Machine tool tracking error control method based on adaptive variable boundary layer thickness nonsingular terminal sliding mode

Abstract

The invention particularly relates to a machine tool tracking error control method based on a self-adaptive variable boundary layer thickness nonsingular terminal sliding mode. The method comprises the following steps: constructing a kinetic model of a machine tool servo feeding translation shaft; a disturbance observer is designed and used for obtaining an estimated value of external disturbance of the machine tool, and a second-order Butterworth low-pass filter is arranged behind the disturbance observer to suppress the influence of high-frequency noise; designing a nonsingular terminal sliding mode surface function based on the tracking error and the derivative thereof; deriving the nonsingular terminal sliding mode surface function, and obtaining an equivalent control law when the derivative is zero; designing an adaptive variable boundary layer thickness saturation function; a switching control law is designed, and the switching control law is composed of an integral of a self-adaptive variable boundary layer thickness saturation function and a proportional reaching law and does not contain a high-frequency switching item; and combining the equivalent control law with the switching control law to generate a total control voltage which is used for controlling a tracking error of the servo feed shaft of the machine tool. According to the method, a better control effect can be realized.

Description

Technical Field

[0001] This invention relates to the field of machine tool feed axis tracking error control, and specifically to a machine tool tracking error control method based on adaptive variable boundary layer thickness non-singular terminal sliding mode. Background Art

[0002] Tracking error is a key indicator for evaluating the machining accuracy of machine tools. The purpose of tracking error control is to shorten the distance between the actual position and the designed position through advanced control theories, thereby improving tracking accuracy. To improve the tracking performance of machine tool servo systems, scholars have proposed many tracking error control methods. Among them, sliding mode control has been widely studied due to its advantages of insensitivity to parameter disturbances and uncertainties, and strong anti-interference ability.

[0003] Reference 1, “Y. Feng, X. Yu, Z. Man, Non-singular terminal sliding mode control of rigid manipulators. Automatica, 2002, 38(12): 2159-2167,” discloses a global non-singular terminal sliding mode control method. Firstly, a new terminal sliding surface is designed for second-order systems to eliminate the singularity-related problems in traditional terminal sliding mode control, ensuring that the time required for the system to reach the equilibrium point from any initial state is within a finite time. However, this method does not consider the impact of chattering on non-singular terminal sliding mode control when controlling second-order systems.

[0004] Reference 2, “J. Wang, L. Zhao, L. Yu, Adaptive terminal sliding mode control for magnetic levitation systems with enhanced disturbance compensation. IEEE Transactions on Industrial Electronics, 2020, 68(1): 756-766,” discloses an improved non-singular terminal sliding mode control method based on adaptive control gain. This method reduces chattering in non-singular terminal sliding mode control by designing an adaptive law for the control gain. However, this method does not eliminate the high-frequency switching term in the switching control law; it only reduces the intensity of chattering, and the impact of chattering on sliding mode control remains significant.

[0005] The typical characteristics of the above literature are: none of them eliminated the high-frequency switching term in the switching control law, and the chattering problem restricted the improvement of the control gain of the non-singular terminal sliding mode control, so that the control accuracy could not be further improved.

[0006] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] To overcome the problems existing in the current non-singular terminal sliding mode control, this invention provides a machine tool tracking error control method based on adaptive variable boundary layer thickness non-singular terminal sliding mode.

[0008] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0009] According to a first aspect of the present invention, a machine tool tracking error control method based on adaptive variable boundary layer thickness nonsingular terminal sliding mode is provided, the method comprising: Step 1: Construct a dynamic model of the machine tool's servo feed translation axis and obtain state variables and machine tool parameters; Step 2: Design a disturbance observer based on state variables, machine tool parameters, and gain matrix to obtain an estimate of the external disturbance of the machine tool, and set a second-order Butterworth low-pass filter after the disturbance observer to suppress the influence of high-frequency noise; Step 3: Design the non-singular terminal sliding surface function based on the tracking error and its derivative; Step 4: Take the derivative of the non-singular terminal sliding surface function. When the derivative is zero, the equivalent control law is obtained. The equivalent control law includes compensation for the disturbance estimate. Step 5: Design an adaptive variable boundary layer thickness saturation function, wherein the boundary layer thickness of the adaptive variable boundary layer thickness saturation function can be adaptively adjusted according to the magnitude of the absolute value of the sliding surface function; Step 6: Design the switching control law, which consists of the integral and proportional approach law of the adaptive variable boundary layer thickness saturation function, and does not contain high-frequency switching terms; Step 7: Combine the equivalent control law and the switching control law to generate a total control voltage, which is used to control the tracking error of the machine tool servo feed axis.

[0010] In some exemplary embodiments, step 1 specifically includes: The dynamic model of the machine tool servo system in state space is as follows:

[0011] in, This is the nominal value of the equivalent inertia. This is the nominal value of the viscous friction coefficient. This refers to the actual position of the feed drive. It is the speed of the feed drive. For the acceleration of the feed drive, To control the voltage, It is an external disturbance to the system; The dynamic model is simplified as

[0012] Among them, state variables Machine tool parameters , , ; acceleration of the linear feed axis Represented as: .

[0013] In some exemplary embodiments, step 2 specifically includes: The disturbance observer is designed as follows:

[0014] in, The observer gain matrix is... and It is a constant. It is an estimate of the disturbance. and As an intermediate variable; A second-order Butterworth low-pass filter is set after the disturbance observer as follows:

[0015] in, It is the natural frequency. It is the damping ratio.

[0016] In some exemplary embodiments, step 3 specifically includes: Design a nonsingular terminal sliding surface function. for:

[0017]

[0018] in, Tracking error The derivative of , All are positive odd integers. It is a parameter that needs to be designed. It is the reference trajectory for the design.

[0019] In some exemplary embodiments, step 4 specifically includes: Depend on Obtain the equivalent control law for: .

[0020] In some exemplary embodiments, step 5 specifically includes: Design an adaptive variable boundary layer thickness saturation function for:

[0021]

[0022] in, It is the thickness of the boundary layer. , , , and All are positive numbers, satisfying and .

[0023] In some exemplary embodiments, step 6 specifically includes: Design switching control law for:

[0024] in, and They are all positive constants. , It is a positive constant.

[0025] In some exemplary embodiments, step 7 specifically includes: The total control voltage is expressed in the following form:

[0026] .

[0027] According to a second aspect of the present invention, a storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the machine tool tracking error control method based on adaptive variable boundary layer thickness nonsingular terminal sliding mode as described in the first aspect.

[0028] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, the machine tool tracking error control method based on adaptive variable boundary layer thickness nonsingular terminal sliding mode described in the first aspect is implemented.

[0029] According to a fourth aspect of the present invention, an electronic device is provided, comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to implement the machine tool tracking error control method based on adaptive variable boundary layer thickness nonsingular terminal sliding mode as described in the first aspect by executing the executable instructions.

[0030] The machine tool tracking error control method based on adaptive variable boundary layer thickness non-singular terminal sliding mode provided by the embodiments of the present invention first designs a disturbance observer for the machine tool servo system to obtain an estimate of the external disturbance of the machine tool. Next, a non-singular terminal sliding surface function is designed, and an equivalent control law is obtained from the derivative of the sliding surface function, which is the continuous control input required for the system state on the ideal sliding surface. The equivalent control law includes compensation for the disturbance observation value, realizing real-time compensation for external disturbances and reducing the impact of external disturbances on the system tracking accuracy. Finally, an adaptive variable boundary layer thickness saturation function is proposed, which can adaptively adjust the boundary layer thickness value according to the magnitude of the absolute value of the sliding surface function. The switching control law consists of the integral and proportional approximation laws of the adaptive variable boundary layer thickness saturation function, which does not contain high-frequency switching terms, and increasing the control gain will not induce obvious chattering. The control voltage is composed of the equivalent control law and the switching control law. The larger control gain in the switching control law makes this method have a more accurate control effect.

[0031] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0032] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0033] Figure 1 This is a flowchart of the method of the present invention.

[0034] Figure 2 This is a rose-shaped trajectory diagram of the tool tip point in the three-axis machining path in an embodiment of the method of the present invention.

[0035] Figure 3 This is a control block diagram of a machine tool tracking error control method based on adaptive variable boundary layer thickness nonsingular terminal sliding mode designed in this invention.

[0036] Figure 4 This is a diagram of the X, Y, and Z axis perturbation observations in an embodiment of the method of the present invention.

[0037] Figure 5 This is a voltage diagram showing the switching of the X, Y, and Z axes in an embodiment of the method of the present invention.

[0038] Figure 6 This is a graph showing the size of the sliding surface functions of the X, Y, and Z axes in an embodiment of the method of the present invention.

[0039] Figure 7 This is a diagram showing the tracking error results of the X, Y, and Z axes in an embodiment of the method of the present invention. Detailed Implementation

[0040] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0041] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0042] To address the shortcomings and deficiencies of existing technologies, this example implementation provides a machine tool tracking error control method based on an adaptive variable boundary layer thickness non-singular terminal sliding mode. Considering the impact of external disturbances on system tracking accuracy, this method first designs a disturbance observer to obtain an estimate of the disturbance. Next, a non-singular terminal sliding surface function is designed. The equivalent control law containing the disturbance estimate is obtained from the fact that the derivative of the sliding surface function is zero, ensuring that the system state is strictly maintained on the sliding surface under ideal conditions (no disturbance, no uncertainty). Finally, an adaptive variable boundary layer thickness saturation function is designed, allowing the boundary layer thickness of the saturation function to adaptively change with the magnitude of the absolute value of the sliding surface function. The integral and proportional approach laws of the adaptive variable boundary layer thickness saturation function together constitute the switching control law. Even under conditions of parameter uncertainty, external disturbances, or unmodeled dynamics, it can still guarantee system stability and tracking performance. The switching control law designed in this method does not contain high-frequency switching terms, suppressing chattering. This invention simultaneously considers machine tool feed axis tracking error control methods under the influence of external disturbances and chattering, resulting in lower chattering and better control performance.

[0043] refer to Figure 1 As shown, the specific steps may include: Step 1: Construct a dynamic model of the machine tool's servo feed translation axis and obtain state variables and machine tool parameters; Step 2: Design a disturbance observer based on state variables, machine tool parameters, and gain matrix to obtain an estimate of the external disturbance of the machine tool, and set a second-order Butterworth low-pass filter after the disturbance observer to suppress the influence of high-frequency noise; Step 3: Design the non-singular terminal sliding surface function based on the tracking error and its derivative; Step 4: Take the derivative of the non-singular terminal sliding surface function. When the derivative is zero, the equivalent control law is obtained. The equivalent control law includes compensation for the disturbance estimate. Step 5: Design an adaptive variable boundary layer thickness saturation function, wherein the boundary layer thickness of the adaptive variable boundary layer thickness saturation function can be adaptively adjusted according to the magnitude of the absolute value of the sliding surface function; Step 6: Design the switching control law, which consists of the integral and proportional approach law of the adaptive variable boundary layer thickness saturation function, and does not contain high-frequency switching terms; Step 7: Combine the equivalent control law and the switching control law to generate a total control voltage, which is used to control the tracking error of the machine tool servo feed axis.

[0044] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and embodiments.

[0045] The method proposed in this invention was tested on an open-type five-axis CNC machining platform. The sampling frequency of the control board was 1000Hz. The experimental trajectory was a three-axis rose trajectory, where the tool tip trajectory was as follows. Figure 2 As shown, the actual positions of each axis are obtained from feedback by an incremental encoder. The machine tool tracking error control algorithm based on adaptive variable boundary layer thickness nonsingular terminal sliding mode in this invention is implemented in Matlab / Simulink 2021a.

[0046] Step 1: Construct a dynamic model of the machine tool's servo feed translation axis.

[0047] A typical ball screw feed drive system consists of a current amplifier, a servo motor, a screw coupling mechanism, a ball screw with a preload nut, a worktable that carries the workpiece, and friction and feedback sensors for the guide rails.

[0048] The dynamic model of the machine tool servo system in state space is as follows:

[0049] in, This is the nominal value of the equivalent inertia. This is the nominal value of the viscous friction coefficient. This refers to the actual position of the workbench. It refers to the speed of the workbench. This refers to the acceleration of the worktable. To control the voltage. It is an external disturbance to the system.

[0050] It can be abbreviated as

[0051] Among them, state variables , , , .

[0052] acceleration of the linear feed axis It can be represented as:

[0053] Step 2: Design a disturbance observer.

[0054] The disturbance observer is designed as follows:

[0055] in, The observer gain matrix is... and It is a constant. It is an estimate of the disturbance. Let be an intermediate variable. Let the estimation error be... We can obtain:

[0056] matrix The matrix is ​​designed to ensure All eigenvalues ​​are located in the left half of the complex plane. Therefore, the disturbance observer can observe disturbances in the machine tool feed drive system.

[0057] Increasing the observer gain improves sensitivity to changes in the input signal, thus accelerating dynamic response characteristics and enabling more accurate tracking of the true state of disturbances. However, while increasing the observer gain improves transient performance and accuracy, it also increases sensitivity to high-frequency noise and interference. This sensitivity can lead to oscillating behavior and even compromise the stability of the disturbance observer.

[0058] Due to the influence of high-frequency noise, a second-order Butterworth low-pass filter needs to be set after the disturbance observer as follows:

[0059] in, It is the natural frequency. It is the damping ratio.

[0060] Step 3: Design a non-singular terminal sliding surface that uses tracking error as the system state.

[0061] The tracking error of the feed axis is:

[0062] It is the reference trajectory for designing the feed axis.

[0063] Design non-singular terminal sliding surface for:

[0064] in, It is the derivative of the tracking error. , All are positive odd integers, satisfying . It is a parameter that needs to be designed.

[0065] The symbolic function is represented as:

[0066] Step 4: Obtain the equivalent control law containing the disturbance estimate by assuming the derivative of the sliding surface is 0.

[0067] Depend on Obtain the equivalent control law for:

[0068] The equivalent control law is obtained by solving for the derivative of the sliding surface, which equals zero. The equivalent control law is obtained. This ensures that the system state is strictly maintained on the sliding surface under ideal conditions (no disturbance, no uncertainty) to avoid deviation from the ideal trajectory.

[0069] Step 5: Design an adaptive variable boundary layer thickness saturation function.

[0070] Design an adaptive variable boundary layer thickness saturation function for:

[0071] in

[0072] in, It is the thickness of the boundary layer. , , , and All are positive numbers, satisfying and . and These represent the upper and lower limits of the boundary layer thickness, respectively. Within the defined boundary layer, The function takes the form of a straight line passing through the origin. From the above equation, it can be seen that a small... This will lead to an increase in boundary layer thickness. Conversely, The larger the value, the thinner the boundary layer. With As the threshold decreases, the boundary layer thickness gradually increases to reduce controller chattering. When increasing, the boundary layer thickness is assigned a minimum value to ensure that the system achieves the desired sliding mode surface. .

[0073] Performance design parameters during system simulation , , , and .

[0074] Step 6: Design the switching control law This forces the system state to arrive at and remain on the sliding surface within a finite time. Even with parameter uncertainties, external disturbances, or unmodeled dynamics, the switching control law can still guarantee system stability and tracking performance as long as the matching conditions are met.

[0075] Switching control laws for:

[0076] in, and They are all positive constants. . It is a positive constant. Switching control law. Composed of a proportionality-reaching law and an integral of an adaptive variable boundary layer thickness saturation function, it contains no high-frequency switching terms and suppresses chattering. This can improve its control gain. and To improve the tracking accuracy of the control.

[0077] Step 7: Based on steps 4 and 6, a control strategy is finally established whereby the disturbance observer compensates for the disturbance value in real time to the adaptive boundary layer non-singular terminal sliding mode controller. The total control voltage can be expressed as follows:

[0078]

[0079] Figure 2 This is a control block diagram of a machine tool tracking error control method based on adaptive variable boundary layer thickness nonsingular terminal sliding mode designed in this invention. Figure 3 The external disturbance values ​​of the servo feed translational axis system, obtained by the disturbance observer method of this invention, are compensated in real time to the controller to suppress the impact of disturbances on tracking accuracy. Figure 4 The switching voltage of the adaptive switching control law designed using the method of this invention shows that the switching voltage of this invention does not exhibit chattering. Figure 5 The value of the sliding surface function obtained experimentally by the method of the present invention is shown. Due to the influence of friction, the sliding surface function of the method of the present invention produces a large peak at the commutation point, indicating that the method of the present invention has better robustness. Figure 6 The tracking error obtained by the method of this invention shows that, since the tracking error of this method is always near zero except for the peak value, it has a smaller tracking error. This is due to the high control gain of the method of this invention. The feed axis model parameter table is shown in Table 1. The tracking error control parameters of the feed axis are shown in Table 2. The tracking error control results of each feed axis are shown in Table 3.

[0080] Table 1 Feed axis model parameter table

[0081] Table 2 Parameters of the Three Axis Controllers

[0082] Table 3 Tracking Error Control Results

[0083] *Note: : Indicates the maximum value of the tracking error; : Represents the mean of the tracking error; : Represents the standard deviation of the tracking error.

[0084] It should be noted that, as another aspect, this application also provides a storage medium, which may be included in an electronic device or may exist independently without being assembled into the electronic device. The storage medium carries one or more programs, which, when executed by an electronic device, cause the electronic device to perform the methods described in the following embodiments.

[0085] In one embodiment, this application provides a computer program product including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0086] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0087] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0088] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.

Claims

1. A machine tool tracking error control method based on adaptive variable boundary layer thickness nonsingular terminal sliding mode, characterized in that, The method includes: Step 1: Construct a dynamic model of the machine tool's servo feed translation axis and obtain state variables and machine tool parameters; Step 2: Design a disturbance observer based on state variables, machine tool parameters, and gain matrix to obtain an estimate of the external disturbance of the machine tool, and set a second-order Butterworth low-pass filter after the disturbance observer to suppress the influence of high-frequency noise; Step 3: Design the non-singular terminal sliding surface function based on the tracking error and its derivative; Step 4: Take the derivative of the non-singular terminal sliding surface function. When the derivative is zero, the equivalent control law is obtained. The equivalent control law includes compensation for the disturbance estimate. Step 5: Design an adaptive variable boundary layer thickness saturation function, wherein the boundary layer thickness of the adaptive variable boundary layer thickness saturation function can be adaptively adjusted according to the magnitude of the absolute value of the sliding surface function; Step 6: Design the switching control law, which consists of the integral and proportional approach law of the adaptive variable boundary layer thickness saturation function, and does not contain high-frequency switching terms; Step 7: Combine the equivalent control law and the switching control law to generate a total control voltage, which is used to control the tracking error of the machine tool servo feed axis.

2. The method according to claim 1, characterized in that, Step 1 specifically involves: The dynamic model of the machine tool servo system in state space is as follows: in, This is the nominal value of the equivalent inertia. This is the nominal value of the viscous friction coefficient. This refers to the actual position of the feed drive. It is the speed of the feed drive. For the acceleration of the feed drive, To control the voltage, It is an external disturbance to the system; The dynamic model is simplified as Among them, state variables Machine tool parameters , , ; acceleration of the linear feed axis Represented as: 。 3. The method according to claim 2, characterized in that, Step 2 specifically involves: The disturbance observer is designed as follows: in, The observer gain matrix is... and It is a constant. It is an estimate of the disturbance. and As an intermediate variable; A second-order Butterworth low-pass filter is set after the disturbance observer as follows: in, It is the natural frequency. It is the damping ratio.

4. The method according to claim 3, characterized in that, Step 3 specifically involves: Design a nonsingular terminal sliding surface function. for: in, Tracking error The derivative of , All are positive odd integers. It is a parameter that needs to be designed. It is the reference trajectory for the design.

5. The method according to claim 4, characterized in that, Step 4 specifically involves: Depend on Obtain the equivalent control law for: 。 6. The method according to claim 5, characterized in that, Step 5 specifically involves: Design an adaptive variable boundary layer thickness saturation function for: in, It is the thickness of the boundary layer. , , , and All are positive numbers, satisfying and .

7. The method according to claim 6, characterized in that, Step 6 specifically involves: Design switching control law for: in, and They are all positive constants. , It is a positive constant.

8. The method according to claim 7, characterized in that, Step 7 specifically involves: The total control voltage is expressed in the following form: 。 9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the machine tool tracking error control method based on the adaptive variable boundary layer thickness non-singular terminal sliding mode as described in any one of claims 1 to 8.

10. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to execute the machine tool tracking error control method based on adaptive variable boundary layer thickness nonsingular terminal sliding mode according to any one of claims 1 to 8 by executing the executable instructions.

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