A kind of air pressure grinding wheel blade self-adaptive grinding method based on multi-sensor feedback

Abstract

The application discloses a kind of based on multi-sensor feedback's air pressure grinding wheel blade adaptive grinding device and method.The device includes mechanical arm, and air pressure grinding wheel end effector installed at the end of mechanical arm;Air pressure grinding wheel end effector includes air pressure grinding wheel grinding head, pressure regulating interface, six-dimensional force sensor, driving motor and sealed shell;The pressure regulating interface is equipped on the sealed shell;Air pressure grinding wheel grinding head is rotatably connected at the outer end of sealed shell;The inner cavity of the air pressure grinding wheel grinding head is communicated with the pressure regulating interface on the sealed shell by flow channel;The air pressure grinding wheel of the present application using attached soft-bond abrasive is processed to blade, air pressure grinding wheel as flexible grinding end effector, can adapt to the complex curved surface processing requirement of blade, reduce stress concentration and damage when processing.In addition, the present application can dynamically correct grinding force and other state parameters, improve the grinding precision of blade.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing, and specifically relates to an adaptive grinding method for pneumatic grinding wheel blades based on multi-sensor feedback. Background Technology

[0002] Aero-engine blades are typical thin-walled, complex free-form surface parts. The materials used are difficult to machine, with low thermal conductivity and elastic modulus. Factors such as thermal deformation and stress deformation directly affect their machining quality.

[0003] Besides aircraft engine blades, blades are also key components of industrial turbines such as compressors, axial flow fans, and gas turbines, and are widely used in energy and power, rail transportation, petrochemicals, and national defense industries.

[0004] Grinding and polishing are essential and critical steps in blade manufacturing. Through processes such as rough polishing, semi-finish polishing, and fine polishing, the machining allowance of the blade is removed, the shape and size are adjusted, and the surface roughness is improved, so as to achieve the blade profile and surface mirror gloss that meet the technical requirements.

[0005] Currently, blade polishing in China is primarily done manually, resulting in low efficiency, high manpower consumption, and significant dust generation that seriously impacts operator health. my country is experiencing a shortage of skilled blade polishing workers, making blade polishing a bottleneck in the industry's development. This hinders the improvement of blade manufacturing companies' precision machining capabilities and affects their sustainable development. There is an urgent need to develop automated and intelligent blade polishing technologies and systems to gradually replace manual polishing, reduce the human resource requirements of blade polishing, and improve grinding tools to enhance processing efficiency and quality consistency. Summary of the Invention

[0006] The purpose of this invention is to provide an adaptive grinding method for pneumatic grinding wheel blades based on multi-sensor feedback, which solves the problems of poor accuracy, low surface positioning accuracy, low grinding efficiency and poor effect in traditional blade grinding.

[0007] In a first aspect, the present invention provides an adaptive control method for pneumatic grinding wheel blade grinding based on multi-sensor feedback. The adaptive grinding device for pneumatic grinding wheel blades used therein includes a robotic arm and a pneumatic grinding wheel end effector installed at the end of the robotic arm. The pneumatic grinding wheel end effector includes a pneumatic grinding wheel grinding head, a pressure regulating interface, a six-dimensional force sensor, a drive motor, and a sealed housing.

[0008] The sealed outer shell is provided with a pressure regulating interface; the pneumatic grinding wheel head is rotatably connected to the outer end of the sealed outer shell; the inner cavity of the pneumatic grinding wheel head is connected to the pressure regulating interface on the sealed outer shell through a flow channel; the drive motor is used to drive the pneumatic grinding wheel head to rotate; the six-dimensional force sensor is used to detect the grinding force of the pneumatic grinding wheel head; the pressure regulating interface is used to adjust the internal pressure of the pneumatic grinding wheel head.

[0009] The adaptive control method for pneumatic grinding wheel blade grinding includes the following steps:

[0010] Step 1: Predict the prior estimate of the current state vector using the state transition matrix. and the prior covariance matrix ;

[0011] Step 2: Collect observation data and construct observation vectors Calculate Kalman gain Correcting prior estimates using Kalman gain Posterior state estimation including grinding force estimation and posterior covariance matrix ;

[0012] Step 3: Estimating the posterior state Extract the filtered grinding force estimate. The data is input to the active disturbance rejection controller (ADRC); the ADRC arranges the transient process through a tracking differentiator, observes the total system disturbance in real time using an extended state observer, and calculates the control quantity through nonlinear error feedback. Adjust the position and internal pressure of the air pressure grinding wheel.

[0013] Preferably, the pneumatic grinding wheel includes a coating layer, granular filler within the coating layer, and abrasive grains attached to the outer surface of the coating layer. The stiffness of the pneumatic grinding wheel is changed by adjusting the internal pressure of the coating layer.

[0014] Preferably, the base of the six-dimensional force sensor is fixed to the end of the robotic arm; the housing of the drive motor is installed in the detection unit; the sealed housing is the same as the housing of the drive motor.

[0015] Preferably, the sealed housing has a rotating inner cavity; the inner cavity of the sealed housing coincides with the axis of the output shaft of the drive motor; the inner end of the pneumatic grinding wheel is coaxially fixed with the output shaft of the drive motor within the inner cavity of the sealed housing.

[0016] Preferably, an inertial sensor is also included; the inertial sensor is fixed on the sealed housing and is used to detect the acceleration of the pneumatic grinding head.

[0017] Preferably, an infrared temperature sensor is also included; the infrared temperature sensor is mounted at the end of the sealed housing.

[0018] Preferably, the grinding area of ​​the pneumatic grinding wheel is hemispherical.

[0019] Preferably, the Kalman gain The expression is as follows:

[0020]

[0021] in, The covariance of the observation noise matrix.

[0022] Preferably, the posterior state estimation and posterior covariance matrix The expression is as follows:

[0023]

[0024]

[0025] in, For the prior state estimation of the current period, Estimate the posterior state for the current period; This is the observation vector for the current period.

[0026] Preferably, the active disturbance rejection controller includes a tracking differentiator, an extended state observer, and a nonlinear state error feedback unit to adjust the internal pressure of the pneumatic grinding wheel head to achieve constant force grinding.

[0027] The discrete form of the tracking differentiator is:

[0028]

[0029] in, , These are the reference grinding force tracking values ​​for the current moment and the next moment, respectively. , These are the reference grinding force change rate tracking values ​​for the current moment and the next moment, respectively. For the desired grinding force, The integration step size is... For speed-movement parameters, These are the filter parameters; It is the optimal nonlinear weighted sum function, used for fast tracking and noise suppression.

[0030] In the extended state observer, the actual control input from the previous sampling period is combined. Real-time estimation of grinding force, rate of change and total disturbance ;

[0031]

[0032] in, This is due to the error in the observation of grinding force; The grinding force estimated for ESO. The rate of change of grinding force estimated by ESO. The total disturbance estimated by ESO; This represents the actual pressure regulation control amount applied in the previous sampling period; To control the gain; The gain of the ESO is tuned according to the bandwidth method.

[0033] In a nonlinear state error feedback system, the current reference grinding force tracking value and the grinding force change rate tracking value are used as the basis for error feedback. , Grinding force and rate of change obtained from the expansion state observer The error between them is used to calculate the virtual control quantity. Then, the total disturbance observed by the extended state observer is used. Compensation is performed to generate the actual control quantity. Adjust the internal pressure of the air pressure grinding wheel head;

[0034]

[0035]

[0036]

[0037]

[0038] in, It is a piecewise function.

[0039]

[0040] in It is a virtual control variable; It is the actual amount under control; For feedback gain; It is a non-linear power; It is a linear factor for a small region.

[0041] The present invention has the following beneficial effects:

[0042] 1. This invention uses a pneumatic grinding wheel with attached soft-bonded abrasive to process blades. As a flexible grinding end effector, the pneumatic grinding wheel can adapt to the complex curved surface processing requirements of blades, reducing stress concentration and damage during processing. Furthermore, this invention can dynamically correct state parameters such as grinding force, improving the grinding accuracy of the blades.

[0043] 2. This invention uses a six-dimensional force sensor to calculate and adjust the grinding angle and force direction in real time, ensuring that the pneumatic grinding wheel and the blade surface always maintain the optimal working posture, thereby improving the grinding quality of the blade.

[0044] 3. This invention adaptively adjusts the rotation and feed speed by monitoring the temperature of the machined surface, thereby extending tool life and improving machining efficiency.

[0045] 4. This invention optimizes key influencing factors in the surface grinding process by using an extended Kalman filter, especially in high-noise and dynamically changing grinding environments, reducing the interference of sensor noise on the control system, and constructing an active disturbance rejection control system by integrating multiple sensors to improve control accuracy and system stability. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the overall structure of the present invention.

[0047] Figure 2 This is a schematic diagram of the pneumatic grinding wheel end effector in this invention.

[0048] Figure 3 This is a force analysis diagram of the pneumatic grinding wheel end effector in the present invention during grinding.

[0049] Figure 4 This is a flowchart illustrating the grinding process used in this invention.

[0050] Figure 5 This is a system block diagram for adaptive grinding control in this invention.

[0051] Figure 6 This is a system block diagram of the active disturbance rejection controller used in the adaptive grinding control of this invention. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings.

[0053] like Figure 1 As shown, an adaptive grinding device for pneumatic grinding wheel blades based on multi-sensor feedback includes a robotic arm 2 and a pneumatic grinding wheel end effector 1 installed at the end of the robotic arm 2.

[0054] like Figure 2As shown, the pneumatic grinding wheel end effector 1 includes a pneumatic grinding wheel grinding head 1-1, an infrared temperature sensor 1-2, a pressure regulating interface 1-3, a six-dimensional force sensor 1-4, a drive motor 1-5, an inertial sensor, and a sealed housing 1-6. The base of the six-dimensional force sensor is fixedly connected to the end of the robotic arm via a flange; the body of the drive motor is connected to the detection part of the six-dimensional force sensor via a flange; the sealed housing 1-6 is fixed to the body of the drive motor. The inertial sensor is fixed to the sealed housing 1-6.

[0055] The sealed housing 1-6 has a rotating inner cavity; the inner cavity of the sealed housing 1-6 coincides with the axis of the output shaft of the drive motor 1-5. The sealed housing 1-6 is provided with a pressure regulating interface 1-3. The pneumatic grinding wheel head 1-1 is coaxially rotatably connected to the outer end of the sealed housing 1-6. The inner end of the pneumatic grinding wheel head 1-1 is coaxially fixed with the output shaft of the drive motor 1-5 within the inner cavity of the sealed housing 1-6. The pneumatic grinding wheel head 1-1 includes a coating layer, granular filler within the coating layer, and abrasive grains attached to the outer surface of the coating layer. The stiffness of the pneumatic grinding wheel head 1-1 is changed by adjusting the internal pressure of the coating layer.

[0056] The interior of the pneumatic grinding wheel head 1-1 is connected to the pressure regulating port 1-3 via a slip ring flow channel. The pressure regulating port 1-3 is connected to an external air source or negative pressure source, thereby adjusting the internal pressure of the rotating pneumatic grinding wheel head 1-1 and thus changing the rigidity of the pneumatic grinding wheel head 1-1.

[0057] Due to the complex grinding surface of the blades, this embodiment employs a hemispherical pneumatic grinding head 1-1 with soft-bonded abrasive for grinding. Simultaneously, since the distribution of grinding speed significantly impacts the processing effect and surface quality during grinding, and because the pneumatic grinding head 1-1 is hemispherical, it is necessary to position the pneumatic grinding wheel at a specific angle to the grinding surface to ensure a more uniform distribution of force and speed within the processing area. Therefore, the essence of grinding control in this embodiment is to ensure that the pressure and processing angle during the curved surface grinding process remain within the error range.

[0058] In this embodiment, as Figure 3 As shown, the state vector X describing the pneumatic grinding head 1-1 is denoted as:

[0059]

[0060] in, The position of the centroid of the pneumatic grinding head 1-1 is specifically the z-axis component; The velocity of the center of mass of the pneumatic grinding head 1-1 is the z-axis component. The force component in the z-axis direction of the pneumatic grinding wheel end effector after gravity compensation is the force component in the z-axis direction of the six-dimensional force sensor 1-4 after gravity compensation (i.e., deducting the projection of the self-weight of the pneumatic grinding wheel end effector 1 in the z-direction), which is consistent with the axis direction of the pneumatic grinding wheel grinding head 1-1. It is the grinding force of the pneumatic grinding wheel 1-1, specifically the normal component of the force exerted by the workpiece on the pneumatic grinding wheel 1-1; The torque about the z-axis experienced by the six-dimensional force sensor; It is the angle between the normal of the machined surface and the axis of the air pressure grinding head 1-1.

[0061] like Figure 4 and Figure 5 As shown, the control method of the pneumatic grinding wheel blade adaptive grinding device includes the following steps:

[0062] Step 1: Estimate the state based on the previous cycle Using state transition function Calculate prior estimates And according to the Jacobian matrix Update prior covariance ;

[0063] The discrete-time state equations for the state vector of the pneumatic grinding head 1-1 are established as follows:

[0064]

[0065] in, This is the state vector from the previous sampling period. For the prior state estimate of the current sampling period; It is a nonlinear discrete-time state transition function. This is the process noise vector of the previous sampling period.

[0066] Write Newton's second law along the Z-axis of the tool (i.e., along the axis of the pneumatic grinding head 1-1):

[0067]

[0068] in, Let t be the position of the centroid of the pneumatic grinding head 1-1 at the current moment; For the quality of the end effector of the pneumatic grinding wheel; The force component of the six-dimensional force sensor in the z-axis direction at the current time t is obtained by the six-dimensional force sensor 1-4. The grinding force at the current time t; The angle between the workpiece normal and the grinding head axis; The z-axis component represents the equivalent disturbance force that includes pressure fluctuations and local stiffness changes in the blades.

[0069] Disturbance force during grinding The statistical properties are modeled through process noise. Therefore, when deriving the discrete-time state equation, process noise is incorporated to obtain a simplified dynamic relationship:

[0070]

[0071] in, , These are the z-axis components of the acceleration and velocity of the pneumatic grinding head 1-1 at the current time t.

[0072] Based on the discretization description of the elastic contact behavior of the end effector in the normal direction, we can obtain:

[0073]

[0074]

[0075] Where k represents the current sampling period; (k-1) represents the previous sampling period.

[0076] Constructing a nonlinear discrete-time state transition matrix Its expression is as follows:

[0077]

[0078] Where T is the sampling time; m is the mass of the pneumatic grinding wheel end effector 1;

[0079] In the discrete-time state equation of the state vector, the noise vector The expression is:

[0080]

[0081]

[0082]

[0083] in, , These represent the position and velocity of the center of mass of the pneumatic grinding head 1-1 in the z-direction, respectively. This refers to random acceleration perturbation in the Z-axis direction; , , , The process noises of the six-dimensional force sensor (z-axis force), grinding head (grinding force), torque around the z-axis, and attitude angle in the previous sampling period are assumed to be zero-mean Gaussian white noise, and their statistical characteristics are derived from the process noise covariance matrix. Decide.

[0084] At the initial moment of system operation ( Initialize the state vector estimate. and the initial error covariance matrix . Let be a diagonal matrix, where the diagonal elements represent the degree of uncertainty about the initial state. Let be the filter that converges quickly in subsequent iterations. Set to a relatively large value. After the sampling cycle begins, use the posterior error covariance matrix updated in the previous sampling cycle. Combined with process noise covariance Derive the prior error covariance matrix at the current time. :

[0085]

[0086]

[0087] in, This is the prior covariance matrix updated for this sampling period; The posterior error covariance matrix of the previous period; State of the previous moment State transition function For the state vector The Jacobian matrix; Let be the process noise covariance matrix.

[0088] Step 2: Collect data from the six-dimensional force sensor, inertial sensor, and robot encoder to construct observation vectors. Calculate based on the observation function h(·) and observation and prediction ;

[0089] Observation vector The expression is:

[0090]

[0091] Wherein, the subscript m represents the quantity measured by the sensor; , The end-effector displacement and velocity are calculated using the robot encoder and geometric model; Force in the z-axis direction after gravity compensation for a six-dimensional force sensor; The tool's Z-axis acceleration is measured by an inertial sensor. The torque about the z-axis; The included angle is obtained from the attitude calculation.

[0092] Observation vector With state vector The following relationship must be satisfied:

[0093]

[0094]

[0095] in, Let be the observation noise vector, representing the computational error introduced by the sensor measurement error. Assume... , , where is the observation noise covariance matrix, and each variance can be determined by sensor specifications or calibration tests. The observation function... The correspondence between the ideal output of each sensor and the state vector is given.

[0096] Step 3: Based on prior covariance Observation noise covariance Calculate Kalman gain and update the state estimate. With covariance ;

[0097] Calculate Kalman gain The expression is as follows:

[0098]

[0099] in, Let X be the Jacobian matrix of the observation function with respect to the state vector X; To observe the noise covariance matrix.

[0100] The current cycle state vector estimate is corrected using Kalman gain. and posterior covariance matrix as follows:

[0101]

[0102]

[0103] in, Estimate the prior state for the current period; The posterior state estimate for the current period serves as the state vector for the next period; This is the observation vector for the current period; It is a 6×6 identity matrix.

[0104] Thus, from the updated posterior state vector In this process, the filtered and corrected estimate of the normal grinding force can be extracted. .

[0105] Step 4: In the tracking differentiator TD, adjust the grinding force according to the set step desired force. A smooth transition process is arranged to generate a reference grinding force trajectory. and its differential signal (Grinding force change rate reference value), for NLSEF and ESO alignment.

[0106]

[0107] in, For reference grinding force tracking value; This is a reference value for the rate of change of grinding force. The desired grinding force; This is the integration step size; For speed-movement parameters; These are the filter parameters; It is the optimal nonlinear weighted sum function, used for fast tracking and noise suppression.

[0108] Step 5: Estimate the grinding force in the extended state observer (ESO). The input is observed and combined with the actual control input from the previous sampling period. Real-time estimation of grinding force, rate of change and total disturbance ;

[0109]

[0110] in, This is due to the error in the observation of grinding force; Grinding force estimated for ESO; The rate of change of grinding force estimated by ESO. The total disturbance estimated by ESO; This represents the actual pressure regulation control amount applied in the previous sampling period; To control the gain; The gain of the ESO is tuned according to the bandwidth method.

[0111] Step Six: In the nonlinear state error feedback (NLSEF), according to ( , )and The error is used to calculate the virtual control quantity. Then, using the total perturbation observed by ESO Compensation is performed to generate the actual control quantity. Adjust the internal pressure of the air pressure grinding wheel head;

[0112]

[0113]

[0114]

[0115]

[0116] Where fal(·) is a piecewise function

[0117]

[0118] in, It is a virtual control variable; It is the actual amount under control; For feedback gain; It is a non-linear power; It is a linear factor for a small region.

[0119] Step 7: Repeat steps 1 through 6 for the next sampling period, iterating k = k + 1. This process estimates the state vector. The iterative update utilizes the grinding force estimate after Kalman filtering. As a feedback input to the active disturbance rejection controller, it enables stable and rapid grinding force control under highly uncertain working conditions such as air pressure fluctuations and changes in contact stiffness.

Claims

1. An adaptive control method for pneumatic grinding wheel blade grinding based on multi-sensor feedback, characterized in that: The pneumatic grinding wheel blade adaptive grinding device includes a robotic arm (2) and a pneumatic grinding wheel end effector (1) installed at the end of the robotic arm (2); the pneumatic grinding wheel end effector (1) includes a pneumatic grinding wheel grinding head (1-1), a pressure regulating interface (1-3), a six-dimensional force sensor (1-4), a drive motor (1-5), and a sealed housing (1-6). The sealing shell (1-6) is provided with a pressure regulating port (1-3); the pneumatic grinding wheel head (1-1) is rotatably connected to the outer end of the sealing shell (1-6); the inner cavity of the pneumatic grinding wheel head (1-1) is connected to the pressure regulating port (1-3) on the sealing shell (1-6) through a flow channel; the drive motor (1-5) is used to drive the pneumatic grinding wheel head (1-1) to rotate; the six-dimensional force sensor (1-4) is used to detect the grinding force of the pneumatic grinding wheel head (1-1); the pressure regulating port (1-3) is used to adjust the internal pressure of the pneumatic grinding wheel head (1-1); The pneumatic grinding wheel end effector (1) also includes an inertial sensor; the inertial sensor is fixed on the sealed housing (1-6) and is used to detect the acceleration of the pneumatic grinding wheel grinding head (1-1); The adaptive control method for pneumatic grinding wheel blade grinding includes the following steps: Step 1: Describe the state vector of the pneumatic grinding head (1-1). Recorded as: in, The position of the centroid of the pneumatic grinding head (1-1); The velocity of the center of mass of the pneumatic grinding head (1-1); The force exerted on the end effector of the pneumatic grinding wheel after gravity compensation Force component in the axial direction; It is the grinding force of the pneumatic grinding wheel (1-1); The force sensor subjected to the six-dimensional force The torque of the shaft; It is the angle between the normal of the machined surface and the axis of the air pressure grinding head (1-1). Based on the state estimate of the previous period Using state transition function Calculate prior estimates And according to the Jacobian matrix Update prior covariance ; Prior estimation as follows: in, This is the state vector from the previous sampling period. For the prior state estimate of the current sampling period; This is the process noise vector of the previous sampling period; State transition function The expression is as follows: Where T is the sampling time; m is the mass of the pneumatic grinding wheel end effector (1); Prior covariance : in, The posterior error covariance matrix of the previous period; State of the previous moment State transition function For the state vector The Jacobian matrix; Step 2: Collect data from the six-dimensional force sensor, inertial sensor, and robot encoder to construct observation vectors. ; Observation vector The expression is: Among them, subscript This represents the quantity measured by the sensor; , The end-effector displacement and velocity are calculated using the robot encoder and geometric model; After performing gravity compensation on the six-dimensional force sensor Force in the axial direction; Tools measured by inertial sensors Axial acceleration; To bypass Axial torque; The included angle is obtained from the attitude calculation; Observation vector With state vector The following relationship must be satisfied: For the observed noise vector; Based on prior covariance Observation noise covariance Calculate Kalman gain The prior estimate is corrected using Kalman gain to obtain the posterior state estimate, which includes the grinding force estimate. and posterior covariance matrix ; The posterior state estimation and posterior covariance matrix The expression is as follows: in, For the prior state estimation of the current period, Estimate the posterior state for the current period; This is the observation vector for the current period; Let X be the Jacobian matrix of the observation function with respect to the state vector X; Step 3: Estimating the posterior state Extract the filtered grinding force estimate. The data is input to the active disturbance rejection controller (ADRC); the ADRC arranges the transient process through a tracking differentiator, observes the total system disturbance in real time using an extended state observer, and calculates the control quantity through nonlinear error feedback. Adjust the position and internal pressure of the pneumatic grinding head (1-1).

2. The adaptive control method for pneumatic grinding wheel blade grinding according to claim 1, characterized in that: The pneumatic grinding wheel (1-1) includes a coating layer, granular filler inside the coating layer, and abrasive grains attached to the outer surface of the coating layer. The stiffness of the pneumatic grinding wheel (1-1) can be changed by adjusting the internal pressure of the coating layer.

3. The adaptive control method for pneumatic grinding wheel blade grinding according to claim 1, characterized in that: The base of the six-dimensional force sensor is fixed to the end of the robotic arm; the housing of the drive motor is installed in the detection unit. The sealed housing (1-6) and the housing of the drive motor.

4. The adaptive control method for pneumatic grinding wheel blade grinding according to claim 1, characterized in that: The sealed housing (1-6) has a rotating inner cavity; the inner cavity of the sealed housing (1-6) coincides with the axis of the output shaft of the drive motor (1-5); the inner end of the pneumatic grinding head (1-1) and the output shaft of the drive motor (1-5) are coaxially fixed in the inner cavity of the sealed housing (1-6).

5. The adaptive control method for pneumatic grinding wheel blade grinding according to claim 1, characterized in that: It also includes an infrared temperature sensor (1-2); the infrared temperature sensor (1-2) is mounted on the end of the sealed housing (1-6).

6. The adaptive control method for pneumatic grinding wheel blade grinding according to claim 1, characterized in that: The grinding area of ​​the pneumatic grinding wheel is hemispherical.

7. The adaptive control method for pneumatic grinding wheel blade grinding according to claim 1, characterized in that: Kalman gain The expression is as follows: in, The covariance of the observation noise matrix.

8. The adaptive control method for pneumatic grinding wheel blade grinding according to claim 1, characterized in that: The active disturbance rejection controller includes a tracking differentiator, an extended state observer, and a nonlinear state error feedback device, which adjusts the internal pressure of the pneumatic grinding head to achieve constant force grinding. The discrete form of the tracking differentiator is: in, , These are the reference grinding force tracking values ​​for the current moment and the next moment, respectively. , These are the reference grinding force change rate tracking values ​​for the current moment and the next moment, respectively. For the desired grinding force, For the integration step size, For speed-movement parameters, These are the filter parameters; It is the optimal nonlinear weighted sum function; In the extended state observer, the actual control input from the previous sampling period is combined. Real-time estimation of grinding force, rate of change and total disturbance ; In a nonlinear state error feedback system, the current reference grinding force tracking value and the grinding force change rate tracking value are used as the basis for error feedback. , Grinding force and rate of change obtained from the expansion state observer The error between them is used to calculate the virtual control quantity. Then, the total disturbance observed by the extended state observer is used. Compensation is performed to generate the actual control quantity. .

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