A linear fitting analysis method for a dual-frequency induction heating power output frequency control system

Abstract

This invention provides a linearization fitting analysis method for the output frequency control system of a dual-frequency induction heating power supply. It unifies the coordinated compensation triggered by frequency increment limiting, frequency increment rate of change limiting, and minimum frequency interval constraints into a synthetic nonlinear module. Under quasi-steady-state and small-disturbance conditions, a describing function is used to equivalently linearize this synthetic nonlinear module, obtaining the equivalent gain related to the fundamental amplitude of the two input channels and forming an equivalent linear frequency domain model. Subsequently, frequency domain windows are selected near the high-frequency and low-frequency operating bands, and a unified structure second-order equivalent model is fitted to the equivalent frequency response, obtaining two sets of isomorphic low-order model parameters for the high-frequency and low-frequency channels. Based on these parameters, the frequency compensation increment required for feedforward compensation is quickly calculated to reduce online computation and improve real-time performance. When the fitting residual exceeds a preset threshold or enters a strongly nonlinear operating condition, model parameter updates and model calls are stopped, and the linearization fitting analysis is exited.

Description

Technical Field

[0001] This invention belongs to the field of automatic control and power electronic control technology, and relates to an analysis method for the output frequency control system of an induction heating power supply, specifically a linear fitting analysis method for the output frequency control system of a dual-frequency induction heating power supply. Background Technology

[0002] Dual-frequency induction heating power supplies utilize high-frequency and low-frequency channels working in tandem to meet the process requirements of different workpiece materials, geometries, and heating depths. In such systems, the output frequency typically needs to be adjusted around the load's equivalent resonant characteristics to effectively track the resonant point and reduce reactive power and operational fluctuations. In engineering, resonant point search signals are often used to characterize the deviation between the operating frequency and the resonant state, and a frequency error signal is constructed based on this to drive output frequency updates.

[0003] From a control theory perspective, the dual-frequency induction heating power supply output frequency control system is a closed-loop control system with the output frequency as the controlled variable and the frequency error signal as the feedback information. Its frequency update link typically includes constrained execution stages such as frequency increment limiting and frequency increment rate limiting, while also needing to satisfy the minimum frequency interval constraint and perform inter-channel coordination compensation when this constraint is triggered. The aforementioned constrained execution and coordination compensation exhibit segmented, saturated, and switching characteristics, resulting in a significantly nonlinear mapping between the frequency increment command and the actual frequency update action. Furthermore, the equivalent load parameters drift with changes in workpiece position, temperature rise, and coupling state, causing the system's dynamic characteristics to vary over time, exhibiting time-varying characteristics. Simultaneously, the combined effect of load parameter uncertainty and external disturbances (such as coupling changes and operating condition switching) gives the system parameter uncertainty and disturbance-driven characteristics. In terms of control structure, engineering often employs a composite control combining feedback regulation and feedforward compensation to balance steady-state accuracy and dynamic performance.

[0004] The aforementioned nonlinear, time-varying, and uncertain characteristics bring a series of engineering challenges: First, traditional linear time-invariant models often struggle to accurately characterize the dynamic characteristics of a system across the entire operating range. This is especially true when amplitude limiting, speed limiting, or minimum frequency interval constraints are involved, as the system's equivalent gain and phase characteristics change with signal amplitude, variation process, and constraint triggering state, making it difficult for fixed-parameter linear models to maintain consistency and interpretability. Second, attempting to rely entirely on nonlinear mechanism models for online analysis and parameter calculation is not only difficult in terms of model establishment and parameter identification, but also prone to model mismatch under parameter drift, disturbance effects, and operating condition switching conditions, thus affecting compensation effectiveness and system robustness. Third, due to the minimum frequency interval constraint and coordinated compensation between the two channels, the frequency update processes of the two channels are coupled in a control sense, making it difficult to directly apply single-channel independent analysis and tuning methods, further increasing the complexity of online analysis and real-time control.

[0005] Meanwhile, dual-frequency induction heating power supplies are primarily designed for high-end industrial applications where operating conditions change rapidly, disturbances are intense, and control update cycles are limited. The computational load of the compensation stage directly impacts the real-time performance and dynamic response of the output frequency adjustment. For feedforward compensation, the generation of compensation amounts typically relies on rapid estimation of the system's dynamic characteristics. Without a readily computable and condition-updated low-order equivalent model, it is difficult to ensure both real-time performance and compensation effectiveness and fault tolerance. Conversely, relying solely on fixed parameters or empirical compensation strategies is insufficient to adapt to changes in system dynamics and constraint intervention levels under different operating conditions, potentially leading to undercompensation or overcompensation.

[0006] Therefore, it is necessary to establish an analysis method for the output frequency control system of dual-frequency induction heating power supply, focusing on the key nonlinear links in the frequency update link. Within the operating window that meets the applicable conditions such as quasi-steady state and small disturbance, an equivalent representation that can be used for frequency domain analysis can be obtained by using the concept of equivalent linearization of nonlinear systems. Furthermore, a low-order equivalent model that is easy to calculate online can be formed to provide a rapid calculation basis for feedforward compensation. At the same time, it should have clear applicable boundaries and error criteria so that when the system enters strongly nonlinear or rapidly time-varying operating conditions, the model parameter update and model call can be stopped in time to avoid unreliable model results from adversely affecting the system operation. Summary of the Invention

[0007] This invention addresses the nonlinear, time-varying, and uncertain characteristics of a dual-frequency induction heating power supply output frequency control system, proposing a linearization fitting analysis method for this system. The system is a dual-channel closed-loop system, with the frequency update link involving coordinated compensation triggered by amplitude limiting, speed limiting, and minimum frequency interval constraints. It exhibits piecewise, saturated, and switching nonlinearities, and load parameter drift and disturbances make traditional fixed-parameter linear models difficult to apply. To reduce the computational complexity of online analysis and feedforward compensation, this invention performs equivalent linearization within a limited operating window, forming a low-order model suitable for frequency domain fitting, providing a basis for rapid calculation of frequency compensation increments.

[0008] To achieve the above objectives, the present invention adopts the following technical solution.

[0009] A linear fitting analysis method for a dual-frequency induction heating power supply output frequency control system includes:

[0010] S110 abstracts the frequency increment limiting, frequency increment rate limiting, and coordinated compensation triggered by dual-frequency minimum frequency interval constraints, which are directly related to the output frequency update, into a unified synthetic nonlinear module.

[0011] S120, within the operating window where the system satisfies quasi-steady state, small disturbances, and infrequent intervention of the synthetic nonlinear module, the synthetic nonlinear module is represented by an equivalent linearization based on the idea of ​​the describing function, obtaining the equivalent gain related to the amplitude of the input fundamental wave, and together with the linear dynamic part of the system, it constitutes an equivalent linear frequency domain model.

[0012] S130, based on the equivalent linear frequency domain model, construct relative frequency domain windows near the operating frequency bands of the high-frequency channel and the low-frequency channel respectively, and form an equivalent frequency response based on natural operating data; within the relative frequency domain window, fit the equivalent frequency response into a second-order equivalent model with a unified structure, and obtain two sets of low-order model parameters for the high-frequency channel and the low-frequency channel respectively.

[0013] S140, the second-order equivalent model calculates and directly outputs the frequency compensation increment required for feedforward compensation at the current operating point, so as to reduce the complexity of online analysis and compensation calculation, and improve the compensation update speed without changing the existing feedback control structure.

[0014] S150: When the frequency domain fitting residual exceeds the preset threshold or the operating condition does not meet the limited operating condition window, stop the update of the second-order equivalent model parameters and the invocation of the second-order equivalent model, exit the linearization fitting analysis, and the feedforward compensation reverts to the existing conservative strategy. When the operating condition recovers and meets the applicable boundary, the update of the second-order equivalent model and the compensation calculation are resumed.

[0015] A computing device includes: at least one processor and a memory storing program instructions; when the program instructions are read and executed by the processor, the computing device performs the method.

[0016] A readable storage medium storing program instructions that, when read and executed by a computing device, cause the computing device to perform the method.

[0017] Beneficial effects:

[0018] 1. To address the nonlinear characteristics such as segmentation, saturation, and switching introduced by the coordinated compensation under the constraints of amplitude limiting, speed limiting, and minimum frequency interval triggering in the frequency update link of the dual-frequency induction heating power supply output frequency control system, the key nonlinear links are uniformly abstracted into a synthetic nonlinear module within the limited operating window. The equivalent gain related to the amplitude of the two-channel input fundamental wave is obtained through the equivalent linearization of the describing function. Thus, an equivalent linear frequency domain model that can be used for frequency domain analysis is established while maintaining the consistency of control meaning, avoiding the mismatch risk caused by relying solely on a linear model with fixed parameters.

[0019] 2. The equivalent frequency response is fitted in the frequency domain within the relative frequency domain window of the high-frequency channel and the low-frequency channel respectively. The low-order model parameters of the two channels are output using a second-order equivalent model with a unified structure. The number of parameters is small and the amount of calculation is small, which can provide a fast calculation basis for feedforward compensation and improve the real-time performance and engineering usability of compensation calculation.

[0020] 3. The validity criterion is based on the fitting residual threshold and the limited working condition window conditions. When the system enters a strongly nonlinear or rapidly time-varying state, or when the fitting residual exceeds the limit, the model parameter update and model call are stopped and the linearization fitting analysis is exited. The feedforward compensation is rolled back to the existing strategy. When the conditions are restored, the update and call are resumed, thereby improving real-time performance while taking into account the clear applicable boundaries and fault tolerance. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the overall process of linearization fitting analysis for a dual-frequency induction heating power supply output frequency control system.

[0022] Figure 2 This is a schematic diagram of the internal structure of the synthetic nonlinear module and the dual-channel coordinated compensation.

[0023] Figure 3 A schematic diagram illustrating the equivalent linearization and equivalent gain construction of the control system description function.

[0024] Figure 4 This is a schematic diagram illustrating the relationship between the second-order fitting of the dual-channel relative frequency domain window and the residual gating. Detailed Implementation

[0025] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0026] This invention provides a linear fitting analysis method for the output frequency control system of a dual-frequency induction heating power supply. The method is applicable to the output frequency control system of a dual-frequency induction heating power supply. The output frequency control system includes at least a high-frequency channel and a low-frequency channel. The two channels adjust the output frequency within their respective operating frequency bands and satisfy the dual-channel cooperative constraint during operation.

[0027] To ensure consistency in the description of the linearization fitting analysis method of this invention, this embodiment makes unified conventions regarding the analysis object and related signals. The output frequency of the high-frequency channel is denoted as... The output frequency of the low-frequency channel is denoted as The target frequency of the high-frequency channel is denoted as . The target frequency of the low-frequency channel is denoted as The frequency error signal of the high-frequency channel is denoted as... The frequency error signal of the low-frequency channel is denoted as The frequency error signal is a resonant point search signal.

[0028] This implementation uses a frequency increment command as the analysis input. The frequency increment command for the high-frequency channel is denoted as... The frequency increment command for the low-frequency channel is denoted as The frequency increment instruction is used to characterize the incremental adjustment requirement of the output frequency within the current update cycle. The linearized fitting analysis method of this invention is used for fast calculation of feedforward compensation, and the frequency compensation increment of the feedforward compensation output is denoted as... and It is used to provide compensation increment support for the existing frequency regulation process. This invention does not change the existing feedback control structure, and the frequency compensation increment participates in the frequency update as a feedforward compensation result.

[0029] The core content of this invention is as follows: Within a limited operating window, the constrained frequency execution and dual-channel coordination, directly related to output frequency updates, are uniformly abstracted into a synthetic nonlinear module; based on the equivalent linearization of the describing function, second-order equivalent models for the high-frequency and low-frequency channels are fitted in the frequency domain, thereby providing a basis for the rapid calculation of frequency compensation increments. To avoid unnecessary implementation limitations, this embodiment only describes the content directly related to the core method. For example... Figure 1As shown, this method uses frequency increment commands and frequency error signals as the main lines to complete the synthesis of nonlinear equivalents, dual-window second-order fitting, and residual gating, and exits the linearization fitting analysis when the operating conditions exceed the limits. Figure 1 As shown, the method includes the following steps:

[0030] S110 abstracts the frequency increment limiting, frequency increment rate limiting, and coordinated compensation triggered by the minimum frequency interval constraint of the two frequencies, which are directly related to the output frequency update, into a unified synthetic nonlinear module.

[0031] S120, within the operating window where the system satisfies quasi-steady state, small disturbances, and infrequent intervention of the synthetic nonlinear module, uses the describing function concept to perform an equivalent linearization representation of the synthetic nonlinear module, obtaining an equivalent gain related to the amplitude of the input fundamental wave, and together with the linear dynamic part of the system, constitutes an equivalent linear frequency domain model.

[0032] S130, based on the equivalent linear frequency domain model, relative frequency domain windows are constructed near the operating frequency bands of the high-frequency and low-frequency channels respectively, and equivalent frequency responses are formed based on natural operating data. Within the relative frequency domain windows, the equivalent frequency responses are fitted to a second-order equivalent model with a unified structure, obtaining two sets of low-order model parameters for the high-frequency and low-frequency channels respectively. When the frequency domain data quality is insufficient, it is permissible to superimpose small identification excitations to enhance the identifiability of the equivalent frequency response.

[0033] S140, the second-order equivalent model calculates and directly outputs the frequency compensation increment required for feedforward compensation at the current operating point, so as to reduce the complexity of online analysis and compensation calculation, and improve the compensation update speed without changing the existing feedback control structure.

[0034] S150: When the frequency domain fitting residual exceeds a preset threshold or the operating condition does not meet the defined operating condition window, the update of the second-order equivalent model parameters and the invocation of the second-order equivalent model are stopped, the linearization fitting analysis is exited, and the feedforward compensation reverts to the existing conservative strategy. Once the operating condition recovers and meets the applicable boundary, the update of the second-order equivalent model and the compensation calculation are resumed. This invention uses the frequency domain fitting residual as the validity criterion to limit the applicability of the method and improve its fault tolerance.

[0035] It should be noted that the dual-frequency induction heating power supply output frequency control system is a dual-channel closed-loop system. The coordinated compensation triggered by amplitude limiting, speed limiting, and minimum frequency interval constraints in the frequency update link introduces nonlinearities such as segmentation, saturation, and switching. At the same time, the equivalent load parameters are affected by factors such as coupling and temperature rise, exhibiting slow drift and superimposed disturbances. To ensure the interpretability and online availability of the frequency domain fitting, this embodiment only provides an equivalent linearization expression for the above nonlinearities within a limited operating window.

[0036] This invention performs linearization fitting analysis only within a limited operating condition window. The limited operating condition window includes four conditions: quasi-steady state, small disturbance, slowly varying parameters, and infrequent intervention of the synthetic nonlinear module. If any condition is not met, model parameter updates and model calls are stopped, and feedforward compensation reverts to the existing strategy. Fitting updates and compensation calculations resume only after the conditions are restored.

[0037] Under the aforementioned limited operating window conditions, in order to obtain an equivalent linear description suitable for frequency domain fitting, it is necessary to limit the sources of nonlinearity in the dual-frequency induction heating power supply output frequency control system and focus the nonlinear analysis range on the frequency update link directly related to the output frequency update. The frequency update link described in this invention refers to the frequency increment command. , Acting on the output frequency , The update process and the constraints and coordination links directly coupled to this update process are described. For nonlinear factors in the power conversion, load coupling, and measurement links that are not directly logically coupled to the frequency update link, this invention does not elaborate on their mechanisms, but rather includes their impact on small disturbance dynamics within a limited operating window in the subsequent equivalent linear frequency domain characterization range, in order to avoid introducing complex descriptions unrelated to the core method.

[0038] In addition to constrained execution characteristics, the coordinated compensation triggered by the dual-frequency minimum frequency interval constraint further introduces nonlinearity in dual-channel coupling. When the output frequencies of the high-frequency channel and the low-frequency channel are close and trigger the minimum frequency interval constraint, the system needs to coordinate and adjust the frequency update action between the channels while maintaining the constraint, so that the frequency update result of one channel is correlated with the update result of the other channel. This correlation is not only manifested as a linkage adjustment when the constraint is triggered, but also causes the mapping between the frequency increment command of the two channels and the frequency update action to switch with the constraint trigger state, forming a nonlinear relationship with channel coupling and piecewise characteristics. Since this coupling relationship directly affects the frequency update link, this invention incorporates it into the input variable of the equivalent gain of the describing function, so that the equivalent gain depends on the fundamental amplitude of the input of both channels simultaneously, thereby ensuring that the fitted model still has a consistent control meaning when the dual-channel cooperative constraint exists.

[0039] In summary, this invention limits the scope of nonlinear analysis to the frequency update link in its specific implementation, and takes the piecewise, saturated, and coupled characteristics formed by frequency increment limiting, frequency increment rate of change limiting, and coordinated compensation triggered by the minimum frequency interval constraint of the two frequencies as the main sources of nonlinearity. Based on this limitation, the above-mentioned nonlinear effects can be uniformly abstracted and equivalently described in the following content, providing a consistent object basis for the equivalent linearization of the describing function and the second-order fitting in the frequency domain.

[0040] The input to the synthesis nonlinear module is the frequency increment command of the high-frequency channel. Frequency increment command for low-frequency channel The output is the actual frequency update. and And update the output frequency accordingly. and . and Under the combined effect of frequency increment limiting, frequency increment rate of change limiting, and minimum frequency interval constraint-triggered coordinated compensation, it exhibits segmented saturation, process dependence, and dual-channel linkage adjustment characteristics; therefore, the synthesized nonlinear module provides a unified object for the subsequent equivalent linearization of the describing function.

[0041] in, This indicates the frequency increment command of the synthesized nonlinear module for the high-frequency channel. The output frequency used to update the high-frequency channel output frequency after coordinated compensation triggered by frequency increment limiting, frequency increment rate of change limiting, and minimum frequency interval constraint of dual frequencies. The actual frequency increment; This indicates the frequency increment command of the synthesized nonlinear module for the low-frequency channel. The output after performing the above processing is used to update the low-frequency channel output frequency. The actual frequency increment.

[0042] like Figure 2 As shown, the frequency increment command is sequentially processed by amplitude limiting and speed limiting to form an updated action, and inter-channel coordination compensation is performed when the minimum frequency interval constraint is triggered, outputting... and .

[0043] To ensure consistency with subsequent frequency domain equivalence, this embodiment treats the input signal of the synthesized nonlinear module as a periodic variable under fundamental frequency dominance. In subsequent sections, the fundamental amplitude of the input signal is used as the key characteristic for equivalent linearization, thus equivaling the synthesized nonlinear module to an equivalent gain that varies with amplitude within a defined operating window. Based on the combination of this equivalent gain and the linear dynamic component, an equivalent linear frequency domain model can be further formed, and second-order frequency domain fitting and feedforward compensation calculations can be performed rapidly within the dual-channel relative frequency domain window.

[0044] Based on the unified input and output of the aforementioned synthetic nonlinear module, to ensure that the equivalent linearization object of the subsequent describing function is clear and consistent throughout the text, this implementation further clarifies the constrained execution and coordination compensation characteristics included in the synthetic nonlinear module. It is important to emphasize that the following characteristics are not modeled as multiple independent components, but rather collectively constitute the internal action of the same synthetic nonlinear module, and are... , arrive , The mapping relationship is uniformly reflected.

[0045] The synthesized nonlinear module includes a frequency increment limiting feature. This frequency increment limiting feature is used to limit the range of frequency increment variation in the amplitude direction. or When the amplitude exceeds the preset allowable range, the output of the synthesized nonlinear module is... or It will no longer exhibit a saturation trend as the input amplitude continues to increase, thus making the input-output relationship exhibit piecewise characteristics.

[0046] The synthesized nonlinear module includes a frequency increment rate of change limiting feature, which limits the rate of change of the frequency increment over time. This feature is used to restrict the rate at which the frequency increment changes over time. (The text also mentions a frequency increment command in a high-frequency channel, but this seems unrelated to the main topic and is likely a separate point.) Or frequency increment command for low-frequency channels When the absolute value of the difference between adjacent update cycles exceeds the first change threshold, the output of the synthesized nonlinear module... or The absolute value of the difference between adjacent update cycles is limited to not exceeding a second change threshold, thereby... or Respond with a limited rate of change.

[0047] Wherein, the first change threshold is 20 to 2000 Hz / update cycle, the second change threshold is 1 to 500 Hz / update cycle, and the second change threshold is not greater than the first change threshold.

[0048] The synthesized nonlinear module includes a coordinated compensation feature triggered by a dual-frequency minimum frequency interval constraint. This coordinated compensation feature is used to output the frequency in the high-frequency channel. With low-frequency channel output frequency When the minimum frequency interval constraint is approached and triggered, the frequency update function of at least one channel is adjusted so that the updated output frequencies of the two channels meet the minimum frequency interval requirement.

[0049] Within the defined operating window, the intensity and intervention status of the above three features remain relatively stable over several consecutive update cycles, and the synthesized nonlinear module does not exhibit frequent switching. This allows the synthesized nonlinear module to be represented by an equivalent linearization under the condition of fundamental frequency dominance. Based on this, the following will employ the describing function concept, using the fundamental amplitude of the input signal to the synthesized nonlinear module as the characterizing quantity, to establish the equivalent gain relationship of the synthesized nonlinear module. This will be further combined with the linear dynamic part to form an equivalent linear frequency domain model, providing a unified foundation for rapid calculation of second-order frequency domain fitting and feedforward compensation.

[0050] Based on the clearly defined synthetic nonlinear module and its internal characteristics, in order to establish an equivalent linear description that can be used for frequency domain fitting within a limited operating window, such as... Figure 3 As shown, the input fundamental amplitude is extracted. , And the output fundamental component, to obtain the equivalent gain , This method forms an equivalent frequency domain representation for frequency domain fitting. The implementation uses the describing function concept to represent the synthesized nonlinear module in an equivalent linearized manner. The basic idea of ​​this equivalent linearization is: under the condition of fundamental frequency dominance, the output fundamental component of the synthesized nonlinear module under a given input fundamental frequency amplitude is regarded as an equivalent amplification and equivalent phase shift of the input fundamental component. Thus, the equivalent gain that varies with amplitude characterizes the main influence of the module on the frequency domain characteristics, while the higher harmonic components introduced by nonlinearity are ignored as secondary influences within a limited operating window.

[0051] In this embodiment, the fundamental frequency selected for equivalent linearization analysis is [frequency value missing]. Its corresponding period is Within the defined operating window, the frequency increment commands for the high-frequency and low-frequency channels are considered as periodic variations dominated by the fundamental frequency, and can be represented in fundamental form as follows:

[0052] ,

[0053] in, for The fundamental amplitude, for The fundamental amplitude, and , The above expression describes the definition and derivation of the equivalent linearization of a function. It does not require that the frequency increment command be an ideal sine wave in actual operation, but only that its fundamental component dominates within a limited operating window.

[0054] Under the condition of fundamental frequency dominance, the effect of the synthesized nonlinear module on the fundamental frequency component can be equivalently represented as a complex gain that varies with the amplitude of the input fundamental frequency. The equivalent gain of the high-frequency channel describing function is defined as follows: The equivalent gain of the low-frequency channel describing function is And:

[0055] ,

[0056] ,

[0057] in, for The input fundamental amplitude, for The input fundamental amplitude; , These are the equivalent amplitude amplification factors for the high-frequency channel and the low-frequency channel, respectively. , These are the equivalent phase shifts for the high-frequency channel and the low-frequency channel, respectively. , , , Through the , The fundamental component and the corresponding input fundamental component are obtained by conventional Fourier analysis and are regarded as slowly changing quantities within a limited operating window.

[0058] Based on the definition of the equivalent gain of the describing function mentioned above, the following section will further explain how to... , Combined with the linear dynamic part of the system, an equivalent linear frequency domain model is formed, so that the main influence of the synthesized nonlinear module is uniformly incorporated in the frequency domain, thus laying the foundation for second-order frequency domain fitting within the dual-channel relative frequency domain window.

[0059] To combine the equivalent gain of the describing function with the linear dynamic part, this embodiment synthesizes the output of the nonlinear module. , Considered as the equivalent input to the linear dynamic part of the system, the output of the linear dynamic part of the system is the frequency error signal. , The linear dynamic part is used to characterize the dynamic relationship between the frequency update link (excluding the synthesis nonlinear module) and the resonant point search to form the frequency error signal within a defined operating window; this part can be equivalent to a linear system, and its specific implementation does not affect the scope of protection of this invention.

[0060] The linear dynamic parts are respectively used and This represents the equivalent linear dynamic relationship between the actual frequency increments of the high-frequency and low-frequency channels and the frequency error signal, let... express Laplace transform, express Laplace transform, , They represent , Laplace transform, , They represent , The Laplace transform, where Let be a Laplace variable. Then we have:

[0061] ,

[0062] ,

[0063] In the frequency domain with small perturbations, the equivalent gain from the describing function of the synthesized nonlinear module can be obtained as follows:

[0064] ,

[0065] ,

[0066] Combining the above relationships, we obtain the equivalent linear frequency domain model from the frequency increment command to the frequency error signal:

[0067] ,

[0068] ,

[0069] The equivalent linear frequency domain transfer function for the two channels is defined as follows:

[0070] ,

[0071] ,

[0072] in, This is a small perturbation angular frequency variable, not equivalent to the output frequency. , The trajectory of change.

[0073] Based on the above equivalent linear frequency domain model, the following sections will further explain how to form [the model] within the respective relative frequency domain windows of the high-frequency and low-frequency channels. , The frequency response data is used to fit a second-order equivalent model with a unified structure, providing directly callable low-order model parameters for the rapid calculation of the frequency compensation increment of feedforward compensation.

[0074] Based on the established equivalent linear frequency domain model, this implementation method requires obtaining the equivalent linear frequency domain transfer functions of the high-frequency channel and the low-frequency channel. , Frequency response data within the range of interest is used to perform subsequent relative frequency domain window selection and second-order frequency domain fitting. This implementation only illustrates the principles for forming frequency response data and its correspondence with the equivalent model, without limiting the sampling structure, excitation injection method, or implementation platform.

[0075] Within a defined operating window, this implementation method preferentially generates frequency response data based on natural operating data. Natural operating data refers to the frequency error signal generated during normal system operation. , and frequency increment command , The observation data sequence evolves over time. Based on this observation data sequence, the fundamental frequency dominance relationship between the frequency increment command and the frequency error signal can be extracted within the selected observation interval, and the frequency can be estimated accordingly. , The amplitude and phase characteristics.

[0076] When the frequency domain components of the natural operating data within the selected observation interval are insufficient to form a stable frequency response estimation result, it is permissible to superimpose a small identification excitation to enhance frequency domain identifiability, provided that the existing feedback control structure of the system is not altered and the normal heating process is not affected. The small identification excitation, designed not to cause significant operational disturbances, can be superimposed on the frequency increment command. With / or This allows for the formation of excitation components usable for frequency domain estimation within the range of small perturbation frequencies of interest. The present invention does not limit the specific form of the micro-identification excitation, only requiring that its amplitude be sufficiently small and satisfy the defined operating window conditions.

[0077] To ensure consistency between the frequency response data and the aforementioned equivalent linear frequency domain model, this embodiment uniformly selects the equivalent frequency domain relationship from the frequency increment command to the frequency error signal when generating the frequency response data. For input, with To output frequency response data forming a high-frequency channel, in For input, with This is to output frequency response data that forms a low-frequency channel. The frequency response data obtained in this way can be considered as a response within a limited operating condition window. , The observations can be directly used for subsequent second-order frequency domain fitting within the relative frequency domain window.

[0078] To ensure the reliability of the fit, a consistency check can be performed on the frequency response data; if the check fails, the model parameters will not be updated.

[0079] Based on the above equivalent linear frequency domain model establishment and frequency response data formation, in order to ensure that the subsequent frequency domain fitting can take into account the differences between the two channels and keep the model order simple, this implementation method constructs relative frequency domain windows near the working frequency bands of the high-frequency channel and the low-frequency channel respectively, and performs frequency domain fitting analysis within each window.

[0080] The relative frequency domain window is used to limit the frequency range covered by the frequency domain fitting, so that the fitting object is concentrated on the frequency band most relevant to the dynamic characteristics of the current operating point, thereby avoiding unnecessary fitting complexity and model mismatch risk introduced by simultaneously covering two channels with a single wideband model. Figure 4 As shown, in the relative frequency domain window of the high-frequency channel Relative frequency domain window of low-frequency channel Internal selection of frequency point set , Complete the second-order fitting and calculate the residuals. , The model is then compared with a threshold to determine whether it is allowed to be used for feedforward compensation calculations.

[0081] In this embodiment, the relative frequency domain window of the high-frequency channel revolves around the current output frequency of the high-frequency channel. The relative frequency domain window of the low-frequency channel is constructed around the current output frequency of the low-frequency channel. Construction. For ease of description, the relative frequency domain window of the high-frequency channel is denoted as... The relative frequency domain window of the low-frequency channel is denoted as .in, Indicates the current output angular frequency of the high-frequency channel. The set of angular frequencies within a preset relative bandwidth range centered on the angular frequency. Indicates the current output angular frequency of the low-frequency channel. The set of angular frequencies within a preset relative bandwidth range centered on the operating point. The preset relative bandwidth reflects the range of small perturbation frequencies around the operating point, and its value can be determined based on the typical bandwidth of the system's dynamic response and the frequency domain identifiability within the observation interval; this invention does not limit its specific numerical form. The specific boundary form of the relative frequency domain window is not limited.

[0082] It should be noted that the relative frequency domain window described in this embodiment targets small perturbation frequency variables used for frequency domain analysis, rather than the trajectory of the output frequency itself. In other words, and Used to characterize the equivalent linear frequency domain transfer function , The amplitude and phase characteristics vary within a small disturbance frequency range, with the center determined based on the current output frequency of each channel to ensure the window remains consistent with the current operating point. When the system operating point changes slowly, and Can be followed , Adaptive updates ensure that the second-order fitting always revolves around the current operating point. When the system exceeds the defined operating window, this invention stops updating model parameters and calling the model, and exits the linear fitting analysis, avoiding updates under rapidly changing or strongly nonlinear conditions that could lead to unreliable fitting results.

[0083] The two channels have different operating frequency bands and dynamic characteristics, and relative frequency domain windows are set to improve the approximation capability of the second-order model near their respective operating points.

[0084] Based on the definition of the relative frequency domain window mentioned above, we will further explain how to... and The frequency point set and its distribution rules for fitting are selected within the window so that the obtained frequency response data can form discrete frequency domain samples that can be used for fitting the second-order model within the window, providing a basis for determining the parameters of the two-channel second-order equivalent model.

[0085] In the aforementioned relative frequency domain window and Based on the established parameters, to transform the frequency response data into discrete frequency domain samples suitable for fitting a second-order equivalent model, this implementation selects frequency point sets within each relative frequency domain window and pre-defines the quantity and distribution of these frequency point sets. The selection of frequency point sets aims to satisfy the identifiability of the second-order model fitting while also considering computational complexity and online update requirements, thereby enabling the fitting process to stably output low-order model parameters for two channels while maintaining simplicity.

[0086] In this embodiment, in the high-frequency channel relative frequency domain window Select high-frequency channel frequency point set In the low-frequency channel relative frequency domain window Select low-frequency channel frequency point set The frequency point set , Each is composed of a finite number of angular frequency points and satisfies , .in, The angular frequency point in the middle is denoted as , The angular frequency point in the middle is denoted as , These are frequency point numbers. The aforementioned angular frequency points are used to indicate the location of sampling or estimating the frequency response within a relative frequency domain window, and their correspondence with the frequency response data is determined by the aforementioned frequency response estimation process.

[0087] The number of frequency points is a preset number, used to satisfy the identifiability of the second-order model fitting while also considering the real-time nature of online updates; this invention does not limit the specific number, value, or interval. The distribution of the frequency point set is a preset distribution method. In one embodiment, frequency points can be selected approximately uniformly at preset intervals within the relative frequency domain window, so that the frequency domain samples cover the low, middle, and high ends of the window, thereby enabling the fitting model to simultaneously consider the changing trends of amplitude and phase characteristics within the window. The selection of the frequency point set should ensure that the fitting residuals can reflect the fitting quality within the window, for use as a subsequent residual threshold criterion.

[0088] In summary, through and Select a frequency point set that meets the preset quantity and preset distribution pattern. , The aforementioned frequency response data can be transformed into discrete frequency domain samples required for fitting a second-order equivalent model. Based on these discrete frequency domain samples, the following section will further present the unified structure of the second-order equivalent model and the expression of the fitting target, and on this basis, determine the parameters of two sets of low-order models for the high-frequency and low-frequency channels. Within the aforementioned relative frequency domain window... , and frequency point set within the window , Based on the established framework, this implementation further provides a unified second-order equivalent model form for frequency domain fitting and clarifies the fitting target expression of the second-order equivalent model parameters, so that the subsequent fitting process can stably output the low-order model parameters of the two channels while maintaining the simplicity of the model order.

[0089] This implementation method defines the equivalent linear frequency domain transfer function. , Both channels are approximated using second-order equivalent models within their respective frequency domain windows. To avoid introducing unnecessary notation, both channels use second-order equivalent models with the same structure, differing only in parameter values. The second-order equivalent model for the high-frequency channel is denoted as... The second-order equivalent model of the low-frequency channel is denoted as ,in For Laplace variables.

[0090] In one implementation, the second-order equivalent model adopts the following unified form:

[0091] ,

[0092] in, , These are the equivalent gain coefficients for the high-frequency channel and the low-frequency channel, respectively. , These are the equivalent time constants for the high-frequency channel and the low-frequency channel, respectively. , ; , These are the equivalent damping coefficients for the high-frequency and low-frequency channels, respectively. , ; , These are the equivalent delays for the high-frequency channel and the low-frequency channel, respectively. , The equivalent delay is used to compensate for the overall lag in the frequency domain phase when needed; when the delay effect is negligible, it can be set as follows: and However, this does not change the unified structure of the second-order model.

[0093] The second-order equivalent model is used to approximate the equivalent frequency domain relationship of each channel within a relative frequency domain window. For high-frequency channels, in any angular frequency point At this point, the frequency response observation is denoted as The predicted value of the second-order equivalent model at this point is denoted as... For low-frequency channels, in any angular frequency point At this point, the frequency response observation is denoted as The predicted value of the second-order equivalent model is denoted as Therefore, the fitting residuals of the two channels at each frequency point are defined as follows:

[0094] ,

[0095] The fitting objective is to fit the set of frequency points in the high-frequency channel. Internally, to make residual The overall error is minimized; in the low-frequency channel frequency point set Internally, to make residual The overall error is minimized. This overall error can be measured using conventional frequency domain error metrics; the present invention does not limit its specific form.

[0096] By unifying the second-order equivalent model form and the fitting target expression as described above, it is possible to achieve the following without increasing the model order: , Within their respective relative frequency domain windows, they approximate as second-order models with fewer parameters, facilitating rapid computation. Based on this, the following section will further explain... and The implementation expression and output results of the two-channel second-order model parameters are determined above, and this lays the foundation for subsequent direct calculation of frequency compensation increments based on the second-order model. , Provides low-level model parameters that can be directly invoked.

[0097] Based on the above-mentioned unified second-order equivalent model form and fitting target, this embodiment further explains the determination method of the two-channel second-order model parameters and their output results, so that the second-order equivalent model can stably characterize the equivalent frequency domain amplitude and phase characteristics within the relative frequency domain window within the limited operating condition window, and provide directly callable model parameters for subsequent feedforward compensation calculation.

[0098] Within a defined operating window, the frequency response data formed over a selected observation interval can be considered as an equivalent linear frequency domain transfer function. , The observation. For the high-frequency channel, at the frequency point set of the high-frequency channel. Angular frequency points within At that location, the corresponding observation value was obtained. For the low-frequency channel, in the low-frequency channel frequency point set Angular frequency points within At that location, the corresponding observation value was obtained. Based on this, the second-order equivalent model is tested on its respective frequency point set. , Frequency domain fitting is performed to minimize the approximation error of the second-order model to the observed frequency response within the relative frequency domain window.

[0099] In one implementation, the second-order equivalent model parameters of the high-frequency channel... By making The parameters of the second-order equivalent model for the low-frequency channel are determined by minimizing the overall fitting error. By making The overall fitting error is determined by minimizing the overall fitting error. This overall fitting error can be determined by the residual... , The structure is such that the parameter values ​​can be obtained using conventional frequency domain fitting methods; however, this invention does not limit the specific solution algorithm. The comprehensive fitting error of the high-frequency channels is the residual of the frequency domain fitting. In frequency point set The error metric obtained by summarizing the results is that the overall fitting error of the low-frequency channel is the residual of the frequency domain fitting. In frequency point set The error metric is obtained by summarizing the results. To ensure the physical rationality and interpretability of the model, basic constraints can be imposed on the parameters during the parameter solution process, including... , , , , , .

[0100] To enhance the stability of online updates, parameter updates can be smoothed or preserved. After the two-channel second-order frequency domain fitting is completed, the output results include: second-order equivalent model parameters for the high-frequency channel. Low-frequency channel second-order equivalent model parameters And residual level information used to characterize the fitting quality. The residual level information can be obtained from... On and On The calculated value reflects the degree to which the second-order model approximates the amplitude and phase characteristics within the relative frequency domain window, and provides a basis for subsequent validity criteria and exit mechanisms.

[0101] Using the above methods, without increasing the model order or introducing a complex parameter system, it is possible to... , Two sets of second-order equivalent model parameters, reflecting the dominant dynamic characteristics near the operating point, are obtained. Based on these two sets of parameters, the following section will further explain how to use the second-order equivalent model to quickly calculate and directly output the frequency compensation increment at the current operating point. , This provides feedforward compensation support for output frequency updates without changing the existing feedback control structure, and forms an effectiveness criterion and fault-tolerant exit loop consistent with the fitting residual.

[0102] In this embodiment, the second-order equivalent model , It approximates the equivalent frequency domain relationship between the frequency increment command and the frequency error signal. Within a defined operating window, the frequency compensation increment can be generated based on the static gain of the second-order equivalent model for rapid calculation.

[0103] Based on the second-order equivalent model form described above, when At that time, the static gains of the second-order equivalent model are as follows:

[0104] ,

[0105] in, , These are the equivalent gain coefficients for the high-frequency and low-frequency channels, respectively, and satisfy the following conditions: , ;when or When the frequency error is less than a preset lower threshold, the frequency compensation increment is not calculated based on the second-order equivalent model. To reduce the frequency error signal, this implementation unifies the compensation direction to the direction that reduces the frequency error signal, and uses the static gain of the second-order equivalent model. , Directly calculate the frequency compensation increment:

[0106] ,

[0107] in, , To compensate for the weighting coefficients, satisfying , .

[0108] In this embodiment, the frequency compensation increment participates in the output frequency update as a feedforward compensation result. To maintain consistency with the aforementioned frequency update link, the feedforward compensation is superimposed with the existing frequency increment command to obtain the frequency increment command participating in the frequency update. Specifically, the frequency increment command for the high-frequency channel participating in the frequency update is denoted as... The frequency increment instruction for low-frequency channels participating in frequency updates is denoted as... , and defined as:

[0109] ,

[0110] in, , The frequency increment command given for the existing frequency regulation process. , This is the input quantity after superimposed feedforward compensation. The frequency increment after superposition is still subject to coordinated compensation constraints triggered by amplitude limiting, speed limiting, and minimum frequency interval constraints.

[0111] Furthermore, to ensure consistency with subsequent validity criteria, when the second-order equivalent model is determined not to meet the usage conditions or when valid model parameters are not currently available, this implementation method will no longer calculate the frequency compensation increment based on the second-order equivalent model. The frequency compensation increment can be set to zero or not participate in the superposition, allowing the output frequency adjustment to revert to the existing conservative strategy. This ensures that feedforward compensation only intervenes when the model is valid and the operating conditions meet the defined operating window, thereby improving real-time performance while maintaining good fault tolerance and engineering applicability.

[0112] Based on the above calculation and superposition method of frequency compensation increment, the next part will further give the validity criterion with frequency domain fitting residual as the core, and explain how to stop model update and call, roll back to the existing strategy, and the recovery method when the fitting error exceeds the limit or the working condition goes out of bounds, so as to form a closed-loop exit mechanism that matches feedforward compensation.

[0113] It is important to emphasize that equivalent linearization and second-order fitting are local frequency domain representations within a limited operating window. When nonlinearity is enhanced, the operating conditions change rapidly over time, or frequency domain observations are unstable, the model approximation error will increase significantly. To avoid unreliable models participating in feedforward compensation calculations and introducing inappropriate compensation, this implementation uses the frequency domain fitting residual as a direct indicator of the effectiveness of the linearization fitting analysis, and constructs an exit and recovery mechanism accordingly.

[0114] Based on the above-mentioned feedforward compensation calculation and superposition method, in order to ensure that the linear fitting analysis method only intervenes when the model is effective and the operating conditions meet the constraints, this implementation method establishes an effectiveness criterion with frequency domain fitting residuals as the core, and forms an exit mechanism to stop model updates and stop model calls accordingly, so as to balance real-time performance and fault tolerance under the changing operating conditions in industrial sites.

[0115] For the sake of consistency, this implementation method will use the high-frequency channel residual. Residual with low-frequency channel This is further summarized into residual level quantities. The residual level quantities for high-frequency channels are denoted as... The residual level of the low-frequency channel is denoted as The residuals are obtained by summing the residuals from their respective frequency point sets. The summing of these residuals can be performed using conventional methods. and In summary, this invention does not limit the specific calculation method. To limit the scope of the model, this embodiment sets residual thresholds for both the high-frequency and low-frequency channels. , and with and As a condition for the usability of the second-order equivalent model; if any channel does not meet the condition, it is considered that the second-order equivalent model is insufficient to approximate the amplitude and phase characteristics within the relative frequency domain window and is not suitable for fast calculation of feedforward compensation.

[0116] When the residual level meets the threshold condition and the system is within the limited operating window, this implementation allows the frequency domain fitting update to continue, and allows the calculation of the frequency compensation increment by calling the current second-order equivalent model parameters. , This implementation will exit the linearization fitting analysis if any of the following conditions occur: First, the residual level exceeds the corresponding threshold, i.e. or Secondly, the system does not meet the limited operating condition window conditions, including conditions such as quasi-steady state, small disturbances, slowly varying parameters, or infrequent intervention of the synthetic nonlinear module. After exiting the linearization fitting analysis, this implementation method stops updating the second-order model parameters and stops calling the second-order model parameters in the feedforward compensation calculation; at this time, the frequency compensation increment... , It no longer participates in the superposition of frequency increment commands, so that the output frequency adjustment returns to the existing conservative strategy, thereby avoiding the introduction of inappropriate feedforward compensation when there is strong nonlinearity, rapid time variation or unreliable frequency domain observation.

[0117] After exiting, continuously monitor the limited operating condition window conditions and residual thresholds. When both are restored to meet the requirements, resume model updates and model calls and recalculate the frequency compensation increment.

[0118] In summary, this invention uses the synthetic nonlinear module as the object to perform equivalent linearization of the describing function, establishes an equivalent linear frequency domain model with dual-channel amplitude correlation, and fits a unified structure second-order equivalent model within the dual-channel relative frequency domain window to support fast calculation of feedforward compensation. At the same time, the fitting residual threshold and the limited operating condition window conditions constitute the validity criterion, forming an exit and recovery mechanism for model update and call, thereby realizing a linear fitting analysis method with low computational load and clear applicable boundaries.

[0119] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0120] Although the invention has been described with respect to a limited number of embodiments, those skilled in the art will understand from the foregoing description that other embodiments are conceivable within the scope of the invention described herein. Furthermore, it should be noted that the language used in this specification has been chosen primarily for readability and instructional purposes, and not for the purpose of explaining or limiting the subject matter of the invention.

Claims

1. A linear fitting analysis method for a dual-frequency induction heating power supply output frequency control system, characterized in that, include: S110 abstracts the frequency increment limiting, frequency increment rate limiting, and coordinated compensation triggered by dual-frequency minimum frequency interval constraints, which are directly related to the output frequency update, into a unified synthetic nonlinear module. S120, within the operating window where the system satisfies quasi-steady state, small disturbances, and infrequent intervention of the synthetic nonlinear module, the synthetic nonlinear module is represented by an equivalent linearization based on the idea of ​​the describing function, obtaining the equivalent gain related to the amplitude of the input fundamental wave, and together with the linear dynamic part of the system, it constitutes an equivalent linear frequency domain model. S130, based on the equivalent linear frequency domain model, construct relative frequency domain windows near the operating frequency bands of the high-frequency channel and the low-frequency channel respectively, and form an equivalent frequency response based on natural operating data; within the relative frequency domain window, fit the equivalent frequency response into a second-order equivalent model with a unified structure, and obtain two sets of low-order model parameters for the high-frequency channel and the low-frequency channel respectively. S140, the second-order equivalent model calculates and directly outputs the frequency compensation increment required for feedforward compensation at the current operating point, so as to reduce the complexity of online analysis and compensation calculation, and improve the compensation update speed without changing the existing feedback control structure. S150: When the frequency domain fitting residual exceeds the preset threshold or the operating condition does not meet the limited operating condition window, stop the update of the second-order equivalent model parameters and the call of the second-order equivalent model, exit the linearization fitting analysis, and the feedforward compensation reverts to the existing conservative strategy. When the operating condition recovers and meets the applicable boundary, the update of the second-order equivalent model and the compensation calculation are resumed.

2. The linearization fitting analysis method for the output frequency control system of a dual-frequency induction heating power supply according to claim 1, characterized in that, In S110, The synthesized nonlinear module includes a frequency increment limiting feature, which limits the range of frequency increment variation in the amplitude direction. When the high-frequency channel's frequency increment command... Or frequency increment command for low-frequency channels When the amplitude exceeds the preset allowable range, the output of the synthesized nonlinear module is... or It will no longer show a saturation trend as the input amplitude continues to increase, thus making the input-output relationship exhibit piecewise characteristics; in, This indicates the frequency increment command of the synthesized nonlinear module for the high-frequency channel. The output frequency used to update the high-frequency channel output frequency after coordinated compensation triggered by frequency increment limiting, frequency increment rate of change limiting, and minimum frequency interval constraint of dual frequencies. The actual frequency increment; This indicates the frequency increment command of the synthesized nonlinear module for the low-frequency channel. The output after performing the above processing is used to update the low-frequency channel output frequency. The actual frequency increment; The synthesized nonlinear module includes a frequency increment rate of change limiting feature, which limits the rate at which the frequency increment changes over time. This feature is used to restrict the rate at which the frequency increment changes over time. (The text also mentions a frequency increment command in a high-frequency channel, but this seems unrelated to the main topic and is likely a separate point.) Or frequency increment command for low-frequency channels When the absolute value of the difference between adjacent update cycles exceeds the first change threshold, the output of the synthesized nonlinear module... or The absolute value of the difference between adjacent update cycles is limited to not exceeding a second change threshold, thereby... or Respond with a limited rate of change; The synthesized nonlinear module includes a coordinated compensation feature triggered by a dual-frequency minimum frequency interval constraint. This coordinated compensation feature is used to output the frequency in the high-frequency channel. With low-frequency channel output frequency When the minimum frequency interval constraint is approached and triggered, the frequency update function of at least one channel is adjusted so that the updated output frequencies of the two channels meet the minimum frequency interval requirement.

3. The linearization fitting analysis method for the output frequency control system of a dual-frequency induction heating power supply according to claim 2, characterized in that, S120 includes: The fundamental frequency chosen for the equivalent linearization analysis is... Its corresponding period is Within the defined operating window, the frequency increment commands for the high-frequency and low-frequency channels are considered as periodic variations dominated by the fundamental frequency, and represented in fundamental form as follows: ， ， in, for The fundamental amplitude, for The fundamental amplitude, and , ; Define the equivalent gain of the high-frequency channel describing function as follows: The equivalent gain of the low-frequency channel describing function is And: ， ， in, for The input fundamental amplitude, for The input fundamental amplitude; , These are the equivalent amplitude amplification factors for the high-frequency channel and the low-frequency channel, respectively. , These are the equivalent phase shifts for the high-frequency channel and the low-frequency channel, respectively. The output of the synthesized nonlinear module , Considered as the equivalent input to the linear dynamic part of the system, the output of the linear dynamic part of the system is the frequency error signal. , ; The linear dynamic parts are respectively used and This represents the equivalent linear dynamic relationship between the actual frequency increments of the high-frequency and low-frequency channels and the frequency error signal, let... Frequency increment command for high-frequency channels Laplace transform, Indicates the frequency increment command for the low-frequency channel. Laplace transform, , They represent , Laplace transform, , They represent , The Laplace transform, where Let Laplace be the variable; then we have: ， ， In the frequency domain with small perturbations, the equivalent gain is obtained from the describing function of the synthesized nonlinear module: ， ， Combining the above relationships, we obtain the equivalent linear frequency domain model from the frequency increment command to the frequency error signal: ， 。 4. The linearization fitting analysis method for the output frequency control system of a dual-frequency induction heating power supply according to claim 3, characterized in that, S130 also includes: when the frequency domain data quality is insufficient, allowing the superposition of small identification stimuli on the frequency increment command to enhance the identifiability of the equivalent frequency response.

5. The linearization fitting analysis method for the output frequency control system of a dual-frequency induction heating power supply according to claim 3, characterized in that, In S130, relative frequency domain windows are constructed near the operating frequency bands of the high-frequency and low-frequency channels, including: The relative frequency domain windows of the high-frequency channels are denoted as follows: The relative frequency domain window of the low-frequency channel is denoted as ;in, Indicates the current output angular frequency of the high-frequency channel. The set of angular frequencies within a preset relative bandwidth range centered on the angular frequency. Indicates the current output angular frequency of the low-frequency channel. The set of angular frequencies within a preset relative bandwidth range centered on; In the relative frequency domain window of the high-frequency channel Select high-frequency channel frequency point set In the low-frequency channel relative frequency domain window Select low-frequency channel frequency point set The frequency point set , Each is composed of a finite number of angular frequency points and satisfies , ;in, The angular frequency point in the middle is denoted as , The angular frequency point in the middle is denoted as , The above angular frequency points are used to indicate the location of sampling or estimating the frequency response within a relative frequency domain window.

6. The linearization fitting analysis method for the output frequency control system of a dual-frequency induction heating power supply according to claim 3, characterized in that, In S130, within the relative frequency domain window, the equivalent frequency response is fitted to a second-order equivalent model with a unified structure, obtaining two sets of low-order model parameters for the high-frequency and low-frequency channels, including: The second-order equivalent model of the high-frequency channel is denoted as The second-order equivalent model of the low-frequency channel is denoted as ,in For Laplace variables: ， ， in, , These are the equivalent gain coefficients for the high-frequency channel and the low-frequency channel, respectively. , These are the equivalent time constants for the high-frequency channel and the low-frequency channel, respectively. , ; , These are the equivalent damping coefficients for the high-frequency and low-frequency channels, respectively. , These are the equivalent delays for the high-frequency channel and the low-frequency channel, respectively. .

7. The linearization fitting analysis method for the output frequency control system of a dual-frequency induction heating power supply according to claim 6, characterized in that, S130 includes: by making the high-frequency channel frequency point set The parameters of the second-order equivalent model for the high-frequency channel are determined by minimizing the overall fitting error. By making the low-frequency channel frequency point set The parameters of the second-order equivalent model for the low-frequency channel are determined by minimizing the overall fitting error. Among them, the comprehensive fitting error of the high-frequency channel is the residual of the frequency domain fitting. In frequency point set The error metric obtained by summarizing the results is that the overall fitting error of the low-frequency channel is the residual of the frequency domain fitting. In frequency point set The error metric is obtained by summarizing the results.

8. The linearization fitting analysis method for the output frequency control system of a dual-frequency induction heating power supply according to claim 7, characterized in that, S140 includes: when At that time, the static gains of the second-order equivalent model are as follows: , ; in, , These are the equivalent gain coefficients for the high-frequency and low-frequency channels, respectively, and satisfy the following conditions: ;when or When the value is less than the preset lower threshold, the frequency compensation increment is not calculated based on this second-order equivalent model. ， ， in, , To compensate for the weighting coefficients, satisfying , .

9. A computing device, characterized in that, include: At least one processor and a memory storing program instructions; When the program instructions are read and executed by the processor, the computing device performs the method as described in any one of claims 1-8.

10. A readable storage medium storing program instructions, characterized in that, When the program instructions are read and executed by the computing device, the computing device performs the method as described in any one of claims 1-8.

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