Cutting force compensation processing method of fast tool servo system based on adaptive control

Abstract

The present invention relates to a cutting force compensation processing method of a fast tool servo system based on adaptive control, belonging to the technical field of ultra-precision processing. The method first establishes an electromechanical model for the fast tool servo system, establishes and sets an adaptive robust control algorithm based on the electromechanical model, then performs a plane turning experiment on the cuttable material to fit the relationship between the cutting force and the cutting area in the turning process, then calculates the ideal cutting area of ​​each cut in the cutting process, and calculates the cutting force, and writes the cutting force into the adaptive robust control algorithm as a new feedforward signal to obtain an adaptive robust control algorithm for feedforward compensation, and finally drives the fast tool to cut using the adaptive robust control algorithm for cutting force feedforward compensation. The method can compensate for the external disturbance of the cutting force in the cutting process, can effectively reduce the surface shape error of the processed surface, and improve the surface shape accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of ultra-precision machining, and in particular relates to a cutting force compensation machining method of a fast tool servo system based on adaptive control. Background Art

[0002] Ultra-precision turning is widely used in the fields of optics, aerospace and semiconductor manufacturing, and is an important technical means to manufacture ultra-high precision parts. Single-point diamond turning uses ultra-precision turning machines with nano-level positioning to drive diamond tools to manufacture workpieces with specific functional surfaces through pre-planned cutting trajectories. In order to improve the processing efficiency and quality of workpieces with complex surface microstructures, the fast tool servo system (referred to as the fast tool servo system) came into being. The fast tool servo system uses a high-frequency response servo mechanism to drive a single-point diamond tool, and cooperates with the machine tool axis movement for ultra-precision cutting. It is an important processing device for processing components with microstructures.

[0003] According to the different driving modes, the fast tool servo system can be mainly divided into piezoelectric ceramic drive, magnetostrictive drive, Maxwell force drive and Lorentz magnetic drive. Compared with the first three driving modes, the Lorentz magnetic drive fast tool servo system has a millimeter-level working stroke, which can meet the processing of large curvature free surfaces and complex microstructure workpieces. Therefore, the Lorentz magnetic drive fast tool servo system has been studied by more and more scholars.

[0004] The Lorentz magnetically driven fast tool servo system is mainly composed of a driving mechanism (voice coil motor), a guiding mechanism (air floating guide rail, flexible hinge) and an end actuator (diamond tool). The mechanical stiffness in the driving direction is relatively low, and the position of the diamond during the cutting process is mainly ensured by the position servo control of the algorithm. However, in the cutting process, the cutting force is a large external disturbance to the fast tool servo system. Some control algorithms with poor robustness will have large following errors under complex cutting conditions with high speed, high frequency and large external disturbances. The diamond tool cannot be processed according to the predetermined trajectory, resulting in poor surface morphology and roughness of the workpiece being processed, and the precision requirements of the workpiece cannot be met. Summary of the invention

[0005] The purpose of the present invention is to provide a cutting force compensation processing method for a fast tool servo system based on adaptive control, so as to solve the problems of poor robustness of the existing fast tool servo system control algorithm, poor surface morphology and roughness of the processed workpiece caused by errors under high speed, high frequency and large external disturbances.

[0006] In order to achieve the above object, the technical solution of the present invention is as follows:

[0007] The present invention relates to a cutting force compensation processing method of a fast tool servo system based on adaptive control, which comprises the following steps:

[0008] S1. Establish an electromechanical model for the fast tool servo system;

[0009] S2. Establish and set an adaptive robust control algorithm based on the electromechanical model;

[0010] S3. Use the fast tool servo system to conduct plane turning experiments on machinable materials and fit the relationship between cutting force and cutting area during turning;

[0011] S4. Calculate the ideal cutting area of ​​each cut in the cutting process according to the feed rate, tool radius and the required cutting pattern, and calculate the cutting force according to the fitted relationship between the cutting force and the cutting area;

[0012] S5. The cutting force is taken as a new feedforward signal and written into the adaptive robust control algorithm to obtain an adaptive robust control algorithm with feedforward compensation;

[0013] S6. Adaptive robust control algorithm with cutting force feedforward compensation is used to drive fast tool cutting.

[0014] Preferably, the electromechanical model in S1 is expressed as:

[0015] (1),

[0016] (2),

[0017] (3),

[0018] in, m , c f and k f They represent the mass, damping coefficient and elastic coefficient of the moving part of the fast tool servo system respectively. x , and They represent the displacement, first-order derivative and second-order derivative of the fast tool servo system respectively. F v Represents the output thrust of the voice coil motor, F dis Indicates the external disturbance to the fast tool servo system. T l represents the force constant of the voice coil motor, i and i’ denote the current driving the voice coil motor and the derivative of the current, respectively, k u represents the magnification of the linear actuator, u Indicates the control amount, tRepresents the time constant of the linear actuator.

[0019] Preferably, the electromechanical model is also transformed in the following manner:

[0020] S1.1. Perform Laplace transform on the electromechanical model. The electromechanical model after Laplace transform is expressed as:

[0021] (4),

[0022] (5),

[0023] (6),

[0024] in, s is a complex frequency variable, X ( s ) is the frequency domain function of displacement, F v ( s ) is the frequency domain function of the output thrust of the voice coil motor, F dis ( s ) is the frequency domain function of the external disturbance, I ( s ) is the frequency domain function of the current, U ( s ) is the frequency domain function of voltage;

[0025] S1.2. Arrange the expression of the electromechanical model after Laplace transformation and obtain:

[0026] (7),

[0027] S1.3. Perform an inverse Laplace transform on the rearranged expression and obtain:

[0028] (8),

[0029] in, Represents the third-order derivative of the displacement of the fast tool servo system, It represents the first-order derivative of the external disturbance to the fast tool servo system;

[0030] Since the first-order derivative of the external disturbance on the fast tool servo system is Much smaller than the external disturbance of the fast tool servo system F dis , ignoring the first-order derivative of the external disturbance on the fast tool servo system The final electromechanical model expression is obtained:

[0031] (9).

[0032] Preferably, the specific steps of establishing the adaptive robust control algorithm in S2 are:

[0033] S2.1. Rewrite the final electromechanical model expression into a state space form equation, which is expressed as:

[0034] (10),

[0035] in, x 1. x 2 and x 3 represent displacement, velocity and acceleration respectively, , and Represent the first-order derivatives of displacement, velocity and acceleration respectively, and the matrix of unknown parameters is defined as i , i =[ i 1, i 2, i 3. i 4. i 5] T , i 1. i 2. i 3. i 4 and i 5 indicates unknown parameters, and , , , , i 5 for The nominal value of is the time-varying component of uncertainty in the normalized concentration, ;

[0036] And, set the parameters as:

[0037] (11),

[0038] (12),

[0039] in, i min and i max represent the upper and lower bounds of the unknown parameters, respectively. d represents the actual disturbance, Ω θ and Ω d Represents position variables i The value range and actual disturbance d The value range of d d Represents the time-varying component Upper bound of size;

[0040] S2.2. Design a continuous mapping parameter adaptation law, which is expressed as:

[0041] (13),

[0042] in, represents the estimated value of parameter θ, represents the first derivative of the estimate, is the adaptive rate diagonal matrix, and >0,τ a represents the adaptive function, represents a discontinuous mapping function, which is expressed as:

[0043] ,

[0044] and is given by the following definition:

[0045] (14),

[0046] in, represents the discontinuous mapping function of the jth parameter, represents the estimated value of the jth parameter.

[0047] Preferably, the specific steps of setting the adaptive robust control algorithm in S2 are:

[0048] S2.3. Define the ideal tracking trajectory of the fast tool servo system and the three tracking errors of the ideal tracking trajectory. The three tracking errors are expressed as:

[0049] (15),

[0050] in, e 1. e 2 and e 3 represent the first tracking error, the second tracking error and the third tracking error respectively, and Represent the first-order derivatives of the first tracking error and the second tracking error, respectively. , and represent the ideal tracking trajectory, the first-order derivative and the second-order derivative of the ideal tracking trajectory respectively;

[0051] S2.4. Define a synovial variable p , the expression of the synovial variable p is:

[0052] (16),

[0053] in, k 1 and k 2 are any non-negative numbers, x 3eq is the acceleration x 3, which is defined as:

[0054] ;

[0055] S2.5. For a synovial variable p Taking the derivative and plugging the equation into the state-space form, we get:

[0056] (17),

[0057] in is the first-order derivative of the synovial-like variable, express x 3eq The first derivative of f represents the regression vector of the system, and ;

[0058] S2.6. According to the ideal feedforward compensation-robust adaptive control algorithm, the required control quantity u is generated, which is expressed as:

[0059] (18),

[0060] (19),

[0061] (20),

[0062] (twenty one),

[0063] in, u a is the online adaptive model feedforward compensation term, u s1 is the linear stabilizing feedback term, u s2 is the nonlinear stabilizing feedback term, f d is the regression vector calculated from the ideal signal, and , used to reduce noise interference, k s1 represents the feedback gain parameter, e is a limiting parameter used to limit the upper bound of the steady-state error. h M It is the maximum value of the system smoothing function and is used to ensure the robustness of the system.

[0064] Preferably, the S5 writes the cutting force into the adaptive robust control algorithm as a new feedforward signal, that is, the cutting force is added to the final electromechanical model as a newly added part of the external disturbance, the unknown parameters are redefined, the regression vector formula of the system is updated and the regression vector is recalculated, and the unknown parameters and regression vector in the ideal feedforward compensation-robust adaptive control algorithm are replaced by the redefined unknown parameters and the recalculated regression vector to obtain an adaptive robust control algorithm for feedforward compensation.

[0065] Preferably, after the cutting force is added as a newly added part of the external disturbance to the final electromechanical model in S5, the expression of the electromechanical model is:

[0066] (twenty two),

[0067] in, F cut is the cutting force.

[0068] Preferably, the unknown parameters redefined in S5 are:

[0069] i n =[ i 1, i 2, i 3. i 4. i 5. i 6] T ,

[0070] in, i n is the matrix of the redefined unknown parameters, i 6 is a newly added unknown parameter, and .

[0071] Preferably, the regression vector formula of the system updated in S5 is:

[0072] ,

[0073] in, f n represents the regression vector of the system, F cut is the cutting force;

[0074] The recalculated regression vector is:

[0075] ,

[0076] in, f dn represents the calculated regression vector, Fcutd The ideal cutting force obtained by calculation.

[0077] Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0078] The present invention relates to a cutting force compensation processing method of a fast tool servo system based on adaptive control. First, an electromechanical model is established for the fast tool servo system, and then an adaptive robust control algorithm is established and set based on the electromechanical model. Then, a plane turning experiment is performed on the cuttable material to fit the relationship between the cutting force and the cutting area in the turning process, and then the ideal cutting area of ​​each cut in the cutting process is calculated, and the cutting force is calculated according to the fitted relationship between the cutting force and the cutting area. The cutting force is used as a new feedforward signal and written into the adaptive robust control algorithm to obtain an adaptive robust control algorithm for feedforward compensation, and finally the adaptive robust control algorithm for cutting force feedforward compensation is used to drive the fast tool for cutting. The external disturbance of the cutting force in the cutting process can be compensated, and the surface shape error of the processed surface can be effectively reduced, and the error is reduced by about 40%, thereby improving the surface shape accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a flow chart of the cutting force compensation processing method of the fast tool servo system based on adaptive control;

[0080] Figure 2 It is a calibration fitting diagram of cutting force and cutting area in the present invention;

[0081] Figure 3 It is a flow chart of the adaptive robust control algorithm of the cutting force feedforward compensation of the present invention;

[0082] Figure 4 Schematic diagram of the internal structure of the fast tool servo system used in the present invention;

[0083] Figure 5 Compensate cutting results for no cutting force;

[0084] Figure 6 To compensate the cutting results with cutting force. DETAILED DESCRIPTION

[0085] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with examples. The following examples are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0086] See attached Figure 1 The present invention relates to a cutting force compensation processing method of a fast tool servo system based on adaptive control, which comprises the following steps:

[0087] S1. Establish an electromechanical model for the fast tool servo system;

[0088] The electromechanical model is expressed as:

[0089] (1),

[0090] (2),

[0091] (3),

[0092] in, m , c f and k f They represent the mass, damping coefficient and elastic coefficient of the moving part of the fast tool servo system respectively. x , and They represent the displacement, first-order derivative and second-order derivative of the fast tool servo system respectively. F v Represents the output thrust of the voice coil motor, F dis Indicates the external disturbance to the fast tool servo system. T l represents the force constant of the voice coil motor, i and i’ They represent the current driving the voice coil motor and the derivative of the current, respectively, k u represents the magnification of the linear actuator, u represents the control amount, and τ represents the time constant of the linear actuator.

[0093] The above electromechanical model is transformed in the following way:

[0094] S1.1. Perform Laplace transform on the electromechanical model. The electromechanical model after Laplace transform is expressed as:

[0095] (4),

[0096] (5),

[0097] (6),

[0098] in, s is a complex frequency variable, X ( s ) is the frequency domain function of displacement, F v ( s ) is the frequency domain function of the output thrust of the voice coil motor, F dis ( s ) is the frequency domain function of the external disturbance, I (s ) is the frequency domain function of the current, U ( s ) is the frequency domain function of voltage;

[0099] S1.2. Arrange the expression of the electromechanical model after Laplace transformation and obtain:

[0100] (7),

[0101] S1.3. Perform an inverse Laplace transform on the rearranged expression and obtain:

[0102] (8),

[0103] in, Represents the third-order derivative of the displacement of the fast tool servo system, It represents the first-order derivative of the external disturbance to the fast tool servo system;

[0104] Since the first-order derivative of the external disturbance on the fast tool servo system is Much smaller than the external disturbance of the fast tool servo system F dis , ignoring the first-order derivative of the external disturbance on the fast tool servo system The final electromechanical model expression is obtained:

[0105] (9).

[0106] S2. Establish and set an adaptive robust control algorithm based on the electromechanical model;

[0107] The specific steps of establishing the adaptive robust control algorithm are:

[0108] S2.1. Rewrite the final electromechanical model expression into a state space form equation, which is expressed as:

[0109] (10),

[0110] in, x 1. x 2 and x 3 represent displacement, velocity and acceleration respectively, , and Represent the first-order derivatives of displacement, velocity and acceleration respectively, and the matrix of unknown parameters is defined as i , i =[ i 1, i 2, i 3. i 4. i 5]T , i 1. i 2. i 3. i 4 and i 5 indicates unknown parameters, and , , , , i 5 for The nominal value of is the time-varying component of uncertainty in the normalized concentration, ;

[0111] And, set the parameters as:

[0112] (11),

[0113] (12),

[0114] in, i min and i max represent the upper and lower bounds of the unknown parameters, respectively. d represents the actual disturbance, Ω θ and Ω d Represents position variables i The value range and actual disturbance d The value range of d d Represents the time-varying component Upper bound of size;

[0115] S2.2. Design a continuous mapping parameter adaptation law, which is expressed as:

[0116] (13),

[0117] in, represents the estimated value of parameter θ, represents the first derivative of the estimate, is the adaptive rate diagonal matrix, and >0, t a represents the adaptive function, represents a discontinuous mapping function, which is expressed as:

[0118] ,

[0119] and is given by the following definition:

[0120] (14),

[0121] in, represents the discontinuous mapping function of the jth parameter, represents the estimated value of the jth parameter.

[0122] The specific steps of setting the adaptive robust control algorithm are:

[0123] S2.3. Define the ideal tracking trajectory of the fast tool servo system and the three tracking errors of the ideal tracking trajectory. The three tracking errors are expressed as:

[0124] (15),

[0125] in, e 1. e 2 and e 3 represent the first tracking error, the second tracking error and the third tracking error respectively, and Represent the first-order derivatives of the first tracking error and the second tracking error, respectively. , and represent the ideal tracking trajectory, the first-order derivative and the second-order derivative of the ideal tracking trajectory respectively;

[0126] S2.4. Define a synovial variable p , the expression of the synovial variable p is:

[0127] (16),

[0128] in, k 1 and k 2 are any non-negative numbers, x 3eq is the acceleration x 3, which is defined as:

[0129] ;

[0130] S2.5. Taking the derivative of a synovial variable p and substituting the state-space equation into it, we obtain:

[0131] (17),

[0132] in is the first-order derivative of the synovial-like variable, express x 3eq The first derivative of f represents the regression vector of the system, and ;

[0133] S2.6. According to the ideal feedforward compensation-robust adaptive control algorithm, the required control quantity u is generated, which is expressed as:

[0134] (18),

[0135] (19),

[0136] (20),

[0137] (twenty one),

[0138] in, u a is the online adaptive model feedforward compensation term, u s1 is the linear stabilizing feedback term, u s2 is the nonlinear stabilizing feedback term, f d is the regression vector calculated from the ideal signal, and , used to reduce noise interference, t a is an adaptive function, k s1 represents the feedback gain parameter, k s1 =0.001, e is a limiting parameter used to limit the upper bound of the steady-state error. e =1, h M It is the maximum value of the system smoothing function and is used to ensure the robustness of the system.

[0139] S3. Use the fast tool servo system to perform a plane turning experiment on the cuttable material, and fit the relationship between the cutting force and the cutting area during the turning process; in this embodiment, beryllium copper is used for the turning experiment. The plane turning experiment is to integrate the fast tool servo system on the ultra-precision turning machine tool, control the tool to be fixed at the 0 position, and feed through the z-axis of the machine tool to achieve cutting. During the cutting process, the machine tool rotary axis is in C-axis mode, the speed is 60 rpm, and the feed speed of the X-axis is 10μm / r, which is 0.6 mm / min. Using the same cutting conditions, a series of variable cutting depth experiments were carried out, with cutting depths of 1~10μm and an interval of 1μm. Since the cutting force is affected by many factors, in order to calibrate the relationship between cutting force and cutting depth as accurately as possible, 3 cutting experiments were carried out for the same cutting depth, and the final experimental results were averaged.

[0140] In this embodiment, the cutting force is obtained by controlling the control voltage of the host computer. During the plane cutting process, the motor is fixed at position 0 and does not move, so there is no influence of inertia force, damping force and elastic force. The output force of the voice coil motor is equal to the cutting force. In this case, there is a correlation between the cutting force and the control voltage output by the host computer. Then, the cutting force signal during the cutting process can be calculated by the output voltage of the host computer. In this embodiment, the relationship between the cutting force and the control voltage is 1volt=10N.

[0141] In this embodiment, the cutting area is calculated by calculating the surface profile before cutting, the current tool profile and the tool profile before a feed step. Before cutting, the surface profile of the workpiece needs to be measured first, and the tool trajectory needs to be calculated based on the ideal workpiece profile after cutting, and the tool profile at this time and the tool profile at the previous feed step are calculated by the tool trajectory. By calculating the intersection of the three profiles and integrating them, the area enclosed by the three profiles is calculated, that is, the cutting area of ​​this cut.

[0142] According to the above experiments and the calculation method of cutting force and cutting area, the experimental calibration results of cutting force and cutting area can be obtained, such as Figure 2 shown.

[0143] S4. Calculate the ideal cutting area of ​​each cut in the cutting process according to the feed rate, tool radius and the required cutting pattern, and calculate the cutting force according to the fitted relationship between the cutting force and the cutting area;

[0144] S5. Write the cutting force into the adaptive robust control algorithm as a new feedforward signal to obtain the adaptive robust control algorithm of feedforward compensation. The specific process is as follows: Figure 3 As shown:

[0145] The cutting force is taken as a new feedforward signal and written into the adaptive robust control algorithm, that is, the cutting force is taken as a new part of the external disturbance and added to the final electromechanical model. The expression of the electromechanical model is:

[0146] (twenty two),

[0147] in, F cut is the cutting force.

[0148] Through the above equation, redefine the unknown parameter θ n :

[0149] i n =[ i 1, i 2, i 3. i 4. i 5. i 6] T ,

[0150] in, i n is the matrix of the redefined unknown parameters, i 6 is a newly added unknown parameter. ,and i 6min ≤ i 6≤ i 6max , among which i 6min =0.8, i 6max =1.2, at the same time, take i The initial value of 6 is 0.9.

[0151] Update the regression vector formula of the system and recalculate the regression vector. The updated regression vector formula is:

[0152] ,

[0153] in, f n represents the regression vector of the system, F cut is the cutting force;

[0154] At the same time, the recalculated regression vector is:

[0155] ,

[0156] in, f dn represents the calculated regression vector, F cutd To calculate the ideal cutting force;

[0157] With the redefined unknown parameters i n and the recalculated regression vector i dn Instead of the unknown parameters θ and regression vector in the ideal feedforward compensation-robust adaptive control algorithm f d , and the adaptive robust control algorithm of feedforward compensation is obtained. Based on this, the online adaptive model feedforward compensation term in the original control system u a Change to the feedforward compensation term of the new control algorithm u an , the expression of the feedforward compensation term of the new control algorithm is:

[0158] ,

[0159] in, represents the estimated value of the updated parameter θ, is the first-order derivative of the estimated value of the updated parameter θ, is the updated adaptive rate diagonal matrix, τ an represents the updated adaptive function.

[0160] S6. Adaptive robust control algorithm with cutting force feedforward compensation is used to drive fast tool cutting.

[0161] like Figure 4 As shown, in this embodiment, all structures of the fast tool servo system are connected to the base plate 5 and the back plate 8, and the shell can also play the role of electromagnetic shielding. When in use, the system is connected to the machine tool through the right-angle connecting plate and the connecting plate on the symmetrical side. The stator 19 of the driving voice coil motor is fixed to the shell back plate 8 by screws, and the air-floating guide rail sleeve 16 is installed on the shell bottom plate 5. The mover 18 of the driving voice coil motor is connected to the air-floating guide rail shaft 15 through the connecting plate 17, and the air-floating guide rail shaft 15 is constrained by the air-floating guide rail sleeve 16 and has only one axial degree of freedom. When the control current flows through the voice coil motor mover 18 coil, the voice coil motor will generate Lorentz magnetic force, which drives the air-floating guide rail shaft 15 and the mechanism connected to the shaft to move within the stroke. The movement generated by the driving voice coil motor and the air-floating guide rail is displacement feedback through a linear grating encoder. The grating scale 13 of the linear grating encoder is fixed to the air-floating guide rail shaft 15 through a support frame 14. The reading head 12 is connected to the housing side plate 10 through the connecting plate 11. The grating ruler moves with the air-floating guide rail, and then the reading head can measure the displacement of the air-floating guide rail, and through the algorithm, perform position closed-loop feedback control on the long-stroke fast tool servo system. In this example, the positioning resolution of the long-stroke fast tool servo system is 20 nm, and the full stroke length is 10 mm. The diamond tool 3 is fixed on the air-floating guide rail shaft 15 through the tool holder 2 and the tool holder connecting plate 4. The tool holder 2 is designed with threaded holes and through holes, which can be used to fine-tune the diamond tool in conjunction with the tool holder connecting plate.

[0162] This control algorithm was used to conduct a cutting experiment on a lens array on beryllium copper. In the cutting experiment, a comparison was made between the cutting force compensation and the cutting force compensation. Figure 5 and Figure 6The figure shows the morphological errors of two lenses after cutting. It can be found that the peak-to-valley value of the lens morphological error without cutting force compensation is 967.39 nm, and the standard deviation is 132.82 nm; while the peak-to-valley value of the lens morphological error with cutting force compensation is 606.01 nm, and the standard deviation is 76.82 nm, which are decreased by 37.36% and 42.16% respectively. This shows that the cutting force compensation processing method based on the fast tool servo system of adaptive control of the present invention can effectively improve the surface shape accuracy of the processed workpiece.

[0163] The present invention is described in detail above in conjunction with the embodiments, but the contents described are only preferred embodiments of the present invention and cannot be considered to limit the scope of implementation of the present invention. All equivalent changes and improvements made according to the scope of application of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A cutting force compensation processing method of a fast tool servo system based on adaptive control, characterized in that: It includes the following steps: S1. Establish an electromechanical model for the fast tool servo system; S2. Establish and set an adaptive robust control algorithm based on the electromechanical model; S3. Use the fast tool servo system to conduct plane turning experiments on machinable materials and fit the relationship between cutting force and cutting area during turning; S4. Calculate the ideal cutting area of ​​each cut in the cutting process according to the feed rate, tool radius and the required cutting pattern, and calculate the cutting force according to the fitted relationship between the cutting force and the cutting area; S5. Write the cutting force into the adaptive robust control algorithm as a new feedforward signal, that is, add the cutting force as a newly added external disturbance into the final electromechanical model, redefine the unknown parameters, update the regression vector formula of the system and recalculate the regression vector, and replace the unknown parameters and regression vector in the ideal feedforward compensation-robust adaptive control algorithm with the redefined unknown parameters and the recalculated regression vector to obtain the feedforward compensation adaptive robust control algorithm; S6. Adaptive robust control algorithm with cutting force feedforward compensation is used to drive fast tool cutting.

2. The cutting force compensation processing method of the fast tool servo system based on adaptive control according to claim 1 is characterized in that: The electromechanical model in S1 is expressed as: （1）， （2）， （3）， in, m , c f and k f They represent the mass, damping coefficient and elastic coefficient of the moving part of the fast tool servo system respectively. x , and They represent the displacement, first-order derivative and second-order derivative of the fast tool servo system respectively. F v Represents the output thrust of the voice coil motor, F dis Indicates the external disturbance to the fast tool servo system. T l represents the force constant of the voice coil motor, i and i’ denote the current driving the voice coil motor and the derivative of the current, respectively, k u represents the magnification of the linear actuator, u Indicates the control amount, τ Represents the time constant of the linear actuator.

3. The cutting force compensation processing method of the fast tool servo system based on adaptive control according to claim 2 is characterized in that: The electromechanical model is also transformed in the following way: S1.

1. Perform Laplace transform on the electromechanical model. The electromechanical model after Laplace transform is expressed as: （4）， （5）， （6）， in, s is a complex frequency variable, X ( s ) is the frequency domain function of displacement, F v ( s ) is the frequency domain function of the output thrust of the voice coil motor, F dis ( s ) is the frequency domain function of the external disturbance, I ( s ) is the frequency domain function of the current, U ( s ) is the frequency domain function of voltage; S1.

2. Arrange the expression of the electromechanical model after Laplace transformation and obtain: （7）， S1.

3. Perform an inverse Laplace transform on the rearranged expression and obtain: （8）， in, Represents the third-order derivative of the displacement of the fast tool servo system, It represents the first-order derivative of the external disturbance to the fast tool servo system; Since the first-order derivative of the external disturbance on the fast tool servo system is Much smaller than the external disturbance of the fast tool servo system F dis , ignoring the first-order derivative of the external disturbance on the fast tool servo system The final electromechanical model expression is obtained: （9）。 4. The cutting force compensation processing method of the fast tool servo system based on adaptive control according to claim 3 is characterized in that: The specific steps of S2 to establish the adaptive robust control algorithm are: S2.

1. Rewrite the final electromechanical model expression into a state space form equation, which is expressed as: （10）， in, x 1. x 2 and x 3 represent displacement, velocity and acceleration respectively, , and Represent the first-order derivatives of displacement, velocity and acceleration respectively, and the matrix of unknown parameters is defined as θ , θ =[ θ 1, θ 2, θ 3. θ 4. θ 5] T , θ 1. θ 2. θ 3. θ 4 and θ 5 indicates unknown parameters, and , , , , θ 5 for The nominal value of is the time-varying component of the uncertainty in the normalized concentration, ; And, set the parameters as: （11）， （12）， in, θ min and θ max represent the upper and lower bounds of the unknown parameters, respectively. d represents the actual disturbance, Ω θ and Ω d Represents position variables θ The value range and actual disturbance d The value range of δ d Represents the time-varying component Upper bound of size; S2.

2. Design a continuous mapping parameter adaptation law, which is expressed as: （13）， in, represents the estimated value of parameter θ, represents the first derivative of the estimate, is the adaptive rate diagonal matrix, and >0, τ a represents the adaptive function, represents a discontinuous mapping function, which is expressed as: ， and is given by the following definition: （14）， in, represents the discontinuous mapping function of the jth parameter, Indicates j The estimated values ​​of the parameters.

5. The cutting force compensation processing method of the fast tool servo system based on adaptive control according to claim 4 is characterized in that: The specific steps of setting the adaptive robust control algorithm in S2 are: S2.

3. Define the ideal tracking trajectory of the fast tool servo system and the three tracking errors of the ideal tracking trajectory. The three tracking errors are expressed as: （15）， in, e 1. e 2 and e 3 represent the first tracking error, the second tracking error and the third tracking error respectively, and Represent the first-order derivatives of the first tracking error and the second tracking error, respectively. , and represent the ideal tracking trajectory, the first-order derivative and the second-order derivative of the ideal tracking trajectory respectively; S2.

4. Define a synovial variable p , the expression of the synovial variable p is: （16）， in, k 1 and k 2 are any non-negative numbers, x 3eq is the acceleration x 3, which is defined as: ; S2.

5. For a synovial variable p Taking the derivative and plugging the equation into the state-space form, we get: （17）， in is the first-order derivative of the synovial-like variable, express x 3eq The first derivative of φ represents the regression vector of the system, and ; S2.

6. According to the ideal feedforward compensation-robust adaptive control algorithm, the required control quantity u is generated, which is expressed as: （18）， （19）， （20）， （21）， in, u a is the online adaptive model feedforward compensation term, u s1 is the linear stabilizing feedback term, u s2 is the nonlinear stabilizing feedback term, φ d is the regression vector calculated from the ideal signal, and , used to reduce noise interference, τ a is an adaptive function, k s1 represents the feedback gain parameter, ε is a limiting parameter used to limit the upper bound of the steady-state error, h M It is the maximum value of the system smoothing function and is used to ensure the robustness of the system.

6. The cutting force compensation processing method of the fast tool servo system based on adaptive control according to claim 1, characterized in that: After the cutting force is added as a new part of the external disturbance to the final electromechanical model in S5, the expression of the electromechanical model is: （22）， in, F cut is the cutting force.

7. The cutting force compensation processing method of the fast tool servo system based on adaptive control according to claim 1 is characterized in that: The unknown parameters redefined in S5 are: θ n =[ θ 1， θ 2， θ 3， θ 4， θ 5， θ 6] T ， in, θ n is the matrix of the redefined unknown parameters, θ 6 is a newly added unknown parameter, and .

8. The cutting force compensation processing method of the fast tool servo system based on adaptive control according to claim 1, characterized in that: The regression vector formula of the S5 updated system is: ， in, φ n represents the regression vector of the system, F cut is the cutting force; The recalculated regression vector is: ， in, φ dn represents the calculated regression vector, F cutd To calculate the ideal cutting force; Based on this, the online adaptive model feedforward compensation term in the original control system u a Change to the feedforward compensation term of the new control algorithm u an , the expression of the feedforward compensation term of the new control algorithm is: ， in, represents the estimated value of the updated parameter θ, is the first-order derivative of the estimated value of the updated parameter θ, is the updated adaptive rate diagonal matrix, τ an represents the updated adaptive function.

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