CN116909210B - Precision motion platform motion trail planning system and method based on frequency selection - Google Patents
Precision motion platform motion trail planning system and method based on frequency selection Download PDFInfo
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Abstract
A motion trail planning system and method for a precision motion platform based on frequency selection belong to the technical field of precision motion platforms. The track generator outputs a reference S curve; the reference S-curve is obtained by a flexible system, and the resonance frequency of the flexible system and the residual oscillation information of the system output are jointly provided to a track generator to correct the reference S-curve. The method comprises the following steps: determining the order of a reference S curve; designing a S-shaped motion track containing parameters and obtaining a zero point containing parameters of the track; determining parameters of an S-shaped motion track; judging whether the parameters are reasonable; and judging whether the residual oscillation meets the requirement or not, and determining the motion trail design standard. The invention solves the problem that the traditional precise motion platform motion track planning parameter design only focuses on the geometric smoothness of the motion track to neglect the flexibility characteristic of the controlled object, and does not need to add an additional damping device, thereby reducing the overall weight and the economic cost.
Description
Technical Field
The invention relates to a frequency selection-based precision motion platform motion track planning system and method, and belongs to the technical field of precision motion platforms.
Background
The motion trail design needs to ensure accuracy and adjustment time while meeting objective physical condition constraints such as travel, counter potential, friction, actuator output and the like. Flexible links can occur in the device due to special mechanical design, mechanical safety protection, cost saving, etc. Meanwhile, certain frequency components of the reference motion trail excite the flexible system to cause residual oscillation, so that the adjustment time and the positioning accuracy are difficult to ensure.
The ultra-precise motion system is an important component of ultra-precise manufacturing and processing equipment, and has important application in the fields of aerospace, laser technology, semiconductor industry and the like. In order to reduce the adverse effect of impact caused by high acceleration and deceleration of a motion platform and heat generated in the motion process on a system, the motion track needs to be planned and controlled. The trapezoidal motion track algorithm is relatively simple, but sudden changes of acceleration exist in the motion process, so that the system oscillation is easily excited, and the accuracy of the positioning system is influenced; the algorithm of the S-shaped motion track is more complex than that of the trapezoidal motion track, but the curve edge of the S-shaped track is smooth, and acceleration abrupt change is not easy to occur. The higher the order of the trajectory curve, the higher the positioning accuracy of the motion system, but the complexity of the corresponding trajectory planning algorithm is increased, and the response speed of the system is affected. Typical positioning and scanning motions in actual production often use third-order, fourth-order or fifth-order S-shaped curves.
In the prior art, a discrete numerical integration method is adopted to plan the track of the ultra-precise motion system, the algorithm of the method is simple and easy to realize, but the traditional precise motion platform motion track planning parameter design only aims at the problem that the geometric smoothness of the motion track ignores the flexible characteristic of the controlled object, and the problems of weight increase and higher economic cost caused by adding an additional damping device for inhibiting the residual oscillation of the traditional flexible structure.
Disclosure of Invention
In order to solve the problems in the background technology, the invention provides a frequency selection-based motion track planning system and method for a precision motion platform.
The invention adopts the following technical scheme: a motion track planning system of a precision motion platform based on frequency selection comprises a track generator C R A flexible system P and a system output Y;
the track generator C R The output of (2) is a reference S curve;
the motion trail of the reference S curve comprises a position delta, a speed V, an acceleration A, a jerk J, an acceleration second derivative S, an acceleration third derivative C and a robust adjustment parameter beta;
the reference S curve is used for obtaining a system output Y through the flexible system P, and the resonance frequency fn of the flexible system P and the information of the residual oscillation of the system output Y are jointly provided to the track generator C R To modify the reference S-curve.
The invention relates to a planning method of a precision motion platform motion trail planning system based on frequency selection, which comprises the following steps:
s1: selecting n f The resonance frequency fn of the controlled flexible system P to be suppressed and the corresponding robust adjustment coefficient β, { n f ∈Z|n f ＜4}，{β∈Z|β＜5-n f Z represents a positive integer, thereby determining the order of the reference S curve as n f +β+1；
S2: designing a parameter-containing S-shaped motion track based on parameters according to the order of the reference S curve selected in the S1, and obtaining a track parameter-containing zero point;
s3: determining parameters of an S-shaped motion track;
s4: judging whether the parameters of the S-shaped motion track are reasonable or not according to the track generation conditions, and if so, generating the S-shaped motion track; repeating S1-S3 to be reasonable if not;
s5: judging whether the residual oscillation meets the requirement according to the system requirement, and if so, correcting the resonance frequency fn and the corresponding robust adjustment coefficient beta by the information of the residual oscillation of the system output Y; if the requirement is not met, extracting residual oscillation information of the system output Y to carry out FFT analysis, selecting three frequency points with the largest frequency components to correct the resonance frequency fn, and repeating S1-S4 until the residual oscillation inhibition meets the system requirement, and determining a motion trail design standard.
Compared with the prior art, the invention has the beneficial effects that:
the invention solves the problem that the traditional precise motion platform motion track planning parameter design only focuses on the geometric smoothness of the motion track to neglect the flexibility characteristic of the controlled object, and does not need to add an additional damping device, thereby reducing the overall weight and the economic cost.
Drawings
FIG. 1 is a schematic illustration of a flexible system of the present invention;
FIG. 2 is a schematic diagram of a third order S-curve acceleration and above;
FIG. 3 is a schematic diagram of a four-order S-curve acceleration and above composition plan;
FIG. 4 is a schematic diagram of a five-order S-curve acceleration and above;
fig. 5 is a schematic diagram of the system pole and trajectory zero distribution.
Fig. 6 is a schematic diagram of a planning system of the present invention.
Detailed Description
The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the invention, but not all embodiments, and all other embodiments obtained by those skilled in the art without making creative efforts based on the embodiments of the present invention are all within the protection scope of the present invention.
A motion track planning system of a precision motion platform based on frequency selection comprises a track generator C R A flexible system P and a system output Y;
the track generator C R The output of (2) is a reference S curve; the order is three or more, and the specific order is determined according to the number of the selected resonant frequencies.
The motion trail of the reference S curve comprises a position delta, a speed V, an acceleration A, a jerk J, an acceleration second derivative S, an acceleration third derivative C and a robust adjustment parameter beta;
the reference S curve is used for obtaining a system output Y through the flexible system P, and the resonance frequency fn of the flexible system P and the information of the residual oscillation of the system output Y are jointly provided to the track generator C R To modify the reference S-curve.
The invention discloses a planning method of a motion trail planning system of a precision motion platform based on frequency selection, in particular to a method for inhibiting residual oscillation of a flexible structure of the motion of the precision motion platform, which comprises the following steps:
s1: when the resonance frequency is obtained, the stiffness coefficient k of the flexible system P is obtained by utilizing ansys finite element stress analysis, and then the resonance frequency is calculated according to the known load mass mSelecting n f The resonance frequency fn of the controlled flexible system P to be suppressed and the corresponding robust adjustment coefficient β, { n f ∈Z|n f ＜4}，{β∈Z|β＜5-n f Z represents a positive integer, thereby determining the order of the reference S curve as n f +β+1；
S2: according to the selection in S1Referring to the order of the S-curve, the method is based on parameters (including: target position delta max Maximum speed V max Maximum acceleration A max Maximum jerk J max Second derivative of maximum acceleration S max Third-order derivative C of maximum acceleration max ) Designing a S-shaped motion track containing parameters, and analyzing in a Laplace domain to obtain a zero point containing parameters of the track;
in the second step, the motion path is restricted by the actual working condition, and the motion path is required to be strictly restricted during the motion path planning, namely the target position delta max The values are determined for the known values. The motor, an indispensable actuator in a motion control system, determines the maximum running speed V of the motor due to the factors such as counter potential, magnetic pole strength, coil turns and the like max And maximum acceleration A under a fixed load and maximum force max The values are determined for the known values. Meanwhile, the necessary motion board card in the motion control system also determines related parameters, and the control period is T s 。
S3: obtaining a pole of the flexible system P according to the resonance frequency fn in the S1, determining parameters of the S-shaped motion track based on a zero pole allocation principle according to the track containing a parameter zero point in the S2;
in order to ensure the integrity of physical information during motion trail planning, the constraint conditions of the higher-order parameters of the third-order S-curve, the fourth-order S-curve and the fifth-order S-curve are respectively as follows:
in the formula (1):
A max representing the maximum amplitude of acceleration;
J max representing the maximum magnitude of jerk;
S max representing the maximum amplitude of the second derivative of acceleration;
C max representing the maximum amplitude of the third-order derivative of the acceleration;
T s and controlling the control period of the system.
S4: judging whether the parameters of the S-shaped motion track are reasonable or not according to the track generation conditions, and if so, generating the S-shaped motion track; repeating S1-S3 to be reasonable if not;
s5: judging whether the residual oscillation meets the requirement according to the system requirement, and if so, correcting the resonance frequency fn and the corresponding robust adjustment coefficient beta by the information of the residual oscillation of the system output Y; if the requirement is not met, extracting residual oscillation information of the system output Y to carry out FFT analysis, selecting three frequency points with the largest frequency components to correct the resonance frequency fn, and repeating S1-S4 until the residual oscillation inhibition meets the system requirement, and determining a motion trail design standard.
The following three cases are classified according to the difference of the robust adjustment parameter β:
when the robust adjustment parameter β is 1:
when the resonance frequency fn of the system inhibition is a single frequency point, f is used 1 For example, a third-order S-curve is used as a reference motion track, and fig. 2 shows a schematic plan of the acceleration of the third-order S-curve and above, the acceleration is obtained by integrating the jerk, the speed is obtained by integrating the acceleration, and the position is obtained by integrating the speed. In the method, the jerk is a series of continuous pulses, and the maximum amplitude of the jerk is J max Minimum amplitude of jerk is-J max 。
Maximum jerk amplitude J max The calculation mode of (a) is as follows:
since the system vibration pole can be approximated as: si= ±j2pi fi, j represents an imaginary unit;
therefore, based on the zero pole allocation principle, the minimum required track zero to be used for residual oscillation corresponds to the system vibration pole, taking a third-order S curve as an example:
so that
In the formula (2):
α 1 is a positive integer, if α is for time optimization 1 Taken as 1.
When the resonance frequency fn of the system suppression is two frequency points, the frequency f is 1 And f 2 For example, and f 1 ＜f 2 And combining the constraint of time optimization, and adopting a fourth-order S curve as a reference motion track. FIG. 3 shows a schematic diagram of the four-order S-curve acceleration and above, the jerk is calculated by the second derivative of the acceleration, the acceleration is calculated by the jerk integral, the velocity is calculated by the acceleration integral, and the position is calculated by the velocity integral. In the method, the second derivative of the acceleration is a series of continuous pulses, and the maximum amplitude of the second derivative of the acceleration is S max The minimum amplitude of the second derivative of the acceleration is-S max The maximum amplitude of the jerk obtained after integration is J max Minimum amplitude of jerk is-J max 。
Maximum jerk amplitude J max And maximum amplitude S of acceleration max The calculation mode of (a) is as follows:
in the formula (3):
α 1 and alpha 2 Are all positive integers, if for time optimization, alpha 1 And alpha 2 All are taken as 1, constraint condition J max /S max ≤A max /J max In the case of (2), a fourth order S-curve may be generated.
When the resonance frequency fn of the system inhibition is three frequency points, f is adopted 1 、f 2 And f 3 For example, at f 1 ＜f 2 ＜f 3 Under the condition of combining the constraint of time optimization, a fifth-order S curve is adopted as a reference motion track. FIG. 4 shows a schematic diagram of the five-order S-curve acceleration and above, the second derivative of the acceleration is calculated by the third derivative of the acceleration, and the jerk is calculated by the second derivative of the accelerationThe acceleration is calculated by the jerk integral, the velocity is calculated by the acceleration integral, and the position is calculated by the velocity integral. In the method, the third-order guide of the acceleration is a series of continuous pulses, and the maximum amplitude of the third-order guide of the acceleration is C max The minimum amplitude of the third-order derivative of the acceleration is-C max The maximum amplitude of the acceleration second derivative obtained after integration is S max Minimum amplitude-S of acceleration second derivative max The maximum amplitude of the jerk obtained after continuous integration is J max Minimum amplitude of jerk is-J max 。
Maximum jerk amplitude J max Maximum amplitude S of acceleration second derivative max The method for calculating the maximum amplitude of the third-order derivative of the acceleration is as follows:
in the formula (4):
α 1 、α 2 and alpha 3 Are all positive integers, if for time optimization, alpha 1 、α 2 And alpha 3 All are taken as 1, constraint condition S max /C max ≤J max /S max ≤A max /J max In the case of (2), a fifth order S-curve may be generated.
When the robust adjustment parameter β is 2:
when the resonance frequency fn of the system inhibition is a single frequency point, f is used 1 For example, a fourth-order S curve is used as a reference motion trajectory, and in the method, the maximum amplitude of jerk is J max Minimum amplitude of jerk is-J max The second derivative of acceleration is a series of continuous pulses, and the maximum amplitude of the second derivative of acceleration is S max The minimum amplitude of the second derivative of the acceleration is-S max 。
Maximum jerk amplitude J max Sum acceleration second derivative maximum amplitude S max The calculation mode of (a) is as follows:
in the formula (3):
α 1 and alpha 2 Are all positive integers, if for time optimization, alpha 1 And alpha 2 All are taken as 1, constraint condition J max /S max ≤A max /J max In the case of (2), a fourth order S-curve may be generated.
When two frequency points needing simultaneous suppression exist in the system, f is adopted 1 And f 2 For example, and f 1 ＜f 2 To a vibration frequency point f where robustness needs to be improved 1 For example, a fifth-order S curve is used as a reference motion track, in the method, the third-order guide of the acceleration is a series of continuous pulses, and the maximum amplitude of the third-order guide of the acceleration is C max The minimum amplitude of the third-order derivative of the acceleration is-C max The maximum amplitude of the acceleration second derivative obtained after integration is S max Minimum amplitude-S of acceleration second derivative max The maximum amplitude of the jerk obtained after continuous integration is J max Minimum amplitude of jerk is-J max 。
Maximum jerk amplitude J max Maximum amplitude S of acceleration second derivative max Acceleration third-order derivative maximum amplitude C max The calculation mode of (a) is as follows:
in the formula (4):
α 1 、α 2 and alpha 3 Are all positive integers, if for time optimization, alpha 1 、α 2 And alpha 3 All are taken as 1, constraint condition S max /C max ≤J max /S max ≤A max /J max In the case of (2), a fifth order S-curve may be generated.
When the robust adjustment parameter β is 3:
with a single frequency point of system rejection being f 1 For example, a 5 th order S curve is usedIn the method, the acceleration third-order guide is a series of continuous pulses, and the maximum amplitude of the acceleration third-order guide is C max The minimum amplitude of the third-order derivative of the acceleration is-C max The maximum amplitude of the acceleration second derivative obtained after integration is S max Minimum amplitude-S of acceleration second derivative max The maximum amplitude of the jerk obtained after continuous integration is J max Minimum amplitude of jerk is-J max 。
Maximum jerk amplitude J max Maximum amplitude S of acceleration second derivative max Acceleration third-order derivative maximum amplitude C max The calculation mode of (a) is as follows:
in the formula (4):
α 1 、α 2 and alpha 3 Are all positive integers, if for time optimization, alpha 1 、α 2 And alpha 3 All are taken as 1, constraint condition S max /C max ≤J max /S max ≤A max /J max In the case of (2), a fifth order S-curve may be generated.
α 1 、α 2 And alpha 3 The value selection should be obtained by combining the tolerable time delay of the controlled system, and the higher-order S curve can be obtained by analogy according to the method.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (1)
1. A planning method of a precision motion platform motion track planning system based on frequency selection is realized through a track planning system, wherein the track planning system comprises a track generator C R A flexible system P and a system output Y;
the track generator C R The output of (2) is a reference S curve;
the motion trail of the reference S curve comprises a position delta, a speed V, an acceleration A, a jerk J, an acceleration second derivative S, an acceleration third derivative C and a robust adjustment parameter beta;
the reference S curve is used for obtaining a system output Y through the flexible system P, and the resonance frequency fn of the flexible system P and the information of the residual oscillation of the system output Y are jointly provided to the track generator C R To modify the reference S-curve;
the method is characterized in that: the method comprises the following steps:
s1: selecting n f The resonance frequency fn of the controlled flexible system P to be suppressed and the corresponding robust adjustment coefficient β, { n f ∈Z|n f ＜4}，{β∈Z|β＜5-n f Z represents a positive integer, thereby determining the order of the reference S curve as n f +β+1；
S2: designing a parameter-containing S-shaped motion track based on parameters according to the order of the reference S curve selected in the S1, and obtaining a track parameter-containing zero point;
s3: determining parameters of an S-shaped motion track;
s4: judging whether the parameters of the S-shaped motion track are reasonable or not according to the track generation conditions, and if so, generating the S-shaped motion track; repeating S1-S3 to be reasonable if not;
s5: judging whether the residual oscillation meets the requirement according to the system requirement, and if so, correcting the resonance frequency fn and the corresponding robust adjustment coefficient beta by the information of the residual oscillation of the system output Y; if the requirement is not met, extracting residual oscillation information of the system output Y to carry out FFT analysis, selecting three frequency points with the largest frequency components to correct the resonance frequency fn, and repeating S1-S4 until the residual oscillation inhibition meets the system requirement, and determining a motion trail design standard;
when the robust adjustment parameter β is 1:
when the resonance frequency fn of the system inhibition is a single frequency point, a third-order S curve is adopted as a reference motion track, acceleration is obtained by calculation of jerk integral, speed is obtained by calculation of acceleration integral, and position is obtained by calculation of speed integral; jerk is a series of continuous pulses with a maximum amplitude of J max Minimum amplitude of jerk is-J max ；
The system vibration pole is as follows: si= ±j2pi fi, j represents an imaginary unit;
therefore, based on the pole-zero configuration principle, the track zero corresponds to the system vibration pole to minimize residual oscillation:
so that
In the formula (2):
α 1 is a positive integer, alpha 1 ＝1；
When the resonance frequency fn of the system suppression is two frequency points and f 1 ＜f 2 When the motion track is used, a fourth-order S curve is used as a reference motion track; jerk is calculated from the second derivative integral of acceleration, acceleration is calculated from the integral of jerk, velocity is calculated from the integral of acceleration, and position is calculated from the velocity productCalculating to obtain the product; the second derivative of acceleration is a series of continuous pulses, and the maximum amplitude of the second derivative of acceleration is S max The minimum amplitude of the second derivative of the acceleration is-S max The maximum amplitude of the jerk obtained after integration is J max Minimum amplitude of jerk is-J max ；
Maximum jerk amplitude J max And maximum amplitude S of acceleration max The calculation mode of (a) is as follows:
in the formula (3):
α 1 and alpha 2 Are all positive integers, alpha 1 ＝1，α 2 =1, constraint J max /S max ≤A max /J max Generating a fourth-order S curve;
when the resonance frequency fn of the system suppression is three frequency points and f 1 ＜f 2 ＜f 3 When the motion trail is used, a fifth-order S curve is used as a reference motion trail; the second derivative of the acceleration is calculated by the third derivative of the acceleration, the jerk is calculated by the second derivative of the acceleration, the acceleration is calculated by the second derivative of the jerk, the speed is calculated by the integral of the acceleration, and the position is calculated by the integral of the speed; the third-order guide of acceleration is a series of continuous pulses, and the maximum amplitude of the third-order guide of acceleration is C max The minimum amplitude of the third-order derivative of the acceleration is-C max The maximum amplitude of the acceleration second derivative obtained after integration is S max Minimum amplitude-S of acceleration second derivative max The maximum amplitude of the jerk obtained after continuous integration is J max Minimum amplitude of jerk is-J max ；
Maximum jerk amplitude J max Maximum amplitude S of acceleration second derivative max The method for calculating the maximum amplitude of the third-order derivative of the acceleration is as follows:
in the formula (4):
α 1 、α 2 and alpha 3 Are all positive integers, alpha 1 ＝1，α 2 ＝1，α 3 =1, constraint S max /C max ≤J max /S max ≤A max /J max Generating a fifth-order S curve;
when the robust adjustment parameter β is 2:
when the resonance frequency fn of the system inhibition is a single frequency point, a fourth-order S curve is adopted as a reference motion track, and the maximum amplitude of the jerk is J max Minimum amplitude of jerk is-J max The second derivative of acceleration is a series of continuous pulses, and the maximum amplitude of the second derivative of acceleration is S max The minimum amplitude of the second derivative of the acceleration is-S max ；
Maximum jerk amplitude J max Sum acceleration second derivative maximum amplitude S max The calculation mode of (a) is as follows:
in the formula (3):
α 1 and alpha 2 Are all positive integers, alpha 1 ＝1，α 2 =1, constraint J max /S max ≤A max /J max Generating a fourth-order S curve;
when two frequency points needing simultaneous suppression exist in the system and f 1 ＜f 2 When the method is used, a fifth-order S curve is used as a reference motion track, the acceleration third-order guide is a series of continuous pulses, and the maximum amplitude of the acceleration third-order guide is C max The minimum amplitude of the third-order derivative of the acceleration is-C max The maximum amplitude of the acceleration second derivative obtained after integration is S max Minimum amplitude-S of acceleration second derivative max The maximum amplitude of the jerk obtained after continuous integration is J max The minimum amplitude of the jerk is-J max ；
Maximum jerk amplitude J max Maximum amplitude S of acceleration second derivative max Acceleration third-order derivative maximum amplitude C max The calculation mode of (a) is as follows:
in the formula (4):
α 1 、α 2 and alpha 3 Are all positive integers, alpha 1 ＝1，α 2 ＝1，α 3 =1, constraint S max /C max ≤J max /S max ≤A max /J max Generating a fifth-order S curve;
when the robust adjustment parameter β is 3:
when the resonance frequency fn of the system inhibition is a single frequency point, a 5-order S curve is adopted as a reference motion track, the acceleration third-order guide is a series of continuous pulses, and the maximum amplitude of the acceleration third-order guide is C max The minimum amplitude of the third-order derivative of the acceleration is-C max The maximum amplitude of the acceleration second derivative obtained after integration is S max Minimum amplitude-S of acceleration second derivative max The maximum amplitude of the jerk obtained after continuous integration is J max Minimum amplitude of jerk is-J max ；
Maximum jerk amplitude J max Maximum amplitude S of acceleration second derivative max Acceleration third-order derivative maximum amplitude C max The calculation mode of (a) is as follows:
in the formula (4):
α 1 、α 2 and alpha 3 Are all positive integers, alpha 1 ＝1，α 2 ＝1，α 3 =1, constraint S max /C max ≤J max /S max ≤A max /J max In the case of (2), a fifth-order S-curve is generated.
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