CN112596389B - Crystal grinding control method and system based on closed-loop cross-coupling iterative learning - Google Patents
Crystal grinding control method and system based on closed-loop cross-coupling iterative learning Download PDFInfo
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Abstract
The invention discloses a crystal grinding control method and a crystal grinding control system based on closed-loop cross-coupling iterative learning, wherein the method comprises the following steps: s10, establishing a mathematical model of the crystal grinding servo system; s20, establishing a discrete closed-loop cross-coupling iterative learning controller to control the position; s30, generating a new control signal by the discrete closed-loop iterative learning controller; s40, the controller obtains a new tracking error according to the expected position information and the actual information; s50, compensating each axis through the contour error distribution model to eliminate the influence of each axis on other axes.
Description
Technical Field
The invention belongs to the technical field of servo control, and particularly relates to a crystal grinding control method and system based on closed-loop cross-coupling iterative learning.
Background
With the development of science and technology and industry, grinding processing is developed towards high speed, high precision and high productivity. The glass processing is also developed towards numerical control mechanization, but due to the particularity of glass materials, the problems of edge abrasion and surface smoothness are easily caused in the processing. In the fields of numerical control machining, robot control, high-precision machining and the like, the permanent magnet synchronous motor has important application. Because the mathematical model of the permanent magnet synchronous motor is a nonlinear and strongly coupled multivariable system, the mathematical model cannot be completely adapted to a speed regulating system or a servo system with high dynamic performance.
Disclosure of Invention
In order to solve the above problems, the present invention aims to provide a crystal grinding control method and system based on closed-loop cross-coupling iterative learning, which is a discrete cross-coupling iterative learning control method independent of a system precision model to improve the grinding precision of a crystal profile, wherein a permanent magnet synchronous motor is used as a driving system for both an x axis and a y axis, and vector control is adopted to realize characteristics similar to a direct current motor.
In order to solve the technical problems, the invention adopts the following technical scheme:
one aspect of the embodiments of the present invention provides a crystal grinding control system based on closed-loop cross-coupling iterative learning, including a profile distribution model, a storage module, an X-axis iterative learning controller, and a Y-axis iterative learning controller, wherein the profile distribution model is used to decompose a profile expected curved surface or curve into expected curves of an X-axis and a Y-axis, the storage module is used to store historical control information, the X-axis iterative learning controller is used to calculate a control quantity of the X-axis at a current time according to a current error, the Y-axis iterative learning controller is used to calculate a control quantity of the Y-axis at the current time according to the current error, first, expected advancing distance information required by the crystal profile grinding system is obtained according to a point cloud data acquisition algorithm, expected motion information of the X-axis and the Y-axis is respectively given through the profile error distribution model, then, actual motion information obtained in real time according to a position sensor in the system, the controller calculates an error according to expected movement and actual movement information, and finally calculates a control output quantity of the iteration according to a discrete cross-coupling iterative learning controller algorithm in combination with a control output quantity of the last time and an error of the current time, and simultaneously stores the error and the control quantity in the memory, and meanwhile, the cross-coupling iterative learning controller calculates coupling compensation information according to error information of an X axis and a Y axis and further controls the motor to work according to an expected advancing distance.
Another aspect of the embodiments of the present invention provides a crystal grinding control method based on closed-loop cross-coupling iterative learning, which is applied to the above crystal contour grinding control system based on discrete cross-coupling iterative learning, and includes the following steps:
s10, establishing a mathematical model of the crystal grinding servo system;
s20, establishing a discrete closed-loop cross-coupling iterative learning controller to control the position;
s30, generating a new control signal by the discrete closed-loop iterative learning controller;
s40, the controller obtains a new tracking error according to the expected position information and the actual information;
and S50, compensating the contour error distribution model to each axis to eliminate the influence of each axis on other axes.
Preferably, S10, the establishing of the mathematical model of the crystal polishing servo system specifically includes:
s11, using a vector control method to enable the crystal grinding servo motor to obtain the characteristics similar to a direct current motor, and simplifying the mathematical model as follows:
in the formula: t ise(T) is the electromagnetic torque, TL(t) is load torque, theta (t) is mechanical angular position of the motor, omega (t) is mechanical angular velocity of the motor, BfIs viscous friction coefficient, J is system equivalent moment of inertia, output variable is theta (T), control variable is Te(t)，
Writing equation (1) as a state space equation and discretizing can yield the following form:
s12, rewriting the formula (1) into a state space equation, and then discretizing to obtain:
where x is [ θ (j) ω (j)]TIs a system state variable, u (j) ═ Te(j)＝kTiq(j) To control the input variables, the system matrices are as follows:
s13, for the controlled system including the x-axis and the y-axis, the mathematical model of each axis is represented by formula (2), and the discretized models of the x-axis and the y-axis are:
wherein A, B, C is as defined in formula (2), x1，k(j +1) and x2，k(j +1) states of the x-axis and y-axis models at time j +1, respectively, y1，k(j +1) and y2，k(j +1) are the outputs of the x-axis and y-axis models at time j +1, respectively.
Preferably, S40, the obtained tracking error is specifically:
s41, defining the contour error epsilon at the j momentk(j) The calculation of (d) is closely related to the cross-coupling gain coefficient, and the cross-coupling gain coefficient tau is calculated firstx(j) And τy(j) And tracking error e of single axis1，k(j) And e2，k(j) Defining x-axis, y-axis and profile errors as:
e1，k(j)＝y1，d(j)-y1，k(j) (5)
e2，k(j)＝y2，d(j)-y2，k(j) (6)
wherein, y1，d(j) And y2，d(j) Given the desired signals on the x-axis and y-axis at time j respectively,
s42, the formula (5) and the formula (6) are arranged to obtain
ek(j)＝yd(j)-yk(j) (7)
Wherein the content of the first and second substances,
s43, the calculation formula of the contour error is as follows:
εk(j)＝τy(j)e2,k(j)-τx(j)e1,k(j) (8)
wherein
Wherein, theta is an included angle between an expected track at a certain moment or the tangential direction of the expected track and the x axis; p is the curvature half of the expected general curve profile motion track at the momentPath, defined τ (j) as:
equation (8) in S44, S43 is re-described as:
preferably, S50, the compensation to the axes by the profile error distribution model to eliminate the influence of each axis on the other axes is:
s51, for the cross-coupling systems described in equation (3) and equation (4), designing a cross-coupling iterative learning control law as follows:
ux,k+1(j)＝ux,k(j)+Γx,dex,k+1(j-1)+τx(j-1)Γε,dεk+1(j-1) (11)
uy,k+1(j)＝uy,k(j)+Γy,dey,k+1(j-1)+τy(j-1)Γε,dεk+1(j-1) (12)
wherein, gamma isx,d、Γy,dProportional gains, Γ, for the x-axis and y-axis respectivelyε,dFor proportional gain of profile error control, writing equation (11) and equation (12) in matrix form:
wherein u isk+1(j)＝[ux,k+1(j),uy,k+1(j)]T，
Then, for the cross-coupling control systems described in equation (3) and equation (4), the cross-coupling iterative learning control algorithms shown in equation (11) and equation (12) are designed, and when the number of iterations is large enough, the x-axis sumThe y-axis and profile errors tend to 0, i.e.
The invention has the following beneficial effects: the embodiment of the invention can eliminate the contour error of the multi-axis motion system, not only reduce the tracking error of a single axis, but also effectively improve the contour tracking capability of the multi-axis motion system, reduce the contour error of the system and improve the tracking performance.
Drawings
FIG. 1 is a schematic structural diagram of a crystal contour grinding control system based on discrete cross-coupling iterative learning according to an embodiment of the present invention;
FIG. 2 is a flowchart illustrating steps of a crystal contour polishing control method based on discrete cross-coupling iterative learning according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
System embodiment
Referring to fig. 1, a profile grinding control system based on discrete cross-coupling iterative learning according to an embodiment of the present invention is shown, which includes a profile assignment model 10, a storage module 20, an X-axis iterative learning controller 30, and a Y-axis iterative learning controller 40, wherein the profile assignment model 10 is configured to decompose a profile expected curved surface or curve into expected curves of an X-axis and a Y-axis, the storage module 20 is configured to store historical control information, the X-axis iterative learning controller 30 is configured to calculate a control quantity of the X-axis at a current time according to a current error, and the Y-axis iterative learning controller 30 is configured to calculate a control quantity of the Y-axis at the current time according to the current error. Firstly, obtaining the expected advancing distance information required by the crystal contour grinding system according to a point cloud data acquisition algorithm, respectively providing expected motion information of an X axis and a Y axis through a contour error distribution model, then, according to the actual motion information obtained by a position sensor in the system in real time, the controller calculates the error according to the expected motion and the actual motion information, finally, according to a discrete cross-coupling iterative learning controller algorithm, the control output quantity of the current iteration is calculated by combining the control output quantity of the last iteration (if the iteration is the first iteration, the previous control output quantity is 0) and the error of the current iteration, and the error and the control quantity are simultaneously stored in a memory, meanwhile, the cross-coupling iterative learning controller calculates coupling compensation information according to error information of an X axis and a Y axis, and then controls the motor to work according to an expected advancing distance.
Method example 1
For the above contour grinding control system based on discrete cross-coupling iterative learning, referring to fig. 2, a flowchart of steps of a contour grinding control method based on discrete cross-coupling iterative learning according to an embodiment of the present invention is shown, which includes the following steps:
s10, establishing a mathematical model of the crystal grinding servo system;
s20, establishing a discrete closed-loop cross-coupling iterative learning controller to control the position;
s30, generating a new control signal by the discrete closed-loop iterative learning controller;
s40, the controller obtains a new tracking error according to the expected position information and the actual information;
s50, compensating each axis through the contour error distribution model to eliminate the influence of each axis on other axes.
In a specific implementation, S10 includes the following steps:
s11, using vector control method to make the crystal grinding servo motor obtain the characteristics similar to the DC motor, simplifying the mathematical model as:
in the formula: t ise(T) is the electromagnetic torque, TL(t) is load torque, theta (t) is mechanical angular position of the motor, omega (t) is mechanical angular velocity of the motor, BfIs viscous friction coefficient, J is system equivalent moment of inertia, output variable is theta (T), control variable is Te(t)。
S12, rewriting the formula (1) in S11 into a state space equation, and then discretizing to obtain:
where x is [ θ (j) ω (j)]TIs a system state variable, u (j) ═ Te(j)＝kTiq(j) To control the input variables, the system matrices are as follows:
s13, for the controlled system of the x-axis and the y-axis, the mathematical model of each axis is represented by formula (2) in S12, and then the models of the x-axis and the y-axis after discretization are respectively:
wherein A, B and C are as defined in formula (2), and x1,k(j +1) and x2,k(j +1) states of the x-axis and y-axis models at time j +1, respectively, y1,k(j +1) and y2,k(j +1) are the outputs of the x-axis and y-axis models at time j +1, respectively.
In a specific implementation, S40 includes the following steps:
s41, as shown in FIG. 2, the contour error ε at the time jk(j) The calculation of (c) is closely related to the cross-coupling gain factor. Therefore, the contour error ε of the motion system is calculatedk(j) Must first countCalculating the cross-coupling gain coefficient taux(j) And τy(j) And tracking error e of single axis1,k(j) And e2,k(j) In that respect Defining x-axis, y-axis and profile errors as
e1,k(j)＝y1,d(j)-y1,k(j) (5)
e2,k(j)＝y2,d(j)-y2,k(j) (6)
Wherein, y1，d(j) And y2，d(j) The x-axis and y-axis signals are expected for time j, respectively.
S42, the formula (5) and the formula (6) are arranged to obtain:
ek(j)＝yd(j)-yk(j) (7)
wherein the content of the first and second substances,
in a specific implementation, S40 includes the following steps:
s43, according to the contour error modeling method, the calculation formula of the contour error is as follows:
εk(j)＝τy(j)e2，k(j)-τx(j)e1，k(j) (8)
wherein
Wherein, theta is an angle between an expected track at a certain moment or a tangential direction thereof and an x axis; ρ is the curvature radius of the expected general curve profile motion track at the moment. Define τ (j) as:
s44, formula (8) in S43 is described again as:
in a specific implementation, S50 includes the following steps:
s51, for the cross-coupling systems described in equation (3) and equation (4), designing a cross-coupling iterative learning control law as follows:
ux,k+1(j)＝ux,k(j)+Γx,dex,k+1(j-1)+τx(j-1)Γε,dεk+1(j-1) (11)
uy,k+1(j)＝uy,k(j)+Γy,dey,k+1(j-1)+τy(j-1)Γε,dεk+1(j-1) (12)
wherein, gamma isx,d、Γy,dProportional gains, Γ, for the x-axis and y-axis respectivelyε,dIs the proportional gain of the profile error control. Writing equations (11) and (12) in matrix form:
wherein u isk+1(j)＝[ux,k+1(j),uy,k+1(j)]T，
Then, for the cross-coupling control systems described in (3) and (4), the cross-coupling iterative learning control algorithms shown in (11) and (12) are designed, and when the number of iterations is large enough, the x-axis and y-axis and the contour error tend to 0, i.e., the contour error tends to be 0
It is to be understood that the exemplary embodiments described herein are illustrative and not restrictive. Although one or more embodiments of the present invention have been described with reference to the accompanying drawings, it will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the following claims.
Claims (2)
1. A crystal grinding control method based on closed-loop cross-coupling iterative learning is characterized by comprising the following steps:
s10, establishing a mathematical model of the crystal grinding servo system;
s20, establishing a discrete closed-loop cross-coupling iterative learning controller to control the position;
s30, generating a new control signal by the discrete closed-loop iterative learning controller;
s40, the controller obtains a new tracking error according to the expected position information and the actual information;
s50, compensating each axis through a contour error distribution model to eliminate the influence of each axis on other axes;
wherein, S10, the mathematical model of the crystal grinding servo system is specifically:
s11, using a vector control method to enable the crystal grinding servo motor to obtain the characteristics similar to a direct current motor, and simplifying the mathematical model as follows:
in the formula: t ise(T) is the electromagnetic torque, TL(t) is load torque, theta (t) is mechanical angular position of the motor, omega (t) is mechanical angular velocity of the motor, BfIs viscous friction coefficient, J is system equivalent moment of inertia, output variable is theta (T), control variable is Te(t)，
Writing equation (1) into a state space equation and discretizing to obtain the following form:
s12, rewriting the formula (1) into a state space equation, and then discretizing to obtain:
where x is [ θ (j) ω (j)]TIs a system state variable, u (j) ═ Te(j)＝kTiq(j) To control the input variables, the system matrices are as follows:
s13, for the controlled system including the x-axis and the y-axis, the mathematical model of each axis is represented by formula (2), and the discretized models of the x-axis and the y-axis are:
wherein A, B, C is as defined in formula (2), x1，k(j +1) and x2，k(j +1) states of the x-axis and y-axis models at time j +1, respectively, y1，k(j +1) and y2，k(j +1) are respectively the outputs of the x-axis model and the y-axis model at the j +1 th moment;
s40, the controller obtains a new tracking error according to the expected position information and the actual information, specifically:
s41, defining the contour error epsilon at the j momentk(j) The calculation of (d) is closely related to the cross-coupling gain coefficient, and the cross-coupling gain coefficient tau is calculated firstx(j) And τy(j) And tracking error e of single axis1，k(j) And e2，k(j) Defining x-axis, y-axis and profile errors as:
e1，k(j)＝y1，d(j)-y1，k(j) (5)
e2，k(j)＝y2，d(j)-y2，k(j) (6)
wherein, y1，d(j) And y2，d(j) The x-axis and y-axis signals are expected at time j,
s42, the formula (5) and the formula (6) are arranged to obtain
ek(j)＝yd(j)-yk(j) (7)
Wherein the content of the first and second substances,
s43, the calculation formula of the contour error is as follows:
εk(j)＝τy(j)e2，k(j)-τx(j)e1，k(j) (8)
wherein
Wherein, theta is an angle between an expected track at a certain moment or a tangential direction thereof and an x axis; ρ is the curvature radius of the expected general curve profile motion track at the moment, and τ (j) is defined as:
equation (8) in S44, S43 is re-described as:
wherein, S50, the compensation to the axes by the profile error distribution model to eliminate the influence of each axis on the other axes is specifically:
s51, for the cross-coupling systems described in equation (3) and equation (4), designing a cross-coupling iterative learning control law as follows:
wherein the content of the first and second substances,
proportional gains for the x-axis and y-axis respectively,
for proportional gain of profile error control, writing equation (11) and equation (12) in matrix form:
wherein, the first and the second end of the pipe are connected with each other,
then, for the cross-coupling control systems described by the formulas (3) and (4), the cross-coupling iterative learning control algorithms shown by the formulas (11) and (12) are designed, and when the number of iterations is large enough, the x-axis and the y-axis and the profile error tend to 0, that is, the x-axis and the y-axis and the profile error tend to be 0
2. A crystal grinding control system based on closed-loop cross-coupling iterative learning is characterized in that the crystal grinding control method based on the closed-loop cross-coupling iterative learning of claim 1 is adopted, and the crystal grinding control system comprises a profile distribution model, a storage module, an X-axis iterative learning controller and a Y-axis iterative learning controller, wherein the profile distribution model is used for decomposing a profile expected curved surface or curve into X-axis and Y-axis expected curves, the storage module is used for storing historical control information, the X-axis iterative learning controller is used for calculating the X-axis control quantity at the current moment according to the current error, the Y-axis iterative learning controller is used for calculating the Y-axis control quantity at the current moment according to the current error, firstly, expected forward distance information required by the crystal grinding system is obtained according to a point cloud data obtaining algorithm, and expected motion information of the X-axis and the Y-axis is respectively given through a profile error distribution model, and finally, calculating to obtain the control output quantity of the iteration according to a discrete cross-coupling iterative learning controller algorithm by combining the last control output quantity and the current error, simultaneously storing the error and the control quantity in a memory, meanwhile, calculating to obtain coupling compensation information according to the error information of the X axis and the Y axis by the cross-coupling iterative learning controller, and further controlling the motor to work according to the expected advancing distance.
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