Composite current loop parameter setting method

Abstract

The application relates to a composite current loop parameter setting method, relates to the technical field of digital control and parameter setting, and solves the problem that, in the prior art, when a current loop is set, the closed-loop peak value of a closed-loop transfer function is ignored, resulting in that, in the super-high-precision scene such as a lithography machine, the high-frequency component tracking error of the setting result is large, and the positioning precision is difficult to improve. The application obtains system fixed parameters, establishes an equivalent composite current loop model, calculates the upper limit of the cross-over frequency according to the effective total delay of the system and takes the upper limit as the cross-over frequency constraint boundary of the main loop, determines the discrete candidate set of the main loop parameters to be set, sequentially executes main loop parameter setting and feedforward loop parameter setting, obtains a candidate parameter combination, sets the closed-loop peak value as a screening hard constraint, fuses multi-dimensional indexes such as phase margin, sensitivity, complementary sensitivity and system bandwidth to construct a comprehensive scoring system, and outputs optimal setting parameters. Under the premise of ensuring system stability and robustness, the application effectively suppresses the closed-loop peak value and improves current tracking and positioning precision.

Description

Technical Field

[0001] This invention relates to the field of digital control and parameter tuning technology, specifically to a composite current loop parameter tuning method, applicable to high-precision, high-bandwidth current loop control scenarios, including but not limited to voice coil motor actuation systems in semiconductor manufacturing equipment. Background Technology

[0002] In integrated circuit manufacturing, nanometer-level precision positioning relies on ultra-high-precision voice coil motor (VRM) actuation systems. The thrust of the VRM is directly proportional to the coil current; therefore, the control accuracy of the current loop directly determines the positioning accuracy. To meet nanometer-level positioning requirements, the current loop must simultaneously possess the following characteristics:

[0003] (1) High bandwidth to achieve fast dynamic response;

[0004] (2) High tracking accuracy to ensure that the actual current accurately follows the given current command.

[0005] Traditional current loop control architectures typically employ PI controllers in conjunction with a main feedback loop to achieve closed-loop current control. These traditional control architectures and parameter tuning methods focus only on classic metrics such as bandwidth, phase margin, and stability, neglecting the peak value of the closed-loop transfer function. However, for ultra-high precision equipment such as lithography machine stages, excessively large closed-loop peak values ​​imply significant amplitude amplification near the crossover frequency. This causes the voice coil motor to generate additional output, which directly translates into minute vibrations of the stage. High-frequency component tracking errors are large, further degrading the voice coil motor's positioning accuracy in ultra-high precision scenarios like lithography machines, making further improvements difficult. These problems urgently need to be addressed. Summary of the Invention

[0006] The purpose of this invention is to solve the problem that existing technologies, when tuning the current loop, neglect the closed-loop transfer function peak value, resulting in large high-frequency component tracking errors and difficulty in improving positioning accuracy in ultra-high precision scenarios such as lithography machines. This invention provides a composite current loop parameter tuning method.

[0007] Methods for tuning composite current loop parameters include:

[0008] S1. Determine the system fixed parameters: This includes obtaining the known parameters of the composite current loop controlled object and its composite current loop digital control link; the composite current loop digital control link consists of a main loop and a feedforward loop.

[0009] S2. Based on the fixed parameters of the system, establish an equivalent composite current loop model that includes a PI controller, load voltage feedforward, reference current feedforward, and active damping.

[0010] S3. Calculate the upper bound of the crossing frequency based on the effective total delay of the open loop in the equivalent composite current loop model. and with that upper bound As a constraint boundary for the main circuit crossing frequency, based on the upper bound of the crossing frequency. Based on this, the parameters of the main circuit to be tuned are determined, the range of values ​​is set, and the parameters are discretized into a candidate set to obtain the candidate set of each parameter of the main circuit to be tuned.

[0011] S4. Based on the candidate set, perform main loop parameter tuning to obtain multiple sets of candidate main loop parameter values;

[0012] S5. Using the values ​​of each group of main loop parameters as a basis, and combining them with the candidate set of parameters to be tuned, perform feedforward loop parameter tuning to obtain multiple sets of candidate feedforward loop parameter values ​​corresponding to the current group of main loop parameter values. Combine the current group of main loop parameter values ​​and the corresponding sets of candidate feedforward loop parameter values ​​to obtain a set of candidate parameter combinations.

[0013] S6. Calculate the closed-loop peak value under each candidate parameter combination. If it is greater than the preset threshold, discard the combination.

[0014] S7. For the candidate parameter combinations that meet the closed-loop peak constraint, use the equivalent composite current loop model to comprehensively evaluate the phase margin, sensitivity, complementary sensitivity and -3dB bandwidth, calculate the comprehensive score, and after traversing the comprehensive scores corresponding to all candidate parameter combinations, output the tuning result with the best comprehensive score.

[0015] Preferably, the equivalent composite current loop model includes a closed-loop transfer function. and open-loop transfer function ;and

[0016] ;

[0017] ;

[0018] in,

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] Represents complex frequency. For the PI controller expression, and These are the proportional and integral coefficients of the PI controller. For feedforward objects, For the controlled object of the composite current loop Domain expression, For the equivalent output inductance, For output capacitor, Here are the inductance parameters of the load. The resistance parameter of the load. For reference current feedforward coefficient, For active damping, the virtual resistance. It is a natural constant. Delay for capacitor current sampling link, For voltage feedforward coefficients, For load voltage sampling link delay, It is a second-order low-pass filter. Here is the expression for a first-order lead compensator. and These are the zero-point angular frequency and the pole angular frequency, respectively. This is the first-order advance compensation multiple. , It is the first-order lead-compensated center frequency, and , This represents the square root operation. To simultaneously consider the load voltage feedforward and the active damped virtual resistance of the equivalent controlled object, For load current sampling link delay, To extract the delay of the decimation filter, As a reference current feedforward, It serves as a load voltage feedforward.

[0025] Preferably, in step S3, the upper bound of the crossover frequency is calculated based on the effective total open-loop delay. The expression is: ;

[0026] in, , For the effective total delay of the open loop, For load current sampling link delay, To extract the delay of the decimation filter, It is the discretization time.

[0027] Preferably, the parameters to be tuned include the zero-point position coefficient of the PI controller. Crossover frequency proportionality coefficient Load voltage feedforward coefficient Reference current feedforward coefficient First-order advance compensation multiple and first-order lead compensation center frequency ;

[0028] The parameter values ​​for each group of candidate feedforward loops are determined by the reference current feedforward coefficient. First-order advance compensation multiple and first-order lead compensation center frequency The values ​​are determined by the load voltage feedforward coefficient; the values ​​of each main circuit parameter group are determined by the load voltage feedforward coefficient. Target crossing frequency PI controller zero position coefficient The proportional gain of the PI controller Integral coefficient of PI controller The possible values ​​constitute the composition.

[0029] Preferably, in step S4, the main loop parameter tuning is performed based on the candidate set to obtain the parameter values ​​for each group of candidate main loops, as follows:

[0030] S41. Select one load voltage feedforward coefficient from each of the candidate sets of load voltage feedforward coefficients, crossover frequency proportional coefficients, and PI controller zero-point position coefficients. The value of , a crossover frequency scaling factor The value of and a PI controller zero position coefficient The values ​​can be selected to form a set of candidate values;

[0031] S42, according to the selected The value of and the upper bound of the crossover frequency Calculate the target crossover frequency ;

[0032] S43. Based on the target crossing frequency and the selected Find the value of and solve for the proportional coefficient of the corresponding PI controller. and integral coefficient The possible values ​​of ;

[0033] S44, to and The values ​​of are used to perform target crossover frequency calibration, ensuring that the open-loop transfer function in the equivalent composite current loop model satisfies the unity-gain condition at the target crossover frequency, thus obtaining the calibrated value. and The value of is thus obtained from . , , , and The values ​​of constitute a set of candidate main loop parameter values.

[0034] Preferably, in step S5, the feedforward loop parameter tuning is performed based on the values ​​of each group of main loop parameters and combined with the candidate set of parameters to be tuned. The implementation method for obtaining the corresponding set of candidate feedforward loop parameter values ​​under the current group of main loop parameter values ​​is as follows:

[0035] Given the current values ​​of the main circuit parameters, select one reference current feedforward coefficient from each of the candidate sets of the reference current feedforward coefficient, the first-order lead compensation multiple, and the first-order lead compensation center frequency. The value of , a first-order advance compensation multiple The value of and the first-order lead compensation center frequency The value of is used to form a set of candidate feedforward loop parameter values ​​corresponding to the current set of main loop parameter values.

[0036] Preferably, in step S6, the method for calculating the closed-loop peak value under each candidate parameter combination is as follows:

[0037] Substitute the current candidate parameter combination into the closed-loop transfer function. In the middle, take As the closed-loop peak value.

[0038] Preferably, in step S7, the calculation of the comprehensive score is performed as follows:

[0039] S71, Adjust the load voltage feedforward coefficient in the current candidate parameter combination. Reference current feedforward coefficient First-order advance compensation multiple First-order lead compensation center frequency The proportional gain of the PI controller Integral coefficient of PI controller Substituting the values ​​of into the open-loop transfer function of the equivalent composite current loop model Then, based on the open-loop transfer function in the equivalent composite current loop model... Calculate sensitivity and complementary sensitivity ;in, , ;

[0040] S72. Based on the target crossing frequency in the current candidate parameter combination. and PI controller zero position coefficient The value of is used to obtain the phase margin. ;

[0041] S73, Based on phase margin Phase margin with target Calculate the phase margin score ;

[0042] S74, Based on phase margin Sensitivity and complementary sensitivity Calculate penalty item scores ;

[0043] S75. Obtain the -3dB bandwidth when the closed-loop transfer function gain drops from 0dB to -3dB under the current candidate parameter combination. ,according to Calculate bandwidth score , As a weight for bandwidth scoring;

[0044] S76. Scoring based on phase margin Penalty item scoring and bandwidth rating Calculate the overall score .

[0045] Preferably,

[0046] ;

[0047] ;

[0048] ;

[0049] in, For the effective total delay of the open loop, This is the phase margin saturation coefficient. For phase score weighting, , and These are phase default weights, sensitivity default weights, and complementary sensitivity default weights, respectively. The target sensitivity value, This represents the target value for complementary sensitivity.

[0050] The beneficial effects of this invention are:

[0051] This invention provides a method for tuning parameters of a composite current loop. It establishes an equivalent composite current loop model by using a hierarchical traversal search of the main loop and feedforward loop of the composite current loop as the core. The closed-loop peak value is set as a hard constraint for screening. A comprehensive scoring system is constructed by integrating multiple dimensions of indicators such as phase margin, sensitivity, complementary sensitivity, and system bandwidth. The optimal tuning parameters are then output. This method achieves low closed-loop peak value, large control bandwidth, and high-precision current tracking while ensuring system stability and robustness, and further improves positioning accuracy.

[0052] This invention uses the closed-loop peak value as a hard constraint for pre-screening (step S6): combinations of candidate parameters whose closed-loop peak value exceeds a preset threshold (e.g., 0.5dB) are directly discarded, ensuring that all schemes entering the final evaluation meet the closed-loop peak value index, thus eliminating the impact of resonance peaks on high-frequency tracking accuracy from the source. This ensures that the tuning results do not exhibit significant amplitude spikes near the crossover frequency, avoiding additional current fluctuations caused by closed-loop resonance. Implementation results show that the maximum tracking error in the frequency band below 10kHz is only 0.34dB, a 90.4% reduction compared to the traditional scheme (peak value approximately 3.25dB).

[0053] A first-order lead compensator is introduced for the reference current feedforward (step S5): To address the phase lag introduced by discretization and delay in the reference current feedforward branch, a first-order lead compensator provides phase lead correction near the crossover frequency, realigning the equivalent feedforward effect with the delayed object response. This compensation only enters the numerator of the closed-loop transfer function and does not change the denominator of the main feedback loop, thus effectively suppressing closed-loop peak values ​​without sacrificing basic stability.

[0054] The hierarchical tuning strategy of this invention ensures stability before optimization (steps S4 to S5): First, the main circuit parameters are tuned to ensure that the basic stability and crossover frequency meet the requirements. Then, the advance compensation parameters are configured in the feedforward circuit to suppress the closed-loop peak value, so that the peak suppression process does not interfere with the stability design of the main circuit, ensuring that the final solution has both safety and high precision.

[0055] This invention achieves synergistic optimization of multi-dimensional performance indicators. Specifically, it integrates phase margin, sensitivity, complementary sensitivity, and bandwidth into a comprehensive scoring system. By combining penalty terms with scoring terms, it selects the optimal tuning result from a large number of candidate parameter combinations while satisfying basic stability and robustness constraints, thus avoiding the disadvantages caused by optimizing a single indicator.

[0056] This invention fully considers the actual delay of digital control: the equivalent model incorporates various practical factors such as sampling delay, anti-aliasing filter delay, and decimation filter delay, making the tuning results more in line with physical implementation and avoiding performance deviations between the ideal model and the actual system.

[0057] This invention achieves a balance between bandwidth and stability. Implementation results show that, while suppressing closed-loop peak values, the system bandwidth is increased from approximately 13kHz to 14kHz in the traditional scheme, the phase margin is increased to approximately 61°, and the settling time is shortened to approximately 20% of the traditional scheme, thus achieving a balance between high bandwidth and high damping. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the digital control link of the composite current loop in the power amplifier control system.

[0059] Figure 2 This is a flowchart of the composite current loop parameter tuning method of the present invention;

[0060] Figure 3 The diagrams show a comparison of the frequency response before and after using the tuning method of the present invention; wherein, (a) is the frequency response diagram without using the parameter tuning method proposed in the present invention; and (b) is the frequency response diagram using the parameter tuning method proposed in the present invention.

[0061] Figure 4 The diagrams show a comparison of the frequency sweep response and step response under the conventional method and the method of the present invention; wherein, (a) is a schematic diagram of the frequency sweep result under the conventional method; (b) is a schematic diagram of the bandwidth under the conventional method; (c) is a schematic diagram of the frequency sweep result under the method proposed in the present invention; (d) is a schematic diagram of the bandwidth under the method proposed in the present invention; (e) is a schematic diagram of the step response under the conventional method; and (f) is a schematic diagram of the step response under the method proposed in the present invention.

[0062] Figure 5 The diagrams show a detailed comparison of the current tracking performance of the conventional method and the method of the present invention in the frequency band below 10kHz; wherein, (a) is a schematic diagram comparing the sinusoidal current waveforms of the conventional method and the method of the present invention at 25Hz; (b) is a schematic diagram comparing the sinusoidal current waveforms of the conventional method and the method of the present invention at 50Hz; (c) is a schematic diagram comparing the sinusoidal current waveforms of the conventional method and the method of the present invention at 75Hz; (d) is a schematic diagram comparing the sinusoidal current waveforms of the conventional method and the method of the present invention at 100Hz; (e) is a schematic diagram comparing the sinusoidal current waveforms of the conventional method and the method of the present invention at 250Hz; (f) is a schematic diagram comparing the sinusoidal current waveforms of the conventional method and the method of the present invention at 500Hz; (g ... (h) is a schematic diagram comparing the sinusoidal current waveforms of the traditional method and the method of the present invention at 750Hz; (i) is a schematic diagram comparing the sinusoidal current waveforms of the traditional method and the method of the present invention at 1000Hz; (j) is a schematic diagram comparing the sinusoidal current waveforms of the traditional method and the method of the present invention at 2.5kHz; (k) is a schematic diagram comparing the sinusoidal current waveforms of the traditional method and the method of the present invention at 5kHz; (l) is a schematic diagram comparing the sinusoidal current waveforms of the traditional method and the method of the present invention at 7.5kHz; (m) is a schematic diagram comparing the sinusoidal current waveforms of the traditional method and the method of the present invention at 10kHz; and (d) is a closed-loop peak comparison diagram of the sinusoidal current waveforms of the traditional method and the method of the present invention within 10kHz. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0065] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0066] Invention Concept: Addressing the problem that existing technologies neglect the closed-loop transfer function and peak value during current loop tuning, leading to large tracking errors and difficulty in improving positioning accuracy in ultra-high precision scenarios such as lithography machines due to this neglect, this invention provides a composite current loop parameter tuning method. Centered on a hierarchical traversal search of the composite current loop main loop and feedforward loop, an equivalent composite current loop model incorporating all digital delays and multiple compensation branches is established. The closed-loop peak value is set as a hard constraint for screening. A comprehensive scoring system is constructed by integrating phase margin, sensitivity, complementary sensitivity, and system bandwidth, outputting the optimal tuning parameters. This achieves low closed-loop peak value, large control bandwidth, and high-precision current tracking while ensuring system stability and robustness, further improving positioning accuracy.

[0067] Specific Implementation Method 1: Combination Figure 1 and Figure 2 This embodiment describes a method for tuning the parameters of a composite current loop, which includes:

[0068] S1. Determine system fixed parameters (basic data preparation): This includes obtaining the known parameters of the composite current loop controlled object and its composite current loop digital control link; the composite current loop digital control link consists of a main loop and a feedforward loop.

[0069] S2. Establish an equivalent composite current loop model (mathematical representation of the controlled object): Based on the fixed parameters of the system, establish an equivalent composite current loop model that includes a PI controller, load voltage feedforward, reference current feedforward, and active damping; the model is used for the calculation of all subsequent performance indicators and parameter search.

[0070] S3. Calculate the upper bound of the crossing frequency and discretize the candidate set of parameters (constraint boundary setting and search space construction):

[0071] The upper bound of the crossover frequency is calculated based on the effective total delay of the open loop in the equivalent composite current loop model. and with that upper bound As a constraint boundary for the crossover frequency of the main loop in the composite current loop, based on the upper bound of the crossover frequency. Based on this, the parameters of the main circuit to be tuned are determined, the range of values ​​is set, and the parameters are discretized into a candidate set to obtain the candidate set of each parameter of the main circuit to be tuned.

[0072] The parameters to be tuned include the zero-point position coefficient of the PI controller. Crossover frequency proportionality coefficient Load voltage feedforward coefficient Reference current feedforward coefficient First-order advance compensation multiple and first-order lead compensation center frequency ;

[0073] This step calculates the upper bound of the main loop crossing frequency based on the system's effective total delay, using this as a hard constraint to limit the feasible range of the main loop parameters (especially the target crossing frequency); and further discretizes each parameter to be tuned into a candidate set, transforming the continuous parameter optimization problem into an traversable discrete search problem;

[0074] S4. Perform main circuit parameter tuning (first layer of hierarchical tuning):

[0075] Based on the candidate set of main circuit parameters to be tuned, the main circuit parameters (load voltage feedforward coefficient) are executed. Target crossing frequency PI controller zero position coefficient The proportional gain of the PI controller Integral coefficient of PI controller The parameters of the main circuit are adjusted to obtain multiple sets of candidate main circuit parameter values.

[0076] This step ensures the basic stability of the system and meets the crossover frequency requirements. S5, Perform feedforward loop parameter tuning (second layer of layered tuning):

[0077] Using the values ​​of the main circuit parameters in each group as a basis, and combining them with the candidate set of parameters to be tuned, the feedforward circuit parameters (reference current feedforward coefficient) are then executed. First-order advance compensation multiple and first-order lead compensation center frequency The parameters are tuned to obtain the corresponding multiple sets of candidate feedforward loop parameters under the current set of main loop parameters. The current set of main loop parameters and the corresponding sets of candidate feedforward loop parameters are combined to obtain a set of candidate parameter combinations.

[0078] This step improves tracking performance and suppresses closed-loop peaks without changing the stability of the main loop.

[0079] S6. Hard Constraint Screening (Feasibility Filtering):

[0080] Calculate the closed-loop peak value for each candidate parameter combination and set the closed-loop peak value as a hard constraint. If the closed-loop peak value corresponding to the current candidate parameter combination is greater than a preset threshold, the current candidate parameter combination is discarded. In specific applications, the preset threshold value is 0.5 dB, and the closed-loop peak value is strictly suppressed within 0.5 dB. This step ensures that all candidate combinations entering the subsequent evaluation meet the minimum requirements for closed-loop peak value in high-precision applications.

[0081] S7. Overall Score and Optimal Output (Performance Evaluation and Decision Output):

[0082] For the candidate parameter combinations that meet the closed-loop peak constraint, the phase margin, sensitivity, complementary sensitivity and -3dB bandwidth are comprehensively evaluated using the equivalent composite current loop model. The comprehensive score is calculated, and after iterating through the comprehensive scores corresponding to all candidate parameter combinations, the tuning result with the best comprehensive score is output.

[0083] Step S7 calculates a comprehensive score (covering multiple indicators such as phase margin, sensitivity, complementary sensitivity, and bandwidth) for the candidate combinations that have passed the hard constraint screening, using the equivalent composite current loop model. After traversing all candidate combinations, the tuning result with the best comprehensive score is output as the final engineering implementation method.

[0084] This invention establishes an equivalent model by fixing system parameters, constrains the range of main loop parameters with the upper limit of the crossover frequency, and then sequentially performs discretized tuning and combination screening of the main loop and feedforward loop, finally outputting the parameter combination with the optimal comprehensive score. This process realizes automated and systematic tuning of composite current loop parameters, avoids manual trial and error, and can take into account the hard constraint of closed-loop peak value, ensuring that the tuning result meets the requirements of system stability and dynamic response.

[0085] This invention provides a high-precision, wide-bandwidth current loop parameter tuning method. The current loop is a core component of the power amplifier control system, and the controller uses the current loop to precisely manage the power amplifier's output current. This invention's method does not rely solely on empirical adjustment of a single PI parameter, but rather addresses... Figure 1 The PI controller, active damping, load voltage feedforward, reference current feedforward, and the first-order lead compensation stage in the feedforward are uniformly and collaboratively tuned in the control architecture shown. By establishing a discrete-time equivalent model that includes sampling delay, calculation delay, anti-aliasing filter delay, and decimation filter delay, and by incorporating closed-loop peak value, phase margin, sensitivity, complementary sensitivity, and bandwidth into the parameter search and evaluation process, this invention can obtain current loop parameters with both high bandwidth and low closed-loop peak value while ensuring system stability and robustness, thereby improving current tracking accuracy and dynamic response performance.

[0086] I. Composite Current Loop Control Architecture

[0087] like Figure 1 As shown, the composite current loop control architecture involved in this invention is based on current closed-loop control. This architecture consists of a main loop and a feedforward loop, specifically including:

[0088] Main loop: A feedback loop consisting of a PI controller, an equivalent controlled object considering active damping and load voltage feedforward, and a load current sampling / decimation delay. Its stability margin is determined by the closed-loop denominator. Decide.

[0089] Load voltage feedforward is used to compensate for the effect of load voltage changes on the output current.

[0090] Feedforward loop: It is a reference current feedforward, in which a first-order lead compensator is connected in series to compensate for the phase lag introduced by discretization and delay of the feedforward, so that the feedforward injection signal is re-aligned with the dynamic response of the object containing the delay.

[0091] The reference current feedforward is determined by the feedforward object. First-order lead compensator Second-order low-pass filter and reference current feedforward coefficient The first-order lead compensator is designed to improve the tracking characteristics between the reference input and the output current. Since the first-order lead compensator only enters the numerator of the closed-loop transfer function and not the denominator, its main function is not to change the basic stability of the main feedback loop, but to compensate for the phase lag caused by discretization and delay in the feedforward branch near the crossover frequency, so that the feedforward injection signal is dynamically re-aligned with the actual object, thereby suppressing the closed-loop peak and improving the tracking performance.

[0092] Figure 1 middle For reference current, This is the filter capacitor current. For load current, This is the load voltage.

[0093] II. Establishment of Equivalent Composite Current Loop Model

[0094] The equivalent composite current loop model includes the closed-loop transfer function. and open-loop transfer function ;and

[0095] ;

[0096] ;

[0097] in,

[0098] ;

[0099] , ;

[0100] ;

[0101] ;

[0102] Represents complex frequency. For the PI controller expression, and These are the proportional and integral coefficients of the PI controller. For feedforward objects, For the controlled object of the composite current loop Domain expression, For the equivalent output inductance, For output capacitor, Here are the inductance parameters of the load. The resistance parameter of the load. For reference current feedforward coefficient, For active damping, the virtual resistance. It is a natural constant. Delay for capacitor current sampling link, For voltage feedforward coefficients, For load voltage sampling link delay, It is a second-order low-pass filter. Here is the expression for a first-order lead compensator. and These are the zero-point angular frequency and the pole angular frequency, respectively. This is the first-order advance compensation multiple. , It is the first-order lead-compensated center frequency, and , This represents the square root operation. For the equivalent controlled object that simultaneously considers load voltage feedforward and active damped virtual resistance in the complex frequency domain, For load current sampling link delay, To extract the delay of the decimation filter, As a reference current feedforward, It serves as a load voltage feedforward.

[0103] The above-described explicit mathematical definitions of open-loop and closed-loop transfer functions quantify the coupling relationship between the main loop and feedforward loop in the composite current loop, various actual delays (sampling delay, filter delay), and the interactions of various control elements (PI controller, feedforward object, lead compensator, active damper) into computable analytical expressions. This provides a unified, programmable mathematical foundation for subsequent steps such as crossover frequency calculation, closed-loop peak value determination, and sensitivity and complementary sensitivity analysis, ensuring that the parameter tuning process is based on an accurate description of the system's dynamic characteristics, rather than relying on experience or simplified models.

[0104] Furthermore, in step S3, the upper bound of the crossover frequency is calculated based on the effective total delay of the open loop. The expression is: ;

[0105] in, , For the effective total delay of the open loop, For load current sampling link delay, To extract the delay of the decimation filter, It is the discretization time.

[0106] In this preferred embodiment, a formula for calculating the upper limit of the crossover frequency is defined. The upper limit of the crossover frequency is directly calculated based on the total effective system delay (the sum of the load current sampling link delay, the decimation filter delay, and the discretization time), and this upper limit is used as a hard constraint boundary for the main circuit crossover frequency. This calculation method takes into account the unavoidable multi-source delays in the digital control system, ensuring that the subsequent parameter tuning process will not exceed the actual phase lag tolerance of the system due to an excessively high set crossover frequency. This avoids instability problems caused by delays from the source and guarantees the reliability of the tuning results within the physically realizable range.

[0107] Furthermore, in step S4, based on the candidate set of parameters to be tuned, the main circuit parameters are tuned, and the implementation method for obtaining the values ​​of each group of candidate main circuit parameters is as follows:

[0108] S41. Select one load voltage feedforward coefficient from each of the candidate sets of load voltage feedforward coefficients, crossover frequency proportional coefficients, and PI controller zero-point position coefficients. The value of , a crossover frequency scaling factor The value of and a PI controller zero position coefficient The values ​​can be selected to form a set of candidate values;

[0109] S42, according to the selected The value of and the upper bound of the crossover frequency Calculate the target crossover frequency ;

[0110] S43. Based on the target crossing frequency and the selected Find the value of and solve for the proportional coefficient of the corresponding PI controller. and integral coefficient The possible values ​​of ;

[0111] ;

[0112] , ;

[0113] ;

[0114] This is the equivalent controlled object considering both load voltage feedforward and active damped virtual resistance at the angular frequency. This is the expression for the angular frequency of the controlled object in the composite current loop. The imaginary unit, The target crossover frequency is the angular frequency.

[0115] S44, to and The values ​​of are used to perform target crossover frequency calibration, ensuring that the open-loop transfer function in the equivalent composite current loop model satisfies the unity-gain condition at the target crossover frequency, thus obtaining the calibrated value. and The value of is thus obtained from . , , , and The values ​​of constitute a set of candidate main loop parameter values.

[0116] The main loop parameter tuning process is decomposed into selecting the load voltage feedforward coefficient, crossover frequency proportional coefficient, and PI controller zero-point position coefficient sequentially from three candidate sets. Based on this, the target crossover frequency is calculated, and the corresponding proportional and integral coefficients are solved. Then, crossover frequency calibration ensures that the open-loop transfer function satisfies the unity-gain condition at the target crossover frequency. This process transforms the originally coupled multi-parameter tuning problem into an operable procedure of sequential selection and iterative calibration. This ensures that the main loop parameter combination strictly meets the crossover frequency constraint and unity-gain requirement, guaranteeing the consistency of basic stability among the candidate main loop parameters and providing a unified benchmark condition for subsequent feedforward loop tuning.

[0117] Furthermore, in step S5, using the values ​​of each group of main loop parameters as a basis, and combining them with the candidate set of parameters to be tuned, the feedforward loop parameters are tuned. The implementation method for obtaining the corresponding set of candidate feedforward loop parameter values ​​under the current group of main loop parameter values ​​is as follows:

[0118] Given the current values ​​of the main circuit parameters, select one reference current feedforward coefficient from each of the candidate sets of the reference current feedforward coefficient, the first-order lead compensation multiple, and the first-order lead compensation center frequency. The value of , a first-order advance compensation multiple The value of and the first-order lead compensation center frequency The value of is used to form a set of candidate feedforward loop parameter values ​​corresponding to the current set of main loop parameter values.

[0119] Furthermore, in step S6, the method for calculating the closed-loop peak value under each candidate parameter combination is as follows:

[0120] Substitute the current candidate parameter combination into the closed-loop transfer function. In the middle, take As the closed-loop peak value.

[0121] Furthermore, in step S7, the method for comprehensively scoring the current candidate parameter combination using the equivalent composite current loop model is as follows:

[0122] S71, Adjust the load voltage feedforward coefficient in the current candidate parameter combination. Reference current feedforward coefficient First-order advance compensation multiple First-order lead compensation center frequency The proportional gain of the PI controller Integral coefficient of PI controller Substituting the values ​​of into the open-loop transfer function of the equivalent composite current loop model Then, based on the open-loop transfer function in the equivalent composite current loop model... Calculate sensitivity and complementary sensitivity ;in, , ;

[0123] S72. Based on the target crossing frequency in the current candidate parameter combination. and PI controller zero position coefficient The value of is used to obtain the phase margin. , The effective total delay for the open loop;

[0124] S73, Based on phase margin Phase margin with target Calculate the phase margin score ;

[0125] ;

[0126] This is the phase margin saturation coefficient, used to control... The degree to which the phase margin tends to saturate as it increases. The smaller the phase margin, the sooner the reward will reach saturation. For phase score weights;

[0127] S74, Based on phase margin Sensitivity and complementary sensitivity Calculate penalty item scores ;

[0128] ;

[0129] , and These are phase default weights, sensitivity default weights, and complementary sensitivity default weights, respectively. The target sensitivity value, The target value for complementary sensitivity;

[0130] S75. Obtain the frequency at which the closed-loop transfer function gain drops from 0dB to -3dB under the current candidate parameter combination. ,according to Calculate bandwidth score , As a weight for bandwidth scoring;

[0131] S76. Scoring based on phase margin Penalty item scoring and bandwidth rating Calculate the overall score .

[0132] In this preferred embodiment, four performance indicators—phase margin, sensitivity, complementary sensitivity, and -3dB bandwidth—are quantified into computable scoring terms. Penalty terms apply a penalty to parameter combinations that do not meet the stability margin and robustness requirements. The phase margin score and bandwidth score are used to distinguish the superiority of candidate combinations among those that pass the hard constraints. This scoring system, through normalization and weight allocation, ensures that the tuning results, while satisfying the closed-loop peak hard constraints, prioritize system stability margin, and then consider robustness and bandwidth. This allows for the selection of the optimal set of parameters from numerous candidate combinations, avoiding performance degradation caused by single-indicator optimization.

[0133] The performance indicators of this invention include: phase margin, sensitivity, complementary sensitivity, and -3dB bandwidth. In addition, the closed-loop peak value is also used as a performance indicator.

[0134] (1) Closed-loop peak index

[0135] The closed-loop peak value is calculated based on the overall closed-loop transfer function and is used to characterize whether there are unacceptable amplitude spikes near the crossover frequency. To avoid the adverse effects of the closed-loop transfer function peak value on trajectory tracking accuracy, its peak value is usually required to be strictly suppressed to within 0.5dB.

[0136] (2) Phase margin and -3dB bandwidth specifications

[0137] Phase margin characterizes the system's stability margin; the -3dB bandwidth, calculated based on the closed-loop transfer function, characterizes the system's dynamic response speed. The upper bound of the delay-dominated crossover frequency... It is calculated from the effective total delay of the open loop and used as the constraint boundary for the target crossing frequency of the main loop.

[0138] (3) Sensitivity and complementary sensitivity index

[0139] Sensitivity and complementary sensitivity are used to characterize the system’s robustness to model uncertainty and measurement noise, respectively.

[0140] Verification experiment:

[0141] Figure 3 The frequency response of the system before and after adopting the tuning method proposed in this invention was compared. All curves were obtained based on the discrete-time model and used the actual circuit parameters and delay terms summarized in Table 1.

[0142] Table 1

[0143]

[0144] Figure 3 (a) shows the frequency response without using the parameter tuning method proposed in this invention. Figure 3 Figure (b) shows the frequency response diagram when using the parameter tuning method proposed in this invention. Figure 3 As shown in (a), the original controller (tuned by MATLAB / ControlSystemDesigner) exhibits a significant resonant peak of about 5 dB in its closed-loop amplitude-frequency response near the crossover frequency, which is unacceptable for high-precision applications. Figure 3 The closed-loop response in (b) is more ideal, with the closed-loop peak suppressed to below 0.5 dB and the phase margin increased to approximately 61°, indicating a significant enhancement in damping and robustness. Overall, the proposed tuning strategy can effectively eliminate the closed-loop peak and improve the phase margin.

[0145] for Figure 4 In traditional methods, the reference current feedforward does not include a lead element, and parameter tuning is performed using MATLAB / ControlSystemDesigner. Its results for a 1A current and a sinusoidal sweep frequency of 25Hz~15kHz are as follows: Figure 4 As shown in Figures (a) and (b), the bandwidth is approximately 13 kHz, the peak value is approximately 1.45 A, and there is a closed-loop peak value of approximately 3.25 dB. However, under the control loop and parameter tuning method proposed in this invention, the sinusoidal frequency sweep result is as follows... Figure 4 (c) and Figure 4 As shown in (d), the bandwidth is slightly increased to 14kHz, while the closed-loop peak is suppressed, and there are no obvious closed-loop spikes within the 14kHz bandwidth. This demonstrates that the method proposed in this invention can significantly improve current tracking accuracy. This can be achieved through... Figure 4 (e) and Figure 4 The step response shown in (f) further demonstrates the current tracking capabilities of both the conventional method and the method of this invention. The current rise times of both methods are essentially the same, but the overshoot of the conventional method reaches 1.550A, while the overshoot of the method of this invention is only 1.034A, a decrease of 93.81%. Furthermore, the settling time of the method of this invention is approximately 20% of that of the conventional method. This significantly improves the current tracking accuracy and dynamic response capability.

[0146] This invention targets semiconductor manufacturing equipment applications where commercial drivers typically have a target bandwidth of around 6kHz. While the method described in this invention can achieve a bandwidth of 14kHz, it still focuses primarily on the frequency band below 10kHz. Figure 5 (a) Figure 5 Figure (l) shows a waveform comparison between the traditional method and the present invention in the range of 25Hz to 10kHz. It can be seen that the current shows obvious tracking error starting from 250Hz under the traditional method, while the present invention does not have obvious overshoot in the frequency band below 10kHz, and only shows attenuation when close to 10kHz, showing extremely high tracking accuracy. Figure 5 The two methods were compared in terms of tracking error variation. The traditional method's tracking error peaked at 3.05 dB at 2.5 kHz and then began to decrease, dropping to -1.5 dB at 10 kHz. In contrast, the maximum tracking error of the present invention was only 0.34 dB in the frequency band below 10 kHz, a reduction of 90.4% compared to the traditional method.

[0147] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for tuning parameters of a compound current loop, characterized in that, include: S1. Determine the system's fixed parameters: This includes obtaining the known parameters of the composite current loop control object and its digital control link; S2. Based on the fixed parameters of the system, establish an equivalent composite current loop model that includes a PI controller, load voltage feedforward, reference current feedforward, and active damping. S3. Calculate the upper bound of the crossing frequency based on the effective total delay of the open loop in the equivalent composite current loop model. and with that upper bound As a constraint boundary for the main circuit crossing frequency, based on the upper bound of the crossing frequency. Based on this, the parameters of the main circuit to be tuned are determined, the range of values ​​is set, and the parameters are discretized into a candidate set; S4. Based on the candidate set, perform main loop parameter tuning to obtain multiple sets of candidate main loop parameter values; S5. Using the values ​​of each group of main loop parameters as a basis, and combining them with the candidate set of parameters to be tuned, perform feedforward loop parameter tuning to obtain multiple sets of candidate feedforward loop parameter values ​​corresponding to the current group of main loop parameter values. Combine the current group of main loop parameter values ​​and the corresponding sets of candidate feedforward loop parameter values ​​to obtain a set of candidate parameter combinations. S6. Calculate the closed-loop peak value under each candidate parameter combination. If it is greater than the preset threshold, discard the combination. S7. For the candidate parameter combinations that meet the closed-loop peak constraint, use the equivalent composite current loop model to comprehensively evaluate the phase margin, sensitivity, complementary sensitivity and -3dB bandwidth, calculate the comprehensive score, and after traversing the comprehensive scores corresponding to all candidate parameter combinations, output the tuning result with the best comprehensive score.

2. The method for tuning the parameters of the composite current loop according to claim 1, characterized in that, The equivalent composite current loop model includes the closed-loop transfer function. and open-loop transfer function ;and ； ； in, , ; ; ； ； Represents complex frequency. For the PI controller expression, and These are the proportional and integral coefficients of the PI controller. For feedforward objects, For the controlled object of the composite current loop Domain expression, For the equivalent output inductance, For output capacitor, Here are the inductance parameters of the load. The resistance parameter of the load. For reference current feedforward coefficient, For active damping, the virtual resistance. It is a natural constant. Delay for capacitor current sampling link, For voltage feedforward coefficients, For load voltage sampling link delay, It is a second-order low-pass filter. Here is the expression for a first-order lead compensator. and These are the zero-point angular frequency and the pole angular frequency, respectively. This is the first-order advance compensation multiple. , It is the first-order lead-compensated center frequency, and , This represents the square root operation. To simultaneously consider the load voltage feedforward and the active damped virtual resistance of the equivalent controlled object, For load current sampling link delay, To extract the delay of the decimation filter, As a reference current feedforward, It serves as a load voltage feedforward.

3. The method for tuning the parameters of the composite current loop according to claim 1, characterized in that, In step S3, the upper bound of the crossover frequency is calculated based on the effective total delay of the open loop. The expression is: ; in, , For the effective total delay of the open loop, For load current sampling link delay, To extract the delay of the decimation filter, It is the discretization time.

4. The method for tuning the parameters of the composite current loop according to claim 1, characterized in that, The parameters to be tuned include the zero-point position coefficient of the PI controller. Crossover frequency proportionality coefficient Load voltage feedforward coefficient Reference current feedforward coefficient First-order advance compensation multiple and first-order lead compensation center frequency ; The parameter values ​​for each group of candidate feedforward loops are determined by the reference current feedforward coefficient. First-order advance compensation multiple and first-order lead compensation center frequency The values ​​are determined by the load voltage feedforward coefficient; the values ​​of each main circuit parameter group are determined by the load voltage feedforward coefficient. Target crossing frequency PI controller zero position coefficient The proportional gain of the PI controller Integral coefficient of PI controller The possible values ​​constitute the composition.

5. The method for tuning the parameters of the composite current loop according to claim 4, characterized in that, In step S4, based on the candidate set, the main loop parameter tuning is performed to obtain the parameter values ​​for each group of candidate main loops. The implementation method is as follows: S41. Select one load voltage feedforward coefficient from each of the candidate sets of load voltage feedforward coefficients, crossover frequency proportional coefficients, and PI controller zero-point position coefficients. The value of , a crossover frequency scaling factor The value of and a PI controller zero position coefficient The values ​​can be selected to form a set of candidate values; S42, according to the selected The value of and the upper bound of the crossover frequency Calculate the target crossover frequency ; S43. Based on the target crossing frequency and the selected Find the value of and solve for the proportional coefficient of the corresponding PI controller. and integral coefficient The possible values ​​of ; S44, to and The values ​​of are used to perform target crossover frequency calibration, ensuring that the open-loop transfer function in the equivalent composite current loop model satisfies the unity-gain condition at the target crossover frequency, thus obtaining the calibrated value. and The value of is thus obtained from . , , , and The values ​​of constitute a set of candidate main loop parameter values.

6. The method for tuning the parameters of the composite current loop according to claim 4, characterized in that, In step S5, the parameter values ​​of each group of main loops are used as a basis, and combined with the candidate set of parameters to be tuned, the feedforward loop parameters are tuned. The implementation method of obtaining the corresponding set of candidate feedforward loop parameter values ​​under the current group of main loop parameter values ​​is as follows: Given the current values ​​of the main circuit parameters, select one reference current feedforward coefficient from each of the candidate sets of the reference current feedforward coefficient, the first-order lead compensation multiple, and the first-order lead compensation center frequency. The value of , a first-order advance compensation multiple The value of and the first-order lead compensation center frequency The value of is used to form a set of candidate feedforward loop parameter values ​​corresponding to the current set of main loop parameter values.

7. The method for tuning the parameters of the composite current loop according to claim 2, characterized in that, In step S6, the method for calculating the closed-loop peak value under each candidate parameter combination is as follows: Substitute the current candidate parameter combination into the closed-loop transfer function. In the middle, take As the closed-loop peak value.

8. The method for tuning the parameters of the composite current loop according to claim 1, characterized in that, In step S7, the calculation of the comprehensive score is performed as follows: S71, Adjust the load voltage feedforward coefficient in the current candidate parameter combination. Reference current feedforward coefficient First-order advance compensation multiple First-order lead compensation center frequency The proportional gain of the PI controller Integral coefficient of PI controller Substituting the values ​​of into the open-loop transfer function of the equivalent composite current loop model Then, based on the open-loop transfer function in the equivalent composite current loop model... Calculate sensitivity and complementary sensitivity ; S72. Based on the target crossing frequency in the current candidate parameter combination. and PI controller zero position coefficient The value of is used to obtain the phase margin. ; S73, Based on phase margin Phase margin with target Calculate the phase margin score ; S74, Based on phase margin Sensitivity and complementary sensitivity Calculate penalty item scores ; S75. Obtain the -3dB bandwidth when the closed-loop transfer function gain drops from 0dB to -3dB under the current candidate parameter combination. ,according to Calculate bandwidth score , As a weight for bandwidth scoring; S76. Scoring based on phase margin Penalty item scoring and bandwidth rating Calculate the overall score .

9. The method for tuning the parameters of the composite current loop according to claim 8, characterized in that, ， 。 10. The method for tuning the parameters of the composite current loop according to claim 8, characterized in that, ； ； ； in, For the effective total delay of the open loop, This is the phase margin saturation coefficient. For phase score weighting, , and These are phase default weights, sensitivity default weights, and complementary sensitivity default weights, respectively. The target sensitivity value, This represents the target value for complementary sensitivity.

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