Control method for suppressing low-frequency disturbance force of a motion stage

Abstract

The application discloses a control method for inhibiting low-frequency disturbance force of a motion platform, and belongs to the technical field of signal processing.The control method comprises the following steps: obtaining measurement data of the motion platform; configuring disturbance observer-based control (DOBC) in a control loop; optimizing the DOBC control architecture to build a realizable causal system; designing a filter unit Q(s) to meet the realizability of the DOBC control loop and reduce high-frequency noise interference; calculating a disturbance force compensation amount for compensating for the disturbance; and superimposing the disturbance force compensation amount u d on the control input u c to realize real-time compensation of the low-frequency disturbance force.The application can flexibly cope with disturbance changes under different working conditions by combining adaptive adjustment of the disturbance observer and the filter, and can significantly improve the anti-interference ability of the system.The optimally designed Q(s) filter effectively separates the low-frequency disturbance force and the high-frequency noise, ensures accurate compensation of the disturbance in the medium and low frequency bands, and simultaneously suppresses the high-frequency noise interference, so that the control precision and stability are greatly improved.

Description

Technical Field

[0001] This application belongs to the field of signal processing technology, specifically relating to a control method for suppressing low-frequency disturbances in a motion table. Background Technology

[0002] In semiconductor precision equipment, the control performance of the motion stage is crucial. Compared with traditional photolithography equipment, the motion stage of nanoimprint equipment has physical contact with the imprinting module. Therefore, the motion stage is affected by the imprinting force disturbance and the vibration of the imprinting module itself, which puts forward higher requirements for control stability.

[0003] Imprinting disturbances are typically addressed by using PID control with pressure feedforward compensation to reduce their impact on the motion table control performance.

[0004] External disturbances (imprinting force and vibration of the imprinting module) are low-frequency random disturbances. Pressure feedforward compensation cannot effectively suppress random disturbances. While PID control enhances the ability to suppress low-frequency disturbances, it also reduces the stability margin and easily causes the motion table to vibrate.

[0005] Chinese patent application CN109164700A discloses a control method for suppressing full-frequency disturbances, the method comprising "step (2): according to the appendix..." Figure 2 A disturbance observer based on error is constructed, and an improved control compensator is inserted into the existing feedback control loop; Step (3): Design a scientific and reasonable sensitivity function to generate a new Q filter to effectively suppress vibrations in the telescope. This invention adopts a new way to design the Q filter, that is, starting from the design sensitivity function ESF(s) (ESF(s)=1-Q(s)), the form of the Q filter is derived in reverse. "(See paragraphs

[0032] and

[0033] of its specification), the "disturbance observer" here is actually adjusting the structure of the feedback control system through the error signal, not DOBC. It cannot independently estimate the disturbance force, nor can it perform active disturbance compensation. The low-pass filter has fixed parameters, does not involve adaptive disturbance compensation, nor does it involve causal optimization. It is suitable for full-frequency disturbance suppression of optoelectronic systems, but does not have adaptive adjustment capability and cannot be adjusted in real time according to the change of disturbance force.

[0006] In summary, there is an urgent need to develop a control technology that can estimate disturbance forces in real time and perform adaptive compensation to meet the high-precision and stable control requirements of motion tables under low-frequency random disturbance forces. Summary of the Invention

[0007] This application aims to at least partially solve one of the aforementioned technical problems in the related art.

[0008] Therefore, this application provides a control method for suppressing low-frequency disturbances of a motion table, comprising the following steps:

[0009] Based on the control loop of the motion table system, the measurement data of the motion table is acquired, and the transfer function P(s) of the controlled object of the motion table system is determined. The measurement data includes the system output y and the control input u. c ;

[0010] A disturbance observer is configured in the control loop to determine the disturbance force estimate; wherein the disturbance observer includes a filtering unit;

[0011] The disturbance compensation amount u is determined based on the disturbance force estimate and the transfer function Q(s) of the filter unit. d ;

[0012] Based on the disturbance compensation amount u d For the control input u c The final control input u is obtained through updating to compensate for low-frequency disturbances.

[0013] Preferably, in the structure of the disturbance observer, the filtering unit is respectively disposed in its two parallel branches.

[0014] Preferably, the filtering unit is close to 1 in the low-to-mid frequency range and gradually attenuates in the high-frequency range to achieve low-frequency disturbance compensation and high-frequency noise suppression.

[0015] Preferably, the filtering unit is a second-order low-pass filter.

[0016] Preferably, the frequency band f of the main disturbance force that needs to be suppressed is determined by estimating the disturbance force through spectral analysis. d .

[0017] Preferably, the design of the filter unit transfer function Q(s) is determined based on the process sensitivity transfer function.

[0018] The process sensitivity transfer function is determined based on the response characteristics between the system output and the disturbance force, as well as the transfer function of the controlled object.

[0019] Preferably, the design of the filter unit transfer function Q(s) is also determined based on the noise sensitivity transfer function.

[0020] The noise sensitivity transfer function is determined based on the response characteristics between the system output and external measurement noise, as well as the transfer function of the controlled object.

[0021] Preferably, it further includes adjusting the cutoff frequency f of the Q(s) filter based on the perturbation spectral characteristics. c Specifically, it includes the following steps:

[0022] Obtain the disturbance frequency band f d ;

[0023] Set the low-frequency disturbance threshold f th ;

[0024] Adjust the cutoff frequency f of the Q(s) filter c :

[0025] When f d ≤f th Then set f c =1.2-1.5×f d ;

[0026] When f d >f th Then maintain the cutoff frequency f c This is a preset reference value.

[0027] Preferably, it further includes a cutoff frequency f c The transfer function Q(s) of the filter is calculated and updated, and the updated Q(s) is applied to the DOBC control loop to improve the disturbance suppression capability.

[0028] Preferably, the method further includes adjusting the gain G of the Q(s) filter based on spectral analysis of the disturbance force estimate, specifically including the following steps:

[0029] Collect system outputs and control inputs, and calculate estimated disturbance forces.

[0030] Spectral analysis was performed on the estimated disturbance forces to extract the main disturbance force frequency band f. d and corresponding amplitude G d ;

[0031] Based on the disturbance amplitude G d Calculate the filter gain G;

[0032] Based on the real-time amplitude G of the disturbance force d The gain G of the filter Q(s) is dynamically adjusted so that the suppression strength of the disturbance force changes adaptively with the magnitude of the disturbance force.

[0033] Based on the above technical solution, it can be seen that this application has at least one of the following beneficial effects compared with the prior art:

[0034] 1. The Disturbance Observer-Based Control Strategy (DOBC) can estimate and compensate for disturbances in real time.

[0035] This method employs a Disturbance Observer (DOBC) to monitor the disturbance force on the system in real time. By calculating the equivalent disturbance force d', a compensation amount is added to the control signal to effectively suppress low-frequency disturbances.

[0036] Traditional control methods (such as PID) can only rely on fixed parameters for adjustment, while DOBC can dynamically adjust the compensation strategy based on real-time measured data. Compared with traditional PID control and feedforward compensation methods, this strategy is better able to adapt to the characteristics of low-frequency random disturbances, enhancing the system's dynamic adaptability and disturbance rejection capability.

[0037] 2. Optimization of Q-filter design

[0038] A second-order Q(s) low-pass filter is used for estimation and compensation of disturbance forces. By adjusting its parameters to maintain a value of 1 in the low-frequency band and attenuate it in the high-frequency band, it can both compensate for low-frequency disturbance forces and suppress the influence of measurement noise. Compared with existing single low-pass filters or notch filters, this filter design is more flexible and can be dynamically adjusted according to different disturbance conditions.

[0039] 3. Adaptive disturbance compensation

[0040] By combining real-time FFT spectrum analysis, the cutoff frequency f of the Q(s) filter can be dynamically adjusted according to the dominant frequency of the disturbance. c With gain G, adaptive disturbance compensation is achieved. Specifically, when the frequency or amplitude of the disturbance changes, the system can synchronously update the filter parameters to ensure that the best disturbance suppression effect is maintained under different operating conditions.

[0041] Compared to traditional methods, this scheme not only adjusts f based on the spectral characteristics of the disturbance force. c Furthermore, it adaptively adjusts the gain G to accommodate changes in the amplitude of the disturbance force. This collaborative optimization approach improves the estimation accuracy of the disturbance force, enabling the system to provide precise compensation under different disturbance force levels, thereby enhancing the disturbance force suppression capability and system stability.

[0042] 4. Improve the control accuracy of the system

[0043] This application employs a Disturbance Observer (DOBC) + Q(s) filter control method to enable the actual motion trajectory of the motion stage to more closely approximate the set trajectory. Compared to traditional PID control and pressure feedforward compensation, DOBC can more accurately identify and compensate for random low-frequency disturbances, thereby effectively reducing the error amplitude, suppressing the error of the motion stage under the action of low-frequency random disturbances, and improving control accuracy.

[0044] Other features and advantages of this application will be set forth in the following description and will be apparent in part from the description, or may be realized by practicing the application. The purpose and other advantages of this application can be realized and obtained by means of the structures particularly pointed out in the written description and the accompanying drawings. Attached Figure Description

[0045] Figure 1This is the basic control principle diagram of DOBC;

[0046] Figure 2 This is a general control architecture diagram for DOBC;

[0047] Figure 3 This is an exemplary DOBC equivalent optimized control architecture diagram for this application;

[0048] Figure 4(a) is an exemplary analysis of the low-frequency disturbance suppression effect based on DOBC control in this application;

[0049] Figure 4(b) is an exemplary trend diagram of the perturbation force over time in this application;

[0050] Figure 4(c) is a frequency distribution diagram of the exemplary perturbation force of this application;

[0051] Figure 5(a) shows the effect of the exemplary DOBC of this application on the sensitivity transfer function phase;

[0052] Figure 5(b) shows the effect of the exemplary DOBC of this application on the sensitivity transfer function amplitude;

[0053] Figure 6(a) shows the effect of the exemplary DOBC of this application on the process sensitivity transfer function phase;

[0054] Figure 6(b) shows the effect of the exemplary DOBC of this application on the amplitude of the process sensitivity transfer function;

[0055] Figure 7(a) is an exemplary control error over time diagram of this application;

[0056] Figure 7(b) is a spectrum analysis diagram of an exemplary error of this application. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0058] The terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to limit the embodiments of this application. The singular forms "a," "the," and "the" as used in the embodiments of this application are also intended to include the plural forms unless the context clearly indicates otherwise.

[0059] To address the shortcomings of existing technologies, the purpose of this application is to provide a control method for suppressing low-frequency disturbances in a motion stage. Specifically, the control method for suppressing low-frequency disturbances in a motion stage provided by this application includes the following steps:

[0060] S1: Acquire the measurement data of the motion table and calculate the transfer function P(s) of the controlled object of the system;

[0061] To accurately model the dynamic behavior of the motion table and achieve effective disturbance suppression control, it is first necessary to acquire the measurement data of the motion table system in the control loop and calculate the controlled object transfer function P(s) based on this data. The motion table, as the controlled object, can be considered as a combination of a rigid body and a flexible modal structure, and its transfer function expression is as follows:

[0062]

[0063] in:

[0064] P(s): The transfer function of the controlled object of the motion table, which reflects the input-output relationship of the system in the Laplace transform domain (s-domain);

[0065] m: represents the equivalent mass of the motion table, reflecting the inertial characteristics of the system;

[0066] s: is the Laplace transform variable, used to describe the dynamic characteristics of the system;

[0067] N s The number of flexible modes reflects the complexity of the motion table structure.

[0068] k i : is the gain coefficient of the i-th flexible mode, representing the degree of influence of the flexible mode on the system;

[0069] β i : is the damping ratio of the i-th mode, representing the effect of damping on the system;

[0070] ω i : is the natural frequency of the i-th mode, representing the resonant frequency of the system.

[0071] Measurement data acquisition and processing

[0072] Data Acquisition: Real-time acquisition of displacement, velocity, and acceleration data of the motion table under different operating conditions is achieved using high-precision sensors (such as displacement sensors and accelerometers). Measurement data includes system output y and control input u. c Simultaneously, record the control input u. c (Motor driving force or current) and the corresponding system response to obtain the complete input-output relationship.

[0073] Data preprocessing: The collected raw data is preprocessed by filtering, denoising, and other operations to improve the accuracy and reliability of the data.

[0074] Spectrum analysis: Using Fast Fourier Transform (FFT) or Power Spectral Density (PSD) analysis methods, the spectral characteristics of the motion stage are extracted from the time-domain data to identify the main perturbation frequencies and modal parameters.

[0075] Calculation of transfer function P(s)

[0076] Modal parameter identification: Based on the spectral analysis results, the main modal parameters of the motion table are identified, including the natural frequency ω. i Damping ratio β i and gain coefficient k i .

[0077] Transfer function modeling: Based on the identified modal parameters, a transfer function P(s) model of the motion table is constructed. This model will serve as the basis for the design of the Disturbance Observer (DOBC) for real-time estimation and compensation of external disturbances.

[0078] Model validation: The accuracy of the transfer function P(s) model is verified by comparing the system response predicted by the model with the actual measured data. If necessary, the model parameters are adjusted and optimized to improve the model's fit.

[0079] Through the above steps, the measurement data of the motion table can be accurately obtained, and the transfer function P(s) of the controlled object of the system can be calculated accordingly, providing a solid foundation for achieving high-precision disturbance suppression control.

[0080] S2: Configure a disturbance observer (DOBC) in the control loop to observe and compensate for low-frequency disturbances;

[0081] Configuring a Disturbance Observer-based Control (DOBC) in the control loop is an effective method for suppressing random disturbances. Similar to feedforward control, DOBC performs feedforward compensation on the observed random disturbance at the control input, thereby reducing the impact of random disturbances on the control system. The basic control principle diagram of DOBC is shown below. Figure 1 As shown, the general control architecture is as follows: Figure 2 As shown.

[0082] In the DOBC (Disturbance Observer) control strategy, the controlled object P (i.e., the motion table) of the system is simultaneously subjected to external disturbance force d and final control input u, causing the output response y to change.

[0083] Disturbance force observation: Due to the dynamic characteristics of the motion table, the estimated value of the disturbance force d′ is calculated by measuring the system output y and the final control input u.

[0084] d'=y / P(s)-u

[0085] Since the disturbance force cannot be directly measured, DOBC derives the estimated value d′ of the disturbance force through the dynamic relationship between the system's final control input u and output y, thereby achieving indirect observation of the disturbance force.

[0086] Disturbance compensation: The disturbance estimate d′ is processed using filter Q(s) to generate the disturbance compensation amount u. d and the control input u of the main controller c The superposition forms the final control input u, which counteracts the effects of the disturbance force.

[0087] u d =Q(s)d'

[0088] in:

[0089] d′: The estimated disturbance force, i.e. the external disturbance effect calculated by DOBC;

[0090] y: The actual output of the motion table;

[0091] P(s): The transfer function of the controlled object (motion table), representing the dynamic characteristics of the system (inertia, flexible vibration, etc.);

[0092] u: Final control input (control input u) c and disturbance force compensation amount u d The sum of, i.e., u = u c +u d ).

[0093] DOBC employs a feedback control strategy to compensate for d′, thereby enhancing the system's disturbance rejection capability and improving control accuracy.

[0094] S3: Optimize the DOBC control architecture by using Q(s) / P(s) to approximate 1 / P(s) in order to build an achievable causal system;

[0095] Ideally, if d' could be directly calculated, compensation would be straightforward. However, according to the transfer function expression, P(s) is a general causal system, meaning the order of the numerator is less than or equal to the order of the denominator. Therefore, 1 / P(s) is a non-causal system, requiring future information to correctly calculate the output, which is unrealistic and cannot be directly used for perturbation estimation. To ensure DOBC is feasible, a method needs to be found to approximate 1 / P(s) so that the entire system remains causal and can achieve the required functionality. Therefore, for Figure 2 The control architecture is optimized equivalently, and the optimized control architecture is as follows: Figure 3 As shown. In the optimized DOBC control architecture, the disturbance observer includes a filtering unit. Figure 3 By Figure 2The filter unit Q(s) on the main branch is placed in two parallel branches, which ensures that both branches are causal systems. By introducing Q(s) for equivalent transformation, the DOBC control system becomes a causal system, which can be implemented in the actual physical system.

[0096] In the traditional DOBC structure ( Figure 2 In this context, the formula for calculating the disturbance force estimation is:

[0097]

[0098] Since 1 / P(s) leads to non-causality, which is difficult to achieve directly in real physical systems, in order to solve the non-causality problem, the optimized DOBC structure ( Figure 3 In this context, Q(s) / P(s) is used to approximate 1 / P(s), that is:

[0099]

[0100] in,

[0101] d′: Estimated value of disturbance force;

[0102] P(s): Represents the transfer function of the controlled object;

[0103] yP(s)u: represents the difference between the measured output and the ideal model output, which can be understood as "the part of the system that is not compensated by the control force";

[0104] This method estimates the disturbance force by designing an appropriate filter unit Q(s), thus avoiding the non-causal problem caused by directly calculating 1 / P(s).

[0105] Q(s): A well-designed filter unit that ensures computational feasibility.

[0106] To ensure the causality of the system, it is necessary to ensure that Q(s) / P(s) is a causal system, that is, the order of its numerator does not exceed the order of its denominator. According to the above formula #1, P(s) is a second-order transfer function. To ensure that Q(s) / P(s) is a causal system, the order of Q(s) must be greater than or equal to the order of P(s).

[0107] S4: Design the filter unit Q(s) to make it approach 1 in the low and medium frequency range and gradually attenuate in the high frequency range, so as to meet the feasibility of the DOBC control loop;

[0108] The filtering unit can effectively separate the low-frequency disturbance signal that needs to be compensated from the high-frequency noise that should be suppressed. It can allow the low-frequency disturbance signal to pass through for system compensation while suppressing high-frequency noise. By selectively filtering signals of different frequencies, it ensures that the DOBC strategy responds only to meaningful disturbances, thereby improving the accuracy and stability of the control system.

[0109] In the DOBC equivalent optimized control architecture ( Figure 3 In order to accurately estimate the disturbance force and perform effective compensation, it is necessary to solve the overall closed-loop transfer function of the control system to ensure that the system can achieve high-precision trajectory tracking control. Here, d represents the external force disturbance, n represents the measurement disturbance, P(s) represents the controlled object, and P(n) and Q(s) are the key parameters that DOBC needs to optimize.

[0110] To construct a complete DOBC control loop, it is first necessary to solve for the overall closed-loop transfer function including the DOBC compensation mechanism, and then analyze the system's error characteristics. Based on the equivalent optimized control block diagram, the mathematical expression of the overall closed-loop transfer function can be derived as follows:

[0111]

[0112] in:

[0113] y: System output;

[0114] r: Reference input, i.e., the control objective that the system expects to achieve.

[0115] P: The actual transfer function of the controlled object (short for P(s)), which describes the dynamic characteristics of the controlled object, usually including rigid body and flexible mode structures.

[0116] P n The nominal transfer function of the controlled object (the transfer function in the ideal case) is an idealized model used when designing control strategies.

[0117] C: The transfer function of the controller, which is usually used to adjust the control algorithm for the system response.

[0118] FF: Represents the transfer function of feedforward control. In motion table control, FF is usually acceleration feedforward, and its expression is FF = m*s. 2 , where m is mass and s is the Laplace variable.

[0119] Q: The transfer function of the filter unit in the Disturbance Observer (DOBC) (short for Q(s)) is responsible for estimating the disturbance force and compensating for it.

[0120] PP nThis indicates the deviation between the actual system model and the ideal model, which usually stems from factors such as disturbance forces and modeling errors.

[0121] Ideally, to ensure that the tracking error e is close to 0, that is, the system can strictly follow the given instructions for motion control, it is necessary to ensure that the error term is effectively eliminated in the closed-loop control system, that is, ry = 0.

[0122]

[0123] As can be seen, the numerator in the above formula #3 contains two parts:

[0124] 1. Q*(PP) n ), introduced by the DOBC structure;

[0125] 2. P n *(1-P*FF), is determined by the compensation characteristics of the feedforward controller.

[0126] To ensure that the tracking error e approaches zero, the feedforward controller FF needs to accurately compensate for the dynamic characteristics of the motion table, i.e., eliminate P. n The term *(1-P*FF), i.e., P n *(1-P*FF)=0 (from this equation, we can deduce that P=1 / FF), then the above equation can be simplified to:

[0127]

[0128] In this control architecture, the FF typically employs acceleration feedforward, and its input signal is the position command POS. Therefore, the mathematical expression of the FF can be determined as m*s. 2 According to the above formula, in order to ensure that the tracking error e = 0, P is required. n =P, therefore we can get P n The expression is as follows:

[0129]

[0130] in:

[0131] P n : Represents the ideal or nominal model of the controlled object. In the DOBC control architecture, P n It is the ideal transfer function of the controlled object, used to estimate and compensate for external disturbances;

[0132] P: Represents the actual transfer function of the controlled object (short for P(s)). P describes the dynamic characteristics of the controlled object, usually including the structure of rigid body and flexible modes.

[0133] FF: Represents the transfer function of feedforward control. In motion table control, FF is usually acceleration feedforward, and its expression is FF = m*s. 2 , where m is the mass and s is the Laplace variable;

[0134] m: represents the mass of the motion table;

[0135] s: The complex frequency variable in the Laplace transform, used to describe the dynamic response of the system;

[0136] The above formula represents the ideal model P of the controlled object. n The actual model P can be represented by feedforward control FF, which is determined by the system mass m and the Laplace variable s.

[0137] This solution process provides a mathematical basis for the DOBC scheme and a theoretical basis for the subsequent optimization design of the filter unit Q(s), so as to ensure the feasibility and robustness of the DOBC control loop.

[0138] In the design of the DOBC control loop, the appropriate selection of the filter unit Q(s) plays a crucial role in the system's disturbance rejection capability and feasibility. To clarify the design requirements of Q(s), it is necessary to analyze the system's process sensitivity transfer function (output / force disturbance) and noise sensitivity transfer function (output / measurement disturbance), and, in conjunction with the dynamic characteristics of the motion table, derive the filter unit structure that meets the DOBC control requirements.

[0139] 1. Process sensitivity transfer function analysis

[0140] Based on the equivalent optimized control block diagram, the process sensitivity (output / force disturbance) transfer function expression containing the DOBC control loop can be solved:

[0141]

[0142] The process sensitivity transfer function reflects the influence of external disturbance force d on the system output y.

[0143] As shown in formula #5, when Q approaches 1, the process sensitivity transfer function also approaches 0, meaning that DOBC can offset the disturbance force d to the greatest extent and reduce the impact of the disturbance force on the output.

[0144] This conclusion indicates that in order to effectively suppress external disturbance forces, Q(s) should be as close as possible to 1 in the frequency band (mid-low frequency) where the disturbance forces mainly act, so as to ensure that DOBC can accurately estimate and compensate for the disturbance forces in the low frequency range.

[0145] 2. Noise Sensitivity Transfer Function Analysis

[0146] Under the DOBC control loop, the noise sensitivity transfer function (output / measurement disturbance) expression containing the DOBC control loop is as follows:

[0147]

[0148] in:

[0149] The noise sensitivity transfer function reflects the effect of the measured noise n on the system output y.

[0150] When Q → -PC, the noise sensitivity transfer function → 0, meaning the impact of measurement noise on the output is minimized. PC is the open-loop transfer function expression in a conventional control architecture (excluding DOBC), which typically exhibits amplitude and phase attenuation characteristics in the high-frequency range. Measurement noise is generally high-frequency noise; therefore, DOBC needs to reduce its impact in the high-frequency range. That is, Q(s) should be attenuated in the high-frequency range to prevent high-frequency noise from being amplified by DOBC and affecting the output, thereby achieving suppression of high-frequency noise.

[0151] 3. Design principle of filter unit Q(s)

[0152] Based on the above two points:

[0153] External disturbances are generally low- to mid-frequency disturbances. Q(s) should be as close to 1 as possible in the low- to mid-frequency range to ensure that DOBC can accurately estimate and compensate for the disturbance.

[0154] Measurement noise is generally high-frequency noise, and Q(s) should be attenuated in the high-frequency range to prevent DOBC amplification of measurement noise from affecting the system output.

[0155] By designing the filter unit to approach 1 in the low-to-mid frequency range and gradually attenuate in the high-frequency range, it is possible to effectively compensate for low-frequency disturbances and suppress high-frequency noise, thereby improving the stability and control accuracy of the system.

[0156] 4. Reasons for choosing a second-order filter unit

[0157] From the transfer function expression of P(s) above, we know that the motion table is a second-order system, and the order of its numerator does not exceed the order of its denominator. Therefore, it is a causal system, and 1 / P(s) is a non-causal system. To ensure that Q(s) / P(s) is a general causal system,

[0158] because

[0159]

[0160] Therefore, Q(s) only needs to be a second-order or higher filter to satisfy the condition that Q(s) / P(s) is a general causal system. However, if the order of the Q(s) filter unit is higher, the computational complexity will increase, and the phase loss will be greater, which will have an adverse effect on the system stability and the system response speed. Especially in applications requiring fast disturbance compensation, this may reduce control accuracy. Moreover, higher-order filter units involve more free parameters (such as additional poles and zeros), making the adjustment more complex. Therefore, in the application scenario of low-frequency disturbance suppression of motion tables, the Q(s) filter unit is preferably a second-order low-pass filter with the same order as the controlled object.

[0161] A second-order low-pass filter is expressed as follows:

[0162]

[0163] in:

[0164] Q(s): The transfer function of the filter;

[0165] s: Laplace transform variable (complex frequency domain variable), used in control theory and signal processing to analyze the dynamic characteristics of a system;

[0166] ω c The cutoff angular frequency of a filter determines its frequency response, measured in radians per second (rad / s), and also determines its bandwidth (the starting point of attenuation from low to high frequencies). ω c =2πf c (f c (cutoff frequency);

[0167] ζ: Damping ratio, which controls the dynamic characteristics of the filter, including overshoot, peak response, and frequency response;

[0168] G: is the variable gain parameter of the filter, which determines the suppression strength of the disturbance.

[0169] The updated Q(s) is applied to the DOBC control loop, and the disturbance suppression capability is improved by the updated filter Q(s), thereby optimizing the system's stability and disturbance rejection capability.

[0170] Cutoff angular frequency ω c ω represents the starting point of signal attenuation in the frequency domain. This can be achieved by adjusting ω. c It can control the frequency range within which the filter effectively suppresses disturbances, f c =ω c / 2π can be used to more intuitively represent the cutoff point of the filter.

[0171] When ω c At higher frequencies, the filter's cutoff frequency f cThe higher the frequency, the more likely it is to be, meaning the filter allows higher frequencies to pass through, making it suitable for wider filtering needs.

[0172] When ω c At lower levels, f c The lower value means that the filter tends to retain only lower frequency signals, making it suitable for low-frequency disturbance suppression.

[0173] Furthermore, the cutoff frequency f c The preferred setting is 1.2f. d -1.5f d f d The main disturbance frequency band is represented by f. d This refers to the low-frequency range where the main energy of external disturbances (such as imprinting force and vibration of the imprinting module) is concentrated. This frequency range is where external disturbances have the most significant impact on the motion table, and it is also the frequency region that needs to be focused on and optimized when designing disturbance suppression measures for the system. This is achieved by using the cutoff frequency f... c Set to 1.2f d -1.5f d This ensures that the disturbance observer can effectively cover f. d It can effectively suppress the main disturbance frequency band f d The disturbance is reduced, while the high-frequency noise is weakened without affecting the effective disturbance compensation.

[0174] The perturbations experienced by the motion table of semiconductor precision equipment (such as nanoimprint lithography equipment) typically include the imprinting force and the vibration of the imprinting module itself. These perturbations usually have the following characteristics:

[0175] Low-frequency characteristics: The imprinting force and vibration of the imprinting module are usually low-frequency disturbances with a relatively low frequency range.

[0176] Randomness: These disturbances are random and may vary due to equipment operating conditions, environmental factors, etc.

[0177] Since the imprinting force and vibration of the imprinting module are typically low-frequency disturbances, the main disturbance frequency bands are often concentrated in the low-frequency range. By acquiring time-domain data and estimating the disturbance force through spectrum analysis, the main disturbance frequency bands can be identified.

[0178] Time-domain signal acquisition: First, it is necessary to acquire the disturbance force signals experienced by the motion table during actual operation. These signals can be measured by high-precision sensors (such as accelerometers, force sensors, etc.).

[0179] Spectrum analysis methods

[0180] Fast Fourier Transform (FFT): This process performs a fast Fourier transform on the acquired time-domain signal, converting it into a frequency-domain signal. FFT can decompose a time-domain signal into amplitude and phase information of different frequency components.

[0181] Power spectral density (PSD) analysis: Calculating the power spectral density of the disturbance signal to determine the energy distribution of different frequency components. The power spectral density can visually reflect which frequency bands have greater disturbance energy.

[0182] By acquiring time-domain data and performing spectrum analysis, the main disturbance frequency bands can be identified: Fast Fourier Transform (FFT) or Power Spectral Density (PSD) analysis is performed on the acquired time-domain data to convert it into frequency-domain data. After conversion, the spectrum will display the amplitude distribution of each frequency component.

[0183] By analyzing the spectrum, such as using FFT (Fast Fourier Transform) or PSD (Power Spectral Density Analysis), the perturbation signal can be analyzed to identify low-frequency bands with abnormally increased amplitudes, thereby determining the main perturbation frequency bands f that need to be suppressed. d .

[0184] After identifying the frequency bands that require disturbance suppression, adjust the parameters of the Q filter (such as cutoff frequency and damping ratio) to effectively suppress disturbances in these frequency bands.

[0185] Damping ratio ζ is a key parameter in filter design, as it affects the dynamic response characteristics of the filter.

[0186] An appropriate damping ratio helps ensure system stability, meaning that the system can give the expected response to the input signal without exhibiting unstable behavior due to excessive oscillation or delay.

[0187] The damping ratio ζ is preferably 0.707. For a second-order low-pass filter, the filter's natural resonant frequency (the frequency at which the system freely vibrates) is located at the cutoff frequency f. c of At times, the system is It has the smoothest amplitude-frequency response in the vicinity, without unnecessary oscillations (underdamped) or excessive attenuation (overdamped).

[0188] This is a typical second-order system parameter, which provides good transition band characteristics and sufficient damping to ensure system stability. It ensures that the filter will not introduce additional oscillations while suppressing disturbances, thus maintaining system stability.

[0189] If the damping ratio is too small (<0.707): the filter will cause additional oscillations, which may lead to system instability;

[0190] If the damping ratio is too high (>0.707), the filter response will be slower, affecting the real-time performance of disturbance compensation.

[0191] 0.707 is the critical damping of a second-order system, which can achieve an optimal balance: it can effectively attenuate high-frequency noise, avoid DOBC miscompensation of measurement noise, and ensure a fast enough response speed so that DOBC can quickly observe and compensate for disturbance forces.

[0192] Furthermore, the equipment may encounter disturbances of different frequency ranges under different operating conditions (different loads, environmental vibrations), which limits the control effect of a fixed Q(s) parameter. The spectral characteristics of external disturbances may change over time (e.g., different vibration characteristics under different operating conditions). If the cutoff frequency f of Q(s) c If the gain G is fixed, the filter may not suppress the problem effectively in certain situations and may not be able to adapt to different disturbance environments.

[0193] Adjust the gain G and cutoff frequency f c This is to adapt to different disturbance conditions and ensure the system remains stable under various circumstances. If the disturbance spectrum drifts, f is dynamically adjusted. c And G, to follow the drift frequency, to improve the disturbance suppression effect.

[0194] An adaptive Q(s) filter design is preferred, which can dynamically adjust the cutoff frequency f of Q(s) according to the spectral characteristics of external disturbances. c And gain G, to improve the adaptability and robustness of disturbance suppression.

[0195] Q(s) adaptive adjustment scheme

[0196] Real-time FFT spectrum analysis is used to identify the main frequency range of the disturbance signal, and the cutoff frequency f of Q(s) is dynamically adjusted according to the spectral characteristics of the disturbance. c And gain G, to ensure that Q(s) provides optimal disturbance compensation capability in the critical frequency band.

[0197] Option 1: Dynamically adjust the cutoff frequency f of Q(s) c

[0198] 1.2-1.5 times cutoff frequency method: Adjusted only during initial disturbance detection, and then kept at a fixed parameter; suitable for situations where the disturbance is relatively stable, but cannot dynamically adapt to frequency drift. However, in practical applications, the frequency of the disturbance may drift with time and operating conditions, for example:

[0199] Equipment load changes: Disturbance forces may cause frequency drift;

[0200] Different environmental vibrations: Different external environments cause changes in the spectrum of disturbance forces;

[0201] Different equipment operating modes: High-frequency components are enhanced in some modes.

[0202] This scheme allows for real-time adjustment of the cutoff frequency f. c This ensures that the filter is always in optimal working condition, thus improving its robustness.

[0203] Specific steps:

[0204] Disturbance spectrum analysis: The output disturbance signal y of the motion table is acquired in real time and subjected to real-time spectrum analysis to extract the spectrum distribution and obtain the main disturbance frequency band f. d .

[0205] Set the low-frequency disturbance threshold f th ;

[0206] Low-frequency disturbance threshold f th This refers to a preset frequency threshold used to distinguish between low-frequency disturbances and high-frequency noise or other disturbances, serving as a boundary point to determine whether a disturbance belongs to the low-frequency range. th The value setting should cover the main low-frequency disturbance frequency bands to ensure the compensation effect, and can be set in combination with the system's flexible mode frequency and control bandwidth requirements.

[0207] Dynamically adjust the cutoff frequency f of the Q(s) filter c :

[0208] When f d ≤f th This indicates that the disturbance frequency is in the low-frequency range, so f is set. c =1.2-1.5×f d This is to ensure that Q(s) has optimal compensation capability in the main disturbance frequency band;

[0209] When f d >f th This indicates that the disturbance frequency has exceeded the range of low-frequency disturbances, so the cutoff frequency f should be maintained. c This is a preset reference value to avoid unnecessary adjustments to the high-frequency band, which could affect system stability. The preset reference value can be set based on empirical values.

[0210] Based on the cutoff frequency f c The filter's transfer function Q(s) is calculated and updated, and the updated Q(s) is applied to the DOBC control loop to improve disturbance rejection capability. This is achieved by adjusting the cutoff frequency f in real time. cThis allows Q(s) to maintain high gain in the main disturbance frequency band and effectively attenuate in the high frequency band. It can dynamically match the compensation bandwidth according to the changes in the disturbance spectrum, ensuring that the disturbance observer always focuses on low-frequency disturbance compensation under different operating conditions, while suppressing high-frequency measurement noise, thereby improving the disturbance suppression effect and the overall stability and robustness of the system.

[0211] Option 2: Dynamically adjust the gain G of Q(s)

[0212] Gain G: is the suppression strength of Q(s) on the disturbance force. The larger the value, the stronger the suppression.

[0213] Option 1 only adjusts the cutoff frequency f c This is done to optimize the frequency characteristics of the filter, enabling it to compensate for specific disturbance frequency ranges. However, simply adjusting f... c It primarily optimizes the frequency distribution of the disturbance force, but cannot adapt to changes in the amplitude of the disturbance force. When the amplitude of the disturbance force changes, the frequency characteristics themselves may not change; therefore, a fixed f... c It remains effective, but the filter's compensation strength may be insufficient or excessive, resulting in poor suppression of disturbance forces. Different disturbance force amplitudes require different suppression strengths. This scheme calculates the disturbance force amplitude G in real time. d By dynamically adjusting the gain G of the Q(s) filter, the DOBC can more accurately estimate and compensate for disturbance forces in the low-frequency band.

[0214] For high-amplitude disturbances, if only f is adjusted c Without increasing the filter gain G, the filter's suppression capability may be insufficient, and the disturbance force cannot be fully compensated.

[0215] For low-amplitude disturbances, if the filter gain G is too high, it may lead to overcompensation, causing the system to overreact to the disturbance and even affecting the system stability.

[0216] Therefore, this scheme determines a suitable f c Then, adaptive gain adjustment is further introduced, and the specific steps are as follows:

[0217] 1. Perturbation based on DOBC observations

[0218] During operation, the system calculates the equivalent disturbance force d′ based on the sensor output signal y and the final control input u.

[0219]

[0220] in:

[0221] d′: Estimated disturbance force (equivalent disturbance force estimated by the disturbance observer);

[0222] y: System output;

[0223] P(s): The transfer function of the controlled object;

[0224] u: Final control input.

[0225] 2. Perform frequency domain analysis on the disturbance signal d′

[0226] Fast Fourier Transform (FFT) or Power Spectral Density (PSD) analysis is employed. For example, an FFT is performed on the estimated disturbance force d′ to convert the time-domain signal into a frequency-domain signal. The output of the FFT is a sequence of complex numbers, where each complex number represents the amplitude and phase of a frequency component. The main active frequency band f of the disturbance force is then extracted. d and its amplitude G d :

[0227] Perform an FFT transform on d′ to obtain the frequency domain signal G. d :G d =FFT(d′)

[0228] 3. Calculate the filter gain G

[0229] Gain G is based on G d The calculation formula, which is calculated and dynamically adjusted, is as follows:

[0230] G = G base +k*G d

[0231] in:

[0232] G base Initial filter gain (default value for normal disturbances);

[0233] k: Gain adjustment coefficient, which determines the amplitude of the disturbance force G. d The degree of impact on G (generally based on experimental or simulation optimization);

[0234] G d : The real-time amplitude of the disturbance force, calculated by FFT;

[0235] G: Used to adjust the gain of filter Q(s), which is the amplification factor of the Q(s) filter to match the DOBC compensation strength with the magnitude of the disturbance.

[0236] Preferably, a threshold constraint is applied to the overall gain G, and the threshold constraint value can be set to (0.9~1.1)G. baseThis avoids the problem of the Q(s) filter further amplifying vibrations and causing system divergence when the system experiences high-frequency vibrations. When the overall gain G exceeds the threshold constraint, a limiting strategy can be adopted to ensure that the filter Q(s) does not excessively amplify the disturbance force. The limiting strategy can be implemented by direct truncation or smooth adjustment.

[0237] Direct threshold constraint method

[0238] For general application scenarios, the direct threshold constraint method can be used, which is simple and efficient.

[0239] When G exceeds the upper limit of 1.1G base At that time, set it to 1.1G base ;

[0240] The above methods are simple to implement, ensure that the gain will not exceed the threshold constraint value, are applicable to most DOBC scenarios, and do not introduce additional dynamic adjustment complexity.

[0241] Adaptive adjustment method

[0242] When G exceeds the threshold, the value of k is dynamically reduced so that G slowly returns to the threshold range.

[0243] Improved formula:

[0244] When G > 1.1G base hour:

[0245]

[0246] Then calculate the new G using the new k′:

[0247] G = G base +k'G d

[0248] The adaptive adjustment method allows G to slowly return to the threshold range, making it suitable for systems requiring high-precision adjustment.

[0249] 4. Dynamically adjust the filter gain G

[0250] According to formula #7,

[0251]

[0252] Where G is the variable gain parameter of the filter, which determines the suppression strength of the disturbance.

[0253] Based on the real-time calculated disturbance amplitude G d The gain G of the filter Q(s) is dynamically adjusted to enhance or weaken the ability to suppress disturbances.

[0254] By dynamically adjusting G, DOBC can adaptively adjust the compensation intensity under different disturbance amplitudes, thereby improving the disturbance suppression effect.

[0255] f c Co-regulatory mechanism with G:

[0256] f c It mainly affects the system's response to disturbances of different frequencies. When the disturbance spectrum changes, f needs to be adjusted. c To match the new frequency characteristics;

[0257] G is mainly used to adjust the strength of disturbance suppression, ensuring that appropriate compensation can be provided for disturbances of different amplitudes within the same frequency range.

[0258] Compared to traditional methods, this scheme not only adjusts f based on the spectral characteristics of the disturbance force. c Furthermore, it adaptively adjusts the gain G to accommodate changes in the amplitude of the disturbance force. This collaborative optimization approach improves the estimation accuracy of the disturbance force, enabling the system to provide precise compensation under different disturbance force levels, thereby enhancing the disturbance force suppression capability and system stability.

[0259] S5: Calculate the disturbance compensation amount based on the relationship between the system output y and the final control input u, and in conjunction with the filter transfer function Q(s). d Used to compensate for disturbances;

[0260] Based on the input / output relationship of the DOBC system:

[0261] y = P(s)(u + d)

[0262] in:

[0263] y: System output;

[0264] u: Final control input (control input u) c and disturbance force compensation amount u d The sum of, i.e., u = u c +u d );

[0265] P(s): The transfer function of the controlled object;

[0266] d: Actual disturbance force (unknown);

[0267] Since the disturbance force d cannot be directly measured, DOBC determines the estimated disturbance force d′ through the final control input u and the system output y.

[0268] The formula for calculating the disturbance force estimate d′ is as follows:

[0269]

[0270] according to Figure 3 u is the final control input, determined by u c and u d Overlay:

[0271] u = u c +u d

[0272] in:

[0273] u: The final actual control input, calculated by the main controller. c The disturbance compensation amount u calculated by DOBC d The superposition is used to drive the system to compensate for the effects of disturbance forces;

[0274] u c : Control inputs calculated by the main controller;

[0275] u d The disturbance force compensation amount is the estimated disturbance force value after filtering and optimization, which is used to compensate for the disturbance force d in order to reduce the impact of the disturbance force d on the system.

[0276] Calculate the disturbance force compensation amount u d

[0277] Based on the DOBC structure, the disturbance force compensation amount u is determined by filtering the disturbance force estimate d′ and the transfer function Q(s) of the filtering unit. d The calculation formula is:

[0278] u d =Q(s)d'

[0279] Substituting the expression for d′ into the equation, the final solution is obtained for the disturbance force compensation amount u. d :

[0280]

[0281] in:

[0282] u d Disturbance compensation amount, calculated by DOBC, is used to suppress the impact of disturbance forces on the system;

[0283] Q(s): Filter transfer function;

[0284] P(s): The transfer function of the controlled object, which represents the dynamic relationship between the system input and output;

[0285] y: System output;

[0286] u c: Control inputs calculated by the main controller (such as PID, feedforward control).

[0287] S6: Adjust the disturbance compensation amount u d Introducing a control terminal, and connecting it to the control input u c Superimposed to suppress the impact of low-frequency disturbances on the motion table.

[0288] according to Figure 3 It can be seen that the final control input u is controlled by the main controller. c and disturbance force compensation amount u d Formed by superposition, that is:

[0289] u = u c +u d

[0290] Among them, u d The disturbance compensation amount is calculated by DOBC, u d It is obtained by processing the disturbance force estimate through filter Q(s), based on the disturbance force compensation amount u. d For control input u c The updated final control input u is used to compensate for low-frequency disturbances and suppress their impact. This compensation mechanism ensures that the system can effectively cancel out disturbances in the low-frequency band while avoiding interference from high-frequency noise on system stability, thereby improving the motion stage's anti-disturbance performance and ensuring that the system can still accurately track the target input under external disturbances, achieving high-precision motion control.

[0291] To verify the effectiveness of the low-frequency disturbance suppression method of this application, multiple sets of comparative experiments were conducted.

[0292] Figure 4 shows a DOBC (Disturbance Observer) simulation model built using MATLAB / Simulink to simulate the disturbance suppression and self-vibration characteristics of the imprinting module. It is used to analyze the disturbance distribution of the system across different frequency ranges. This figure consists of three sub-figures:

[0293] Figure 4(a): Analysis of the low-frequency disturbance suppression effect based on DOBC control

[0294] This curve describes the change of the disturbance force experienced by the imprinting module over time during operation.

[0295] As shown in the figure, the amplitude of the disturbance is relatively large in the initial stage, but it decays rapidly with the intervention of the control method and tends to stabilize within a certain range. This trend indicates that the DOBC method can effectively suppress low-frequency disturbances and improve the stability and control accuracy of the system.

[0296] Figure 4(b): Trend of disturbance force over time

[0297] As can be seen from the figure, the disturbance signal exhibits certain fluctuation characteristics throughout the sampling range and contains low-frequency components. This analysis method helps to identify the main disturbance frequency components and optimize the DOBC filter parameters accordingly, thereby enhancing the control system's ability to suppress low-frequency disturbances and improving the dynamic stability of the motion table.

[0298] Figure 4(c) Distribution of disturbance force at different frequency components

[0299] This figure shows the spectral analysis of the disturbance signal using Fast Fourier Transform (FFT), illustrating the distribution of the disturbance force across different frequency ranges.

[0300] As can be seen from the figure, the disturbance force is mainly concentrated in the low frequency band (1-10Hz) and attenuates rapidly with the increase of frequency, which verifies that the low frequency disturbance force is the main source of interference in the system and compensation design is needed for the low frequency part.

[0301] Conclusion: The disturbance forces of the imprinting module are mainly concentrated in the low-frequency region; therefore, using a low-pass filter Q(s) for disturbance force compensation is effective. Furthermore, FFT spectrum analysis can provide a basis for optimizing the control strategy, making the compensation strategy more targeted and improving the system's stability and disturbance rejection capability.

[0302] Figure 5 illustrates the impact of the DOBC (Disturbance Observer) control loop on the sensitivity transfer function, used to analyze the improvement of the system's disturbance rejection capability by DOBC across different frequency ranges. This figure contains two sub-figures:

[0303] Figure 5(a) Phase effect of DOBC control loop on noise sensitivity transfer function

[0304] The curve shows the phase change of the noise sensitivity transfer function with and without DOBC control (blue curve).

[0305] In the mid-to-low frequency range (below approximately 10 Hz), the introduction of DOBC results in significant phase changes.

[0306] The DOBC loop improves the phase characteristics of the system, reduces the impact of low-frequency disturbances, and enhances system stability.

[0307] Figure 5(b) shows the effect of the DOBC control loop on the amplitude of the noise sensitivity transfer function.

[0308] This curve describes the change in the gain G of the system's noise sensitivity transfer function at different frequencies.

[0309] In the low frequency band (10 0 Up to 10 2DOBC significantly reduces the amplitude of the noise sensitivity transfer function (Hz), thus improving the system's anti-interference capability.

[0310] High frequency band (10 3 The amplitudes of the two (above Hz) are basically the same, indicating that DOBC mainly optimizes low-frequency disturbances, while having little impact on high-frequency bands.

[0311] Conclusion: DOBC control significantly reduces the sensitivity amplitude, reduces the impact of low-frequency disturbances, improves the system's anti-disturbance capability, and makes the motion table more stable.

[0312] Figure 6(a) Phase effect of DOBC control loop on process sensitivity transfer function

[0313] In the low-frequency range (around 10Hz), DOBC control slightly reduces the phase angle of the system, which can better suppress low-frequency disturbances compared to when there is no DOBC.

[0314] In the high frequency band (10 3 Above Hz, the phases of the two are basically the same, indicating that the main function of DOBC is concentrated in the low frequency range.

[0315] Figure 6(b) Effect of DOBC control loop on the amplitude of process sensitivity transfer function

[0316] Low frequency band (below 10Hz): DOBC control significantly reduces the sensitivity amplitude of the system, making the system less responsive to low-frequency disturbances and improving its anti-disturbance capability.

[0317] High frequency band (10 3 (above Hz): The curves of DOBC control and no DOBC basically overlap, indicating that DOBC mainly optimizes low-frequency disturbances, while having little impact on high frequencies.

[0318] Conclusion: DOBC control mainly optimizes the disturbance suppression capability in the low-frequency band, making the system more stable, while having less impact on the high-frequency band.

[0319] Figure 7(a) Control error changes over time

[0320] Comparison of three control methods:

[0321] Blue curve (PID control): Traditional PID control schemes have larger errors and wider fluctuation ranges;

[0322] Black curve (PID control + pressure feedforward compensation): After adding pressure feedforward compensation, the error is reduced, but there is still some fluctuation.

[0323] Red curve (PID control + DOBC control): After introducing DOBC, the error is further reduced, and the overall fluctuation amplitude is significantly smaller than the other two schemes.

[0324] Figure 7(b) Control error spectrum distribution

[0325] Low frequency band (10 0 Up to 10 2 Hz):

[0326] The error amplitude of DOBC control (red curve) decreases significantly in this region, proving that DOBC has a strong ability to suppress low-frequency disturbances.

[0327] Traditional PID control (blue curve) has a large error amplitude in the low-frequency range, indicating that it has poor immunity to low-frequency disturbances.

[0328] Mid-to-high frequency band (10 2 (above Hz):

[0329] The error spectra of each control scheme gradually converge, indicating that the optimization of DOBC mainly plays a role in suppressing low-frequency disturbances, while having little impact on high-frequency noise.

[0330] Conclusion: FFT analysis shows that DOBC control can effectively reduce low-frequency errors, reduce the impact of low-frequency disturbances on system stability, and make the control system more accurate and stable in the low-frequency range.

[0331] The foregoing has described specific embodiments of this application. Furthermore, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0332] In the description of this application, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In the embodiments of this application, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in a suitable manner in any one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this application, as well as the features of different embodiments or examples.

[0333] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features, excluding any ordering. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature and is used to distinguish it from another. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0334] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0335] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A control method for suppressing low-frequency disturbances in a motion table, characterized in that, Includes the following steps: Based on the control loop of the motion table system, the measurement data of the motion table is acquired, and the transfer function P(s) of the controlled object of the motion table system is determined. The measurement data includes the system output y and the control input u. c ; A disturbance observer is configured in the control loop to determine the disturbance force estimate; wherein the disturbance observer includes a filtering unit; The disturbance compensation amount u is determined based on the disturbance force estimate and the transfer function Q(s) of the filter unit. d ; Based on the disturbance compensation amount u d For the control input u c The final control input u is obtained through updating to compensate for low-frequency disturbances.

2. The control method according to claim 1, characterized in that, In the structure of the disturbance observer, the filtering unit is respectively set in its two parallel branches.

3. The control method according to claim 1, characterized in that, The filtering unit is close to 1 in the low-to-mid frequency range and gradually attenuates in the high-frequency range to achieve low-frequency disturbance compensation and high-frequency noise suppression.

4. The control method according to claim 1, characterized in that, The filtering unit is a second-order low-pass filter.

5. The control method according to claim 1, characterized in that, By estimating the disturbance force through spectral analysis, the main disturbance force frequency band f that needs to be suppressed can be determined. d .

6. The control method according to claim 1, characterized in that, Also includes: The design of the filter unit transfer function Q(s) is determined based on the process sensitivity transfer function. The process sensitivity transfer function is determined based on the response characteristics between the system output and the disturbance force, as well as the transfer function of the controlled object.

7. The control method according to claim 1, characterized in that, The design of the filter unit transfer function Q(s) is also based on the noise sensitivity transfer function. The noise sensitivity transfer function is determined based on the response characteristics between the system output and external measurement noise, as well as the transfer function of the controlled object.

8. The control method according to claim 1, characterized in that, Further, it includes adjusting the cutoff frequency f of the Q(s) filter based on the perturbation spectral characteristics. c Specifically, it includes the following steps: Obtain the main disturbance frequency band f d ; Set the low-frequency disturbance threshold f th ; Adjust the cutoff frequency f of the Q(s) filter c : When f d ≤f th Then set f c =1.2-1.5×f d ; When f d >f th Then maintain the cutoff frequency f c This is a preset reference value.

9. The control method according to claim 8, characterized in that, Further including based on the cutoff frequency f c The filter's transfer function Q(s) is calculated and updated, and the updated Q(s) is applied to the control loop to improve the disturbance suppression capability.

10. The control method according to claim 1, characterized in that, Further, it includes adjusting the gain G of the Q(s) filter based on spectral analysis of the disturbance force estimate, specifically including the following steps: Collect system outputs and control inputs, and calculate estimated disturbance forces. Spectral analysis was performed on the estimated disturbance forces to extract the main disturbance force frequency band f. d and corresponding amplitude G d ; Based on the disturbance amplitude G d Calculate the filter gain G; Based on the real-time amplitude G of the disturbance force d The gain G of the filter Q(s) is dynamically adjusted so that the suppression strength of the disturbance force changes adaptively with the magnitude of the disturbance force.

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