Active anti-interference method, system and device based on high-order low-pass filter

Abstract

The present invention belongs to the field of anti-interference technology, and discloses an active anti-interference method, system and device based on a high-order low-pass filter. The method includes obtaining system disturbances according to a state space model of a motion control system, extracting matching disturbances in the system disturbances, and decomposing the matching disturbances into differentiable parts and bounded parts; using the differentiable parts as extended states, performing an expansion operation on the system state using the extended states, and reconstructing the state space model based on the expanded system state to obtain an extended state space model; according to the extended state space model of the motion control system, establishing an extended state observer based on a high-order low-pass filter, including a high-order low-pass filter, an extended state observer and an output feedback controller. The present invention is used for high-performance disturbance suppression and noise suppression of motion control systems to improve the control accuracy of motion control systems.

Description

Technical Field

[0001] The present invention belongs to the technical field of anti-interference, and in particular relates to an active anti-interference method, system and device based on a high-order low-pass filter. Background Art

[0002] In the processing of automated equipment such as CNC machine tools, industrial robots, cutting machines and engraving machines, the processing accuracy is often affected by changes in load inertia, tool wear, uncertainty in external forces and uncertainty in the model itself. As one of the core skills in the field of mechanical processing, anti-interference technology is particularly important for improving the accuracy of control systems. At the same time, noise in the measurement process will also have an adverse effect on the processing effect. Excessive noise levels can significantly reduce the overall performance of the system. Therefore, exploring effective methods to simultaneously suppress external disturbances and reduce the impact of noise on the system has become a key challenge to improve processing accuracy and optimize system performance, which is of extremely important practical value for meeting the requirements of high-precision manufacturing.

[0003] Disturbance suppression is one of the widely studied issues in automation equipment control systems. The main methods used for this purpose include sliding mode control, model predictive control, robust control, and disturbance / uncertainty estimation and attenuation (DUEA). The DUEA method uses an observer to estimate disturbances and then compensates them in the control input channel to effectively mitigate the impact of disturbances on system performance. Unlike other methods with only one degree of freedom, the DUEA method adds additional degrees of freedom, making the controller design more flexible. So far, several DUEA methods and their variants have emerged, including disturbance observers, extended state observers (ESO), unknown input observers, and equivalent input disturbances. As a key component of active disturbance rejection control, the ESO method treats system uncertainty as a total disturbance, also known as an extended state. By estimating the extended state of the system, an output feedback control with disturbance compensation is designed.

[0004] However, actual systems often have measurement noise, which can lead to measurement errors, which directly affect the accuracy and performance of the control system, and also affect the control system based on the observer method. Traditional high-gain observers are robust to system uncertainties. Higher observer gains can improve the accuracy of disturbance suppression, but they also amplify noise. The trade-off between disturbance suppression and noise attenuation becomes a key challenge in the design. Summary of the invention

[0005] The object of the present invention is to provide an active anti-interference method, system and device based on a high-order low-pass filter for high-performance disturbance suppression and noise suppression of a motion control system to improve the control accuracy of the motion control system.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] In a first aspect, the present invention provides an active anti-interference method based on a high-order low-pass filter, which is applied to a motion control system. The active anti-interference method based on a high-order low-pass filter comprises:

[0008] Obtain system disturbances according to the state space model of the motion control system, extract matching disturbances from the system disturbances, and decompose the matching disturbances into differentiable parts and bounded parts;

[0009] The differentiable part is used as an expanded state, the system state is expanded using the expanded state, and the state space model is reconstructed based on the expanded system state to obtain an expanded state space model;

[0010] According to the extended state space model of the motion control system, an extended state observer based on a high-order low-pass filter is established, including a high-order low-pass filter, an extended state observer and an output feedback controller;

[0011] Given a reference input of a motion control system, the internal model state is obtained through the internal model system. Using an extended state observer based on a high-order low-pass filter, the control input of the extended state space model is obtained according to the internal model state, and the output of the motion control system is obtained from the extended state space model.

[0012] Preferably, the step of acquiring the system disturbance according to the state space model of the motion control system and extracting the matching disturbance in the system disturbance comprises:

[0013] Establish the state space model of the motion control system, the formula is as follows:

[0014] ;

[0015] In the formula, for The state of the motion control system at all times, for The derivative of for The control input of the motion control system at all times, for External disturbance at any time, for The output of the motion control system at all times, for The measurement noise of the motion control system at all times, is the system matrix, is the input matrix, is the output matrix, is the disturbance input matrix, the specific form is as follows:

[0016] ;

[0017] In the formula, , , As a constant, take , , for , , The nominal value of , the state space model of the motion control system is rewritten as follows:

[0018] ;

[0019] In the formula, , is the nominal value of the system matrix, is the nominal value of the input matrix;

[0020] Pick The system disturbance at time ,in for The mismatch disturbance at the moment, for Matching disturbance at the moment, setting mismatching disturbance , then we get the matching disturbance , express The location of the control system at all times, express Always run the system to control the speed.

[0021] Preferably, decomposing the matching disturbance into a differentiable part and a bounded part comprises:

[0022] ;

[0023] In the formula, for The matching disturbance at time, To match the disturbance The approximation of represents the differentiable part of the matching perturbation, To match the disturbance The remaining term of , represents the bounded part of the matching perturbation.

[0024] Preferably, the method of using the differentiable part as an expanded state, using the expanded state to perform an expansion operation on the system state, and reconstructing the state space model based on the expanded system state to obtain the expanded state space model includes:

[0025] Will Moments match the differentiable part of the disturbance As The expansion state at time , then the system state expands to , express The system state after time expansion, express The state of the motion control system at all times The transpose of Represents the system state after expansion The location of the motion control system, Represents the system state after expansion The speed of the motion control system;

[0026] The expanded state space model of the motion control system is obtained as follows:

[0027] ;

[0028] In the formula, for The derivative of for The control input of the motion control system at all times, for The output of the motion control system at all times, for The measurement noise of the motion control system at all times, is the system matrix in the extended state space model, is the input matrix in the extended state space model, is the output matrix in the extended state space model, It is an intermediate parameter, and its specific form is as follows:

[0029] ;

[0030] In the formula, is a constant in the state space model The nominal value of is a constant in the state space model The nominal value of is a constant in the state space model The nominal value of represents the bounded part of the matching perturbation, represents the derivative of the differentiable part of the matching perturbation.

[0031] Preferably, the high-order low-pass filter is expressed as follows:

[0032] ;

[0033] In the formula, for Time filter The state of the stage, , is the filter order, for The derivative of for Time filter The state of the stage, for The derivative of is the bandwidth of the extended state observer, is the gain of the high-order low-pass filter, for The output of the motion control system at all times, is estimated by the extended state observer value, express The position of the motion control system in the system state after time expansion, is the output of a high-order low-pass filter.

[0034] Preferably, the extended state observer is expressed as follows:

[0035] ;

[0036] In the formula, is the estimated value of the system state after expansion, is the estimated value of the position of the motion control system, is the estimated value of the velocity of the motion control system, is the estimated value of the expansion state, is the gain of the extended state observer, which is designed as follows:

[0037] ;

[0038] In the formula, the parameters , is the bandwidth of the highly extended state observer, is a constant matrix and .

[0039] Preferably, the output feedback controller is expressed as follows:

[0040] Using the internal model principle, the output feedback controller is designed as follows:

[0041] ;

[0042] In the formula, for Output the output of the feedback controller at all times, that is, The control input of the motion control system at all times, represents the intermediate parameter, are feedback gains, Inner mold state:

[0043] ;

[0044] In the formula, for The derivative of and are the internal model system matrix and the input matrix respectively, Represents the reference input of the motion control system.

[0045] In a second aspect, the present invention provides an active anti-interference system based on a high-order low-pass filter, comprising a disturbance decomposition module, a state expansion module, an observer design module and an output module, wherein:

[0046] The disturbance decomposition module is configured to: obtain system disturbance according to the state space model of the motion control system, extract matching disturbance in the system disturbance, and decompose the matching disturbance into a differentiable part and a bounded part;

[0047] The state expansion module is configured to: use the differentiable part as an expanded state, use the expanded state to expand the system state, and reconstruct the state space model based on the expanded system state to obtain the expanded state space model;

[0048] The observer design module is configured to: establish an extended state observer based on a high-order low-pass filter according to an extended state space model of the motion control system, including a high-order low-pass filter, an extended state observer and an output feedback controller;

[0049] The output module is configured as follows: given a reference input of the motion control system, the internal model state is obtained through the internal model system, the control input of the extended state space model is obtained according to the internal model state using an extended state observer based on a high-order low-pass filter, and the output of the motion control system is obtained from the extended state space model.

[0050] In a third aspect, the present invention provides an active anti-interference device based on a high-order low-pass filter, comprising a processor and a memory storing a plurality of computer instructions, wherein the computer instructions, when executed by the processor, implement the steps of the active anti-interference method based on the high-order low-pass filter.

[0051] The present invention provides an active anti-interference method, system and device based on a high-order low-pass filter, which decomposes the disturbance into a differentiable part and a bounded part. Compared with the ESO design that directly assumes that all disturbances are differentiable, it is more reasonable, more in line with the actual situation, and can better handle disturbances. By inserting a high-order low-pass filter between the system output and the observer input, the measurement noise is suppressed and the interference suppression performance is improved. The filter is usually added after the output of the observer. The design of adding a high-order low-pass filter between the system output and the observer input can bring about a significant improvement in performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 A control block diagram of an active anti-interference method based on a high-order low-pass filter of the present invention;

[0053] Figure 2 This is a comparison diagram of the output of the magnetic suspension system under different control algorithms in the experiment of the present invention;

[0054] Figure 3 A comparison diagram of the position estimation of the magnetic suspension system under different control algorithms in the experiment of the present invention;

[0055] Figure 4 This is a comparison diagram of the control input of the magnetic suspension system under different control algorithms in the experiment of the present invention;

[0056] Figure 5 This is a comparison chart of disturbance estimation of the magnetic levitation system under different control algorithms in the experiment of the present invention. DETAILED DESCRIPTION

[0057] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] It should be noted that when a component is referred to as being “connected” to another component, it may be directly connected to the other component or there may be a central component; when a component is referred to as being “fixed” to another component, it may be directly fixed to the other component or there may be a central component.

[0059] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0060] In view of the uncertainty, disturbance and measurement noise problems existing in the motion control system of automation equipment, this embodiment designs an active anti-interference method based on a high-order low-pass filter (low-pass filter-based extendedstate observer, LPFESO), which is of great significance for improving mechanical processing accuracy.

[0061] Example 1: Figure 1 As shown, an active anti-interference method based on a high-order low-pass filter (LPF) in this embodiment is applied to a motion control system (MCS), and includes the following steps:

[0062] Step 1: Obtain the system disturbance according to the state space model of the motion control system, extract the matching disturbance in the system disturbance, and decompose the matching disturbance into a differentiable part and a bounded part.

[0063] Establish the state space model of the motion control system, the formula is as follows:

[0064] ;

[0065] In the formula, for The state of the motion control system at all times, for The derivative of for The control input of the motion control system at all times, for External disturbance at any time, for The output of the motion control system at all times, for The measurement noise of the motion control system at all times, is the system matrix, is the input matrix, is the output matrix, is the disturbance input matrix, the specific form is as follows:

[0066] ;

[0067] In the formula, , , is a constant. Due to the limitation of measurement conditions, it is impossible to obtain , , The exact value of can only be obtained from its nominal value, so , , for , , The nominal value of , the state space model of the motion control system is rewritten as follows:

[0068] ;

[0069] In the formula, , is the nominal value of the system matrix, is the nominal value of the input matrix.

[0070] Pick The system disturbance at time ,in for The mismatch disturbance at the moment, for Matching disturbance at the moment, setting mismatching disturbance , then we get the matching disturbance , so the total disturbance Including unmodeled dynamics, model uncertainties, and external disturbances, express The location of the control system at all times, express Always run the system to control the speed.

[0071] Decompose the matching perturbation into differentiable and bounded parts, including:

[0072] ;

[0073] In the formula, for The matching disturbance at time, To match the disturbance The approximation of represents the differentiable part of the matching perturbation, To match the disturbance The remaining term of represents the bounded part of the matching disturbance. This embodiment decomposes the disturbance into a differentiable part and a bounded part, which is more in line with the actual situation, handles the disturbance more reasonably, and is conducive to improving disturbance suppression.

[0074] Step 2: Use the differentiable part as the expanded state, use the expanded state to expand the system state, and reconstruct the state space model based on the expanded system state to obtain the expanded state space model.

[0075] Will Moments match the differentiable part of the disturbance As The expansion state at time , then the system state expands to , express The system state after time expansion, express The state of the motion control system at all times The transpose of Represents the system state after expansion The location of the motion control system, Represents the system state after expansion The speed of the motion control system. Compared with the state-space model Equivalent, the two have the same numerical value. In order to unify the expression of the system state after expansion, the symbol transformation is performed; similarly, Compared with the state-space model equivalence.

[0076] The expanded state space model of the motion control system is obtained as follows:

[0077] ;

[0078] In the formula, for The derivative of for The control input of the motion control system at all times, for The output of the motion control system at all times, for The measurement noise of the motion control system at all times, is the system matrix in the extended state space model, is the input matrix in the extended state space model, is the output matrix in the extended state space model, It is an intermediate parameter, and its specific form is as follows:

[0079] ;

[0080] In the formula, is a constant in the state space model The nominal value of is a constant in the state space model The nominal value of is a constant in the state space model The nominal value of represents the bounded part of the matching perturbation, represents the derivative of the differentiable part of the matching perturbation.

[0081] Step 3: According to the extended state space model of the motion control system, an extended state observer based on a high-order low-pass filter is established, including a high-order low-pass filter, an extended state observer and an output feedback controller.

[0082] Step 3.1, design a high-order low-pass filter, expressed as follows:

[0083] ;

[0084] In the formula, for Time filter The state of the stage, , is the filter order, for The derivative of for Time filter The state of the stage, for The derivative of is the bandwidth of the extended state observer, is the gain of the high-order low-pass filter, for The output of the motion control system at all times, is estimated by the extended state observer value, express The position of the motion control system in the system state after time expansion, is the output of the high-order low-pass filter. In this embodiment, a high-order low-pass filter is introduced between the system output and the observer, which can better suppress the measurement noise and improve the system performance.

[0085] Step 3.2: Based on the output of the high-order low-pass filter, design the extended state observer, which is expressed as follows:

[0086] ;

[0087] In the formula, is the estimated value of the system state after expansion, is the estimated value of the position of the motion control system, is the estimated value of the velocity of the motion control system, is the estimated value of the expansion state, is the gain of the extended state observer, and the gain parameter is designed by bandwidth parameterization method as follows:

[0088] ;

[0089] In the formula, the parameters , is the bandwidth of the highly extended state observer, is a constant matrix and .

[0090] Step 3.3, design the output feedback controller, expressed as follows:

[0091] Using the internal model (IM) principle, an output feedback control (FC) with disturbance compensation is designed, as follows:

[0092] ;

[0093] In the formula, for Output the output of the feedback controller at all times, that is, The control input of the motion control system at all times, represents the intermediate parameter, are feedback gains, Inner mold state:

[0094] ;

[0095] In the formula, for The derivative of and are the internal model system matrix and the input matrix respectively, Represents the reference input of the motion control system.

[0096] Step 4: Given Reference input for the moment motion control system , the internal model state is obtained through the internal model system , using an extended state observer based on a high-order low-pass filter, the control input of the extended state space model is obtained according to the internal model state , and the output of the motion control system is obtained by the expanded state space model .

[0097] In order to verify the superiority of the LPFESO proposed in the method of the present invention in terms of noise suppression and interference suppression, an experimental comparison was carried out on a magnetic levitation system (MLS) with ESO, the cascaded ESO (CaESO) and the parallel ESO (PESO). At the same time, the experimental platform performance of the LPFESO method proposed in the present invention under different orders of LPF was compared, namely, The experimental results are as follows Figure 2-Figure 5 shown.

[0098] Figure 2 The output trajectory of the system is depicted in the figure. The vertical axis is the output of the motion control system. , in millimeters (mm), and the horizontal axis is time (Time), in seconds (s). It can be seen that CaESO, PESO, and LPFESO show smoother trajectories during the disturbance mutation period, while ESO has the largest jitter change. It is worth noting that the noise and interference suppression performance of CaESO and PESO is is better than LPFESO, but as The suppression performance of LPFESO is improved with the increase of . This observation emphasizes the advantage of LPFESO in noise suppression, as well as its interference attenuation capability, demonstrating its robustness under different conditions. Moreover, the effectiveness of noise suppression increases further with the increase of filter order, which emphasizes the key role of filter order in improving the system's immunity to measurement noise.

[0099] Figure 3 The position estimation of the motion control system provides further explanation. The ordinate in the figure is the estimated value of the position of the motion control system , in millimeters (mm), and the horizontal axis is time (Time), in seconds (s). The experimental results show that LPFESO, as a high-gain observer with high bandwidth, still has good noise suppression capability even if the larger observer bandwidth amplifies the measurement noise. It is worth noting that increasing the filter order not only enhances the noise suppression capability, but also improves the accuracy of system state and disturbance estimation, thereby improving the overall system performance.

[0100] Figure 4 and Figure 5 The control input and disturbance estimates are shown. Figure 4 The vertical axis is the control input of the motion control system , with the unit of V, and the horizontal axis is time Time, with the unit of seconds s. The figure shows that although the input voltage fluctuation of LPFESO is more obvious than other methods, it can effectively suppress noise, thereby significantly improving the stability and accuracy of the system in complex environments. Figure 5 The vertical axis is the estimated value of the expansion state , the horizontal axis is time Time, the unit is seconds s. Figure 5 It can be observed that the transformation of the perturbation estimate follows a similar trend as the perturbation itself.

[0101] Embodiment 2: This embodiment provides an active anti-interference system based on a high-order low-pass filter, including a disturbance decomposition module, a state expansion module, an observer design module and an output module, wherein:

[0102] The disturbance decomposition module is configured to: obtain the system disturbance according to the state space model of the motion control system, extract the matching disturbance in the system disturbance, and decompose the matching disturbance into a differentiable part and a bounded part.

[0103] The state expansion module is configured to: use the differentiable part as the expanded state, use the expanded state to expand the system state, and reconstruct the state space model based on the expanded system state to obtain the expanded state space model.

[0104] The observer design module is configured to: establish an extended state observer based on a high-order low-pass filter according to an extended state space model of the motion control system, including a high-order low-pass filter, an extended state observer and an output feedback controller.

[0105] The output module is configured as follows: given a reference input of the motion control system, the internal model state is obtained through the internal model system, the control input of the extended state space model is obtained according to the internal model state using an extended state observer based on a high-order low-pass filter, and the output of the motion control system is obtained from the extended state space model.

[0106] For the specific definition of the active anti-interference system based on the high-order low-pass filter, please refer to the definition of the active anti-interference method based on the high-order low-pass filter in Example 1, which will not be repeated here.

[0107] Embodiment 3: This embodiment provides an active anti-interference device based on a high-order low-pass filter, comprising a processor and a memory storing a plurality of computer instructions, wherein the computer instructions, when executed by the processor, implement the steps of the active anti-interference method based on the high-order low-pass filter.

[0108] For the specific definition of the active anti-interference device based on the high-order low-pass filter, please refer to the definition of the active anti-interference method based on the high-order low-pass filter above, which will not be repeated here.

[0109] The memory and the processor are electrically connected directly or indirectly to achieve data transmission or interaction. For example, these elements can be electrically connected to each other through one or more communication buses or signal lines. The memory stores a computer program that can be run on the processor, and the processor implements the method of the present invention by running the computer program stored in the memory.

[0110] The memory may be, but is not limited to, a random access memory (RAM), a read only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable read-only memory (EEPROM), etc. The memory is used to store a program, and the processor executes the program after receiving an execution instruction.

[0111] The processor may be an integrated circuit chip with data processing capabilities. The above-mentioned processor may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc. The methods, steps and logic block diagrams disclosed in the embodiments of the present invention may be implemented or executed. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0112] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0113] The above-mentioned embodiments only express several implementation modes of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. An active anti-interference method based on a high-order low-pass filter, applied to a motion control system, characterized in that: The active anti-interference method based on the high-order low-pass filter comprises: Obtain system disturbances according to the state space model of the motion control system, extract matching disturbances from the system disturbances, and decompose the matching disturbances into differentiable parts and bounded parts; The differentiable part is used as an expanded state, the system state is expanded using the expanded state, and the state space model is reconstructed based on the expanded system state to obtain an expanded state space model; According to the extended state space model of the motion control system, an extended state observer based on a high-order low-pass filter is established, including a high-order low-pass filter, an extended state observer and an output feedback controller; Given a reference input of a motion control system, an internal model state is obtained through an internal model system, and an extended state observer based on a high-order low-pass filter is used to obtain a control input of an extended state space model according to the internal model state, and the output of the motion control system is obtained from the extended state space model; The step of decomposing the matching disturbance into a differentiable part and a bounded part includes: ； In the formula, for The matching disturbance at time, To match the disturbance The approximation of , which represents the differentiable part of the matching perturbation, To match the disturbance The remaining term of represents the bounded part of the matching perturbation; Wherein, the high-order low-pass filter is expressed as follows: ； In the formula, for Time filter The state of the stage, , is the filter order, for The derivative of for Time filter The state of the stage, for The derivative of is the bandwidth of the extended state observer, is the gain of the high-order low-pass filter, for The output of the motion control system at all times, is estimated by the extended state observer value, express The position of the motion control system in the system state after the time expansion, is the output of the high-order low-pass filter; The extended state observer is expressed as follows: ； In the formula, is the estimated value of the system state after expansion, is the estimated value of the position of the motion control system, is the estimated value of the velocity of the motion control system, is the estimated value of the expansion state, is the gain of the extended state observer, which is designed as follows: ； In the formula, the parameters , is the bandwidth of the highly extended state observer, is a constant matrix and ; Wherein, the output feedback controller is expressed as follows: Using the internal model principle, the output feedback controller is designed as follows: ； In the formula, for Output the output of the feedback controller at all times, that is, The control input of the motion control system at all times, represents the intermediate parameter, are feedback gains, Inner mold state: ； In the formula, for The derivative of and are the internal model system matrix and the input matrix respectively, Represents the reference input of the motion control system.

2. The active anti-interference method based on a high-order low-pass filter according to claim 1 is characterized in that: The method of acquiring the system disturbance according to the state space model of the motion control system and extracting the matching disturbance in the system disturbance comprises: Establish the state space model of the motion control system, the formula is as follows: ； In the formula, for The state of the motion control system at all times, for The derivative of for The control input of the motion control system at all times, for External disturbance at any time, for The output of the motion control system at all times, for The measurement noise of the motion control system at all times, is the system matrix, is the input matrix, is the output matrix, is the disturbance input matrix, the specific form is as follows: ； In the formula, , , As a constant, take , , for , , The nominal value of , the state space model of the motion control system is rewritten as follows: ； In the formula, , is the nominal value of the system matrix, is the nominal value of the input matrix; Pick The system disturbance at time ,in for The mismatch disturbance at the moment, for Matching disturbance at the moment, setting mismatching disturbance , then we get the matching disturbance , express The location of the control system at all times, express Always run the system to control the speed.

3. The active anti-interference method based on a high-order low-pass filter according to claim 1 is characterized in that: The method uses the differentiable part as an expanded state, uses the expanded state to perform an expansion operation on the system state, and reconstructs the state space model based on the expanded system state to obtain the expanded state space model, including: Will Moments match the differentiable part of the disturbance As The expansion state at time , then the system state expands to , express The system state after time expansion, express The state of the motion control system at all times The transpose of Represents the system state after expansion The location of the motion control system, Represents the system state after expansion The speed of the motion control system; The expanded state space model of the motion control system is obtained as follows: ； In the formula, for The derivative of for The control input of the motion control system at all times, for The output of the motion control system at all times, for The measurement noise of the motion control system at all times, is the system matrix in the extended state space model, is the input matrix in the extended state space model, is the output matrix in the extended state space model, It is an intermediate parameter, and its specific form is as follows: ； In the formula, is a constant in the state space model The nominal value of is a constant in the state space model The nominal value of is a constant in the state space model The nominal value of represents the bounded part of the matching perturbation, represents the derivative of the differentiable part of the matching perturbation.

4. An active anti-interference system based on a high-order low-pass filter, characterized in that: The active anti-interference system based on high-order low-pass filter includes a disturbance decomposition module, a state expansion module, an observer design module and an output module, wherein: The disturbance decomposition module is configured to: obtain system disturbance according to the state space model of the motion control system, extract matching disturbance in the system disturbance, and decompose the matching disturbance into a differentiable part and a bounded part; The state expansion module is configured to: use the differentiable part as an expanded state, use the expanded state to expand the system state, and reconstruct the state space model based on the expanded system state to obtain the expanded state space model; The observer design module is configured to: establish an extended state observer based on a high-order low-pass filter according to an extended state space model of the motion control system, including a high-order low-pass filter, an extended state observer and an output feedback controller; The output module is configured to: given a reference input of the motion control system, obtain an internal model state through the internal model system, use an extended state observer based on a high-order low-pass filter to obtain a control input of an extended state space model according to the internal model state, and obtain an output of the motion control system from the extended state space model; The step of decomposing the matching disturbance into a differentiable part and a bounded part includes: ； In the formula, for The matching disturbance at time, To match the disturbance The approximation of , which represents the differentiable part of the matching perturbation, To match the disturbance The remaining term of represents the bounded part of the matching perturbation; Wherein, the high-order low-pass filter is expressed as follows: ； In the formula, for Time filter The state of the stage, , is the filter order, for The derivative of for Time filter The state of the stage, for The derivative of is the bandwidth of the extended state observer, is the gain of the high-order low-pass filter, for The output of the motion control system at all times, is estimated by the extended state observer value, express The position of the motion control system in the system state after time expansion, is the output of the high-order low-pass filter; Wherein, the extended state observer is expressed as follows: ； In the formula, is the estimated value of the system state after expansion, is the estimated value of the position of the motion control system, is the estimated value of the velocity of the motion control system, is the estimated value of the expansion state, is the gain of the extended state observer, which is designed as follows: ； In the formula, the parameters , is the bandwidth of the highly extended state observer, is a constant matrix and ; Wherein, the output feedback controller is expressed as follows: Using the internal model principle, the output feedback controller is designed as follows: ； In the formula, for Output the output of the feedback controller at all times, that is, The control input of the motion control system at all times, represents the intermediate parameter, are feedback gains, Inner mold state: ； In the formula, for The derivative of and are the internal model system matrix and the input matrix respectively, Represents the reference input of the motion control system.

5. An active anti-interference device based on a high-order low-pass filter, comprising a processor and a memory storing a plurality of computer instructions, characterized in that: When the computer instructions are executed by the processor, the steps of the active anti-interference method based on the high-order low-pass filter described in any one of claims 1 to 3 are implemented.

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