Non-circular contour part position domain high-precision turning method and device and medium

Abstract

The invention discloses a non-circular contour part position domain high-precision turning method and device and a medium. The method comprises the steps that for a rotating system, a motor voltage excitation signal is given, a tool position output signal is collected, and a system identification tool box is adopted to obtain a rotating system second-order state space model in a time domain; for the problem that the control performance of the rotating system is obviously reduced by the change of a time period, a definition of a position domain is given, and a time domain model of the rotating system is converted into a position domain model; discretizing the position domain model according to the obtained position domain model, converting the position domain model into a high-order all-drive model, and then designing a corresponding all-drive stabilization controller to stabilize the rotating system; and designing a model prediction controller to solve an optimal control law and inversely transforming the optimal control law into an all-drive control law through a corresponding relational expression. According to the method, the rotation system in the position domain is represented by adopting the all-drive system model, so that the physical interpretation of the model can be maintained, and the problem of bad matrixes frequently occurring in the traditional means can be avoided.

Description

Technical Field

[0001] The present invention relates to the field of precision machining, and in particular to a method, device and medium for high-precision turning machining of non-circular contour parts. Background Art

[0002] CNC machine tools play a vital role in the machining of non-circular contour parts in the automotive, marine and aerospace industries. Components such as cams, camshafts and convex elliptical pistons usually require high-precision turning to ensure their performance and durability. The shape of these parts determines that the reference input of the cutting tool depends on the rotation angle of the workpiece rather than the time process, resulting in the actual signal having periodic characteristics in position rather than time. Specifically, when the workpiece rotates around the spindle, the cutting tool needs to be precisely adjusted according to the change in rotation angle to achieve the desired cutting shape. This position-related periodic characteristic poses significant challenges to traditional time-domain repetitive control systems.

[0003] To solve the above problems, researchers have integrated some adaptive methods into time-domain repetitive control systems, such as improving performance by adjusting the sampling period or buffer length of the repetitive controller. However, these methods not only increase the computational complexity, but may also cause stability problems. Therefore, when dealing with the high-precision control requirements of rotating systems, choosing to adopt a position-domain control strategy becomes a more effective approach. The position-domain control strategy focuses on periodic signals related to position. Since the period of these signals is constant relative to the position and is independent of the rotation speed, the controller designed in the position domain can more effectively cope with the challenges brought by changes in rotation speed. The concept of position domain was originally introduced to suppress angle-related interference in constant-speed rotating systems. Compared with the time domain, control in the position domain can more accurately track and suppress spatial periodic interference, ensuring efficient suppression of position-related periodic interference, and therefore has received widespread attention.

[0004] It is worth noting that many existing methods still rely on state-space models to describe rotating systems, which leads to the fuzziness of the physical meaning of the system and may cause ill-conditioned matrix problems when the model is simplified, thus affecting the control performance and stability. In contrast, the all-wheel drive system is modeled based on physical laws, which can more accurately reflect the dynamic characteristics of the real system, while avoiding the numerical calculation problems caused by ill-conditioned matrices and retaining the physical meaning of the system. This modeling method not only improves the accuracy of the model, but also simplifies the control system design, making it more suitable for high-precision machining of complex non-circular contour parts. Summary of the invention

[0005] The purpose of the present invention is to provide a method, device and medium for high-precision turning of non-circular contour parts based on high-order full drive in position domain. First, for the rotating system, a motor voltage excitation signal is given to collect the tool position output signal, and the second-order state space model of the rotating system in the time domain is obtained by using the Matlab system identification toolbox; secondly, in view of the problem that the change of time period will significantly reduce the control performance of the system, the definition of the position domain and a transformation method for converting the rotating system model from the time domain to the position domain are given; then, according to the obtained position domain model, it is further discretized and converted into a high-order full drive model; then, the corresponding full drive control law is designed to stabilize the system; finally, a model predictive controller is designed to solve the optimal control law and inversely transform it into the full drive control law through the corresponding relationship, so as to realize high-precision turning of non-circular contour parts.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A high-precision turning method for a non-circular contour part position domain, comprising:

[0008] Step S1: for a rotating system, a motor voltage excitation signal is given, a tool position output signal is collected, and a system identification toolbox is used to obtain a second-order state space model of the rotating system in the time domain;

[0009] Step S2: In view of the problem that the change of time period will significantly reduce the control performance of the rotating system, a definition of the position domain is given, and a transformation method is used to convert the time domain model of the rotating system into a position domain model;

[0010] Step S3: discretize the position domain model and convert it into a high-order all-wheel drive model according to the obtained position domain model, and then design a corresponding all-wheel drive stabilization controller to stabilize the rotating system;

[0011] Step S4: Design a model predictive controller to solve the optimal control law and inversely transform it into the full-drive control law through the corresponding relationship.

[0012] Furthermore, the second-order state space model of the rotating system obtained in step S1 is:

[0013] (1)

[0014] in, represents the state of the rotating system, represents the time derivative of the rotating system state, Represents the tool position output signal, represents the motor voltage excitation signal, represents the state matrix of the rotating system, represents the control matrix of the rotation system, Represents the output matrix of the rotation system.

[0015] Furthermore, the step S2 comprises:

[0016] definition is the rotation speed of the rotating system, , then any position in the time domain can be expressed as:

[0017] (2)

[0018] in, For the moment The corresponding position, is the integral variable, the position domain is a set of positions defined by a series of equations (2), and the time domain signal In the location domain it is represented as :

[0019] (3)

[0020] and The relationship is , the inverse function of formula (2) is given by:

[0021] (4)

[0022] in, represents the system speed in the position domain. Substituting equation (2) into equation (1), the state of the rotating system is The derivative of can be expressed as:

[0023] (5)

[0024] in, Represents the state of the rotating system in the position domain, As the independent variable of the rotating system state, the rotating system state space model in the position domain is:

[0025] (6)

[0026] in, and They are the tool position output signal and motor voltage excitation signal in the position domain respectively.

[0027] Furthermore, the step S3 comprises:

[0028] Defining constants With the current turntable speed The relationship is , while considering the rotation system identification parameters and , then the equation of the rotating system is written as:

[0029] (7)

[0030] in, is the system identification parameter, Taking the derivation, we can get ,in express The second-order derivative of The equation Substituting into the elimination we get:

[0031] (8)

[0032] Formula (8) is converted into After discretization, the following high-order all-wheel drive model can be obtained:

[0033] (9)

[0034] in, , Respectively 1,2 step recursion, , , are all intermediate variables. , , ;

[0035] Based on the high-order full-drive theory, if the coefficient matrix reversible, the rotating system is fully driven; the direct parameter method is used to design the fully driven stabilizing controller, and the design There are the following forms:

[0036] (10)

[0037] in is the parameter matrix of the designed all-wheel drive stabilization controller, is an external signal;

[0038] Substitute equation (9) into equation (8) to convert the original rotating system into full-drive form:

[0039] (11).

[0040] Furthermore, the step S4 comprises:

[0041] remember for The augmented matrix is ​​formed by , , , then:

[0042] (12)

[0043] in, express 1-step recursion, is the identity matrix of appropriate dimension;

[0044] For the reference input position signal in the position domain derived from the rotation angle of the spindle motor , design a model predictive controller to solve the optimal control law; set the prediction interval , the recursive expression is as follows:

[0045] (13)

[0046] in for The augmented matrix is ​​formed by Indicates that of Step by step, Indicates that of Step by step, Respectively 2. , , Power;

[0047] Defining quadratic performance indicators for:

[0048] (14)

[0049] in, represents the state weight matrix of the rotating system, represents the control weight matrix of the rotation system, represents the matrix transpose symbol, for The augmented matrix is ​​formed by , for The augmented matrix is ​​formed by Input position signal for reference in position domain, and The relationship is as follows:

[0050]

[0051] in, Respectively for of Step recursion;

[0052] Quadratic performance indicators through Yalmip toolbox Solve and obtain the optimal control sequence ;

[0053] Take the first element of the sequence as the system control law at the current moment, and according to formula (10), convert the external signal obtained by the MPC controller into Through the inverse transformation of formula (10), ,Will Substituting the high-order full-drive model in the position domain shown in equation (9) into the high-precision turning of non-circular contour parts can be achieved.

[0054] The present invention also provides a high-precision turning processing device for non-circular contour parts in the position domain, characterized in that it includes one or more processors for implementing the high-precision turning processing method for non-circular contour parts in the position domain as described above.

[0055] The present invention also provides a readable storage medium on which a program is stored. When the program is executed by a processor, the method for high-precision turning of a non-circular contour part in position domain as described above is implemented.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1) In view of the problem that the change of time period will significantly reduce the control performance of the system, the present invention provides a definition of the position domain and a transformation method for converting the rotating system model from the time domain to the position domain;

[0058] 2) The present invention adopts the full-drive system model to characterize the rotation system in the position domain, which can not only maintain the physical interpretability of the model, but also avoid the bad matrix problem that often occurs in traditional methods, and also significantly improve the efficiency and simplicity of the design process;

[0059] 3) The present invention proposes an MPC method based on a high-order all-wheel drive model, which converts the obtained optimal control law back into control instructions suitable for the all-wheel drive system through the corresponding inverse transformation relationship, and finally achieves high-precision tracking of periodic reference inputs in the position domain. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 The present invention is a flow chart of a method for high-precision turning of non-circular contour parts in the position domain.

[0061] Figure 2 The present invention is a comparison curve diagram of the actual cutting trajectory of a turning tool and the reference trajectory in a method for high-precision turning of a non-circular contour part in the position domain.

[0062] Figure 3 It is a structural schematic diagram of a high-precision turning processing device for non-circular contour parts in the position domain of the present invention. DETAILED DESCRIPTION

[0063] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] See also Figure 1 and Figure 2 , a high-precision turning method for non-circular contour parts, comprising the following steps:

[0065] Step S1: for the rotating system (rotating drive system of the lathe spindle), a motor voltage excitation signal is given, the tool position output signal is collected, and a system identification toolbox is used to obtain a second-order state space model of the rotating system in the time domain. The system identification toolbox can be Matlab:

[0066] Among them, the second-order state space model of the rotating system is as follows:

[0067] (1)

[0068] in, represents the state of the rotating system, represents the time derivative of the rotating system state, Represents the tool position output signal, represents the motor voltage excitation signal, represents the state matrix of the rotating system, represents the control matrix of the rotation system, Represents the output matrix of the rotation system. .

[0069] Step S2: In view of the problem that the change of time period will significantly reduce the control performance of the rotating system, a definition of the position domain is given, and the rotating system model is converted from the time domain model to the position domain model through a transformation method, which specifically includes:

[0070] definition is the rotation speed of the rotating system, , then any position in the time domain can be expressed as:

[0071] (2)

[0072] in, For the moment The corresponding position, is the integral variable. The position domain is a set of positions defined by a series of equations (2). In the present invention, the time domain signal In the location domain it is represented as :

[0073] (3)

[0074] and The relationship is , the inverse function of formula (2) is given by:

[0075] (4)

[0076] in, represents the system speed in the position domain. Substituting equation (2) into equation (1), the state of the rotating system is The derivative of can be expressed as:

[0077] (5)

[0078] in, Represents the state of the rotating system in the position domain, As the independent variable of the rotating system state, the rotating system state space model in the position domain is:

[0079] (6)

[0080] in, and They are the tool position output signal and motor voltage excitation signal in the position domain respectively.

[0081] Step S3: based on the obtained position domain model, further discretize the position domain model and convert it into a high-order all-wheel drive model, and then design a corresponding all-wheel drive stabilization controller to stabilize the rotating system, specifically including:

[0082] Defining constants With the current turntable speed The relationship is In the present invention , while considering the rotation system identification parameters and , then the equation of the rotating system can be written as:

[0083] (7)

[0084] In the present invention, , , then formula (7) is:

[0085]

[0086] right Taking the derivation, we can get ,in express The second-order derivative of The equation Substituting into the elimination we get:

[0087] (8)

[0088] Formula (8) is converted into the increment of the rotation angle After discretization, the following high-order all-wheel drive model can be obtained:

[0089] (9)

[0090] in, , Respectively 1,2 step recursion, , , are all intermediate variables. , , . Specifically, , , .

[0091] Based on the high-order full-drive theory, if the coefficient matrix If the rotation system is reversible, then the rotation system is fully driven. The direct parameter method is used to design the fully driven stabilization controller. There are the following forms:

[0092] (10)

[0093] in is the parameter matrix of the designed all-wheel drive stabilization controller. , An external signal.

[0094] Substitute equation (9) into equation (8) to convert the original rotating system into full-drive form:

[0095] (11).

[0096] Step S4, designing a model predictive controller to solve the optimal control law and inversely transforming it into the full-drive control law through the corresponding relationship, specifically including:

[0097] remember for The augmented matrix is ​​formed by , , , then:

[0098] (12)

[0099] in, express 1-step recursion, is the identity matrix of appropriate dimension.

[0100] For the reference input position signal in the position domain derived from the rotation angle of the spindle motor , , design a model predictive controller to solve the optimal control law. Set the prediction interval , the recursive expression is as follows:

[0101] (13)

[0102] in for The augmented matrix is ​​formed by Indicates that of Step by step, Indicates that of Step by step, Respectively 2, 3, 4, 5 powers, and

[0103] ,

[0104] .

[0105] Where T represents the matrix transpose symbol.

[0106] Defining quadratic performance indicators for:

[0107] (14)

[0108] in, represents the state weight matrix of the rotating system, represents the control weight matrix of the rotation system, represents the matrix transpose symbol, for The augmented matrix is ​​formed by , An external signal. for The augmented matrix is ​​formed by Input position signal for reference in position domain, and The relationship is as follows:

[0109]

[0110] in, Respectively for of Step recursion.

[0111] The quadratic performance index J is solved by the Yalmip toolbox to obtain the optimal control sequence .

[0112] Take the first element of the sequence as the system control law at the current moment, and according to formula (10), convert the external signal obtained by the MPC controller into Through the inverse transformation of formula (10), ,Will Substituting the position domain high-order full-drive model shown in equation (9) into the high-precision turning process of non-circular contour parts, the final machining trajectory of the non-circular contour parts is as follows: Figure 2 shown.

[0113] See also Figure 3 An embodiment of the present invention provides a high-precision turning processing device for non-circular contour parts in the position domain, including one or more processors for implementing a high-precision turning processing method for non-circular contour parts in the position domain in the above-mentioned embodiment.

[0114] An embodiment of a high-precision turning processing device for position domain of non-circular contour parts of the present invention can be applied to any device with data processing capability, and the device with data processing capability can be a device or apparatus such as a computer. The device embodiment can be implemented through software, or through hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of any device with data processing capability in which it is located reading the corresponding computer program instructions in the non-volatile memory into the internal memory for execution. From the hardware level, if Figure 3 As shown, it is a hardware structure diagram of a non-circular contour part position domain high-precision turning processing device of the present invention, in which any device with data processing capability is located, except Figure 3 In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities in the embodiments may also include other hardware, usually based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0115] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0116] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0117] An embodiment of the present invention further provides a readable storage medium having a program stored thereon. When the program is executed by a processor, a high-precision turning method for position domain of a non-circular contour part in the above embodiment is implemented.

[0118] The readable storage medium may be an internal storage unit of any device with data processing capability described in any of the aforementioned embodiments, such as a hard disk or a memory. The readable storage medium may also be an external storage device, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. equipped on the device. Furthermore, the readable storage medium may also include both an internal storage unit of any device with data processing capability and an external storage device. The readable storage medium is used to store the computer program and other programs and data required by any device with data processing capability, and may also be used to temporarily store data that has been output or is to be output.

[0119] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A high-precision turning method for non-circular contour parts, characterized in that: include: Step S1: for a rotating system, a motor voltage excitation signal is given, a tool position output signal is collected, and a system identification toolbox is used to obtain a second-order state space model of the rotating system in the time domain; Step S2: In view of the problem that the change of time period will significantly reduce the control performance of the rotating system, a definition of the position domain is given, and a transformation method is used to convert the time domain model of the rotating system into a position domain model; Step S3: discretize the position domain model and convert it into a high-order all-wheel drive model according to the obtained position domain model, and then design a corresponding all-wheel drive stabilization controller to stabilize the rotating system; Step S4: Design a model predictive controller to solve the optimal control law and inversely transform it into the full-drive control law through the corresponding relationship.

2. A method for high-precision turning of non-circular contour parts according to claim 1, characterized in that: The second-order state space model of the rotating system obtained in step S1 is: (1) in, represents the state of the rotating system, represents the time derivative of the rotating system state, Represents the tool position output signal, represents the motor voltage excitation signal, represents the state matrix of the rotating system, represents the control matrix of the rotation system, Represents the output matrix of the rotation system.

3. A method for high-precision turning of non-circular contour parts according to claim 2, characterized in that: The step S2 comprises: definition is the rotation speed of the rotating system, , then any position in the time domain can be expressed as: (2) in, For the moment The corresponding position, is the integral variable, the position domain is a set of positions defined by a series of equations (2), and the time domain signal In the location domain it is represented as : (3) and The relationship is , the inverse function of formula (2) is given by: (4) in, represents the system speed in the position domain. Substituting equation (2) into equation (1), the state of the rotating system is The derivative of can be expressed as: (5) in, Represents the state of the rotating system in the position domain, As the independent variable of the rotating system state, the rotating system state space model in the position domain is: (6) in, and They are the tool position output signal and motor voltage excitation signal in the position domain respectively.

4. A method for high-precision turning of non-circular contour parts according to claim 3, characterized in that: The step S3 comprises: Defining constants With the current turntable speed The relationship is , while considering the rotation system identification parameters and , then the equation of the rotating system is written as: (7) in, is the system identification parameter, Taking the derivation, we can get ,in express The second-order derivative of The equation Substituting into the elimination we get: (8) Formula (8) is converted into the increment of the rotation angle After discretization, the following high-order all-wheel drive model can be obtained: (9) in, , Respectively 1,2 step recursion, , , are all intermediate variables. , , ; Based on the high-order full-drive theory, if the coefficient matrix reversible, the rotating system is fully driven; the direct parameter method is used to design the fully driven stabilizing controller, and the design There are the following forms: (10) in is the parameter matrix of the designed all-wheel drive stabilization controller, is an external signal; Substitute equation (9) into equation (8) to convert the original rotating system into full-drive form: (11)。 5. A method for high-precision turning of non-circular contour parts according to claim 4, characterized in that: The step S4 comprises: remember for The augmented matrix is ​​formed by , , , then: (12) in, express 1-step recursion, is the identity matrix of appropriate dimension; For the reference input position signal in the position domain derived from the rotation angle of the spindle motor , design a model predictive controller to solve the optimal control law; set the prediction interval , the recursive expression is as follows: (13) in for The augmented matrix is ​​formed by Indicates that of Step by step, Indicates that of Step by step, Respectively 2. , , Power; Defining quadratic performance indicators for: (14) in, represents the state weight matrix of the rotating system, represents the control weight matrix of the rotation system, represents the matrix transpose symbol, for The augmented matrix is ​​formed by , for The augmented matrix is ​​formed by Input position signal for reference in position domain, and The relationship is as follows: in, Respectively for of Step recursion; Quadratic performance indicators through Yalmip toolbox Solve and obtain the optimal control sequence ; Take the first element of the sequence as the system control law at the current moment, and according to formula (10), convert the external signal obtained by the MPC controller into Through the inverse transformation of formula (10), ,Will Substituting the high-order full-drive model in the position domain shown in equation (9) into the high-precision turning of non-circular contour parts can be achieved.

6. A high-precision turning device for non-circular contour parts, characterized in that: It comprises one or more processors for implementing a high-precision turning method for a non-circular contour part position domain as claimed in any one of claims 1 to 5.

7. A readable storage medium, characterized in that: A program is stored thereon, and when the program is executed by a processor, a high-precision turning method for position domain of a non-circular contour part according to any one of claims 1-5 is implemented.

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