CN114114899B - Feedforward coefficient setting method and device for feedforward controller of workpiece table - Google Patents
Feedforward coefficient setting method and device for feedforward controller of workpiece table Download PDFInfo
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Abstract
The invention provides a feedforward coefficient setting method and device of a feedforward controller of a workpiece table, a storage medium and electronic equipment, and relates to the technical field of control engineering, wherein the method comprises the following steps: s1: exciting a preset shaft based on a preset impulse coefficient to obtain impulse response of the preset shaft; s2: operating the workpiece table based on a first feedforward coefficient of the feedforward controller to obtain a position error of the workpiece table and a speed parameter of the feedforward controller; s3: obtaining a second feedforward coefficient of the feedforward controller based on the impulse response, the position error and the speed parameter; s4: judging whether the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold value; when the second feedforward coefficient is not smaller than a preset threshold value, the second feedforward coefficient is obtained to serve as a first feedforward coefficient, and S2-S4 are executed in a circulating mode; otherwise, the second feedforward coefficient is obtained and used as the feedforward coefficient after the setting. The technical scheme provided by the invention can automatically adjust the feedforward coefficient of the feedforward controller, and greatly improves the adjusting efficiency.
Description
Technical Field
The invention relates to the technical field of control engineering, in particular to a feedforward coefficient setting method and device of a feedforward controller of a workpiece table.
Background
The workpiece stage, currently generally referred to as a dry dual workpiece stage, has a feedforward controller and a feedback controller, wherein the feedforward controller takes the form of an FIR (Finite Impulse Response ) controller. In the operation process of the workpiece table, the feedforward coefficient of the feedforward controller needs to be set so as to obtain the optimal feedforward coefficient, thereby minimizing the error of the operation track of the workpiece table.
At present, the feedforward coefficient is adjusted by adopting a manual adjustment mode. In the manual adjustment process, a debugger needs to move the track for many times and observe errors, and needs to consider the adjustment direction and adjustment amount of the feedforward coefficient which reduces the errors. Obviously, this approach is time consuming, laborious and inefficient.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a feedforward coefficient setting method and device for a feedforward controller of a workpiece table, which can automatically set the feedforward coefficient of the feedforward controller and greatly improve the setting efficiency.
In order to achieve the above purpose, the technical scheme of the invention is realized as follows:
in a first aspect, an embodiment of the present invention provides a method for setting a feedforward coefficient of a feedforward controller of a workpiece stage, where the method includes:
S1: exciting a preset axis of the workpiece table based on a preset impulse coefficient to obtain an impulse response of the preset axis;
S2: operating the workpiece stage based on a known first feedforward coefficient of the feedforward controller to obtain a position error of the workpiece stage and a speed parameter of the feedforward controller;
S3: obtaining a second feedforward coefficient of the feedforward controller based on the impulse response of the predetermined axis, the position error of the workpiece stage, and the speed parameter of the feedforward controller;
S4: judging whether the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold value;
When the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is not smaller than the preset threshold value, acquiring the second feedforward coefficient as the first feedforward coefficient, and circularly executing S2-S4;
and when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than the preset threshold value, acquiring the second feedforward coefficient as the feedforward coefficient after the feedforward controller is set.
Preferably, the obtaining the second feedforward coefficient of the feedforward controller based on the impulse response of the predetermined axis, the position error of the workpiece stage, and the speed parameter of the feedforward controller includes:
Obtaining a bias guide of the output of the workpiece table to a feedforward coefficient of the feedforward controller based on the impulse response of the preset shaft and the speed parameter of the feedforward controller;
Obtaining a gradient of a preset objective function based on the position error of the workpiece table and the deviation of the output of the workpiece table to the feedforward coefficient of the feedforward controller; wherein the preset objective function is pre-established based on the relation between the feedforward coefficient of the feedforward controller and the position error of the workpiece table;
Obtaining a Hessian matrix of the preset objective function based on the deviation of the output of the workpiece table on the feedforward coefficient of the feedforward controller;
And obtaining a second feedforward coefficient of the feedforward controller based on the gradient of the preset objective function and the Hessian matrix of the preset objective function.
Preferably, the bias derivative of the output of the workpiece stage to the feedforward coefficient of the feedforward controller is calculated using the following expression:
Wherein, A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; /(I)An impulse response for the predetermined axis; /(I)A speed parameter for the feedforward controller; p is the transfer function of the workpiece table; c fb is a transfer function of a feedback controller of the workpiece stage; c ff is the transfer function of the feedforward controller; r is the input of the workpiece table; y is the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller.
Preferably, the gradient of the preset objective function is calculated using the following expression:
Wherein, A gradient for the preset objective function; j is the preset objective function; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; e is the position error of the workpiece table; /(I)And the bias of the feedforward coefficient of the feedforward controller is conducted for the output of the workpiece stage.
Preferably, the Hessian matrix of the preset objective function is obtained by calculation using the following expression:
wherein R δ,i is a Hessian matrix of the preset objective function; A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the sequence number of the sampling point.
Preferably, the second feedforward coefficient of the feedforward controller is calculated using the following expression:
Wherein δ i+1 is the second feedforward coefficient of the feedforward controller at the ith iteration; delta i is the first feedforward coefficient of the feedforward controller at the ith iteration; gamma i is the preset step size at the ith iteration; r δ,i is a Hessian matrix of the preset objective function; a gradient for the preset objective function.
Preferably, the preset objective function is:
Wherein δ is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; and e is the position error of the workpiece table.
Preferably, the speed parameters of the feedforward controller include: acceleration, jerk, and jerk of the feedforward controller.
In a second aspect, an embodiment of the present invention provides a feedforward coefficient setting apparatus of a feedforward controller of a workpiece table, including:
The excitation unit is used for exciting a preset axis of the workpiece table based on a preset impulse coefficient to obtain an impulse response of the preset axis;
An operation unit, configured to operate the workpiece stage based on a known first feedforward coefficient of the feedforward controller, and obtain a position error of the workpiece stage and a speed parameter of the feedforward controller;
A first acquisition unit configured to obtain a second feedforward coefficient of the feedforward controller based on an impulse response of the predetermined axis, a position error of the workpiece stage, and a speed parameter of the feedforward controller;
The judging unit is used for judging whether the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold value;
the loop execution unit is used for acquiring the second feedforward coefficient as the first feedforward coefficient when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is not smaller than the preset threshold value, and performing S2-S4 in a loop;
And the second acquisition unit is used for acquiring the second feedforward coefficient as the feedforward coefficient after the feedforward controller is set when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than the preset threshold value.
Preferably, the first acquisition unit includes:
a first calculating subunit, configured to obtain, based on an impulse response of the predetermined axis and a speed parameter of the feedforward controller, a bias derivative of an output of the workpiece stage to a feedforward coefficient of the feedforward controller;
A second calculating subunit, configured to obtain a gradient of a preset objective function based on a position error of the workpiece stage and a deviation of an output of the workpiece stage from a feedforward coefficient of the feedforward controller; wherein the preset objective function is pre-established based on the relation between the feedforward coefficient of the feedforward controller and the position error of the workpiece table;
A third calculation subunit, configured to obtain a Hessian matrix of the preset objective function based on a deviation of the output of the workpiece stage from a feedforward coefficient of the feedforward controller;
and a fourth calculation subunit, configured to obtain a second feedforward coefficient of the feedforward controller based on the gradient of the preset objective function and the Hessian matrix of the preset objective function.
Preferably, the first calculating subunit calculates and obtains a bias derivative of the output of the workpiece stage to the feedforward coefficient of the feedforward controller by using the following expression:
Wherein, A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; /(I)An impulse response for the predetermined axis; /(I)A speed parameter for the feedforward controller; p is the transfer function of the workpiece table; c fb is a transfer function of a feedback controller of the workpiece stage; c ff is the transfer function of the feedforward controller; r is the input of the workpiece table; y is the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller.
Preferably, the second calculation subunit calculates the gradient of the preset objective function using the following expression:
Wherein, A gradient for the preset objective function; j is the preset objective function; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; e is the position error of the workpiece table; /(I)And the bias of the feedforward coefficient of the feedforward controller is conducted for the output of the workpiece stage.
Preferably, the third computation subunit computes to obtain the Hessian matrix of the preset objective function using the following expression:
wherein R δ,i is a Hessian matrix of the preset objective function; A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the sequence number of the sampling point.
Preferably, the fourth calculation subunit calculates to obtain the second feedforward coefficient of the feedforward controller using the following expression:
Wherein δ i+1 is the second feedforward coefficient of the feedforward controller at the ith iteration; delta i is the first feedforward coefficient of the feedforward controller at the ith iteration; gamma i is the preset step size at the ith iteration; r δ,i is a Hessian matrix of the preset objective function; a gradient for the preset objective function.
Preferably, the preset objective function is:
Wherein δ is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; and e is the position error of the workpiece table.
Preferably, the speed parameters of the feedforward controller include: acceleration, jerk, and jerk of the feedforward controller.
According to the feedforward coefficient setting method and device for the feedforward controller of the workpiece table, provided by the embodiment of the invention, the predetermined axis of the workpiece table is excited based on the preset impulse coefficient, the impulse response of the predetermined axis is obtained, the workpiece table is operated based on the first feedforward coefficient of the known feedforward controller, the position error of the workpiece table and the speed parameter of the feedforward controller are obtained, and the second feedforward coefficient of the feedforward controller is obtained based on the impulse response of the predetermined axis, the position error of the workpiece table and the speed parameter of the feedforward controller; when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is not smaller than a preset threshold value, the second feedforward coefficient is obtained to serve as the first feedforward coefficient, and the steps are circularly executed; and when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold value, acquiring the second feedforward coefficient as the feedforward coefficient after the feedforward controller is set. Therefore, the technical scheme provided by the invention can automatically adjust the feedforward coefficient of the feedforward controller, thereby greatly improving the adjusting efficiency.
Drawings
The scope of the present disclosure will be better understood from the following detailed description of exemplary embodiments, read in conjunction with the accompanying drawings. The drawings included herein are:
FIG. 1 is a flow chart of a method according to an embodiment of the present invention;
FIG. 2 is a control block diagram of a workpiece stage system in accordance with an embodiment of the invention;
FIG. 3 is a schematic diagram of a workpiece stage motion trajectory error in an embodiment of the invention;
fig. 4 is a block diagram of an apparatus according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the following detailed description of the implementation method of the present invention will be given with reference to the accompanying drawings and examples, by which the technical means are applied to solve the technical problems, and the implementation process for achieving the technical effects can be fully understood and implemented accordingly.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those described herein, and therefore the scope of the present invention is not limited to the specific embodiments disclosed below.
Example 1
According to an embodiment of the present invention, there is provided a feedforward coefficient setting method of a feedforward controller of a workpiece stage, as shown in fig. 1, the method according to the embodiment of the present invention includes:
step S1, exciting a preset axis of the workpiece table based on a preset impulse coefficient to obtain an impulse response of the preset axis;
in this embodiment, the workpiece stage has 6 axes, each axis corresponding to a set of feedforward coefficients to be set. In the tuning process, the feedforward coefficient is tuned for one of the axes at a time, and the predetermined axis is one of the 6 axes.
In this embodiment, the preset impulse coefficient is an impulse coefficient preset by an operator.
Step S2: operating the workpiece stage based on a known first feedforward coefficient of the feedforward controller to obtain a position error of the workpiece stage and a speed parameter of the feedforward controller;
In this embodiment, the first feedforward coefficient of the feedforward controller is the current feedforward coefficient of the feedforward controller. When the step is executed for the first time, the current feedforward coefficient is an initial value preset by an operator; when the step is executed in the subsequent cycle, the current feedforward coefficient is the second feedforward coefficient obtained in the step S3, that is, a new feedforward coefficient, that is, the new feedforward coefficient obtained in the step S3 is used as the current feedforward coefficient of the current cycle to execute the step S2 again.
In this embodiment, the speed parameters of the feedforward controller include: acceleration acc, jerk ierk, and jerk snap of the feedforward controller.
The position error of the workpiece table refers to a difference between an input r and an output y in a control block diagram of the workpiece table system shown in fig. 2, wherein the input r is a position set value of the workpiece table, and the output y is an actual position value of the workpiece table during operation.
Step S3: obtaining a second feedforward coefficient of the feedforward controller based on the impulse response of the predetermined axis, the position error of the workpiece stage, and the speed parameter of the feedforward controller;
Specifically, the second feedforward coefficient of the feedforward controller is obtained in the following manner: obtaining a bias guide of the output of the workpiece table to a feedforward coefficient of the feedforward controller based on the impulse response of the preset shaft and the speed parameter of the feedforward controller; obtaining a gradient of a preset objective function based on the position error of the workpiece table and the deviation of the output of the workpiece table to the feedforward coefficient of the feedforward controller; wherein the preset objective function is pre-established based on the relation between the feedforward coefficient of the feedforward controller and the position error of the workpiece table; obtaining a Hessian matrix of the preset objective function based on the deviation of the output of the workpiece table on the feedforward coefficient of the feedforward controller; and obtaining a second feedforward coefficient of the feedforward controller based on the gradient of the preset objective function and the Hessian matrix of the preset objective function.
In this embodiment, the following expression is used to calculate and obtain the deviation of the output of the workpiece stage from the feedforward coefficient of the feedforward controller:
Wherein, A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; /(I)An impulse response for the predetermined axis; /(I)The speed parameters of the feedforward controller are the acceleration acc, the jerk jerk and the jerk snap of the feedforward controller; p is the transfer function of the workpiece table; c fb is a transfer function of a feedback controller of the workpiece stage; c ff is the transfer function of the feedforward controller; r is the input of the workpiece table; y is the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller.
In this embodiment, the gradient of the preset objective function is calculated using the following expression:
Wherein, A gradient for the preset objective function; j is the preset objective function; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; e is the position error of the workpiece table; /(I)And the bias of the feedforward coefficient of the feedforward controller is conducted for the output of the workpiece stage.
In this embodiment, the following expression is used to calculate and obtain the Hessian matrix of the preset objective function:
wherein R δ,i is a Hessian matrix of the preset objective function; A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the sequence number of the sampling point.
In this embodiment, the following expression is used to calculate and obtain the second feedforward coefficient of the feedforward controller:
Wherein δ i+1 is the second feedforward coefficient of the feedforward controller at the ith iteration; delta i is the first feedforward coefficient of the feedforward controller at the ith iteration; gamma i is the preset step size at the ith iteration; r δ,i is a Hessian matrix of the preset objective function; a gradient for the preset objective function.
In this embodiment, the preset objective function is:
Wherein δ is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; and e is the position error of the workpiece table.
Step S4: judging whether the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold value;
When the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is not smaller than the preset threshold value, acquiring the second feedforward coefficient as the first feedforward coefficient, and circularly executing S2-S4;
and when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than the preset threshold value, acquiring the second feedforward coefficient as the feedforward coefficient after the feedforward controller is set.
In this embodiment, steps S2 to S4 are a process of performing a loop, and it is determined whether the absolute value of the difference between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold, that is, it is determined whether a new feedforward coefficient obtained by the above loop calculation is converged, and when the absolute value of the difference between the second feedforward coefficient and the first feedforward coefficient is smaller than the preset threshold, it is indicated that the new feedforward coefficient obtained by the calculation is converged, and the new feedforward coefficient (that is, the second feedforward coefficient calculated in the last loop) is used as the feedforward coefficient after the feedforward controller is set, and the workpiece stage is operated based on the set feedforward coefficient to obtain the minimum track error.
The calculation principle of each expression described above is described in detail below:
To minimize the trajectory error of a workpiece stage, essentially a set of feedforward coefficients is found such that the value of the objective function J, which is established based on the relationship between the feedforward coefficients of the feedforward controller of the workpiece stage and the position error of the workpiece stage, is minimized:
wherein δ is a feedforward coefficient of the feedforward controller, that is, a feedforward coefficient to be set, specifically k acc、kjerk、ksnap; n is the number of sampling points; t is the serial number of the sampling point; e is the position error of the workpiece table, namely the difference between the position set value of the workpiece table and the actual position value of the workpiece table, and e=r-y.
In this embodiment, the objective function is preferably solved by using the gaussian newton method principle, so as to obtain the value of δ corresponding to the minimum value of the objective function, which is used as the feedforward coefficient after tuning. Then, the iterative expression for δ is:
Wherein δ i+1 is the second feedforward coefficient of the feedforward controller at the ith iteration; delta i is the first feedforward coefficient of the feedforward controller at the ith iteration, i.e., the current feedforward coefficient of the feedforward controller; gamma i is the preset step size at the ith iteration; r δ,i is the Hessian matrix of the above objective function; a gradient that is the objective function described above.
While the Hessian matrix R δ,i of the above objective function and the gradient of the above objective functionThe following expression can be used:
the physical meaning of each parameter in the above formula is described above, and is not described herein.
From the above analysis, it can be seen that delta i+1 is required, only the Hessian matrix R δ,i of the objective function and the gradient of the objective function need be solvedBy solving/>R δ,i can be obtained; by solving/>And e, can obtain/>
It will be appreciated that the error e described above may be derived by operating the workpiece stage based on the current feed forward coefficient of the feed forward controller. The following detailed descriptionIs a solving method of:
As shown in fig. 2, r is the input of the workpiece stage, namely, the position set value of the workpiece stage; y is the output of the workpiece table, namely the actual position value of the workpiece table during operation; v is external disturbance; c ff is the transfer function of the feedforward controller of the workpiece stage, which may be represented in FIG. 2; c fb is the transfer function of the feedback controller of the workpiece stage, which may be represented in FIG. 2; p is the transfer function of the stage, which can be represented in fig. 2. Then, the expression of output y is:
the above formula y is biased with respect to δ to obtain:
Wherein, The impulse response of the preset shaft is obtained after the preset shaft is excited, and the impulse response is specifically a toeplitz matrix of the impulse response. In this embodiment, the predetermined axis of the workpiece table is excited based on the preset impulse coefficient in step S1, and the obtained impulse response is/>
And C ff has the expression:
Cff＝ksnap*s4+kjerk*s3+kacc*s2
wherein, k acc is the coefficient of acceleration acc, k jerk is the coefficient of jerk jerk, k snap is the coefficient of jerk snap, and k acc、kjerk、ksnap is the feedforward coefficient to be set in this embodiment; s is a variable in the transfer function of the feedforward controller, then, The expression of (2) is shown in the following table 1:
TABLE 1
Since the input r of the stage is the set value of the position, the input r isThe expression of (2) is shown in the following table 2:
TABLE 2
The acc, jerk and snap in table 2 are all set values of the trajectory data, and represent the acceleration, jerk and jerk of the feedforward controller, respectively, and these three parameters are collectively referred to as the speed parameter of the feedforward controller.
I.e. as can be seen from table 2,The set values of the acceleration acc, the jerk jerk, and the jerk snap may be used for the representation, and the set values may be obtained by operating the stage based on the current feedforward coefficient of the feedforward controller, i.e., by the above-described step S2.
Practice shows that by adopting the technical scheme provided by the embodiment of the invention, the running track error of the workpiece table is obviously reduced, and as shown in fig. 3, the abscissa is a sampling point, and the ordinate is a corresponding track error. In fig. 3, the portion with larger longitudinal fluctuation is the track error obtained based on the feedforward coefficient before tuning, and the smoother transverse track is the track error obtained based on the feedforward coefficient after tuning, so that the track error is obviously reduced by about 90%; and the setting efficiency is obviously improved, and only one hour is needed for finishing the setting of the degree-of-freedom feedforward of the workpiece table 6.
According to the feedforward coefficient setting method of the feedforward controller of the workpiece table, provided by the embodiment of the invention, a preset shaft of the workpiece table is excited based on a preset impulse coefficient, impulse response of the preset shaft is obtained, the workpiece table is operated based on a first feedforward coefficient of a known feedforward controller, position errors of the workpiece table and speed parameters of the feedforward controller are obtained, and a second feedforward coefficient of the feedforward controller is obtained based on the impulse response of the preset shaft, the position errors of the workpiece table and the speed parameters of the feedforward controller; when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is not smaller than a preset threshold value, the second feedforward coefficient is obtained to serve as the first feedforward coefficient, and the steps are circularly executed; and when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold value, acquiring the second feedforward coefficient as the feedforward coefficient after the feedforward controller is set. Therefore, the technical scheme provided by the invention can automatically adjust the feedforward coefficient of the feedforward controller, thereby greatly improving the adjusting efficiency.
Example two
Corresponding to the embodiment of the method, the invention also provides a feedforward coefficient setting device of a feedforward controller of a workpiece table, as shown in fig. 4, which comprises:
An excitation unit 201, configured to excite a predetermined axis of the workpiece stage based on a preset impulse coefficient, and obtain an impulse response of the predetermined axis;
an operation unit 202, configured to operate the workpiece stage based on a known first feedforward coefficient of the feedforward controller, and obtain a position error of the workpiece stage and a speed parameter of the feedforward controller;
A first obtaining unit 203, configured to obtain a second feedforward coefficient of the feedforward controller based on an impulse response of the predetermined axis, a position error of the workpiece stage, and a speed parameter of the feedforward controller;
A determining unit 204, configured to determine whether an absolute value of a difference between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold;
a loop execution unit 205, configured to obtain the second feedforward coefficient as the first feedforward coefficient when the absolute value of the difference between the second feedforward coefficient and the first feedforward coefficient is not less than the preset threshold, and loop execute S2 to S4;
And a second obtaining unit 206, configured to obtain the second feedforward coefficient as the feedforward coefficient after the feedforward controller is set when the absolute value of the difference between the second feedforward coefficient and the first feedforward coefficient is smaller than the preset threshold.
In this embodiment, the first obtaining unit 203 includes:
a first calculating subunit, configured to obtain, based on an impulse response of the predetermined axis and a speed parameter of the feedforward controller, a bias derivative of an output of the workpiece stage to a feedforward coefficient of the feedforward controller;
A second calculating subunit, configured to obtain a gradient of a preset objective function based on a position error of the workpiece stage and a deviation of an output of the workpiece stage from a feedforward coefficient of the feedforward controller; wherein the preset objective function is pre-established based on the relation between the feedforward coefficient of the feedforward controller and the position error of the workpiece table;
A third calculation subunit, configured to obtain a Hessian matrix of the preset objective function based on a deviation of the output of the workpiece stage from a feedforward coefficient of the feedforward controller;
and a fourth calculation subunit, configured to obtain a second feedforward coefficient of the feedforward controller based on the gradient of the preset objective function and the Hessian matrix of the preset objective function.
In this embodiment, the first calculating subunit calculates and obtains the partial derivative of the output of the workpiece stage to the feedforward coefficient of the feedforward controller by using the following expression:
Wherein, A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; /(I)An impulse response for the predetermined axis; /(I)A speed parameter for the feedforward controller; p is the transfer function of the workpiece table; c fb is a transfer function of a feedback controller of the workpiece stage; c ff is the transfer function of the feedforward controller; r is the input of the workpiece table; y is the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller.
In this embodiment, the second calculating subunit calculates the gradient of the preset objective function using the following expression:
Wherein, A gradient for the preset objective function; j is the preset objective function; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; e is the position error of the workpiece table; /(I)And the bias of the feedforward coefficient of the feedforward controller is conducted for the output of the workpiece stage.
In this embodiment, the third computation subunit computes to obtain the Hessian matrix of the preset objective function by using the following expression:
wherein R δ,i is a Hessian matrix of the preset objective function; A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the sequence number of the sampling point.
In this embodiment, the fourth calculating subunit calculates to obtain the second feedforward coefficient of the feedforward controller using the following expression:
Wherein δ i+1 is the second feedforward coefficient of the feedforward controller at the ith iteration; delta i is the first feedforward coefficient of the feedforward controller at the ith iteration; gamma i is the preset step size at the ith iteration; r δ,i is a Hessian matrix of the preset objective function; a gradient for the preset objective function.
In this embodiment, the preset objective function is:
Wherein δ is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; and e is the position error of the workpiece table.
In this embodiment, the speed parameters of the feedforward controller include: acceleration, jerk, and jerk of the feedforward controller.
The working principle, the working procedure, and the like of the device relate to specific embodiments, and refer to specific embodiments of a feedforward coefficient setting method of a feedforward controller of a workpiece table provided by the invention, and the same technical contents are not described in detail herein.
The feedforward coefficient setting device of the feedforward controller of the workpiece table provided by the embodiment of the invention excites a preset shaft of the workpiece table based on a preset impulse coefficient to obtain an impulse response of the preset shaft, operates the workpiece table based on a first feedforward coefficient of a known feedforward controller to obtain a position error of the workpiece table and a speed parameter of the feedforward controller, and obtains a second feedforward coefficient of the feedforward controller based on the impulse response of the preset shaft, the position error of the workpiece table and the speed parameter of the feedforward controller; when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is not smaller than a preset threshold value, the second feedforward coefficient is obtained to serve as the first feedforward coefficient, and the steps are circularly executed; and when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold value, acquiring the second feedforward coefficient as the feedforward coefficient after the feedforward controller is set. Therefore, the technical scheme provided by the invention can automatically adjust the feedforward coefficient of the feedforward controller, thereby greatly improving the adjusting efficiency.
Example III
According to an embodiment of the present invention, there is also provided a storage medium having stored thereon program code that, when executed by a processor, implements a feed-forward coefficient setting method of a feed-forward controller of a workpiece table as in any of the above embodiments.
Example IV
According to an embodiment of the present invention, there is further provided an electronic device including a memory and a processor, where the memory stores program code executable on the processor, and when the program code is executed by the processor, the feedforward coefficient setting method of the feedforward controller of the workpiece stage according to any one of the foregoing embodiments is implemented.
According to the feedforward coefficient setting method, the feedforward coefficient setting device, the storage medium and the electronic equipment of the feedforward controller of the workpiece table, which are provided by the embodiment of the invention, a preset shaft of the workpiece table is excited based on the preset impulse coefficient, the impulse response of the preset shaft is obtained, the workpiece table is operated based on a first feedforward coefficient of a known feedforward controller, the position error of the workpiece table and the speed parameter of the feedforward controller are obtained, and a second feedforward coefficient of the feedforward controller is obtained based on the impulse response of the preset shaft, the position error of the workpiece table and the speed parameter of the feedforward controller; when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is not smaller than a preset threshold value, the second feedforward coefficient is obtained to serve as the first feedforward coefficient, and the steps are circularly executed; and when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold value, acquiring the second feedforward coefficient as the feedforward coefficient after the feedforward controller is set. Therefore, the technical scheme provided by the invention can automatically adjust the feedforward coefficient of the feedforward controller, thereby greatly improving the adjusting efficiency.
In the several embodiments provided by the present application, it should be understood that the disclosed apparatus and method may be implemented in other manners. For example, the apparatus embodiments described above are merely illustrative, e.g., the division of elements is merely a logical functional division, and there may be additional divisions of actual implementation, e.g., multiple elements or components may be combined or integrated into another system, or some features may be omitted, or not performed.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed over a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the embodiment of the present invention.
In addition, each functional unit in the embodiments of the present invention may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The integrated units may be implemented in hardware or in software functional units.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention is essentially or a part contributing to the prior art, or all or part of the technical solution may be embodied in the form of a software product stored in a storage medium, comprising several instructions for causing an electronic device (which may be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods of the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Although the embodiments of the present invention are disclosed above, the embodiments are only used for the convenience of understanding the present invention, and are not intended to limit the present invention. Any person skilled in the art can make any modification and variation in form and detail without departing from the spirit and scope of the present disclosure, but the scope of the present disclosure is still subject to the scope of the present disclosure as defined by the appended claims.
Claims (14)
1. A method for tuning a feed-forward coefficient of a feed-forward controller of a workpiece table, the method comprising:
S1: exciting a preset axis of the workpiece table based on a preset impulse coefficient to obtain an impulse response of the preset axis;
S2: operating the workpiece stage based on a known first feedforward coefficient of the feedforward controller to obtain a position error of the workpiece stage and a speed parameter of the feedforward controller;
S3: obtaining a second feedforward coefficient of the feedforward controller based on the impulse response of the predetermined axis, the position error of the workpiece stage, and the speed parameter of the feedforward controller;
S4: judging whether the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold value;
When the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is not smaller than the preset threshold value, acquiring the second feedforward coefficient as the first feedforward coefficient, and circularly executing S2-S4;
When the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than the preset threshold value, acquiring the second feedforward coefficient as the feedforward coefficient after the feedforward controller is set;
The obtaining a second feedforward coefficient of the feedforward controller based on the impulse response of the predetermined axis, the position error of the workpiece stage, and the speed parameter of the feedforward controller includes:
Obtaining a bias guide of the output of the workpiece table to a feedforward coefficient of the feedforward controller based on the impulse response of the preset shaft and the speed parameter of the feedforward controller;
Obtaining a gradient of a preset objective function based on the position error of the workpiece table and the deviation of the output of the workpiece table to the feedforward coefficient of the feedforward controller; wherein the preset objective function is pre-established based on the relation between the feedforward coefficient of the feedforward controller and the position error of the workpiece table;
Obtaining a Hessian matrix of the preset objective function based on the deviation of the output of the workpiece table on the feedforward coefficient of the feedforward controller;
And obtaining a second feedforward coefficient of the feedforward controller based on the gradient of the preset objective function and the Hessian matrix of the preset objective function.
2. The method for setting the feedforward coefficient of the feedforward controller of the workpiece stage according to claim 1, wherein the deviation of the feedforward coefficient of the feedforward controller from the output of the workpiece stage is calculated using the following expression:
Wherein, A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; /(I)An impulse response for the predetermined axis; /(I)A speed parameter for the feedforward controller; p is the transfer function of the workpiece table; c fb is a transfer function of a feedback controller of the workpiece stage; c ff is the transfer function of the feedforward controller; r is the input of the workpiece table; y is the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller.
3. The method of setting a feedforward coefficient of a feedforward controller of a workpiece table according to claim 1, wherein the gradient of the preset objective function is calculated using the following expression:
Wherein, A gradient for the preset objective function; j is the preset objective function; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; e is the position error of the workpiece table; /(I)And the bias of the feedforward coefficient of the feedforward controller is conducted for the output of the workpiece stage.
4. The method for setting the feedforward coefficient of the feedforward controller of the workpiece table according to claim 1, wherein the Hessian matrix of the preset objective function is obtained by calculation using the following expression:
Wherein R δ,i is a Hessian matrix of the preset objective function; A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; v is a feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the sequence number of the sampling point.
5. The method of setting a feedforward coefficient of a feedforward controller of a workpiece table according to claim 1, wherein the second feedforward coefficient of the feedforward controller is calculated using the following expression:
Wherein δ i+1 is the second feedforward coefficient of the feedforward controller at the ith iteration; delta i is the first feedforward coefficient of the feedforward controller at the ith iteration; gamma i is the preset step size at the ith iteration; r δ,i is a Hessian matrix of the preset objective function; a gradient for the preset objective function.
6. The method for setting a feedforward coefficient of a feedforward controller of a workpiece table according to claim 1, wherein the preset objective function is:
Wherein δ is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; and e is the position error of the workpiece table.
7. The method of setting a feedforward coefficient of a feedforward controller of a workpiece table according to claim 1, wherein the speed parameter of the feedforward controller includes: acceleration, jerk, and jerk of the feedforward controller.
8. A feed-forward coefficient setting device of a feed-forward controller of a workpiece table, the device comprising:
The excitation unit is used for exciting a preset axis of the workpiece table based on a preset impulse coefficient to obtain an impulse response of the preset axis;
An operation unit, configured to operate the workpiece stage based on a known first feedforward coefficient of the feedforward controller, and obtain a position error of the workpiece stage and a speed parameter of the feedforward controller;
A first acquisition unit configured to obtain a second feedforward coefficient of the feedforward controller based on an impulse response of the predetermined axis, a position error of the workpiece stage, and a speed parameter of the feedforward controller;
The judging unit is used for judging whether the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than a preset threshold value;
A loop execution unit, configured to acquire the second feedforward coefficient as the first feedforward coefficient when an absolute value of a difference value between the second feedforward coefficient and the first feedforward coefficient is not smaller than the preset threshold, and loop execute the steps of the operation unit, the first acquisition unit, and the judgment unit;
the second acquisition unit is used for acquiring the second feedforward coefficient as the feedforward coefficient after the feedforward controller is set when the absolute value of the difference value between the second feedforward coefficient and the first feedforward coefficient is smaller than the preset threshold value;
The first acquisition unit includes:
a first calculating subunit, configured to obtain, based on an impulse response of the predetermined axis and a speed parameter of the feedforward controller, a bias derivative of an output of the workpiece stage to a feedforward coefficient of the feedforward controller;
A second calculating subunit, configured to obtain a gradient of a preset objective function based on a position error of the workpiece stage and a deviation of an output of the workpiece stage from a feedforward coefficient of the feedforward controller; wherein the preset objective function is pre-established based on the relation between the feedforward coefficient of the feedforward controller and the position error of the workpiece table;
A third calculation subunit, configured to obtain a Hessian matrix of the preset objective function based on a deviation of the output of the workpiece stage from a feedforward coefficient of the feedforward controller;
and a fourth calculation subunit, configured to obtain a second feedforward coefficient of the feedforward controller based on the gradient of the preset objective function and the Hessian matrix of the preset objective function.
9. The feedforward coefficient setting device of a feedforward controller of a workpiece stage according to claim 8, wherein the first calculation subunit calculates a bias derivative of the output of the workpiece stage with respect to the feedforward coefficient of the feedforward controller using the following expression:
Wherein, A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; /(I)An impulse response for the predetermined axis; /(I)A speed parameter for the feedforward controller; p is the transfer function of the workpiece table; c fb is a transfer function of a feedback controller of the workpiece stage; c ff is the transfer function of the feedforward controller; r is the input of the workpiece table; y is the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller.
10. The feedforward coefficient setting device of the feedforward controller of the workpiece table according to claim 8, wherein the second calculation subunit calculates the gradient of the preset objective function using the following expression:
Wherein, A gradient for the preset objective function; j is the preset objective function; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; e is the position error of the workpiece table; /(I)And the bias of the feedforward coefficient of the feedforward controller is conducted for the output of the workpiece stage.
11. The feedforward coefficient setting device of the feedforward controller of the workpiece table according to claim 8, wherein the third computation subunit computes a Hessian matrix of the preset objective function using the following expression:
Wherein R δ,i is a Hessian matrix of the preset objective function; A bias guide for the feedforward coefficient of the feedforward controller for the output of the workpiece stage; delta is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the sequence number of the sampling point.
12. The feedforward coefficient setting device of a feedforward controller of a workpiece table according to claim 8, wherein the fourth calculation subunit obtains the second feedforward coefficient of the feedforward controller by calculation using the following expression:
Wherein δ i+1 is the second feedforward coefficient of the feedforward controller at the ith iteration; delta i is the first feedforward coefficient of the feedforward controller at the ith iteration; gamma i is the preset step size at the ith iteration; r δ,i is a Hessian matrix of the preset objective function; a gradient for the preset objective function.
13. The feedforward coefficient setting device of the feedforward controller of the workpiece table of claim 8, wherein the preset objective function is:
Wherein δ is the feedforward coefficient of the feedforward controller; n is the number of sampling points; t is the serial number of the sampling point; and e is the position error of the workpiece table.
14. The feedforward coefficient setting device of a feedforward controller of a workpiece table of claim 8, wherein the speed parameter of the feedforward controller includes: acceleration, jerk, and jerk of the feedforward controller.
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