A friction compensation method and CNC machine tool based on friction model and linear extended state observer

Abstract

The present invention belongs to the technical field related to numerical control technology, and discloses a friction compensation method and a numerical control machine tool based on a friction model and a linear expansion state observer, the steps of which are as follows: (1) based on the command position signal s at the current moment during the motion process; i (k) Calculate the current command speed v i (k); (2)SSV friction model is based on the command speed v i (k) Predict the current feedforward friction force F i (k), and then the feedforward friction force F i (k) is converted into the friction current feedforward value IF i (k); (3) the friction current feedforward IF i (k) The current loop feedforward register of the driver is sent to the CNC system; (4) The LESO inside the driver is based on the feedback speed signal v back_i (k), the signal I output by the current loop cmd_i (k) and the friction current feedforward IF i (k), estimate the external disturbance δ at the current moment i (k), and the external disturbance δ i (k) Feedforward compensation into the current loop. The present invention solves the problem of low precision of existing friction compensation.

Description

Technical Field

[0001] The present invention belongs to the technical field related to numerical control technology, and more specifically, relates to a friction compensation method and a numerically controlled machine tool based on a friction model and a linear expansion state observer. Background Art

[0002] A major technical difficulty in high-precision CNC systems lies in the nonlinearity and uncertainty inherent in complex servo systems, with friction being one of the main factors contributing to the decline in system tracking accuracy and response quality. Friction is widely present between moving contact surfaces and exhibits complex nonlinear characteristics. Friction is not only a function of relative motion speed but is also related to environmental factors such as temperature. Nonlinear friction can cause the servo system to exhibit low-speed creep, position tracking flattening, velocity tracking dead zones, and steady-state limit cycle oscillations, leading to large contour errors on the workpiece surface. Nonlinear friction is particularly severe when the system is running at low speeds. For systems with high low-speed performance requirements, such as precision machining machines, friction is a challenge that must be overcome.

[0003] Currently, friction compensation methods are mainly divided into two categories: model-based compensation methods and model-free compensation methods. The simplest and most effective model-based compensation method is feedforward control based on a fixed parameter inverse model. When performing compensation, the desired speed or feedback speed is usually selected as the input, and the compensation effect depends on the accuracy of the model and parameters. However, friction is an extremely complex process. Although domestic and international research has proposed some sufficiently accurate models to describe friction phenomena, the more accurate the model, the more parameters are involved, making identification more difficult and increasing the cost of compensation.

[0004] Model-free compensation methods primarily include high-gain PID control, iterative learning control, signal jittering, disturbance observer control, and variable structure control. They treat nonlinear friction, along with other disturbances, as external disturbances and suppress the effects of disturbances on the system by changing the control structure or parameters. While model-free compensation methods do not require identification of friction parameters, reducing the cost of friction compensation, the control strategy design is not as concise as that of model-based compensation methods, and the compensation strategy's adjustment capabilities are insufficient to track overly complex friction changes, resulting in poor compensation effectiveness and a high risk of system oscillation. Summary of the Invention

[0005] In response to the above defects or improvement needs of the prior art, the present invention provides a friction compensation method and a CNC machine tool based on a friction model and a linear extended state observer, which aim to solve the problem of low accuracy of existing friction compensation.

[0006] To achieve the above object, according to one aspect of the present invention, a friction compensation method based on a friction model and a linear extended state observer is provided, the method comprising the following steps:

[0007] (1) Based on the current command position signal s after interpolation by the CNC system during motion i (k) Calculate the current command speed v i (k);

[0008] (2) The SSV friction model is based on the command speed v i (k) Predict the current feedforward friction force F i (k), and then the feedforward friction force F i (k) is converted into the friction current feedforward value IF i (k);

[0009] (3) The friction current feedforward IF i (k) Send it to the corresponding current loop feedforward register of the driver of the CNC system, and calculate the friction current feedforward value IF at the current moment. i (k) performing filtering processing;

[0010] (4) The LESO inside the driver is based on the feedback speed signal v back_i (k), the signal I output by the current loop cmd_i (k) and the friction current feedforward IF i (k), estimate the external disturbance δ at the current moment i (k), and the external disturbance δ i (k) Feedforward compensation into the current loop.

[0011] Furthermore, the calculation formula of the friction force predicted by the SSV friction model is:

[0012]

[0013] Where, F s is the maximum static friction force; F c is the Coulomb friction force; v s is the Stribeck velocity; B is the viscous friction;

[0014] ξ(k) is the bristle deformation variable of the SSV friction model; α is the viscous friction correction coefficient; ρ, σ, and n are the SSV dynamic friction parameters.

[0015] Furthermore, the calculation formula of the friction current feedforward is:

[0016]

[0017] Among them Fsc (k) is the friction force that characterizes the Stribeck characteristic, F bw (k) is the friction force that characterizes the friction hysteresis part; K t is the motor torque constant.

[0018] Furthermore, the disturbance z2 estimated by LESO is i (k), calculated as follows:

[0019]

[0020] Where β1 and β2 are the gains of LESO; z1 is the extended state observable of LESO; and J is the inertia of the machine tool feed system.

[0021] Furthermore, before step (1), a step of obtaining relevant parameters of the CNC machine tool is also included.

[0022] Furthermore, the friction parameters of the machine tool feed system are identified by friction feedforward parameter identification software for use in the SSV friction model.

[0023] The present invention also provides a numerically controlled machine tool, which performs friction compensation by using the friction compensation method based on the friction model and the linear extended state observer as described above.

[0024] In general, compared with the prior art, the friction compensation method and CNC machine tool based on the friction model and linear extended state observer provided by the present invention have the following beneficial effects:

[0025] 1. The friction compensation method based on the friction model and linear extended state observer of the present invention takes into account the effects of inaccurate friction model identification, uneven friction parameters and environmental changes in practical applications, and regards them as residual disturbances for compensation through LESO. It expands the friction feedforward calculation model, improves the accuracy of friction feedforward control, and improves the compensation accuracy. Compared with the traditional friction feedforward method, it further improves the dynamic response performance of the machine tool feed system, further reduces the position tracking error of the machine tool feed to within 3μm, and thus improves the machining accuracy of the machine tool.

[0026] 2. The SSV friction model feedforward calculation process is implemented on the CNC system side, while LESO is implemented on the servo side. This ensures real-time estimation of system states and provides strong support for control decisions. Compared to traditional feedforward control methods within servo drives, this method leverages the high computing power of the CNC system to meet the computational requirements of complex models, while providing users with greater flexibility and adaptability. It effectively utilizes the CNC system's software and hardware resources, maximizing the control accuracy of the machine tool feed system.

[0027] 3. The present invention provides a calculation formula for friction force predicted by a friction model based on the friction characteristics of CNC machine tools, which is conducive to improving accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a flow chart of a friction compensation method based on a friction model and a linear extended state observer provided by the present invention;

[0029] Figure 2 Schematic diagram of the command position signal and command speed signal required for the feedforward calculation involved in the present invention;

[0030] Figure 3 yes Figure 1 Implementation principle block diagram of the friction compensation method based on friction model and linear extended state observer;

[0031] Figure 4 (a) and (b) are the curves of velocity and following error respectively. DETAILED DESCRIPTION

[0032] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0033] See also Figure 1 and Figure 3 The present invention provides a friction compensation method based on a friction model and a linear extended state observer. The compensation method uses a single state variable friction (SSV) model based on Bouc-Wen to compensate for the main part of the friction in the feed system. The influence caused by inaccurate friction model identification, uneven friction parameters and environmental changes is then regarded as a residual disturbance force and compensated using a linear extended state observer (LESO). High-precision control based on dynamics is achieved. On the basis of the traditional friction force compensation method, the position tracking error of the machine tool feed system is further reduced, achieving a tracking error control level of micron level (within 3μm).

[0034] The compensation method mainly includes the following steps:

[0035] Step 1: Obtain relevant parameters of the CNC machine tool and identify the friction parameters of the machine tool feed system through friction feedforward parameter identification software for use in a single state variable friction model (SSV friction model).

[0036] The parameters required for this implementation are as follows:

[0037] Table 1 Relevant parameters required to obtain the single state variable friction model

[0038]

[0039] Step 2: Based on the current command position signal s after interpolation by the CNC system during the motion process i (k) Calculate the current command speed v i (k).

[0040] In this embodiment, a command position signal that has been interpolated and planned by the numerical control system and satisfies certain speed and acceleration constraints is obtained, and the command position signal can be further differentially calculated to obtain corresponding command speed and acceleration signals.

[0041] See also Figure 2 , command speed v i The calculation formula for (k) is:

[0042]

[0043] Where i is the selected feed axis number, k is the kth control cycle, and ΔT is the interpolation cycle of the CNC system.

[0044] Step 3: The SSV friction model is based on the command speed v i (k) Predict the current feedforward friction force F i (k), and then the feedforward friction force F i (k) is converted into the friction current feedforward value IF i (k).

[0045] Friction feedforward is generally used on the basis of velocity and acceleration feedforward to further reduce the following error caused by friction in the reverse segment.

[0046] The calculation formula of the friction force predicted by the SSV friction model is:

[0047]

[0048] Where, F s is the maximum static friction force; F c is the Coulomb friction force; v s is the Stribeck velocity; B is the viscous friction;

[0049] ξ(k) is the bristle deformation variable of the SSV friction model; α is the viscous friction correction coefficient; ρ, σ, and n are the SSV dynamic friction parameters.

[0050] The calculation formula of the friction current feedforward is:

[0051]

[0052] Among them F sc (k) is the friction force that characterizes the Stribeck characteristic, F bw (k) is the friction force that characterizes the friction hysteresis part; K t is the motor torque constant.

[0053] Step 4: The friction current feedforward IF i (k) Send it to the corresponding current loop feedforward register of the driver of the CNC system, and calculate the friction current feedforward value IF at the current moment. i (k) Perform filtering processing.

[0054] Among them, it is necessary to ensure that the driver has the corresponding interface inside, and the feedforward amount must be converted according to the speed and current calculation units inside the driver to ensure the accuracy of the feedforward control.

[0055] Step 5: The LESO inside the driver is based on the feedback speed signal v back_i (k), the signal I output by the current loop cmd_i (k) and the friction current feedforward IF i (k), estimate the external disturbance δ at the current moment i (k), and the external disturbance δ i (k) Feedforward compensation into the current loop.

[0056] Among them, LESO requires machine tool commissioning personnel to configure corresponding parameters based on the identified total inertia of the feed system.

[0057] The disturbance z2 estimated by LESO is δ i (k), calculated as follows:

[0058]

[0059] Where β1 and β2 are the gains of LESO; z1 is the extended state observable of LESO; and J is the inertia of the machine tool feed system.

[0060] Steps 2 to 5 are the feedforward control implementation process within a control cycle. During the machining process of the machine tool, the feedforward control implementation process can effectively reduce the position following error of each feed axis within the entire motion cycle, and achieve near-zero following error control in the uniform speed section and micron-level (within 3μm) following error control in the variable speed section. Compared with the traditional friction feedforward method, the specific effects of the present invention are as follows: Figure 4 shown.

[0061] The present invention also provides a numerically controlled machine tool, which performs friction compensation by using the friction compensation method based on the friction model and the linear extended state observer as described above.

[0062] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A friction compensation method based on a friction model and a linear extended state observer, characterized in that: The method comprises the following steps: (1) Based on the current command position signal s after interpolation by the CNC system during motion i (k) Calculate the current command speed v i (k); (2) The SSV friction model is based on the command speed v i (k) Predict the current feedforward friction force F i (k), and then the feedforward friction force F i (k) is converted into the friction current feedforward value IF i (k); (3) The friction current feedforward IF i (k) Send it to the corresponding current loop feedforward register of the driver of the CNC system, and calculate the friction current feedforward value IF at the current moment. i (k) performing filtering processing; (4) The LESO inside the driver is based on the feedback speed signal v back_i (k), the signal I output by the current loop cmd_i (k) and the friction current feedforward IF i (k), estimate the external disturbance δ at the current moment i (k), and the external disturbance δ i (k) Feedforward compensation into the current loop.

2. The friction compensation method based on the friction model and the linear extended state observer according to claim 1, characterized in that: The calculation formula of the friction force predicted by the SSV friction model is: Where, F s is the maximum static friction force; F c is the Coulomb friction force; v s is the Stribeck velocity; B is the viscous friction force; ξ(k) is the bristle deformation of the SSV friction model; α is the viscous friction correction coefficient; ρ, σ, n are the SSV dynamic friction parameters; F sc (k) is the friction force that characterizes the Stribeck characteristic, F bw (k) is the friction force representing the friction hysteresis part.

3. The friction compensation method based on the friction model and the linear extended state observer according to claim 2, characterized in that: The calculation formula of the friction current feedforward is: where K t is the motor torque constant.

4. The friction compensation method based on the friction model and the linear extended state observer according to claim 3, characterized in that: The disturbance z2 estimated by LESO is δ i (k), calculated as follows: Where β1 and β2 are the gains of LESO; z1 is the extended state observable of LESO; and J is the inertia of the machine tool feed system.

5. The friction compensation method based on a friction model and a linear extended state observer according to any one of claims 1 to 4, characterized in that: Before step (1), the method also includes the step of obtaining relevant parameters of the CNC machine tool.

6. The friction compensation method based on the friction model and the linear extended state observer according to claim 5, characterized in that: The friction parameters of the machine tool feed system are identified by friction feedforward parameter identification software and used for the SSV friction model.

7. A CNC machine tool, characterized in that: The CNC machine tool performs friction compensation by adopting the friction compensation method based on the friction model and the linear extended state observer as described in any one of claims 1 to 6.

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