Electromagnetic stirring control method integrating PID (Proportion Integration Differentiation) control and pulse width modulation technology

Abstract

The invention belongs to the field of electromagnetic stirring, and discloses an electromagnetic stirring control method fusing PID (Proportion Integration Differentiation) control and pulse width modulation technology, which comprises the following steps of: 1, initializing stirring; step 2, PWM intervention adjustment is carried out; 3, the PWM duty ratio is adjusted through speed sensor data and PID feedback; and step 4, PWM switching frequency is adjusted through temperature sensor data and PID feedback. According to the invention, a high-frequency and smoothly changing magnetic field can be generated through the PWM technology, so that the stirring speed can be smoothly and quickly adjusted. And meanwhile, two paths of PID control algorithms are introduced, and one path of PID ensures that the stirring speed of the liquid metal solution can reach the speed set by a user all the time. And the other path of PID is responsible for performing real-time adjustment according to whether the current stirring temperature is uniform or not in real time.

Description

Technical Field

[0001] The invention relates to the field of electromagnetic stirring, and in particular to an electromagnetic stirring control method integrating PID control and pulse width modulation technology. Background Art

[0002] Electromagnetic stirring (EMS) is a technology that achieves stirring by inducing eddy currents in liquid metal and generating Lorentz forces. This technology is widely used in the fields of metallurgy and materials science, especially in the casting and processing of metals such as steel and aluminum. Currently, many factories use EMS to stir liquid metal, which often results in uneven stirring, resulting in poor processing results, and it is impossible to quickly respond to the current stirring speed or temperature and make real-time adjustments during the stirring process. Summary of the invention

[0003] The purpose of the present invention is to provide an electromagnetic stirring control method integrating PID control and pulse width modulation technology to solve the problems raised in the above background technology.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] An electromagnetic stirring control method integrating PID control and pulse width modulation technology, comprising:

[0006] Step 1, after power-on, perform initialization operation of stirring work;

[0007] Step 2: Initialize the duty cycle and switch frequency to control the stirring process at the beginning, and then there are two PIDs, one responsible for controlling the uniformity of the stirring temperature and the other responsible for controlling the uniformity of the stirring speed. First, the PID responsible for controlling the uniformity of the stirring speed works first, and then the PID responsible for controlling the uniformity of the stirring temperature works;

[0008] Step 3, adjust the PWM duty cycle through the speed sensor data and PID feedback;

[0009] Step 4: Use temperature sensor data and PID feedback to adjust the PWM switching frequency.

[0010] Furthermore, the step 1 specifically includes:

[0011] Step 1.1, set a stirring speed and stirring temperature deviation value according to the type of liquid metal;

[0012] Step 1.2, set an initial duty cycle. When the power is turned on and the machine starts working, the stirring speed of the liquid metal solution is 0, and the temperature difference of each temperature sensor is also close to 0. At this time, the first PID responsible for controlling the uniformity of the stirring temperature does not intervene in the work, and the output value of the second PID responsible for controlling the stirring speed of the liquid metal solution is superimposed on the initial duty cycle. The specific method is to superimpose the output value of the second PID with the set PWM step limit value ΔD max After the division, it is superimposed with the initial duty cycle to achieve precise control. The duty cycle of PWM is expressed by the following formula:

[0013]

[0014] Where D represents the duty cycle, t high represents the time when the PWM switch is turned on, and T represents the PWM period;

[0015] Step 1.3, the duty cycle after the second PID feedback adjustment is expressed by the following formula:

[0016]

[0017] Where D final Represents the final duty cycle after the second PID adjustment, D initial Represents the initial duty cycle, PID voutput Represents the output adjustment value of the second PID, ΔD max Represents the step limit value.

[0018] Furthermore, the step 2 specifically includes:

[0019] Step 2.1, when the duty cycle of PWM is gradually increased, the equivalent current flowing into the electromagnetic coil will also gradually increase. According to the PWM formula, the equivalent current in the electromagnetic coil can be expressed by the following formula:

[0020]

[0021] Where I avg Represents the equivalent current in the electromagnetic coil, D final Represents the duty cycle adopted after the second PID adjustment, V sta represents the PWM standard input voltage, and R represents the resistance value of the electromagnetic coil;

[0022] Step 2.2, the magnetic field generated by the equivalent current in the electromagnetic coil gradually increases, thereby affecting the stirring speed of the liquid metal solution. At this time, the magnitude of the electromagnetic field generated and the magnitude of the Lorentz force on the liquid metal solution are expressed by the following formulas:

[0023]

[0024] Fl=B×J (5)

[0025] Where I avg represents the equivalent current in the electromagnetic coil, m is the number of turns of the electromagnetic coil, L is the length of the electromagnetic coil, μ0 represents the magnetic permeability in the atmosphere, B represents the magnetic field strength, F l represents the magnitude of the Lorentz force on the liquid metal solution, and J represents the current density inside the liquid metal solution;

[0026] Furthermore, the step 3 specifically includes:

[0027] Step 3.1, since the input source of the second PID is determined by the average value of each position speed sensor installed in the stirring container, the control algorithm of the second PID is expressed by the following formula:

[0028]

[0029] In the formula, e V (t) is the error, i.e., the difference between the user's expected speed value and the actual average speed measurement of sensors at different locations, K p , K i , K d are proportional, integral and differential gains respectively, and the output signal u of the second PID v (t) represents the output value of the second PID, V s (t) represents the average value of each speed sensor, V sta Represents the speed expectation set by the user;

[0030] Step 3.2: If the current actual speed is lower than the expected speed value set by the user, the output value of the second PID will increase. However, in order to prevent the PWM step length from changing too much and causing the speed to increase too quickly, thus affecting the stability of stirring, the output value of the second PID will be different from the PWM step length limit value ΔD. max After division, add it to the existing control quantity.

[0031] Furthermore, the step 4 specifically includes:

[0032] Step 4.1, the first PID uses the temperature difference of the temperature sensors at different positions as the input source to adjust and control the switching frequency of the PWM duty cycle. The temperature difference of the temperature sensors at different positions is defined by the following formula:

[0033]

[0034] Where ΔTtem represents the input source of the first PID, n represents the number of temperature sensors in the stirring container, and Ttem nRepresents the temperature value of the temperature sensor, Ttem sta Indicates that the value of the temperature sensor is used as the reference temperature value;

[0035] Step 4.2: Since the first PID is not always involved in the mixing process, only the current calculated ΔTtem is greater than the user's set value ΔTtem sta After that, the first PID starts to intervene, so set ΔTtem sta The value of must be greater than 0;

[0036] Step 4.3, if the currently calculated ΔTtem is greater than ΔTtem sta , the first PID immediately intervenes and controls the switching frequency of PWM instead of the duty cycle. The switching frequency of PWM is obtained by the following formula:

[0037]

[0038] In the formula, T represents the cycle time of PWM, and ω represents the switching frequency of PWM;

[0039] Step 4.4, when the calculated ΔTtem is greater than ΔTtem sta When it exceeds fifty percent, the output value of the first PID significantly reduces the current PWM switching frequency. PWM has a minimum switching frequency. If the PWM switching frequency adjusted by the first PID is lower than the minimum switching frequency, the minimum switching frequency is used for adjustment.

[0040] Step 4.5, the control equation of the first PID is expressed as follows:

[0041]

[0042] In the formula, PID ωoutput Represents the output value of the first PID, e ω (t) represents the difference between the actual ΔTtem measured by each temperature sensor and the ΔTtem expected by the user sta The error value, n represents the number of temperature sensors in the stirring container, K p , K i , K d are proportional, integral and differential gains respectively, t is the current time, t' is the time variable of the integration, which means the accumulation of past errors;

[0043] Step 4.6: During the control process, once the ΔTtem after the first PID adjustment is less than or equal to the expected temperature deviation ΔTtem set by the user, sta After that, the first PID is immediately disconnected and no longer participates in the electromagnetic stirring work until the next time ΔTtem calculated according to Formula 7 is greater than ΔTtemsta After that, the first PID continues to participate in the stirring work.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows: By using the present invention, a high-frequency and smoothly changing magnetic field can be generated through PWM technology, so that the stirring speed can be adjusted smoothly and quickly. At the same time, the present invention introduces two-way PID control algorithms. One-way PID ensures that the stirring speed of the liquid metal solution can always reach the user-set speed. The other-way PID is responsible for making real-time adjustments according to whether the current stirring temperature is uniform. Description of the Drawings

[0045] Figure 1 is a flow chart of the present invention.

[0046] Figure 2 is a schematic diagram of the effects of different PWM duty cycles in the present invention. In the figure, D1, D2, and D3 represent PWM waveforms with different duty cycles, D1 < D2 < D3, T1, T2, and T3 represent the periods corresponding to different duty cycles, T1 = T2 = T3, and V 等效 represents the equivalent voltage of this PWM under different periods.

[0047] Figure 3 is a schematic diagram of PID adjustment according to the average value of speed sensors at different positions in the stirring container in the present invention.

[0048] Figure 4 is a schematic diagram of the effects of different PWM switching frequencies in the present invention. In the figure, W1, W2, and W3 represent PWM waveforms with different switching frequencies of PWM, W1 > W2 > W3, T1, T2, and T3 represent the periods corresponding to different switching frequencies of PWM, T1 < T2 < T3, and V 等效 represents the equivalent voltage of this PWM under different switching frequencies.

[0049] Figure 5 is a schematic diagram of PID adjustment according to the temperature sensor difference at different positions in the stirring container in the present invention. Detailed Embodiments

[0050] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0051] Please refer to Figure 1-Figure 5 , an electromagnetic stirring control method integrating PID control and pulse width modulation technology, including the following steps.

[0052] Step 1, after power-on, perform the initialization operation of the stirring work, which specifically includes the following steps:

[0053] Step 1.1, when starting to stir the liquid metal, the user first needs to set a stirring speed and a stirring temperature deviation value according to the type of liquid metal.

[0054] Step 1.2, this control method sets an initial duty cycle. When the power is turned on and the work starts, the stirring speed of the liquid metal solution is 0, and the temperature difference of each temperature sensor is also close to 0. At this time, the first PID responsible for controlling the stirring uniformity (PID based on the difference of the temperature sensors at each position as input) does not intervene in the work, and the second PID responsible for controlling the stirring speed of the liquid metal solution will output a larger value and superimpose with the initial duty cycle. However, in order to make the stirring speed of the liquid metal solution rise smoothly and linearly, the duty cycle change step is prevented from changing too fast, resulting in unstable stirring. The present invention compares the output value of the second PID with the step limit value ΔD of the PWM set inside the control method. max After the division, it is added to the initial duty cycle to achieve precise control. The duty cycle of PWM can be expressed by the following formula.

[0055]

[0056] Where D represents the duty cycle, t high Represents the time that the PWM switch is turned on (maintaining a high level), and T represents the PWM period.

[0057] Step 1.3, the duty cycle after PID feedback adjustment can be expressed by the following formula.

[0058]

[0059] Where D final Represents the final duty cycle after the second PID adjustment, D initial Represents the initial duty cycle built into the algorithm, PID voutput Represents the output adjustment value of the second PID, ΔD max Represents the step limit value.

[0060] Step 2, PWM intervention regulation, at the beginning, the initialization duty cycle and switching frequency are used to control the stirring process, and then there are two PIDs, one is responsible for controlling the uniformity of the stirring temperature, and the other is responsible for controlling the uniformity of the stirring speed. First, the PID responsible for controlling the uniformity of the stirring speed works first, and then the PID responsible for controlling the uniformity of the stirring temperature works. Specifically, the following steps are included:

[0061] Step 2.1, when the duty cycle of PWM is gradually increased, the equivalent current flowing into the electromagnetic coil will also gradually increase. This is achieved by the PWM algorithm, as shown in the schematic diagram. Figure 2 According to the PWM formula, the equivalent current in the electromagnetic coil can be expressed by the following formula.

[0062]

[0063] Where I avg Represents the equivalent current in the electromagnetic coil, D final Represents the duty cycle adopted by the algorithm after the second PID adjustment, V sta represents the PWM standard input voltage, and R represents the resistance value of the electromagnetic coil.

[0064] Step 2.2, the magnetic field generated by the equivalent current in the electromagnetic coil will gradually increase and affect the stirring speed of the liquid metal solution. At this time, the magnitude of the electromagnetic field generated and the magnitude of the Lorentz force on the liquid metal solution can be expressed by the following formulas:

[0065]

[0066] F l =B×J(5)

[0067] Where I avg represents the equivalent current in the electromagnetic coil, m is the number of turns of the electromagnetic coil, L is the length of the electromagnetic coil, μ0 represents the magnetic permeability in the atmosphere, and B represents the magnetic field strength. Fl represents the Lorentz force on the liquid metal solution, and J represents the current density inside the liquid metal solution.

[0068] Step 2.3, according to the above formula, when the current inside the liquid metal solution is constant, the higher the duty cycle, the greater the electromagnetic field generated by the electromagnetic coil, the greater the Lorentz force on the liquid metal solution, and ultimately the faster the rotation speed. At the same time, according to the above formula, it can be seen that the stirring speed of the liquid metal solution is closely related to the duty cycle of the PWM.

[0069] Step 3, adjusting the PWM duty cycle through the speed sensor data and PID feedback, specifically including the following steps:

[0070] Step 3.1, since the input source of the second PID is determined by the average value of each position speed sensor installed in the stirring container, the control algorithm of the second PID can be expressed by the following formula.

[0071]

[0072] In the formula, e V(t) is the error, that is, the difference between the user's expected speed value and the actual average speed measurement of sensors at different locations. K p , K i , K d are proportional, integral and differential gains respectively. The output signal u of the second PID v (t) represents the amount of adjustment that needs to be applied to the system. V s (t) represents the average value of each speed sensor, V sta Represents the speed expectation set by the user.

[0073] Step 3.2, if the current actual speed is lower than the expected speed value set by the user, the output value of the second PID will increase. However, in order to prevent the PWM step length from changing too much and causing the speed to increase too quickly, thus affecting the stability of the stirring, the output value of the second PID will be different from the PWM step length limit value ΔD. max After division, add it to the existing control quantity. The second PID control diagram is as follows Figure 3 shown.

[0074] Step 4, using the temperature sensor data and PID feedback to adjust the PWM switching frequency, specifically includes the following steps:

[0075] Step 4.1, during the stirring process, the liquid metal solution itself has a high heat, and during the stirring process, the liquid metal solution particles rub against each other and also against the stirring container, so the temperature of the liquid metal solution will rise. In addition, the more uniform the stirring, the more conducive it is to the internal heat conduction of the liquid metal solution, and the more uniform the internal temperature distribution of the liquid metal solution. Therefore, the first PID uses the temperature difference of the temperature sensors at different positions as the input source to adjust and control the switching frequency of the PWM duty cycle. The temperature difference of the temperature sensors at different positions is defined by the following formula:

[0076]

[0077] Where ΔTtem represents the input source of the first PID (i.e., the difference between the temperature sensors at different locations), n represents the number of temperature sensors in the stirring container, and Ttem n Represents the temperature value of the temperature sensor, Ttem sta Indicates that the value of the temperature sensor is used as the reference temperature value.

[0078] Step 4.2: Since the first PID is not always involved in the mixing process, only the current calculated ΔTtem is greater than the user's set value ΔTtem sta After that, the first PID starts to intervene. It is impossible to ensure that the temperature at each position is absolutely equal during the stirring process, so generally ΔTtem sta The value must be greater than 0.

[0079] Step 4.3, if the ΔTtem calculated by the system is greater than ΔTtem sta , the first PID will immediately intervene. The first PID mainly controls the switching frequency of PWM rather than the duty cycle. The switching frequency of PWM can be obtained by the following formula:

[0080]

[0081] Where T represents the cycle time of PWM, and ω represents the switching frequency of PWM.

[0082] Step 4.4, when the calculated ΔTtem is greater than ΔTtem sta When it exceeds 50%, the output value of the first PID will significantly reduce the current PWM switching frequency. However, in order to ensure that there is no large oscillation during the mixing process, the system will set a minimum PWM switching frequency. If the PWM switching frequency after PID adjustment is lower than this value, the minimum value will be used for adjustment.

[0083] According to formula (8), when the switching frequency of PWM is reduced, when the equivalent current of the same magnitude is output, the cycle of PWM will become longer, the switching speed of high and low levels will be reduced, and the real-time response capability of PWM will be weakened. Then, the equivalent current output of PWM in one cycle will no longer be smooth. This will cause a slight oscillation effect in the liquid metal solution during the stirring process, thereby promoting the uniformity of the temperature inside the liquid metal. In turn, the viscosity and flow behavior of the liquid metal solution at different locations tend to be consistent, which is conducive to the uniformity of stirring. The schematic diagram of the effect of different PWM switching frequencies is shown in Figure 4 shown.

[0084] Step 4.5, the control equation of the first PID can be expressed as follows:

[0085]

[0086] In the formula, PID ωoutput Represents the first PID output value, e ω (t) represents the difference between the actual ΔTtem measured by each temperature sensor and the ΔTtem expected by the user sta The error value is n. n represents the number of temperature sensors in the stirring container. K p , K i , K d are proportional, integral and differential gains respectively. t is the current time, and t' is the time variable of the integration, which means the accumulation of past errors.

[0087] During the adjustment process, if the PID adjustment value is too large and the PWM switching frequency is reduced to the minimum limit value, the system will automatically adopt the minimum limit value. This process can be represented by the following code block:

[0088]

[0089] where ω inital Represents the initial PWM switching frequency of the system, ω min Represents the lowest PWM switching frequency set by the system. ω The final PWM switching frequency used.

[0090] Step 4.6: During the control process, once the ΔTtem after the first PID adjustment is less than or equal to the expected temperature deviation ΔTtem set by the user, sta After that, the first PID is immediately disconnected and no longer participates in the electromagnetic stirring work. The working diagram of the first PID is as follows Figure 5 shown.

[0091] Step 4.9, until the next time ΔTtem calculated according to formula 7 is greater than ΔTtem sta After that, the first PID continues to participate in the stirring work.

[0092] Through the above process, in the whole control method, the switching frequency and duty cycle of PWM are used as the underlying algorithms that can actually affect the stirring effect, and the two-way PID control algorithm adjusts the PWM related variables according to the user set value. Such a control method arrangement can better meet the stirring needs, making the whole stirring process highly controllable and improving the stirring quality.

[0093] The control method of the present invention includes two parts, the first part is the PWM algorithm. This method extracts the switching frequency and duty cycle of PWM separately, and controls them separately by two PIDs respectively. The adjustment of the PWM duty cycle can change the stirring speed of the liquid metal solution. The switching frequency of PWM can affect whether slight oscillation occurs during the stirring process. In the stirring work, it is often required to stir evenly and avoid the phenomenon of local excessive temperature causing inconsistent fluidity of the entire liquid metal solution. Therefore, the adjustment of the PWM frequency allows artificial control to induce an oscillation effect during the stirring process, so as to ensure that the temperature of the entire liquid metal solution tends to be consistent during the stirring process.

[0094] The second major part of the present invention is mainly a two-way PID algorithm, which is mainly designed for the input and output of the two-way PID. The first PID and the PID for feedback adjustment of the PWM duty cycle exist throughout the entire stirring process, and the stirring speed expected by the user is met by changing the size of the duty cycle. However, in order to avoid uncontrollable oscillation effects during operation, this method limits the output of the PID, and acts on the system after dividing the output by the step limit value. At the same time, the stirring is ensured to be uniform as much as possible under the premise of ensuring that the stirring speed meets the requirements, so the input of this PID is the average value of the speed sensors distributed at different positions of the stirring container. The second PID plays a major role in regulating the uniformity of the entire stirring process. By changing the switching frequency of PWM by PID, a slight oscillation phenomenon is artificially induced, thereby promoting the uniformity of the temperature of the entire liquid metal solution during the stirring process. In order to better ensure this, the input of this PID is the difference between the temperature sensors at different positions. However, in order to keep the induced oscillation effect within a controllable range, the output of this PID is compared with the minimum PWM switching frequency set by the system and then output.

[0095] The present invention controls the switching frequency and duty cycle of PWM at the same time, and provides two PIDs to control them separately. The PID that controls the PWM switching frequency starts working only when the temperature difference between different sensors is greater than the user-set value, and stops working once the requirements are met.

[0096] The present invention combines PWM technology with PID control, sets a certain amount of PWM duty cycle step limit value and PWM minimum switching frequency, and then uses two separate PIDs to separately control the PWM duty cycle and switching frequency.

[0097] In order to ensure that the temperature of the liquid metal solution at different positions tends to be consistent during the stirring process, the present invention opens a single PID to control the switching frequency of PWM, and uses the oscillation effect caused by artificial control by reducing the switching frequency of PWM to promote the temperature of the liquid metal solution to be consistent during the stirring process.

[0098] The present invention is characterized in that:

[0099] 1) Combining PWM technology with PID algorithm and introducing it into electromagnetic stirring, PWM can make the current change smoothly at high frequency, thereby generating a high-frequency and smoothly changing magnetic field, which makes the stirring process smoother.

[0100] 2) Two PIDs are introduced to control the duty cycle and switching frequency of PWM respectively, and are combined with PWM in the electromagnetic stirring algorithm.

[0101] 3) The switching frequency of PWM is reduced through PID control, thereby artificially inducing an oscillation effect during the liquid metal stirring process to promote the temperature of the liquid metal solution to be consistent during the stirring process.

[0102] 4) The switching frequency and duty cycle of PWM are extracted separately and controlled by PID, which increases the controllability of the electromagnetic stirring process.

[0103] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An electromagnetic stirring control method integrating PID control and pulse width modulation technology, characterized in that: include: Step 1, after power-on, perform initialization operation of stirring work; Step 2: Initialize the duty cycle and switch frequency to control the stirring process at the beginning, and then there are two PIDs, one responsible for controlling the uniformity of the stirring temperature and the other responsible for controlling the uniformity of the stirring speed. First, the PID responsible for controlling the uniformity of the stirring speed works first, and then the PID responsible for controlling the uniformity of the stirring temperature works; Step 3, adjust the PWM duty cycle through the speed sensor data and PID feedback; Step 4: Use temperature sensor data and PID feedback to adjust the PWM switching frequency.

2. The electromagnetic stirring control method integrating PID control and pulse width modulation technology according to claim 1 is characterized in that: The step 1 specifically includes: Step 1.1, set a stirring speed and stirring temperature deviation value according to the type of liquid metal; Step 1.2, set an initial duty cycle. When the power is turned on and the machine starts working, the stirring speed of the liquid metal solution is 0, and the temperature difference of each temperature sensor is also close to 0. At this time, the first PID responsible for controlling the uniformity of the stirring temperature does not intervene in the work, and the output value of the second PID responsible for controlling the stirring speed of the liquid metal solution is superimposed on the initial duty cycle. The specific method is to superimpose the output value of the second PID with the set PWM step limit value ΔD max After the division, it is superimposed with the initial duty cycle to achieve precise control. The duty cycle of PWM is expressed by the following formula: Where D represents the duty cycle, t high represents the time when the PWM switch is turned on, and T represents the PWM period; Step 1.3, the duty cycle after the second PID feedback adjustment is expressed by the following formula: Where D final Represents the final duty cycle after the second PID adjustment, D initial Represents the initial duty cycle, PID voutput Represents the output adjustment value of the second PID, ΔD max Represents the step limit value.

3. The electromagnetic stirring control method integrating PID control and pulse width modulation technology according to claim 2 is characterized in that: The step 2 specifically includes: Step 2.1, when the duty cycle of PWM is gradually increased, the equivalent current flowing into the electromagnetic coil will also gradually increase. According to the PWM formula, the equivalent current in the electromagnetic coil can be expressed by the following formula: Where I avg Represents the equivalent current in the electromagnetic coil, D final Represents the duty cycle adopted after the second PID adjustment, V sta represents the PWM standard input voltage, and R represents the resistance value of the electromagnetic coil; Step 2.2, the magnetic field generated by the equivalent current in the electromagnetic coil gradually increases, thereby affecting the stirring speed of the liquid metal solution. At this time, the magnitude of the electromagnetic field generated and the magnitude of the Lorentz force on the liquid metal solution are expressed by the following formulas: F l =B×J (5) Where I avg represents the equivalent current in the electromagnetic coil, m is the number of turns of the electromagnetic coil, L is the length of the electromagnetic coil, μ0 represents the magnetic permeability in the atmosphere, B represents the magnetic field strength, F l represents the magnitude of the Lorentz force acting on the liquid metal solution, and J represents the current density inside the liquid metal solution.

4. The electromagnetic stirring control method integrating PID control and pulse width modulation technology according to claim 3 is characterized in that: The step 3 specifically includes: Step 3.1, since the input source of the second PID is determined by the average value of the speed sensors at various positions installed in the stirring container, the control algorithm of the second PID is expressed by the following formula: In the formula, e V (t) is the error, i.e., the difference between the user's expected speed value and the actual average speed measurement of sensors at different locations, K p , K i , K d are proportional, integral and differential gains respectively, and the output signal u of the second PID v (t) represents the output value of the second PID, V s (t) represents the average value of each speed sensor, V sta Represents the speed expectation set by the user; Step 3.2: If the current actual speed is lower than the expected speed value set by the user, the output value of the second PID will increase. However, in order to prevent the PWM step length from changing too much and causing the speed to increase too quickly, thus affecting the stability of stirring, the output value of the second PID will be different from the PWM step length limit value ΔD. max After division, add it to the existing control quantity.

5. The electromagnetic stirring control method integrating PID control and pulse width modulation technology according to claim 4 is characterized in that: The step 4 specifically includes: Step 4.1, the first PID uses the temperature difference of the temperature sensors at different positions as the input source to adjust and control the switching frequency of the PWM duty cycle. The temperature difference of the temperature sensors at different positions is defined by the following formula: Where ΔTtem represents the input source of the first PID, n represents the number of temperature sensors in the stirring container, and Ttem n Represents the temperature value of the temperature sensor, Ttem sta Indicates that the value of the temperature sensor is used as the reference temperature value; Step 4.2: Since the first PID is not always involved in the mixing process, only the current calculated ΔTtem is greater than the user's set value ΔTtem sta After that, the first PID starts to intervene, so set ΔTtem sta The value of must be greater than 0; Step 4.3, if the currently calculated ΔTtem is greater than ΔTtem sta , the first PID immediately intervenes and controls the switching frequency of PWM instead of the duty cycle. The switching frequency of PWM is obtained by the following formula: In the formula, T represents the cycle time of PWM, and ω represents the switching frequency of PWM; Step 4.4, when the calculated ΔTtem is greater than ΔTtem sta When it exceeds fifty percent, the output value of the first PID significantly reduces the current PWM switching frequency. PWM has a minimum switching frequency. If the PWM switching frequency adjusted by the first PID is lower than the minimum switching frequency, the minimum switching frequency is used for adjustment. Step 4.5, the control equation of the first PID is expressed as follows: In the formula, PID ωoutput Represents the output value of the first PID, e ω (t) represents the difference between the actual ΔTtem measured by each temperature sensor and the ΔTtem expected by the user sta The error value, n represents the number of temperature sensors in the stirring container, K p , K i , K d are proportional, integral and differential gains respectively, t is the current time, t' is the time variable of the integration, which means the accumulation of past errors; Step 4.6: During the control process, once the ΔTtem after the first PID adjustment is less than or equal to the expected temperature deviation ΔTtem set by the user, sta After that, the first PID is immediately disconnected and no longer participates in the electromagnetic stirring work until the next time ΔTtem calculated according to Formula 7 is greater than ΔTtem sta After that, the first PID continues to participate in the stirring work.

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