Multi-scale modeling method based on permanent magnet linear motor driven motion stage

Abstract

The application provides a multi-scale modeling method based on a permanent magnet linear motor driven motion platform, and belongs to the technical field of ultra-precision motion control. The method solves the index distribution problem of different physical processes of the motor model in the prior art, and improves the system modeling accuracy and simulation efficiency. The method comprises the following steps: step one, system scale division, the permanent magnet linear motor driven motion platform system is divided into three scales of electromagnetic scale, dynamics scale and control system scale; step two, based on scale division, an electromagnetic thrust model of electromagnetic scale, a structure dynamics model of dynamics scale and a position control system model of control system scale are constructed; step three, a multi-scale coupling mechanism is constructed, and a cross-scale information transmission relationship is established; and step four, multi-scale model joint solution. The application solves the index distribution problem of different physical processes of the existing motor model, minimizes the control error under the condition of certain engineering parameters, and improves the system modeling accuracy and simulation efficiency.

Description

Technical Field

[0001] This invention belongs to the field of ultra-precision motion control technology, and in particular relates to a multi-scale modeling method based on a motion stage driven by a permanent magnet linear motor. Background Technology

[0002] With the development of semiconductor manufacturing, precision machining, and high-end equipment manufacturing technologies, precision motion platforms are increasingly widely used in industrial production and scientific research. Precision motion stages driven by permanent magnet linear motors have become important actuators in high-precision motion control systems due to their advantages such as simple structure, fast response speed, high positioning accuracy, and no mechanical transmission backlash. They are widely used in systems such as lithography equipment, precision measuring equipment, and high-speed machining platforms.

[0003] When designing and researching control strategies for motion tables driven by permanent magnet linear motors, it is usually necessary to establish a mathematical model of the system to describe the electromagnetic characteristics of the motor, the dynamic characteristics of the mechanical structure, and the coupling relationship between the control system. In existing technologies, lumped parameter models or single-scale models are often used to model the motion table system, for example, by establishing an electromagnetic model of the motor and a mechanical dynamic model to describe the overall motion characteristics of the system. However, actual motion table systems typically involve multiple physical processes, and their dynamic behavior is influenced not only by the electromagnetic characteristics of the motor but also by the combined effects of structural vibration modes and the dynamic characteristics of the control system.

[0004] Because a permanent magnet linear motor-driven motion stage is a complex electromechanical system, it often contains different spatial and temporal scales simultaneously. For example, the electromagnetic processes of the motor typically occur on a shorter time scale, while the vibration of the mechanical structure involves spatial scale characteristics such as structural modes, and the control system exhibits macroscopic dynamic behavior. Traditional single-scale modeling methods often fail to accurately describe the coupling relationships between different scales, thus affecting the accuracy of system simulation analysis and control system design.

[0005] Therefore, how to establish a modeling method that can describe the coupling relationship between different scales and achieve index allocation and high-precision modeling of different physical processes of a permanent magnet linear motor driven motion stage system has become a problem that needs to be solved in the field of electromechanical system modeling and motion control. Summary of the Invention

[0006] To address the problems existing in the background technology, this invention provides a multi-scale modeling method based on a motion stage driven by a permanent magnet linear motor. This method solves the problem of index allocation for different physical processes in the existing motor model, thereby improving the system modeling accuracy and simulation efficiency.

[0007] The technical solution adopted by this invention to solve its technical problem is: a multi-scale modeling method based on a motion table driven by a permanent magnet linear motor, comprising the following steps:

[0008] Step 1: System Scale Division. The permanent magnet linear motor driven motion table system is divided into three scales: electromagnetic scale, dynamic scale, and control system scale.

[0009] Step 2: Based on the scale division, construct an electromagnetic thrust model at the electromagnetic scale, a structural dynamics model at the dynamic scale, and a position control system model at the control system scale;

[0010] Step 3: Construct a multi-scale coupling mechanism to establish cross-scale information transmission relationships;

[0011] Step 4: Solve the multi-scale model together.

[0012] The construction of the electromagnetic thrust model in step two: an electromagnetic thrust model with input current:

[0013] (1)

[0014] In the formula Indicates electromagnetic thrust. For a constant motor thrust constant, For input current,

[0015] Due to the presence of ripple disturbance, the derived electromagnetic thrust model of the motor output is as follows:

[0016] (2)

[0017] In the formula, For the current frequency, The average thrust of the motor, ( () represents the amplitude of the motor thrust ripple. This represents the number of pole pairs of the motor.

[0018] The output electromagnetic thrust is affected by the cogging force, and the cogging force model is as follows:

[0019] (3)

[0020] In the formula, For the cogging torque, The length of the iron core. The average width of the air gap in the magnet area. Radial magnetic field strength For the thickness of the magnet, The length of the air gap. Permeability, For slot coefficient, The total magnetic field energy stored for the k-th tooth. The air gap magnetic permeability is a function of position variation. The ripple disturbance and cogging force models are fused, and the electromagnetic thrust model is simulated and analyzed using COMSOL and MATLAB.

[0021] The construction of the structural dynamics model in step two involves obtaining vibration modes through an experimental platform and constructing a low-order structural dynamics model.

[0022] (4)

[0023] In the formula, The quality of the basic modules, It's about the quality of the terminal module. It is the absolute displacement of the basic module. It is the absolute displacement of the terminal module. It is the relative displacement of the terminal module relative to the basic module. The stiffness coefficient in the system, is the damping coefficient of the system.

[0024] Equation (4) and The relationship between them, after being transformed by Laplace, yields the expression for the second-order transfer function of the system:

[0025] (5)

[0026] In the formula, This is the undamped resonant angular frequency of the second-order system. Let be the damping coefficient of the second-order system.

[0027] The construction of the position control system model in step two involves measuring and calculating the position error using sensors, outputting a current control signal, and thus controlling the motion trajectory of the motion table. The expression is as follows:

[0028] (6)

[0029] In the formula, For sensor output current, For sensor constants, To address the position error, the position control system model compares the actual displacement feedback signal of the motion table with the target position signal, generates control commands using the VEM chassis, amplifies them via a power amplifier, and transmits them to the electromagnetic model.

[0030] The multi-scale coupling mechanism described in step three involves the position control system model transmitting current control signals to the electromagnetic thrust model, the electromagnetic thrust model transmitting electromagnetic thrust to the structural dynamics model, and the structural dynamics model feeding back the motion table displacement error to the position control system model.

[0031] The beneficial effects of this invention are: the method solves the problem of index allocation for different physical processes in motor models in the prior art, and improves the system modeling accuracy and simulation efficiency.

[0032] This method provides a detailed analysis of the motor's output mechanism and output disturbances, and considers these disturbances during model building to improve model accuracy and compensate for model errors caused by output disturbances. The method integrates multi-scale models, from electromagnetic output to structural dynamics modeling, and then to a position control system composed of sensors. The position control system controls the input current of the electromagnetic thrust model to form a closed loop, allowing for the allocation of control errors across various stages. By adjusting the parameters of each model, the control error is minimized under given engineering parameters, achieving high-precision modeling and index allocation for different physical processes in a permanent magnet linear motor-driven motion table system. Attached Figure Description

[0033] In the attached diagram:

[0034] Figure 1 This is a schematic diagram of the structural dynamics model of the motion table driven by a permanent magnet linear motor provided by the present invention;

[0035] Figure 2 This is a flowchart of the multi-scale modeling method based on a permanent magnet linear motor driven motion table provided by the present invention;

[0036] Figure 3 This is a schematic diagram of the multi-scale fusion modeling provided by the present invention. Detailed Implementation

[0037] The present invention will now be described in further detail with reference to the accompanying drawings. The drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0038] A multi-scale modeling method based on a motion table driven by a permanent magnet linear motor includes the following steps:

[0039] Step 1: System Scale Division. Based on the physical characteristics and dynamic behavior of the system, the permanent magnet linear motor driven motion table system is divided into three scales: electromagnetic scale, dynamic scale, and control system scale. The electromagnetic scale is used to describe the electromagnetic characteristics of the motor; the dynamic scale is used to describe the vibration characteristics of the mechanical structure of the motion table; and the control system scale is used to describe the dynamic behavior of the motion control system.

[0040] Step 2: Based on the scale division in Step 1, construct the electromagnetic thrust model at the electromagnetic scale, the structural dynamics model at the dynamic scale, and the position control system model at the control system scale.

[0041] Step 3: Construct a multi-scale coupling mechanism to establish cross-scale information transmission relationships between the electromagnetic scale, dynamic scale, and control system scale;

[0042] Step four: The multi-scale model is solved jointly using an iterative calculation method. In each calculation cycle, the control calculation, electromagnetic thrust calculation, and structural response calculation are completed sequentially. The displacement of the motion table is fed back to the control system to form a closed-loop control until the system response reaches a stable state.

[0043] The construction of the electromagnetic thrust model in step two involves establishing an electromagnetic mathematical model of the permanent magnet linear motor, calculating the electromagnetic thrust generated by the motor based on the input current, and using this electromagnetic thrust as the input quantity for the structural dynamics model. Generally, there exists an electromagnetic thrust model generated by the input current.

[0044] (1)

[0045] In the formula Indicates electromagnetic thrust. For a constant motor thrust constant, For input current,

[0046] However, since the armature current and primary back EMF waveforms of the motor are not ideal sinusoidal waveforms, they will cause fluctuations in the motor thrust constant, i.e., there is a ripple disturbance phenomenon. After derivation, the electromagnetic thrust model of the motor output is as follows:

[0047] (2)

[0048] In the formula, The frequency of the current (in rad / s). The average thrust of the motor, ( () represents the amplitude of the motor thrust ripple. This represents the number of pole pairs of the motor.

[0049] Furthermore, the output electromagnetic thrust is also affected by the cogging force, the model of which is:

[0050] (3)

[0051] In the formula, For the cogging torque, The length of the iron core. The average width of the air gap in the magnet area. Radial magnetic field strength For the thickness of the magnet, The length of the air gap. Permeability, For slot coefficient, The total magnetic field energy stored for the k-th tooth. It is a function of air gap permeability as a function of position.

[0052] The above equation shows that cogging force is only related to the motor position and not to the current. This means that cogging force exists even when no current is flowing through the motor. Therefore, it is necessary to fuse the ripple disturbance and cogging force models. COMSOL and MATLAB are used in conjunction to simulate and analyze the electromagnetic inference model to solve the problem of complex model fusion.

[0053] The second step involves constructing the structural dynamics model: A physical model of the motion platform is created, comprising a base module and a terminal module. The base module is directly driven by an external force from a linear motor, while the terminal module is driven by the base module through an elastic damping device. To reduce friction, the base module is guided by an air-bearing guide rail, which carries the terminal module, allowing it to move together with the base module. This system can be modeled as a two-mass system, which can be considered an underdamped second-order system.

[0054] Vibration modes were obtained through an experimental platform, and a low-order structural dynamics model was constructed.

[0055] (4)

[0056] In the formula, The quality of the basic modules, It's about the quality of the terminal module. It is the absolute displacement of the basic module. It is the absolute displacement of the terminal module. It is the relative displacement of the terminal module relative to the basic module. The stiffness coefficient in the system, The damping coefficient of the system is...

[0057] Equation (4) and The relationship between them, after being transformed by Laplace, yields the expression for the second-order transfer function of the system:

[0058] (5)

[0059] In the formula, This is the undamped resonant angular frequency of the second-order system. Let be the damping coefficient of the second-order system.

[0060] The structural dynamics model is used to calculate the displacement, velocity, and acceleration response of the motion platform under electromagnetic thrust.

[0061] The construction of the position control system model in step two involves measuring and calculating the position error using sensors, outputting a current control signal, and thus controlling the motion trajectory of the motion table. The expression is as follows:

[0062] (6)

[0063] In the formula, For sensor output current, For sensor constants, To address the position error, the position control system model compares the actual displacement feedback signal of the motion table with the target position signal, generates control commands using the VEM chassis, amplifies them via a power amplifier, and transmits them to the electromagnetic model.

[0064] The multi-scale coupling mechanism described in step three involves the position control system model transmitting current control signals to the electromagnetic thrust model, the electromagnetic thrust model transmitting electromagnetic thrust to the structural dynamics model, and the structural dynamics model feeding back the motion table displacement error to the position control system model. This multi-scale information transmission mechanism enables the dynamic coupling of multiple models.

[0065] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A multi-scale modeling method based on a motion table driven by a permanent magnet linear motor, characterized in that: Includes the following steps: Step 1: System Scale Division. The permanent magnet linear motor driven motion table system is divided into three scales: electromagnetic scale, dynamic scale, and control system scale. Step 2: Based on the scale division, construct an electromagnetic thrust model at the electromagnetic scale, a structural dynamics model at the dynamic scale, and a position control system model at the control system scale; Step 3: Construct a multi-scale coupling mechanism to establish cross-scale information transmission relationships; Step 4: Solve the multi-scale model together.

2. The multi-scale modeling method based on a permanent magnet linear motor-driven motion stage according to claim 1, characterized in that: The construction of the electromagnetic thrust model in step two: An electromagnetic thrust model exists that generates input current: （1） In the formula Indicates electromagnetic thrust. For a constant motor thrust constant, For input current, Due to the presence of ripple disturbance, the derived electromagnetic thrust model of the motor output is as follows: （2） In the formula, For the current frequency, The average thrust of the motor, ( () represents the amplitude of the motor thrust ripple. This represents the number of pole pairs of the motor. The influence of the output electromagnetic thrust on the cogging force, the cogging force model is as follows: （3） In the formula, For the cogging torque, The length of the iron core. The average width of the air gap in the magnet area. Radial magnetic field strength For the thickness of the magnet, The length of the air gap. Permeability, For slot coefficient, The total magnetic field energy stored for the k-th tooth. The air gap magnetic permeability is a function of position variation. The ripple disturbance and cogging force models are fused, and the electromagnetic thrust model is simulated and analyzed using COMSOL and MATLAB.

3. The multi-scale modeling method based on a permanent magnet linear motor-driven motion stage according to claim 2, characterized in that: The construction of the structural dynamics model in step two: Vibration modes were obtained through an experimental platform, and a low-order structural dynamics model was constructed. （4） In the formula, The quality of the basic modules, It's about the quality of the terminal module. It is the absolute displacement of the basic module. It is the absolute displacement of the terminal module. It is the relative displacement of the terminal module relative to the basic module. The stiffness coefficient in the system, The damping coefficient in the system is... Equation (4) and The relationship between them, after being transformed by Laplace, yields the expression for the second-order transfer function of the system: （5） In the formula, This is the undamped resonant angular frequency of the second-order system. Let be the damping coefficient of the second-order system.

4. The multi-scale modeling method based on a permanent magnet linear motor-driven motion stage according to claim 3, characterized in that: The construction of the position control system model in step two involves measuring and calculating the position error using sensors, outputting a current control signal, and thus controlling the motion trajectory of the motion table. The expression is as follows: （6） In the formula, For sensor output current, For sensor constants, To address the position error, the position control system model compares the actual displacement feedback signal of the motion table with the target position signal, generates control commands using the VEM chassis, amplifies them via a power amplifier, and transmits them to the electromagnetic model.

5. The multi-scale modeling method based on a permanent magnet linear motor-driven motion stage according to claim 4, characterized in that: The multi-scale coupling mechanism described in step three involves the position control system model transmitting current control signals to the electromagnetic thrust model, the electromagnetic thrust model transmitting electromagnetic thrust to the structural dynamics model, and the structural dynamics model feeding back the displacement error of the motion table to the position control system model.

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