CN-122018305-A - Motion instruction time-frequency domain active design method based on short-time Fourier

CN122018305ACN 122018305 ACN122018305 ACN 122018305ACN-122018305-A

Abstract

The invention relates to the technical field of motion planning and discloses a motion instruction time-frequency domain active design method based on short-time Fourier, wherein the process of constructing a motion instruction generation model comprises the steps of defining a motion instruction of a flexible feeding system, constructing an objective function with optimal motion time, obtaining frequency distribution of an acceleration motion instruction in each time period based on short-time Fourier transformation introducing a Hanning window function, constructing a time spectrum component constraint equation of the acceleration motion instruction according to a resonance frequency band of the flexible feeding system and the frequency distribution of the acceleration motion instruction, adopting a method based on sampling sparse observation points to design a motion constraint equation, adopting a linear programming method to construct the motion instruction generation model with optimal frequency spectrum, and solving control peaks of time B splines. The invention basically reduces resonance phenomenon which is easy to generate in the high-speed movement process, and has high robustness.

Inventors

ZHENG HONGMEI
LIU CHUANGCHUANG
XU WEIWEI
HUANG XIAOYONG
CHEN KE
DONG FANGFANG
TIAN XIAOQING

Assignees

合肥工业大学

Dates

Publication Date: 20260512
Application Date: 20251209

Claims (10)

1. A motion instruction time-frequency domain active design method based on short-time Fourier is characterized in that the process of constructing a motion instruction generation model comprises the following steps: defining a motion instruction of the flexible feeding system based on a time B spline curve, and constructing an objective function with optimal motion time; based on short-time Fourier transform introduced into a Hanning window function, dividing an acceleration motion instruction corresponding to the motion instruction into a plurality of short-time fragments, and carrying out Fourier transform on each short-time fragment to obtain the frequency distribution of the acceleration motion instruction in each time period; According to the resonance frequency band of the flexible feeding system and the frequency distribution of the acceleration motion instruction, constructing a time-frequency spectrum component constraint equation of the acceleration motion instruction so as to limit the amplitude of the motion instruction to be solved in the resonance frequency band; designing a kinematic constraint equation by adopting a method based on sampling sparse observation points; And combining the time-frequency spectrum component constraint equation, the kinematic constraint equation and the objective function with optimal motion time, adopting a linear programming method to build a motion instruction generation model with optimal time frequency spectrum, and designing a motion instruction for the flexible feeding system by solving a control vertex of a time B spline.
2. The method for actively designing a time-frequency domain of motion commands based on short-time fourier according to claim 1, wherein the time-based B-spline curve defines the motion commands of the flexible feeding system and constructs an objective function with optimal motion time, specifically comprising: Based on the B spline curve theory, the motion time of the motion instruction is used as a curve parameter, an analysis expression of the motion instruction is constructed through a group of linear combinations of control vertexes and the basis functions of the B spline curve, the motion instruction sequence is represented through the analysis expression of the motion instruction, and an objective function expression with optimal time is constructed on the basis of the analysis expression of the motion instruction.
3. The method for actively designing a time-frequency domain of a motion command based on short-time fourier transform according to claim 2, wherein the method for constructing an analytical expression of the motion command based on the B-spline curve theory uses the motion time of the motion command as a curve parameter by linear combination of a set of basis functions controlling vertices and B-spline curves, specifically comprises: constructing a motion instruction analysis expression based on a time B spline curve: ; Wherein, the Is a motion instruction represented by a time B spline curve; For the index at the time t, Is the first time B spline curve The control vertices of the control system are set, , Representing the number of control vertices; Is the first time B spline curve And (3) a base function.
4. The method for actively designing a time-frequency domain of a motion command based on short-time fourier transform according to claim 3, wherein the representing the sequence of motion commands by an analytical expression of the motion command specifically comprises: Moving an actuator of the flexible feed system from one point to another according to a motion command expression of the time B-spline curve And corresponding speed movement instructions Acceleration movement instruction And jerk motion command Expressed as: ; Wherein, the , Representation of A command for the movement of the moment of time, An index indicating the time corresponding to the nth motion instruction, The transpose is represented by the number, , , Representing the vector of the control vertices, Representing the mth control vertex and, A matrix expression representing a time B-spline basis function, Representing the length of the sequence of motion commands, Representing the m-th basis function of the B-spline, 、、 Is that First derivative, second reciprocal and third reciprocal of time t.
5. The method for actively designing a time-frequency domain of a motion command based on short-time fourier transform according to claim 4, wherein the constructing a time-optimal objective function expression based on an analytical expression of the motion command specifically comprises: under given motion constraint and time-frequency domain active design constraint, the minimum motion time T is taken as a target: ; And Respectively is The command and speed of movement at the moment in time, An index indicating the instant corresponding to the ith motion instruction, Length of the motion instruction sequence; considering the motion command as a quantity to be calculated, simplification is achieved by maximizing the motion command The mode of the sum indirectly realizes the aim of the minimum movement time: 。
6. The method for actively designing a time-frequency domain of a motion command based on short-time fourier according to claim 5, wherein the method for actively designing a time-frequency domain of a motion command based on short-time fourier transform introducing a hanning window function divides the acceleration motion command corresponding to the motion command into a plurality of short-time segments, performs fourier transform on each short-time segment, and obtains a frequency distribution of the acceleration motion command in each time segment, specifically comprising: Construction of hanning window function Is a analytic expression of (2): Wherein, the method comprises the steps of, M is the window length of the Hanning window; by the movement of the hanning window function on the time axis, the acceleration movement is instructed Convolving and windowing short-time segments in each Hanning window and performing Fourier transformation to obtain an acceleration motion instruction Spectral components during the time period of the current hanning window, item First in the Hanning window Spectral components The method comprises the following steps: ; Wherein, the , C is an acceleration movement instruction The total number of the short-time fragments which are decomposed is L, which is the number of preset Fourier transform points; acceleration motion instruction corresponding to the b-th hanning window H is the overlapping length of a pre-set Hanning window; In imaginary units.
7. The method of claim 6, wherein the sequence of motion commands for convolution windowed acceleration motion commands is in a convolution windowing stage Motion instruction information obtained through the b-th hanning window ; Representation of Acceleration at the moment of time is determined, To pair(s) A windowing matrix for the b-th hanning window convolution operation; During the Fourier transform phase, for the motion instruction sequence information in the b-th Hanning window Fourier transforming to obtain Wherein the time domain information is the time corresponding to the b-th Hanning window, and the frequency domain information is the frequency spectrum component : ; Wherein, the , Is the corresponding fourier transform matrix.
8. The method for actively designing a time-frequency domain of a motion command based on short-time fourier transform according to claim 7, wherein the constructing a time-frequency spectrum component constraint equation of the acceleration motion command according to a resonant frequency band of the flexible feeding system and a frequency distribution of the acceleration motion command to limit an amplitude of the motion command to be solved in the resonant frequency band specifically comprises: constructing the amplitude of excitation frequency spectrum component in each Hanning window : ; And Respectively denoted as Real and imaginary parts of (a); Will be Respectively, the real and imaginary parts of (a) are limited: First, the Motion instruction frequency spectrum real virtual vector corresponding to Hanning window From the following components Real and imaginary components of (a) construct: ; Wherein, the , Is a spectral component Is used for the vector of the real part of (c), Is a spectral component Is used to determine the imaginary component vectors of (a), To calculate the resonance frequency interval of flexible system Inner spectral sequence Fourier transform matrices required for the real and imaginary parts of (a): ; Wherein, the Represents the starting frequency of the resonance frequency interval, Represents the end frequency of the resonance frequency interval, For spectral sequences The frequency index vector within the pair of the frequency indices, For the sampling frequency to be the same, Is a Fourier transform matrix In the presence of an element of the group, The operation of taking the real part is represented, Representing an operation of taking an imaginary part; the motion instruction time-frequency domain active design is realized by minimizing the amplitude of the excitation frequency spectrum component of the acceleration motion instruction A in each Hanning window Minimization of the real and imaginary parts of the excitation spectral components within each hanning window translates into real and imaginary vectors of the spectrum within each hanning window The element does not exceed the preset maximum value, the first Within the hanning window, the time-frequency spectrum component constraint equation of the acceleration motion command is expressed as: ; Wherein, the Is the most significant of the real imaginary vector of the spectrum in the b-th hanning window.
9. The method for actively designing a time-frequency domain of a motion command based on short-time fourier transform according to claim 8, wherein the method for designing a kinematic constraint equation based on sampling sparse observation points specifically comprises: At the start time Displacement, displacement Speed and velocity of And acceleration All 0 at the termination time Displacement, displacement Is that Speed of Acceleration of All 0, the motion boundary constraint is expressed as: ; Representation of A matrix is formed which is a combination of the two, Representation of A matrix of components; The motion command speed constraint is: ; Is the maximum speed; The motion instruction acceleration constraint is: ; is the maximum acceleration; the motion instruction jerk constraint is: ; Is the maximum jerk; taking the distortion characteristic of the B spline into consideration, the upper limit and the lower limit of the control vertex of the B spline curve are constrained: ; The lower-bound matrix is represented as such, Representing the upper limit matrix.
10. The method for actively designing a motion command time-frequency domain based on short-time fourier transform according to claim 9, wherein the method for designing a motion command for a flexible feed system by solving control vertices of a time B-spline by constructing a motion command generation model with optimal frequency spectrum by using a linear programming method in combination with the time-frequency spectrum component constraint equation, the kinematic constraint equation, and an objective function with optimal motion time comprises: the motion instruction is represented by a time B spline curve, the control vertex P of the time B spline is the quantity to be solved, and the motion instruction generation model with optimal time spectrum is as follows: ; 。

Description

Motion instruction time-frequency domain active design method based on short-time Fourier Technical Field The invention relates to the technical field of motion planning, in particular to a motion instruction time-frequency domain active design method based on short-time Fourier. Background In precision manufacturing equipment such as semiconductor packaging, testing and the like, the feeding speed and positioning accuracy of a flexible feeding system are core indexes for measuring the performance of equipment. In order to improve production efficiency, it is highly demanded that the equipment realize high acceleration and high precision point-to-point movement in operation while suppressing terminal vibration to the maximum extent. However, the feeding system is easy to generate residual vibration after high-speed and high-acceleration movement, so that the positioning stability time is obviously prolonged, and the improvement of the equipment operation efficiency is restricted. Document 1（LIU W, LIU W, ZHOU M, et al. An active vibration control method based on energy-fuzzy for cantilever structures excited by aerodynamic loads[J]. Chinese Journal of Aeronautics 34.9 (2021): 224-235..） proposes an energy fuzzy self-adaptive PD control method, which adjusts control model parameters in real time based on system vibration energy, so that a vibration active control system can adapt to different load working conditions. However, the vibration active control system needs to install a vibration state monitoring sensor, which increases the hardware cost of the device. Literature 2（TSAY D M, LIN C F. Asymmetrical inputs for minimizing residual response[C]//2005 IEEE International Conference on Mechatronics. IEEE, 2005: 235-240..） proposes an asymmetric S-shaped speed curve (AS-cut) motion planning method, which aims at minimizing residual response and stabilizing time and optimizing vibration response of a feeding system, but searches optimal instruction parameters from a time domain angle to realize residual vibration suppression, the process relies on accurately modeling the system, and robustness and vibration suppression performance are affected by modeling errors. Document 3（SENCER B, TAJIMA S. Frequency optimal feed motion planning in computer numerical controlled machine tools for vibration avoidance[J]. Journal of manufacturing science and engineering, 2017, 139(1): 011006.. ） proposes a polynomial track generation method with minimum frequency spectrum energy in a frequency band as a target, and through actively designing a frequency domain of a motion instruction, residual vibration of a feeding system is obviously restrained, and a new idea is provided for high-speed high-precision speed planning. However, in equipment such as five-axis machine tools, robots, electronic manufacturing equipment, etc., mechanical parameters such as inertia, rigidity, etc. of the feed system may change with the change of the movement position, resulting in the change of dynamic characteristics. At this time, the method has no time resolution capability, and cannot adjust the frequency spectrum vibration suppression range according to the change of the dynamic characteristics of the feeding system in the motion process, so that the residual vibration suppression effect of the feeding system is limited. Therefore, the application aims at the problem of low processing efficiency and precision caused by vibration of the flexible feeding system in the high-speed movement process, introduces a short-time Fourier transform theory, actively designs a time frequency domain of a movement instruction, attenuates the frequency band energy which causes resonance of the system in the movement instruction, prevents the system from generating resonance in the movement process of executing the movement instruction, and fundamentally solves the problem that the system is easy to generate resonance in the high-speed movement process. Disclosure of Invention In order to solve the technical problems, the invention provides a motion instruction time-frequency domain active design method based on short-time Fourier. In order to solve the technical problems, the invention adopts the following technical scheme: A motion instruction time-frequency domain active design method based on short-time Fourier comprises the following steps of: defining a motion instruction of the flexible feeding system based on a time B spline curve, and constructing an objective function with optimal motion time; based on short-time Fourier transform introduced into a Hanning window function, dividing an acceleration motion instruction corresponding to the motion instruction into a plurality of short-time fragments, and carrying out Fourier transform on each short-time fragment to obtain the frequency distribution of the acceleration motion instruction in each time period; According to the resonance frequency band of the flexible feeding system and the frequency distribut