As shown, a microbubble precipitation flotation system comprises:

[0055] The data acquisition module is used to collect the flotation data of the historical micro-bubble precipitation flotation system, including bubble generation data and mineral particle data, and generate a bubble generation data array and a mineral particle data set;

[0056] A feature extraction module is electrically connected to the historical data acquisition module. The feature extraction module is used to screen out features related to bubble generation in the data set based on the bubble generation data set, determine the bubble generation rate, and screen out features related to mineral particle flotation efficiency in the data set based on the mineral particle data set, and determine the mineral particle flotation rate;

[0057] The flotation parameter generation module, the flotation control module and the feature extraction module are electrically connected. The flotation control module is used to establish an automatic control model of the microbubble precipitation flotation system based on the bubble generation rate and the mineral particle flotation rate, adjust the bubbles and mineral particles in the flotation system, and generate flotation control parameters;

[0058] A parameter adjustment module is electrically connected to the flotation parameter generation module and is used to input the flotation control parameters into the microbubble precipitation flotation system for parameter adjustment according to the flotation control parameters;

[0059] By integrating the data acquisition module, feature extraction module, flotation parameter generation module and parameter adjustment module, an automated adjustment and real-time feedback mechanism is implemented to optimize the flotation efficiency of the microbubble precipitation flotation system. This integrated modular design can improve the accuracy and efficiency of the flotation process, reduce manual intervention and enhance the level of automated control.

[0060] The data acquisition module specifically includes:

[0061] The acquisition unit, based on sensors in the flotation system, collects bubble generation data and mineral particle data during the flotation process;

[0062] The data integration unit packages the bubble generation data and mineral particle data within the specified time window into a bubble generation data array and a mineral particle data set according to the start time to the end time of the flotation process and each minute as a time window;

[0063] A data preprocessing unit, which preprocesses the data set based on the bubble generation data array and the mineral particle data set, including denoising and format unification;

[0064] The design of "acquisition unit, data integration unit, and data preprocessing unit" in the data acquisition module ensures the accuracy and real-time performance of flotation process data through multi-level data acquisition and preprocessing. Data preprocessing effectively removes noise and ensures the accuracy of subsequent analysis.

[0065] Reference Figure 2 As shown in Figure 2, the feature extraction module includes:

[0066] The bubble feature extraction unit is used to screen out features related to the bubble generation rate based on the bubble generation data set and determine the bubble generation rate;

[0067] The mineral particle feature extraction unit is electrically connected to the bubble feature extraction unit. The mineral particle feature extraction unit is used to screen out features related to the mineral particle flotation efficiency based on the mineral particle data set and determine the mineral particle flotation rate.

[0068] The bubble feature extraction unit and the mineral particle feature extraction unit specifically include: calculating and determining the bubble generation rate based on the bubble generation features in the bubble generation data set, and calculating and determining the mineral particle flotation rate based on the mineral particle features in the mineral particle data set;

[0069] The design of the feature extraction module optimizes the prediction ability of bubble generation rate and mineral particle flotation rate by accurately screening out features related to bubble generation rate and mineral particle flotation efficiency, providing a basis for refined regulation of the flotation process.

[0070] Based on the bubble generation data set, the features related to the bubble generation rate are screened out, and the bubble generation rate is determined to include:

[0071] The bubble rate calculation formula is:

[0072]

[0073] Where, is the bubble change rate, Generate the value of the bubble corresponding to the t-th time node For the The bubble generation value corresponding to the time node, and is the time difference between two time nodes;

[0074] By establishing a bubble rate calculation formula, the bubble generation rate is accurately calculated and provides quantitative analysis support for flotation control. This makes the adjustment of the bubble generation rate more consistent with the flotation rate requirements of mineral particles, thereby improving flotation efficiency.

[0075] The flotation parameter generation module specifically includes:

[0076] The bubble change rate array unit is used to generate a bubble change rate array based on the bubble generation rate;

[0077] The mineral particle flotation efficiency array unit is used to generate a mineral particle flotation efficiency array based on the mineral particle flotation rate;

[0078] A flotation parameter combination unit, used to combine the bubble generation rate and the mineral particle flotation rate to generate a flotation control parameter;

[0079] The bubble regulating unit is used to adjust the bubble generation process in the flotation system based on the flotation control parameters to optimize the flotation effect;

[0080] The mineral particle adjustment unit is used to adjust the distribution and sedimentation of mineral particles during the flotation process based on the flotation control parameters to improve the flotation efficiency;

[0081] The flotation parameter generation module generates optimized flotation control parameters by combining the bubble change rate array unit with the mineral particle flotation efficiency array unit. The flotation control parameters generated through multi-level data analysis more accurately adapt to the actual needs of the flotation process.

[0082] The flotation control parameters generated by combining the bubble generation rate and the mineral particle flotation rate include:

[0083] According to the bubble generation rate and mineral particle flotation rate, an automatic control model of the flotation system is established based on regression analysis, and the optimized flotation control parameters are generated according to the control model;

[0084] Among them, the automatic control model formula is:

[0085]

[0086] Where, represents the flotation control parameter, is the bubble generation rate, is the flotation rate of mineral particles, is the regression analysis function;

[0087] The automatic control model established based on regression analysis can generate optimized flotation control parameters by correlating the bubble generation rate with the mineral particle flotation rate. This method makes the flotation process more adaptive and intelligent, and improves the efficiency of the flotation process.

[0088] Based on the flotation control parameters, the distribution and sedimentation of mineral particles during the flotation process are adjusted, including:

[0089] receiving a flotation control parameter, a data set derived from a combination of a bubble generation rate and a mineral particle flotation rate, including the bubble generation rate and the mineral particle flotation rate;

[0090] Based on the flotation control parameters, the bubble generation rate is adjusted to ensure that the bubble generation matches the flotation rate of the mineral particles;

[0091] Based on the flotation control parameters, the bubble size is adjusted. The distribution of bubbles affects the interaction between bubbles and mineral particles. The bubble generation rate and bubble size are adjusted to achieve the optimization of bubble distribution.

[0092] Continuously adjust bubble generation rate, size and distribution based on real-time flotation results;

[0093] By adjusting the bubble generation rate, bubble size and bubble distribution in real time, the best match between bubbles and mineral particles is achieved, and the flotation effect is optimized. The real-time feedback mechanism ensures the dynamic optimization of the flotation process, enabling the system to be adjusted instantly according to the actual conditions of the mineral particles.

[0094] The parameter adjustment module specifically includes:

[0095] Flotation control parameter reception and decoding: Receives, decodes and analyzes the flotation control parameters generated by the flotation parameter generation module. The flotation control parameters include bubble generation rate and mineral particle flotation rate.

[0096] Mapping flotation control parameters to specific system parameters, including bubble generation rate, mineral particle distribution, and reactor operating conditions;

[0097] Generate corresponding adjustment plans based on flotation control parameters, calculate the optimal combination between bubble generation rate and mineral particle flotation rate, and formulate adjustment plans to ensure the optimal ratio of bubbles to mineral particles and achieve the best flotation efficiency;

[0098] The control system issues corresponding instructions to adaptively adjust the bubble generator and mineral particle distribution equipment, monitor the changes of bubbles and mineral particles in the flotation system in real time, and ensure that the adjustments reach the expected goals;

[0099] Collect real-time bubble generation and mineral particle flotation data in the flotation system, compare the flotation effects before and after adjustment, and analyze whether the target flotation efficiency has been achieved.

[0100] The control system issues corresponding instructions to adaptively adjust the bubble generator and mineral particle distribution equipment, including:

[0101] Among them, the adaptive adjustment formula is:

[0102]

[0103] Where, is the control signal, Proportional gain constant, Integral gain constant, Differential gain constant, is the error at the current moment, is the integral term of the error, The derivative of the error.

[0104] In summary, the advantages of the present invention are:

[0105] The microbubble precipitation flotation system uses automated regulation and control, based on real-time feedback of bubble generation rate and mineral particle flotation rate, to precisely adjust the matching degree between bubbles and mineral particles, optimize the flotation process, and thus improve flotation efficiency and mineral recovery rate.

[0106] Through the automation of the data acquisition module, feature extraction module and flotation parameter generation module, the dependence on manual adjustment is reduced, the interference of human factors on the flotation effect is avoided, and the stability and reliability of the system are improved;

[0107] This system can monitor the bubble generation and mineral particle flotation in real time during the flotation process. Through real-time data feedback and adaptive control algorithms, it can continuously optimize the flotation process. By adjusting the bubble generation rate, bubble size and mineral particle distribution, it can better achieve precise control of the flotation process and ensure continuous improvement of flotation efficiency.

[0108] By using intelligent methods such as regression analysis to establish an automatic control model, the flotation system can automatically generate optimized control parameters according to different operating conditions. This intelligent control not only improves the automation level of the system, but also adapts to the flotation requirements of different ores, and has strong versatility and adaptability.

[0109] Since the system can adjust control parameters in real time according to the flotation effect, it improves the efficiency of the flotation process, avoids excessive operation and energy waste, and helps reduce energy consumption and flotation costs;

[0110] By precisely adjusting the distribution of mineral particles and matching the flotation of bubbles, the flotation recovery rate of minerals can be increased, the loss of useful minerals can be reduced, and the utilization efficiency of mining resources can be further improved;

[0111] By continuously collecting flotation data and feedback information, the system provides reliable data support for subsequent system optimization and decision-making, promoting the continuous improvement and perfection of the flotation process.

[0112] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions merely illustrate the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A microbubble precipitation flotation system, characterized in that: include: The data acquisition module is used to collect the flotation data of the historical micro-bubble precipitation flotation system, including bubble generation data and mineral particle data, and generate a bubble generation data array and a mineral particle data set; a feature extraction module, the feature extraction module being electrically connected to the historical data acquisition module, and configured to screen out features related to bubble generation in the data set based on the bubble generation data set, and determine the bubble generation rate; and to screen out features related to mineral particle flotation efficiency in the data set based on the mineral particle data set, and determine the mineral particle flotation rate; The flotation parameter generation module and the flotation control module are electrically connected to the feature extraction module. The flotation control module is used to establish an automatic control model of the microbubble precipitation flotation system based on the bubble generation rate and the mineral particle flotation rate, adjust the bubbles and mineral particles in the flotation system, and generate flotation control parameters; The parameter adjustment module is electrically connected to the flotation parameter generation module, and is used to input the flotation control parameters into the microbubble precipitation flotation system for parameter adjustment according to the flotation control parameters.

2. A microbubble precipitation flotation system according to claim 1, characterized in that: The data acquisition module specifically includes: The acquisition unit, based on sensors in the flotation system, collects bubble generation data and mineral particle data during the flotation process; The data integration unit packages the bubble generation data and mineral particle data within the specified time window into a bubble generation data array and a mineral particle data set according to the start time to the end time of the flotation process and each minute as a time window; The data preprocessing unit preprocesses the data set based on the bubble generation data array and the mineral particle data set, wherein the preprocessing includes denoising and format unification.

3. A microbubble precipitation flotation system according to claim 2, characterized in that: The feature extraction module includes: The bubble feature extraction unit is used to screen out features related to the bubble generation rate based on the bubble generation data set and determine the bubble generation rate; The mineral particle feature extraction unit is electrically connected to the bubble feature extraction unit. The mineral particle feature extraction unit is used to screen out features related to the mineral particle flotation efficiency based on the mineral particle data set and determine the mineral particle flotation rate.

4. A microbubble precipitation flotation system according to claim 3, characterized in that: The bubble feature extraction unit and the mineral particle feature extraction unit specifically include: calculating and determining the bubble generation rate based on the bubble generation features in the bubble generation data set, and calculating and determining the mineral particle flotation rate based on the mineral particle features in the mineral particle data set.

5. A microbubble precipitation flotation system according to claim 4, characterized in that: Based on the bubble generation data set, the features related to the bubble generation rate are screened out to determine the specific bubble generation rate. include: The bubble rate calculation formula is: Where, is the bubble change rate, Generate the value of the bubble corresponding to the t-th time node For the The bubble generation value corresponding to the time node, and is the time difference between two time nodes.

6. A microbubble precipitation flotation system according to claim 5, characterized in that: The flotation parameter generation module specifically includes: The bubble change rate array unit is used to generate a bubble change rate array based on the bubble generation rate; The mineral particle flotation efficiency array unit is used to generate a mineral particle flotation efficiency array based on the mineral particle flotation rate; A flotation parameter combination unit, used to combine the bubble generation rate and the mineral particle flotation rate to generate a flotation control parameter; The bubble regulating unit is used to adjust the bubble generation process in the flotation system based on the flotation control parameters to optimize the flotation effect; The mineral particle adjustment unit is used to adjust the distribution and sedimentation of mineral particles during the flotation process based on the flotation control parameters to improve the flotation efficiency.

7. A microbubble precipitation flotation system according to claim 6, characterized in that: The flotation control parameters generated by combining the bubble generation rate and the mineral particle flotation rate specifically include: According to the bubble generation rate and mineral particle flotation rate, an automatic control model of the flotation system is established based on regression analysis, and the optimized flotation control parameters are generated according to the control model; Among them, the automatic control model formula is: Where, represents the flotation control parameter, is the bubble generation rate, is the flotation rate of mineral particles, is the regression analysis function.

8. A microbubble precipitation flotation system according to claim 7, characterized in that: The method of adjusting the distribution and sedimentation of mineral particles during the flotation process based on the flotation control parameters includes: receiving a flotation control parameter, a data set derived from a combination of a bubble generation rate and a mineral particle flotation rate, including the bubble generation rate and the mineral particle flotation rate; Based on the flotation control parameters, the bubble generation rate is adjusted to ensure that the bubble generation matches the flotation rate of the mineral particles; Based on the flotation control parameters, the bubble size is adjusted. The distribution of bubbles affects the interaction between bubbles and mineral particles. The bubble generation rate and bubble size are adjusted to achieve the optimization of bubble distribution. The bubble generation rate, size and distribution are continuously adjusted based on the real-time measured flotation effect.

9. A microbubble precipitation flotation system according to claim 8, characterized in that: The parameter adjustment module specifically includes: Flotation control parameter reception and decoding: Receives, decodes and analyzes the flotation control parameters generated by the flotation parameter generation module. The flotation control parameters include bubble generation rate and mineral particle flotation rate. Mapping flotation control parameters to specific system parameters, including bubble generation rate, mineral particle distribution, and reactor operating conditions; Generate corresponding adjustment plans based on flotation control parameters, calculate the optimal combination between bubble generation rate and mineral particle flotation rate, and formulate adjustment plans to ensure the optimal ratio of bubbles to mineral particles and achieve the best flotation efficiency; The control system issues corresponding instructions to adaptively adjust the bubble generator and mineral particle distribution equipment, monitor the changes of bubbles and mineral particles in the flotation system in real time, and ensure that the adjustments reach the expected goals; Collect real-time bubble generation and mineral particle flotation data in the flotation system, compare the flotation effects before and after adjustment, and analyze whether the target flotation efficiency has been achieved.

10. A microbubble precipitation flotation system according to claim 9, characterized in that: The control system issues corresponding instructions to adaptively adjust the bubble generator and the mineral particle distribution equipment. include: Among them, the adaptive adjustment formula is: Where, is the control signal, Proportional gain constant, Integral gain constant, Differential gain constant, is the error at the current moment, is the integral term of the error, The derivative of the error.

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