Staggered parallel Buck power supply control method for direct-current electric arc furnace

Abstract

The invention relates to the technical field of electric arc furnace power supply control, in particular to a staggered parallel Buck power supply control method for a direct current electric arc furnace, and the method comprises the steps: constructing a system dynamic equation for each Buck module; a fixed time disturbance observer is designed for each Buck module; designing a self-adaptive fixed-time sliding mode controller for each Buck module, wherein a sliding mode surface of the self-adaptive fixed-time sliding mode controller comprises a current error, a disturbance estimation value and a time-varying item of user preset convergence time; designing a control law; the self-adaptive updating of the control parameters is realized; and after the amplitude of the control variable is limited, a multi-phase staggered PWM driving signal is generated. The method has the advantages that the fixed time disturbance observer is designed for each Buck module, lumped disturbance such as load and power grid fluctuation is estimated in real time, feedforward compensation is conducted, and robustness is improved; a self-adaptive fixed-time sliding mode controller is adopted, and a sliding mode surface of the self-adaptive fixed-time sliding mode controller comprises a time-varying item of convergence time preset by a user, so that inductive current can be strictly converged within any set time irrelevant to an initial state.

Description

Technical Field

[0001] This invention relates to the field of power supply control technology for electric arc furnaces, and in particular to a method for controlling an interleaved parallel Buck power supply for a DC electric arc furnace. Background Technology

[0002] As a key piece of equipment in modern metallurgical industry, the stability and dynamic performance of the power supply of a DC electric arc furnace directly determine the stability of the electric arc, smelting efficiency, and the final product quality. A typical DC electric arc furnace power supply system usually adopts a two-stage structure of "rectifier + DC power supply". The DC power supply section, due to its simple structure and convenient control, often uses an interleaved parallel Buck converter topology.

[0003] However, during operation, the equivalent load resistance of a DC electric arc furnace exhibits complex characteristics that are unknown, time-varying, and subject to drastic changes. This places extremely high demands on the current control performance of its power supply. While traditional proportional-integral (PI) control methods are simple in structure and easy to implement, their response speed is limited, and their robustness to parameter changes and external disturbances is poor, making them unsuitable for high-end applications. Specifically, traditional PI control suffers from the following prominent problems in DC electric arc furnace applications: 1. When the grid voltage fluctuates, the arc current will fluctuate significantly, leading to arc instability and seriously affecting the smelting quality; 2. When the arc load changes drastically, the dynamic response of the current control is slow, making it difficult to quickly maintain arc stability and resulting in poor adaptability to load changes. 3. It can easily lead to increased electrode consumption and decreased arc stability, which in turn affects production efficiency and product consistency.

[0004] To improve system robustness, sliding mode control has been widely studied and applied to power electronic converters due to its inherent robustness against parameter perturbations and external disturbances. However, traditional sliding mode control has inherent drawbacks: 1. The vibration problem is serious: Due to the discontinuity of the switching function, high-frequency chattering will occur when the system state crosses the sliding surface. This not only increases switching losses and affects device lifespan, but may also excite unmodeled high-frequency dynamic responses. 2. Convergence performance depends on the initial state: The system's convergence time is closely related to the initial state, which cannot be predicted or set by the user. This is a significant drawback in electric arc furnace applications with specific process timing requirements. 3. Sensitive to mismatch disturbances: Its ability to suppress disturbances that do not meet the matching conditions (such as load disturbances) is limited.

[0005] While some studies have attempted to combine disturbance observers with sliding mode control to improve performance through feedforward compensation, the convergence time of these methods still depends on the initial state of the system. Users cannot freely specify the convergence time according to actual process requirements (such as the different requirements for current stabilization speed during the melting and refining periods of an electric arc furnace). Furthermore, although fixed-time control theory can guarantee that the system's convergence time has an upper bound independent of the initial state, this time boundary is usually tightly coupled with internal system parameters (such as controller gain and inductance value), making it difficult for users to intuitively set and adjust this convergence time directly based on external process requirements.

[0006] Therefore, existing technologies struggle to achieve the comprehensive control objectives of user-defined convergence time, complete robustness against mismatch disturbances, and effective suppression of chattering while ensuring strong robustness. This has become a technical bottleneck restricting further improvements in the performance of DC electric arc furnace power supplies. Summary of the Invention

[0007] The purpose of this invention is to provide a control method for interleaved parallel Buck power supply for DC electric arc furnaces, which solves the problems of existing control methods such as unpredictable convergence time, poor robustness to mismatch disturbances, and chattering. The invention adopts a technical solution that combines an adaptive fixed-time disturbance observer with fixed-time sliding mode control to achieve convergence of the inductor current to a given value within any preset time by the user, and ensures that the system is fully robust to disturbances such as load changes, while also having excellent characteristics of fast dynamic response and low chattering.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A method for controlling an interleaved parallel Buck power supply for a DC electric arc furnace, comprising: Real-time acquisition of inductor current, input voltage, and output voltage of each Buck module; For each Buck module, a system dynamic equation is constructed, which includes inductor current error and lumped disturbance terms. Design a fixed-time perturbation observer for each Buck module to estimate the lumped perturbation within a preset fixed time interval; An adaptive fixed-time sliding mode controller is designed for each Buck module, whose sliding surface includes time-varying terms for current error, disturbance estimate, and user-preset convergence time. Design a control law, which includes an equivalent control term and a switching control term based on the hyperbolic tangent function, to suppress chattering; To achieve adaptive updating of control parameters, dynamically adjust boundary layer thickness, convergence gain, switching gain, and convergence time based on the system error state; After limiting the control variables, multi-phase interleaved PWM drive signals are generated to drive the switching transistors of each Buck module.

[0009] Lumped disturbances include matching disturbances caused by grid voltage fluctuations and mismatch disturbances caused by unknown time-varying load resistance; Inductor current error The inductor current of the k-th Buck module With the total current setpoint The difference is expressed by the following formula: ; N represents the total number of all Buck modules; The system dynamic equations are: ; in: The derivative representing the current error, with units of A / s; This indicates the input DC voltage, in volts (V). This represents the inductance value of the k-th Buck module, in H. This indicates the output voltage, in volts (V). This indicates a lumped disturbance.

[0010] The upper bound of the estimation error convergence time of the fixed-time perturbation observer is independent of the inductor current and the initial state of the perturbation observer.

[0011] The fixed-time disturbance observer adopts the following structure: ①; ②; in: This represents the estimated current error, in A. Indicates the adaptive boundary layer thickness; Indicates the adjustable gain parameter; and Both represent exponential coefficients. , ; Indicates the estimated disturbance value; The derivative representing the current estimation error, in A / s; sat(·) represents the saturation function; This represents the absolute value of the current error estimate.

[0012] The adaptive sliding surface is designed as follows: When t < hour, ③; When t≥ hour, ④; in: This represents the variable of the sliding surface, in units of A; This represents the inductor current error of the k-th module; Indicates the estimated disturbance value; t represents the time variable; Indicates the user-preset convergence time; Represented as a time-varying term, the formula is: ⑤; This represents the convergence gain.

[0013] The control law is designed as follows: ⑥ in: This indicates the input DC voltage, in volts (V). This represents the inductance value of the k-th Buck module, in H. Indicates switching gain, satisfying ; tanh(·) denotes the hyperbolic tangent function; Indicates the smoothing factor; This indicates the output voltage, in volts (V). This represents the ratio of the sliding surface to the smoothing factor; Indicates control variables; when At that time, the equivalent control item is ; when At that time, the equivalent control item is ; Switch control item to .

[0014] Adaptive updating of control parameters, including: (1) Adaptive formula for boundary layer thickness φ: ⑦; In formula ⑦, Indicates the current boundary layer thickness; Indicates the minimum boundary layer thickness; Indicates the maximum boundary layer thickness; The absolute value of the current error estimate is represented by , and k represents the adjustment coefficient. (2) Adaptive formula for convergence gain ζ: ⑧; In formula ⑧, This represents the initial value of the convergence gain; Indicates adaptive gain; Indicates the absolute value of the current error; Indicates the control cycle; (3) Adaptive formula for switching gain η: 9 In formula ⑨, Indicates the initial value of the switching gain; Indicates adaptive gain; Represents the absolute value of the sliding surface; Indicates the control cycle; (4) Convergence time The adaptive formula: ⑩ In formula ⑩, Indicates the current convergence time; Indicates the initial value of the convergence time; Indicates adaptive gain; This represents the absolute value of the current error. Indicates the control cycle.

[0015] It also includes monitoring and safety protection mechanisms, real-time monitoring of system tracking errors and sliding surface variables, and triggering a parameter reset mechanism when the absolute value of the current error exceeds a set threshold and persists for a set time; and controlling variables. Implement amplitude limiting protection to prevent actuator saturation.

[0016] An interleaved parallel Buck power supply control system for a DC electric arc furnace, used to implement an interleaved parallel Buck power supply control method for a DC electric arc furnace, includes a signal acquisition module, a fixed-time disturbance observer module, an adaptive fixed-time sliding mode controller module, and a PWM generation module; The signal acquisition module is used to acquire inductor current, input voltage, and output voltage signals; The fixed-time disturbance observer module is used to estimate the system's lumped disturbance in real time; The adaptive fixed-time sliding mode controller module is used to calculate the control quantity based on the sliding surface and disturbance estimate; The PWM generation module is used to convert control signals into phase-interleaved drive signals.

[0017] A power supply system for a DC electric arc furnace employs an interleaved parallel Buck power supply control method for DC electric arc furnaces to control the output current of the interleaved parallel Buck converter.

[0018] Compared with the prior art, the beneficial effects of the present invention are: 1. By introducing an adaptive fixed-time sliding mode surface with a time-varying term, the inductor current of the system can strictly converge to a given value within any user-preset convergence time. This convergence time is independent of the initial state of the system. Operators can directly set the required current stabilization time according to different process stages of the DC electric arc furnace (such as rapid response required during the melting period and stable and precise response required during the refining period), achieving unprecedented control flexibility, which is impossible to achieve with traditional PI, sliding mode, or even fixed-time control methods. 2. By designing a fixed-time disturbance observer independently for each Buck module, it is possible to quickly and accurately estimate and feedforward the mismatch disturbance caused by the unknown time-varying load impedance (violent arc fluctuations) and the matching disturbance caused by the grid voltage fluctuation. Based on the observer's compensation mechanism, the impact of lumped disturbances on the tracking performance of the control system is fundamentally eliminated, enabling the system to maintain extremely high steady-state accuracy and strong robustness under a wide range of operating conditions. 3. The hyperbolic tangent function is used in the control law to replace the traditional sign function, and adaptive boundary layer technology is combined to achieve smooth switching of the control signal. At the same time, the accurate compensation of the disturbance by the disturbance observer also significantly reduces the switching gain requirement. These two measures work together to greatly suppress the high-frequency chattering phenomenon inherent in traditional sliding mode control, which not only reduces the stress and loss of switching devices and extends their service life, but also reduces electromagnetic interference that may be caused by chattering, and improves the reliability and stability of system operation. 4. A comprehensive parameter adaptive update law is introduced, including key parameters such as convergence gain, switching gain, convergence time, and boundary layer thickness, which can be dynamically adjusted according to the system error state. This enables the controller to automatically adapt to different operating points and disturbance intensities, while ensuring fixed-time convergence performance, further optimizing the dynamic response process, achieving fast tracking without overshoot, and enhancing the system's adaptability to different smelting conditions. 5. The controllers of each Buck module work completely independently, but because each controller is equipped with a high-precision disturbance observer, it can automatically compensate for the imbalance caused by slight differences in parameters or uneven input between modules; therefore, the present invention does not require an additional current sharing control loop, and can naturally achieve automatic balancing of the output current of each parallel Buck module, simplifying the system structure, improving reliability, and is very suitable for DC electric arc furnace power supply scenarios with high current output. 6. When faced with drastic load changes in DC electric arc furnaces, it can achieve faster, more stable, and overshoot-free dynamic recovery; significantly improve the stability of the electric arc, thereby directly improving smelting efficiency, reducing electrode consumption, and ultimately ensuring product quality consistency, providing a high-performance power control solution for high-end metallurgical industrial applications. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the power supply control system for a DC electric arc furnace. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings, but it should be noted that the implementation of the present invention is not limited to the following embodiments.

[0021] The following embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments. Unless otherwise specified, the methods used in the following embodiments are conventional methods.

[0022] Example 1 The core of this invention lies in the independent design of an adaptive fixed-time disturbance observer and an adaptive fixed-time sliding mode controller for each Buck module. This design can accurately estimate and compensate for mismatch disturbances caused by factors such as unknown time-varying loads, achieving intrinsic current sharing among Buck modules without the need for an additional current sharing control loop. By introducing user-specifiable convergence time parameters and a time-varying sliding surface, it ensures that the total system current stabilizes at a given value within any preset fixed time, and the convergence time is independent of the system's initial state. Simultaneously, a parameter adaptive mechanism is employed to adjust the controller parameters in real time based on the system tracking error and the sliding surface state to adapt to different operating conditions. Furthermore, the use of a hyperbolic tangent function effectively suppresses control signal chattering. This invention is particularly suitable for industrial applications such as DC electric arc furnaces that require high current, high robustness, and fast dynamic response, significantly improving control performance.

[0023] Combination Figure 1 The basic topology of the Buck converter shown is a power supply system with N Buck modules connected in an interleaved parallel configuration. The following describes a method for controlling an interleaved parallel Buck power supply for a DC electric arc furnace, with the specific steps as follows: Step 1: Sample the inductor current, input DC voltage, and output voltage of each Buck module.

[0024] Step 2: Using the inductor current tracking the total current setpoint as the control target, calculate the current error of the k-th module: ; in, This represents the inductor current of the k-th module; This indicates the total current setpoint.

[0025] Step 3: Build an adaptive fixed-time disturbance observer for each Buck module to estimate the lumped disturbance of the system in real time. ; ; in: This is the current estimation error; and For exponential coefficients, , ; This is the estimated value of the disturbance; The parameter configuration ensures Hurwitz stability (i.e., all system poles are located in the left half of the complex plane, ensuring system stability). The gain of the disturbance observer needs to be selected based on the system dynamics, disturbance characteristics, and boundaries. sat(·) is the saturation function of the adaptive boundary layer; The design law for the adaptive boundary layer thickness, which is a saturation function, is: ; in: This represents the current boundary layer thickness. Minimum boundary layer thickness; This represents the maximum boundary layer thickness. This represents the absolute value of the current error estimate; k is the adjustment coefficient.

[0026] Step 4: Design an independent adaptive fixed-time sliding mode controller for each module; Design sliding surface : When t < hour, ③; When t≥ hour, ④; in: This represents the variable of the sliding surface, in units of A; This represents the inductor current error of the k-th module; Indicates the estimated disturbance value; t represents the time variable; Indicates the user-preset convergence time; Represented as a time-varying term, the formula is: ⑤; Expressing the convergence gain, the adaptive formula is: ; in: For convergence gain; This is the initial value for the convergence gain; For adaptive gain; This is the absolute value of the current error; To control the cycle.

[0027] Convergence time The adaptive formula: ; in: This is the current convergence time; This is the initial value for the convergence time; For adaptive gain; This is the absolute value of the current error; To control the cycle.

[0028] Step 5: Calculate the control variables : When t < hour: ; When t≥ hour: ; in: This indicates the input DC voltage, in volts (V). This represents the inductance value of the k-th Buck module, in H. Indicates switching gain, satisfying ; tanh(·) denotes the hyperbolic tangent function; Indicates the smoothing factor; This indicates the output voltage, in volts (V). This represents the ratio of the sliding surface to the smoothing factor; Indicates control variables; To switch the gain, satisfy Its adaptive formula is: ; To switch the gain, To switch the initial gain value, For adaptive gain, The absolute value of the sliding surface. To control the cycle.

[0029] Step Six: Control Variables After limiting, a modulated signal is generated. Each Buck module carrier uses phase interleaving, with an adjacent phase difference of 360° / N, where N is the number of Buck modules; the modulated signal is compared with the carrier signal to generate a PWM drive signal.

[0030] Step 7: The real-time monitoring system tracks the error and sliding surface; when the error exceeds the threshold and continues for a certain period of time, the parameter reset mechanism is triggered; and the control output is limited to prevent saturation.

[0031] This invention has the following main advantages: Arbitrary time convergence: Users can directly set the current convergence time according to process requirements (such as the melting period and refining period of the electric arc furnace). This time is independent of the initial state of the system, achieving unprecedented control flexibility. Strong robustness: By using a fixed-time disturbance observer to estimate and compensate for mismatch disturbances caused by factors such as unknown time-varying loads in real time, the impact of these disturbances on control performance is fundamentally eliminated, resulting in high steady-state accuracy. Parameter adaptive mechanism: On the one hand, the controller parameters are adjusted in real time according to the system tracking error and sliding surface state to adapt to different working conditions; on the other hand, the saturation function and tanh function of the adaptive boundary layer are used to smoothly switch the control law, which greatly suppresses the high-frequency chattering phenomenon inherent in traditional sliding mode control while maintaining strong robustness and improving the life of switching devices. Intrinsic current sharing between Buck modules: Each module controller works independently and automatically compensates for the differences in parameters between different Buck modules through disturbance observation, naturally achieving current balance in each phase without the need for additional current sharing control, which is very suitable for constant current control applications in electric arc furnaces; Excellent dynamic performance: Compared with traditional PI, SMC and other methods, this invention can achieve faster and overshoot-free dynamic recovery when the load changes drastically, which significantly improves the process quality and reliability of the power supply system.

[0032] Example 2 In this embodiment, the control method for an interleaved parallel Buck power supply for a DC electric arc furnace is the same as in Embodiment 1. Based on this, a three-phase (N=3) interleaved parallel Buck converter is used as an example for specific explanation. The system parameters are set as follows: Input DC voltage ; Rated output voltage ; Inductance value of each Buck module ; Switching frequency The control period Δt = 0.1 ms; Total output current setpoint (That is, the target current for each module is approximately 500A).

[0033] Step 1: Signal sampling and processing; The inductor current of each Buck module is collected in real time using a current sensor (such as a Hall sensor). Simultaneously, the input voltage is collected. and output voltage The signal is then converted from analog to digital and sent to a digital controller (such as a DSP or FPGA).

[0034] Step 2: Calculate the current error of each module in the digital controller; Current error for each module: ; If the sampling is obtained ,but .

[0035] Step 3: Build and run an adaptive fixed-time perturbation observer; The parameter settings are shown in the following example: Gain coefficient: , ; Exponential coefficient: , ; Boundary layer parameters: , , ; The observer operates in real time according to the following formula: ①; ②; Output of lumped disturbance The estimated value The observer can accurately estimate the disturbance caused by sudden load changes (such as a sudden drop from 100% to 50%) within about 2ms.

[0036] Step 4: Design and calculate the adaptive fixed-time sliding surface; Set initial value for convergence time Sliding surface variables Calculated based on time segments: When t < hour, ③; When t≥ hour, ④; Among them, time-varying terms Calculated using the following formula: ; Time-varying terms The parameters are as follows: Initial convergence gain: Adaptive gain ; Convergence time adaptive gain: ; For example, when a large current error is detected When, the following formula applies: ; Convergence time It will adaptively adjust to within one control cycle. This enables dynamic fine-tuning.

[0037] Step 5: Calculate the control variables; The control law is calculated piecewise according to the following formula: ; The key parameters are set as follows: Switch the initial gain value: Adaptive gain ; Smoothing factor: ; The equivalent control term in the control law is responsible for the ideal dynamics of the system, while the switching control term... It provides robustness; by using a hyperbolic tangent function and adaptive gain, it can effectively suppress the jitter amplitude of the control signal within the safe operating area of ​​the switching device (such as IGBT), and the peak voltage stress is reduced by about 60% compared with the traditional SMC.

[0038] Step 6: Generate interleaved PWM drive signals; The calculated control variables (i.e., the duty cycle signal) is limited to [0, 0.9] to generate the modulated signal. A triangular carrier wave with a 120° (360° / 3) phase difference is provided to the three Buck modules. The modulation signal of each module is compared with the corresponding carrier wave to generate three interleaved PWM drive signals, which drive the switching transistors of the three Buck modules respectively. This method can significantly reduce the total output current ripple, and the theoretical ripple amplitude can be reduced to less than 1 / 3 of that of a single module.

[0039] Step 7: System Monitoring and Protection; Real-time monitoring of current error in each module and sliding surface variables Set error threshold If any module If this threshold is exceeded for more than 1ms, the parameter reset mechanism is triggered to restore the key controller parameters to their initial values, preventing system divergence under abnormal operating conditions; simultaneously, the final control output is also reset. Limiting protection is implemented to ensure that it remains within the physically feasible range and to prevent phenomena such as integral saturation.

[0040] Verification of the effect of this embodiment: In the PSIM / Matlab simulation environment, when the load experiences a 50% step change at t=0.02s, the system using this invention can quickly and without overshoot recover to the given value within a preset 5ms, with a steady-state error of less than ±0.5%. Compared to traditional PI controllers (recovery time >15ms, overshoot >5%) and traditional SMCs (recovery time approximately 8ms, significant chattering), this invention demonstrates significant advantages in dynamic response, steady-state accuracy, and control smoothness.

[0041] This invention introduces an adaptive fixed-time sliding mode surface with a time-varying term, enabling the system's inductor current to strictly converge to a given value within any user-preset convergence time. This convergence time is independent of the system's initial state, allowing operators to directly set the required current stabilization time according to different process stages of the DC electric arc furnace (e.g., rapid response during melting, stable and precise response during refining), achieving unprecedented control flexibility—something traditional PI, sliding mode, and even fixed-time control methods cannot achieve. Furthermore, by independently designing a fixed-time disturbance observer for each Buck module, it can address disturbances caused by unknown time-varying load impedance (violent arc fluctuations). The system performs fast and accurate real-time estimation and feedforward compensation for matching disturbances and those caused by grid voltage fluctuations. Based on the observer-based compensation mechanism, it fundamentally eliminates the impact of lumped disturbances on the tracking performance of the control system, enabling the system to maintain extremely high steady-state accuracy and strong robustness under a wide range of operating conditions. The system uses a hyperbolic tangent function instead of the traditional sign function in the control law, combined with adaptive boundary layer technology, to achieve smooth switching of the control signal. Simultaneously, the accurate compensation of disturbances by the disturbance observer significantly reduces the switching gain requirement. These two measures work together to greatly suppress the high-frequency chattering inherent in traditional sliding mode control, not only reducing the switching gain of the switching... This reduces stress and wear on components, extends their service life, and reduces electromagnetic interference that may be caused by chattering, thereby improving the reliability and stability of system operation. A comprehensive parameter adaptive update law is introduced, allowing key parameters such as convergence gain, switching gain, convergence time, and boundary layer thickness to be dynamically adjusted according to the system error state. This enables the controller to automatically adapt to different operating points and disturbance intensities, further optimizing the dynamic response process while ensuring fixed-time convergence performance, achieving fast, overshoot-free tracking, and enhancing the system's adaptability to different smelting conditions. Each Buck module's controller operates completely independently, but each controller is equipped with high-precision... The perturbation observer can automatically compensate for imbalances caused by subtle differences in parameters or uneven inputs between modules. Therefore, this invention eliminates the need for an additional current sharing control loop, naturally achieving automatic current balancing of the output current of each parallel Buck module. This simplifies the system structure, improves reliability, and is highly suitable for DC arc furnace power supply scenarios with high current output. When faced with drastic load changes in DC arc furnaces, it can achieve faster, smoother, and overshoot-free dynamic recovery. It significantly improves arc stability, thereby directly increasing smelting efficiency, reducing electrode consumption, and ultimately ensuring consistent product quality, providing a high-performance power control solution for high-end metallurgical industrial applications.

Claims

1. A staggered parallel Buck power supply control method for a direct current arc furnace, characterized by, The application relates to a multi-phase Buck converter control method. Real-time acquisition of inductor current, input voltage and output voltage of each Buck module; System dynamic equation is constructed for each Buck module, and the system dynamic equation contains inductor current error and lumped disturbance term; A fixed-time disturbance observer is designed for each Buck module to estimate the lumped disturbance within a preset fixed time; An adaptive fixed-time sliding mode controller is designed for each Buck module, and the sliding mode surface contains current error, disturbance estimation value and time-varying term of user preset convergence time; A control law is designed, which contains an equivalent control term and a switching control term based on a hyperbolic tangent function, and is used for suppressing chattering; Adaptive update of control parameters is realized according to system error state dynamic boundary layer thickness, convergence gain, switching gain and convergence time; After limiting the control variables, multi-phase phase-staggered PWM driving signals are generated to drive the switching tubes of the Buck modules.

2. The interleaved parallel Buck power supply control method for a direct current electric arc furnace according to claim 1, characterized in that, The lumped disturbance includes matching disturbance caused by grid voltage fluctuation and non-matching disturbance caused by unknown time-varying load resistance; The inductance current error The inductance current error of the kth Buck module The difference between the total current given value The difference between the total current given value ； N represents the total number of all Buck modules; The system dynamic equation is as follows: ； Wherein: The derivative representing the current error, with units of A / s; V represents the input DC voltage, in V; This represents the inductance value of the k-th Buck module, in H. V represents output voltage, unit: V; represents a lumped disturbance.

3. The interleaved parallel Buck power supply control method for a DC arc furnace according to claim 1, characterized by, The upper bound of the estimation error convergence time of the fixed-time disturbance observer is independent of the initial state of the inductor current and the disturbance observer.

4. The interleaved parallel Buck power supply control method for a direct current electric arc furnace according to claim 1, characterized in that, The fixed-time disturbance observer adopts the following structure: ①； ②； Wherein: represents the current error estimate value in A; represents the adaptive boundary layer thickness; represents an adjustable gain parameter; with both denote an exponential coefficient, , ; denotes the disturbance estimate; derivative of the current estimation error in A / s; Sat(·) represents a saturation function; represents the absolute value of the current error estimate.

5. The interleaved parallel Buck power supply control method for a DC arc furnace according to claim 1, characterized by, The adaptive sliding mode surface is designed as follows: when t when t ③; when t≥ when t≥ when t≥ when t≥ Wherein: represents a slip surface variable, in A; represents the inductance current error of the kth module; denotes the disturbance estimate; T represents a time variable; represents a convergence time preset by the user; is expressed as a time-varying term, with the formula: ⑤； represents the convergence gain.

6. The interleaved parallel Buck power supply control method for a direct current electric arc furnace according to claim 1, characterized in that, The control law is designed as follows: ⑥ Wherein: V represents the input DC voltage, in V; Lk represents the inductance value of the kth Buck module, in H; represents a switching gain, satisfying ; Tanh(·) represents a hyperbolic tangent function; denotes a smoothing factor; V represents output voltage, unit: V; represents the ratio of the slip surface to the smoothing factor; denotes a control variable; When the equivalent control item is ; When the equivalent control item is ; The switching control item is .

7. The interleaved parallel Buck power supply control method for a DC arc furnace according to claim 1, characterized by, The adaptive update of the control parameters comprises: (1) Adaptive formula of boundary layer thickness phi: ⑦； In formula (6), represents the current boundary layer thickness; represents the minimum boundary layer thickness; represents the maximum boundary layer thickness; represents the absolute value of the current error estimate, and k represents an adjustment coefficient. (2) Adaptive formula of convergence gain zeta: ⑧； In formula (7), represents the convergence gain initial value; represents the adaptive gain; represents the current error absolute value; represents the control period; (3) Adaptive formula of switching gain eta: ⑨ In formula (9), represents a switching gain initial value; represents an adaptive gain; represents an absolute value of a sliding mode surface; represents a control period; (4) Convergence time Adaptive formula: ⑩ in Equation (10), denotes the current convergence time; denotes the initial value of the convergence time; denotes the adaptive gain; denotes the absolute value of the current error, denotes the control period.

8. The interleaved parallel Buck power supply control method for a direct current electric arc furnace according to claim 1, characterized in that, The monitoring and security protection mechanism also includes real-time monitoring of system tracking error and sliding mode surface variable, triggering parameter reset mechanism when the absolute value of current error exceeds the set threshold and lasts for more than a set time; and limiting the protection of control variable ​

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