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

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, and the process of constructing a motion instruction generation model comprises the steps: defining a motion instruction of a flexible feeding system, and constructing a target function with optimal motion time; based on short-time Fourier transform introducing a Hanning window function, obtaining 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; designing a kinematics constraint equation by adopting a method based on sampling sparse observation points; a linear programming method is adopted to establish a motion instruction generation model with an optimal time-frequency spectrum, and a control vertex of a time B spline is solved. According to the method, the resonance phenomenon easily generated in the high-speed movement process is fundamentally reduced, and high robustness is achieved.

Description

Technical Field

[0001] This invention relates to the field of motion planning technology, and specifically to a time-frequency domain active design method for motion commands based on short-time Fourier transform. Background Technology

[0002] In precision manufacturing equipment such as semiconductor packaging and testing, the feed speed and positioning accuracy of flexible feed systems are core indicators for evaluating equipment performance. To improve production efficiency, there is an urgent need for equipment to achieve high-acceleration, high-precision point-to-point movement during operation, while minimizing end-effector vibration. However, feed systems are prone to residual vibration after high-speed, high-acceleration movement, significantly prolonging the positioning stabilization time and hindering the improvement of equipment operating efficiency.

[0003] Reference 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 adaptive PD control method, which adjusts the control model parameters in real time based on the system vibration energy, enabling the active vibration control system to adapt to different load conditions. However, the active vibration control system requires the installation of vibration state monitoring sensors, increasing the hardware cost of the equipment.

[0004] Reference 2 (TSAY DM, LIN C F. Asymmetrical inputs for minimizing residual response[C] / / 2005 IEEE International Conference on Mechatronics. IEEE, 2005:235-240..) proposes an asymmetric S-curve motion planning method, which optimizes the vibration response of the feed system by minimizing the residual response and settling time. However, this method seeks the optimal command parameters from the time domain to achieve residual vibration suppression, and the process depends on accurate modeling of the system. Its robustness and vibration suppression performance are affected by modeling errors.

[0005] Reference 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 trajectory generation method with the goal of minimizing spectral energy within a frequency band. By actively designing the frequency domain of motion commands, it significantly suppresses the residual vibration of the feed system, providing a new approach for high-speed and high-precision speed planning. However, in equipment such as five-axis machine tools, robots, and electronic manufacturing equipment, the mechanical parameters of the feed system, such as inertia and stiffness, may change with the movement position, leading to changes in dynamic characteristics. In this case, the method lacks time resolution and cannot adjust the spectral vibration suppression range according to the changes in the dynamic characteristics of the feed system during motion, resulting in limited residual vibration suppression effect of the feed system.

[0006] Therefore, this application addresses the problem of low processing efficiency and accuracy caused by vibration during high-speed motion of flexible feed systems by introducing short-time Fourier transform theory to actively design the time-frequency domain of motion commands, attenuating the frequency band energy in the motion commands that causes resonance in the system, and preventing the system from resonating during the execution of motion commands, thus fundamentally solving the problem of resonance in the system during high-speed motion. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a time-frequency domain active design method for motion commands based on short-time Fourier transform.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A time-frequency domain active design method for motion commands based on short-time Fourier transform, the process of constructing a motion command generation model includes: The motion command of the flexible feed system is defined based on the time B-spline curve, and the objective function for optimizing the motion time is constructed. Based on the short-time Fourier transform with the introduction of the Hanning window function, the acceleration motion command corresponding to the motion command is divided into multiple short-time segments. The Fourier transform is performed on each short-time segment to obtain the frequency distribution of the acceleration motion command in each time period. Based on the resonant frequency band of the flexible feed system and the frequency distribution of the acceleration motion command, a time-spectrum component constraint equation for the acceleration motion command is constructed to limit the amplitude of the motion command to be solved within the resonant frequency band. Kinematic constraint equations are designed using a method based on sparse sampling observation points; Combining the time-spectrum component constraint equations, kinematic constraint equations, and the objective function for optimal motion time, a time-spectrum optimal motion command generation model is established using linear programming. By solving for the control vertices of the time B-spline, motion commands are designed for the flexible feed system.

[0009] In one embodiment, the step of defining motion commands for the flexible feed system based on time-B-spline curves and constructing an objective function for optimal motion time specifically includes: Based on B-spline curve theory, the motion time of the motion command is used as the curve parameter. An analytical expression for the motion command is constructed by linearly combining a set of control vertices and the basis functions of the B-spline curve. The motion command sequence is represented by the analytical expression of the motion command. Based on the analytical expression of the motion command, a time-optimal objective function expression is constructed.

[0010] In one embodiment, based on B-spline curve theory, the motion time of the motion command is used as a curve parameter. An analytical expression for the motion command is constructed through a linear combination of a set of control vertices and the basis functions of the B-spline curve. Specifically, this includes: Constructing an analytical expression for motion commands based on time-B-spline curves: ; in, It is a motion command represented by a time B-spline curve; This is the index at time t. The first time-space B-spline curve One control vertex, , Indicates the number of control vertices; The first time-spline curve One basis function.

[0011] In one embodiment, representing the motion instruction sequence using a parsed expression of the motion instruction specifically includes: Based on the motion command expression of the time B-spline curve, the motion command sequence for moving the actuator of the flexible feed system from one point to another is obtained. and the corresponding speed and motion commands Acceleration motion command and acceleration motion commands Represented as: ; in, , express Motion instructions at any moment This represents the index of the time corresponding to the nth motion command. Indicates transpose. , , This represents the control vertex vector. This represents the m-th control vertex. The matrix expression representing the basis functions of the time-space B-spline curve. Indicates the length of the motion command sequence. Let m be the basis function of the B-spline curve. , , for The first derivative, second reciprocal, and third reciprocal with respect to time t.

[0012] In one embodiment, the step of constructing a time-optimal objective function expression based on the analytical expression of the motion command specifically includes: Given the motion constraints and the active design constraints in the time and frequency domain, the objective is to minimize the motion time T: ; and They are respectively Motion commands and speed at any given moment This represents the index of the time corresponding to the i-th motion command. The length of the motion command sequence; Considering the motion command as a variable to be determined, simplification is achieved by maximizing the motion command. The goal of minimizing motion time can be indirectly achieved by summing the results: .

[0013] In one embodiment, the short-time Fourier transform based on the Hanning window function divides the acceleration motion command corresponding to the motion command into multiple short-time segments, performs a Fourier transform on each short-time segment, and obtains the frequency distribution of the acceleration motion command in each time period, specifically including: Constructing the Hanning window function The parsing expression: ;in, M is the window length of the Hanning window; By shifting the Hanning window function along the time axis, the acceleration motion command is controlled. Convolution windowing and Fourier transform are performed on short time segments within each Hanning window to obtain acceleration motion commands. The spectral components within the current Hanning window time period, the first The first one inside the Hanning window spectral components for: ; in, , c represents the acceleration motion command. The total number of short time segments into which it is decomposed, where L is the preset number of Fourier transform points; The acceleration motion command corresponding to the b-th Hanning window The starting position; h is the preset Hanning window overlap length; It is the imaginary unit.

[0014] In one embodiment, during the convolution windowing stage, the convolution windowing acceleration motion command sequence The motion command information obtained through the b-th Hanning window ; express acceleration at any moment To The windowing matrix for performing the b-th Hanning window convolution operation; During the Fourier transform stage, the motion command sequence information within the b-th Hanning window is processed. Perform a Fourier transform to obtain The time-domain information and frequency-domain information; where the time-domain information is the time corresponding to the b-th Hanning window, and the frequency-domain information is the spectral components. : ; in, , This is the corresponding Fourier transform matrix.

[0015] In one embodiment, the step of constructing a time-spectrum component constraint equation for the acceleration motion command based on the resonant frequency band of the flexible feed system and the frequency distribution of the acceleration motion command, in order to limit the amplitude of the motion command to be solved within the resonant frequency band, specifically includes: Construct the amplitude of the excitation spectral component within each Hanning window : ; and They are respectively represented as The real and imaginary parts; Will The real and imaginary parts are restricted separately: No. The real and imaginary vectors of the motion command spectrum corresponding to each Hanning window Depend on Construction of the real and imaginary parts: ; in, , It is a spectral component The real part vector, It is a spectral component The imaginary part vector, To calculate the resonant frequency range of the flexible system Inner spectral sequence The Fourier transform matrices required for the real and imaginary parts: ; in, Indicates the starting frequency of the resonance frequency range. Indicates the ending frequency of the resonance frequency range. Spectral sequence Frequency index vector within, Sampling frequency, Fourier transform matrix The elements in This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part; Active time-frequency domain design of motion commands is achieved by minimizing the amplitude of the excitation spectral component within each Hanning window of the acceleration motion command A; the first... Minimizing the real and imaginary parts of the excitation spectrum components within each Hanning window is transformed into: the real and imaginary vectors of the spectrum within each Hanning window. If the element does not exceed the preset maximum value, then the first... Within a Hanning window, the constraint equation for the time-frequency component of the acceleration motion command is expressed as: ; in, It represents the maximum and minimum values ​​of the real and imaginary vectors of the spectrum within the b-th Hanning window.

[0016] In one embodiment, the method of designing kinematic constraint equations based on sampling sparse observation points specifically includes: At the start time displacement ,speed and acceleration All are 0; at the termination time displacement for ,speed acceleration All values ​​are 0, and the motion boundary constraints are expressed as follows: ; express The matrix formed express The matrix formed; The speed constraint for motion commands is: ; Maximum speed; The acceleration constraint for motion commands is: ; This is the maximum acceleration; The motion command jerk constraint is: ; This is the maximum jerk. Considering the distortion characteristics of B-splines, the upper and lower limits of the control vertices of the B-spline curve are constrained: ; Represents the lower bound matrix, This represents the upper bound matrix.

[0017] In one embodiment, by combining the time-spectrum component constraint equations, kinematic constraint equations, and the objective function for optimal motion time, a time-spectrum optimal motion command generation model is established using linear programming. Motion commands are designed for the flexible feed system by solving for the control vertices of the time B-spline. Specifically, this includes: Motion commands are represented by time-B-spline curves, where the control vertex P of the time-B-spline is the variable to be solved. The motion command generation model with optimal time-spectrum is as follows: ; .

[0018] Compared with the prior art, the beneficial technical effects of the present invention are: To reduce resonance during the motion of a flexible feed system, this invention proposes a time-frequency domain active design method for point-to-point linear motion time B-spline commands based on short-time Fourier transform. This method combines the time-frequency analysis capabilities of short-time Fourier transform with the high flexibility in the definition of time B-spline curves. It actively designs motion commands based on the resonant frequency band of the flexible feed system, limiting the spectral components of the motion commands within the resonant frequency band at different time periods. This fundamentally reduces resonance phenomena that easily occur during high-speed motion, exhibiting advantages of high robustness and high stability. Simultaneously, the linear programming model proposed in this invention has significant computational advantages, enabling rapid calculation of the control vertices of the time B-spline to generate high-speed, low-vibration point-to-point motion commands. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method of the present invention.

[0020] Figure 2This is a comparison chart of the displacement and velocity motion commands generated by the method proposed in this invention and the displacement and velocity motion commands solved by the S-shaped velocity planning method.

[0021] Figure 3 This is a comparison chart of the acceleration motion command obtained by the method proposed in this invention and the motion command obtained by the S-shaped velocity planning method, as well as a comparison chart of their Fast Fourier Transform (FFT) results.

[0022] Figure 4 This is a comparison diagram showing the displacement response and residual vibration at the end of a flexible feed system when the motion command obtained by the method proposed in this invention and the motion command obtained by the S-shaped velocity planning method are applied. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] like Figure 1 As shown, the motion command time-frequency domain active design method based on short-time Fourier transform in this invention includes the following steps in constructing the motion command generation model: A time-frequency domain active design method for motion commands based on short-time Fourier transform includes the following steps in constructing a motion command generation model: S1, define the motion command of the flexible feed system based on the time B-spline curve, and construct the objective function for optimal motion time; S2, based on the short-time Fourier transform with the introduction of the Hanning window function, divides the acceleration motion command corresponding to the motion command into multiple short-time segments, performs Fourier transform on each short-time segment, and obtains the frequency distribution of the acceleration motion command in each time period. S3. Based on the resonant frequency band of the flexible feed system and the frequency distribution of the acceleration motion command, construct the time-spectrum component constraint equation of the acceleration motion command to limit the amplitude of the motion command to be solved in the resonant frequency band. S4. Kinematic constraint equations are designed using a method based on sparse sampling observation points. S5. Combining the time-spectrum component constraint equation, kinematic constraint equation, and the objective function for optimal motion time, a time-spectrum optimal motion command generation model is established using linear programming. By solving for the control vertices of the time B-spline, motion commands are designed for the flexible feed system.

[0025] In one embodiment, step S1 specifically includes: First, we construct the position and motion command expression based on the fifth-order time B-spline (t-Bspline) curve, which can be expressed as: ; in, It is a motion command relating to the curve parameter t of the time-b-spline curve; For the curve of the first One control vertex; For the B-spline curve One basis function.

[0026] So, the point-to-point motion command sequence and the corresponding speed and motion commands Acceleration motion command and acceleration motion commands It can be expressed as: ; in, , , , Indicates a sequence of motion commands. This represents the control vertex vector. The matrix expression representing the basis functions of a B-spline curve. Indicates the length of the motion command sequence. Let represent the basis functions of the m-th B-spline curve. This indicates the number of control vertices.

[0027] , and for Regarding time The first, second, and third derivatives of are given by the following elements: , and . To of The first derivative can be expressed as: .

[0028] In the formula, For the first A 4th-order B-spline basis function The first derivative. The recursive formula is as follows: ; also, Represented as: ; in, The values ​​of the node vectors are based on the total time of motion planning. Uniformly distributed design is represented as ,in, This is the predetermined time interval.

[0029] With the goal of minimizing the motion time T, the analytical expression for the objective is as follows: ; In the formula, and They are respectively Motion commands and speed at any given moment.

[0030] By maximizing motion commands The method of indirectly achieving the goal of minimizing motion time through the sum of sequences can be expressed as: .

[0031] In one embodiment, step S2 specifically includes: Using the Short Time Fourier Transform (STFT) of the Hanning window function, the acceleration motion command is divided into multiple short time segments, and a Fourier transform is performed on each short time segment to obtain the frequency distribution of the acceleration motion command in each time segment, enabling active time-frequency domain design of the motion command.

[0032] Constructing the Hanning window function The parsing expression: ; in M is the window length of the Hanning window.

[0033] In response to acceleration motion commands After STFT conversion, the first The first window spectral components It can be represented as: ; Where c is the acceleration motion command. The total number of segments broken down into short time fragments; The acceleration corresponding to the b-th window The starting position can be represented as h is the preset Hanning window overlap length; L is the preset Fourier transform (FFT) point count.

[0034] The total number of short time segments, c, is expressed as: ; in This indicates rounding down to the nearest integer.

[0035] Acceleration Motion Command Sequence The motion command information obtained through the b-th Hanning window It can be represented as: ; in, To The windowing matrix for performing the b-th Hanning window convolution operation can be represented as: ; also, Hanning window function The matrix representation of is expressed as follows: ; During the FFT transform stage, the motion command sequence information within the b-th Hanning window is processed. Perform FFT to obtain the acceleration motion command sequence. The time-domain information and frequency-domain information. The time-domain information is the time corresponding to the b-th Hanning window, i.e. , This indicates the interpolation period. Frequency domain information consists of spectral components. , can be represented as: ; in, The corresponding Fourier transform matrix can be expressed as: ; in, , and Values .

[0036] In one embodiment, step S3 specifically includes: Subsequently, the amplitude of the excitation spectrum component of the acceleration motion command A is minimized within each Hanning window, and the real and imaginary parts of the amplitude of the excitation spectrum component are restricted respectively, thereby realizing the active time-frequency domain design of the motion command for vibration suppression of the flexible feed system.

[0037] Amplitude of each excitation spectral component within the Hanning window The analytical expression is: ; in, and They are respectively represented as The real and imaginary parts.

[0038] No. The real and imaginary vectors of the motion command spectrum corresponding to each Hanning window Depend on The construction of the real and imaginary parts can be represented as: ; in, , yes The real part vector of can be expressed as ; yes The imaginary part vector can be expressed as . To calculate the frequency range Inner spectral sequence The Fourier transform matrix required for the real and imaginary parts of the expression can be expressed as: ; in, Spectral sequence The frequency index vector within can be represented as , The sampling frequency.

[0039] The first Minimizing the real and imaginary parts of the excitation spectrum components within each Hanning window can be transformed into minimizing the real and imaginary vectors of the spectrum within each Hanning window. The number of elements does not exceed the preset maximum value. Based on this, the first... Within a Hanning window, the constraint equation for the time-frequency component of the acceleration motion command can be expressed as: ; in, It represents the maximum and minimum values ​​of the real and imaginary vectors of the spectrum within the b-th Hanning window.

[0040] In one embodiment, step S4 specifically includes: Point-to-point motion boundary constraints and motion constraints are established. Based on the S-shaped velocity curve and combined with preset maximum acceleration and jerk, the durations of acceleration, constant velocity, and deceleration phases are estimated. Observation points are set at a resolution of 15 points / second during the durations of acceleration and deceleration phases; and at a resolution of 30 points / second during the duration of constant velocity phases. This reduces the number of constraint equations, decreases the computational scale of the optimization model, and improves computational efficiency.

[0041] Motion boundary constraints at the start and end points, at the initial moment displacement ,speed and acceleration All are 0; at the termination time displacement for ,speed acceleration All are 0. The motion boundary constraints can be expressed as: ; Motion command speed constraint: To ensure the smoothness of the motion process, the motion command speed should not exceed the maximum speed. , can be represented as: .

[0042] Motion command acceleration constraint: To avoid motor overload, the motion command acceleration should not exceed the maximum acceleration. , can be represented as: .

[0043] Motion command jerk constraint: To avoid unstable motion, high-frequency noise, and vibration, the motion command jerk shall not exceed the maximum jerk. , can be represented as: .

[0044] To prevent fluctuations caused by changes in the B-spline at the target position, upper and lower limits are constrained for the control vertices of the B-spline curve, which can be expressed as: .

[0045] Motion commands are represented by B-splines, and the control vertex P of the time B-spline is the variable to be solved. Combining motion boundary constraints, motion process constraints, and time-frequency domain active design constraints, the time-frequency optimal motion command generation model can be expressed as: ; .

[0046] The motion command generation model can be calculated using the interior point method to solve for the control vertices of the motion command, resulting in a motion trajectory that satisfies kinematic and dynamic constraints while avoiding excitation of vibration amplitude in the system during motion engineering. From a motion planning perspective, short-time Fourier transform theory is introduced to address the problem of strong vibrations generated by the flexible feed system during high-speed motion. Compared to traditional quadratic programming models, the linear programming model proposed in this invention has significant computational advantages, enabling rapid calculation of the control vertices of the time B-spline and generation of high-speed, low-vibration point-to-point motion commands. Based on the above implementation methods, the following conditions are provided for the embodiments: (1) The total displacement in this embodiment is 100mm, the maximum speed is limited to 100mm / s, the maximum acceleration is limited to 2500mm / s2, the maximum jerk is 10000mm / s, the initial and final speeds and accelerations are 0, the window length of the Hanning window is 256, and the overlap length is 192; the total planning time is based on the S-shaped speed planning time as the time template.

[0047] (2) For comparison, this embodiment uses the widely used S-shaped velocity curve and FS-shaped velocity curve to perform velocity planning to obtain the displacement, velocity and acceleration commands of the initial motion trajectory.

[0048] (3) Using the point-to-point motion high-speed vibration suppression method based on short-time Fourier theory proposed in this invention, the S-shaped velocity trajectory is re-optimized under the condition of satisfying kinematic and dynamic constraints, and the optimized displacement, velocity and acceleration commands are obtained. Figure 2 (a) and (b) in the middle. Figure 3 (a) shows a comparison between the motion command obtained by the method proposed in this invention and the motion command obtained by the S-shaped velocity planning method. It can be observed that the method proposed in this invention and the FS-shaped velocity planning method obtain smoother and more adaptively adjusted motion commands (time domain angle) than the S-shaped velocity planning method.

[0049] (4) Apply the motion command obtained by the method proposed in this invention and the motion command obtained by the S-shaped velocity planning and FS-shaped velocity planning methods to the flexible feed system, and observe the energy distribution of the motion command in the excitation spectrum component at the end of the flexible feed system during the motion process. Figure 3 As shown in (b), it can be observed that the sum of the energies of the excitation spectrum components of the method proposed in this invention and the FS-shaped velocity planning method is much smaller than the sum of the energies of the excitation spectrum components obtained by the S-shaped velocity planning method.

[0050] (5) Apply the motion commands obtained by the method proposed in this invention and the motion commands obtained by the S-shaped velocity planning and FS-shaped velocity planning methods to the flexible feed system, and observe the displacement response and residual vibration at the end of the flexible feed system. Figure 4 As shown in (a) and (b) in the figure, it can be seen that the method proposed in this invention can significantly reduce the residual vibration amplitude at the end of the system.

[0051] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0052] It should be understood that although the steps in the flowcharts of the accompanying drawings are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some of the steps in the flowcharts of the accompanying drawings may include multiple steps or stages, which are not necessarily completed at the same time, but may be executed at different times, and the execution order of these steps or stages is not necessarily sequential, but may be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0053] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0054] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0055] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A time-frequency domain active design method for motion commands based on short-time Fourier transform, characterized in that, The process of building a motion command generation model includes: The motion command of the flexible feed system is defined based on the time B-spline curve, and the objective function for optimizing the motion time is constructed. Based on the short-time Fourier transform with the introduction of the Hanning window function, the acceleration motion command corresponding to the motion command is divided into multiple short-time segments. The Fourier transform is performed on each short-time segment to obtain the frequency distribution of the acceleration motion command in each time period. Based on the resonant frequency band of the flexible feed system and the frequency distribution of the acceleration motion command, a time-spectrum component constraint equation for the acceleration motion command is constructed to limit the amplitude of the motion command to be solved within the resonant frequency band. Kinematic constraint equations are designed using a method based on sparse sampling observation points; Combining the time-spectrum component constraint equations, kinematic constraint equations, and the objective function for optimal motion time, a time-spectrum optimal motion command generation model is established using linear programming. By solving for the control vertices of the time B-spline, motion commands are designed for the flexible feed system.

2. The time-frequency domain active design method for motion commands based on short-time Fourier transform as described in claim 1, characterized in that, The motion commands for the flexible feed system are defined based on time-B-spline curves, and an objective function for optimizing motion time is constructed, specifically including: Based on B-spline curve theory, the motion time of the motion command is used as the curve parameter. An analytical expression for the motion command is constructed by linearly combining a set of control vertices and the basis functions of the B-spline curve. The motion command sequence is represented by the analytical expression of the motion command. Based on the analytical expression of the motion command, a time-optimal objective function expression is constructed.

3. The time-frequency domain active design method for motion commands based on short-time Fourier transform according to claim 2, characterized in that, Based on B-spline curve theory, the motion time of the motion command is used as a curve parameter. An analytical expression for the motion command is constructed through a linear combination of a set of control vertices and the basis functions of the B-spline curve. Specifically, this includes: Constructing an analytical expression for motion commands based on time-B-spline curves: ； in, It is a motion command represented by a time B-spline curve; This is the index at time t. The first time-spline curve One control vertex, , Indicates the number of control vertices; The first time-spline curve One basis function.

4. The time-frequency domain active design method for motion commands based on short-time Fourier transform according to claim 3, characterized in that, The representation of the motion instruction sequence through the parsed expression of the motion instructions specifically includes: Based on the motion command expression of the time B-spline curve, the motion command sequence for moving the actuator of the flexible feed system from one point to another is obtained. and the corresponding speed and motion commands Acceleration motion command and acceleration motion commands Represented as: ； in, , express Motion instructions at any moment This represents the index of the time corresponding to the nth motion command. Indicates transpose. , , This represents the control vertex vector. This represents the m-th control vertex. The matrix expression representing the basis functions of the time-space B-spline curve. Indicates the length of the motion command sequence. Let m be the basis function of the B-spline curve. , , for The first derivative, second reciprocal, and third reciprocal with respect to time t.

5. The time-frequency domain active design method for motion commands based on short-time Fourier transform according to claim 4, characterized in that, The construction of a time-optimal objective function expression based on the analytical expression of the motion command specifically includes: Given the motion constraints and the active design constraints in the time and frequency domain, the objective is to minimize the motion time T: ； and They are respectively Motion commands and speed at any given moment This represents the index of the time corresponding to the i-th motion command. The length of the motion command sequence; Considering the motion command as a variable to be determined, simplification is achieved by maximizing the motion command. The goal of minimizing motion time can be indirectly achieved by summing the results: 。 6. The time-frequency domain active design method for motion commands based on short-time Fourier transform according to claim 5, characterized in that, The short-time Fourier transform based on the Hanning window function divides the acceleration motion command corresponding to the motion command into multiple short-time segments, performs a Fourier transform on each short-time segment, and obtains the frequency distribution of the acceleration motion command in each time segment, specifically including: Constructing the Hanning window function The parsing expression: ;in, M is the window length of the Hanning window; By shifting the Hanning window function along the time axis, the acceleration motion command is controlled. Convolution windowing and Fourier transform are performed on short time segments within each Hanning window to obtain acceleration motion commands. The spectral components within the current Hanning window time period, the first The first one inside the Hanning window spectral components for: ； in, , c represents the acceleration motion command. The total number of short time segments into which it is decomposed, where L is the preset number of Fourier transform points; The acceleration motion command corresponding to the b-th Hanning window The starting position; h is the preset Hanning window overlap length; It is the imaginary unit.

7. The time-frequency domain active design method for motion commands based on short-time Fourier transform as described in claim 6, characterized in that, During the convolution windowing stage, the convolution windowing acceleration motion command sequence The motion command information obtained through the b-th Hanning window ; express acceleration at any moment To The windowing matrix for performing the b-th Hanning window convolution operation; During the Fourier transform stage, the motion command sequence information within the b-th Hanning window is processed. Perform a Fourier transform to obtain The time-domain information and frequency-domain information; where the time-domain information is the time corresponding to the b-th Hanning window, and the frequency-domain information is the spectral components. : ； in, , This is the corresponding Fourier transform matrix.

8. The time-frequency domain active design method for motion commands based on short-time Fourier transform according to claim 7, characterized in that, The step of constructing a time-spectrum component constraint equation for the acceleration motion command based on the resonant frequency band of the flexible feed system and the frequency distribution of the acceleration motion command, in order to limit the amplitude of the motion command to be solved within the resonant frequency band, specifically includes: Construct the amplitude of the excitation spectral component within each Hanning window : ； and They are respectively represented as The real and imaginary parts; Will The real and imaginary parts are restricted separately: No. The real and imaginary vectors of the motion command spectrum corresponding to each Hanning window Depend on Construction of the real and imaginary parts: ； in, , It is a spectral component The real part vector, It is a spectral component The imaginary part vector, To calculate the resonant frequency range of the flexible system Inner spectral sequence The Fourier transform matrices required for the real and imaginary parts: ； in, Indicates the starting frequency of the resonance frequency range. Indicates the ending frequency of the resonance frequency range. Spectral sequence Frequency index vector within, Sampling frequency, Fourier transform matrix The elements in This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part; Active time-frequency domain design of motion commands is achieved by minimizing the amplitude of the excitation spectral component within each Hanning window of the acceleration motion command A; the first... Minimizing the real and imaginary parts of the excitation spectrum components within each Hanning window is transformed into: the real and imaginary vectors of the spectrum within each Hanning window. If the element does not exceed the preset maximum value, then the first... Within a Hanning window, the constraint equation for the time-frequency component of the acceleration motion command is expressed as: ； in, It represents the maximum and minimum values ​​of the real and imaginary vectors of the spectrum within the b-th Hanning window.

9. The time-frequency domain active design method for motion commands based on short-time Fourier transform according to claim 8, characterized in that, The method of designing kinematic constraint equations based on sparse sampling observation points specifically includes: At the start time displacement ,speed and acceleration All are 0; at the termination time displacement for ,speed acceleration All values ​​are 0, and the motion boundary constraints are expressed as follows: ； express The matrix formed express The matrix formed; The speed constraint for motion commands is: ; Maximum speed; The acceleration constraint for motion commands is: ; This is the maximum acceleration; The motion command jerk constraint is: ; This is the maximum jerk. Considering the distortion characteristics of B-splines, the upper and lower limits of the control vertices of the B-spline curve are constrained: ； Represents the lower bound matrix, This represents the upper bound matrix.

10. The time-frequency domain active design method for motion commands based on short-time Fourier transform according to claim 9, characterized in that, Combining the time-spectrum component constraint equations, kinematic constraint equations, and the objective function for optimal motion time, a time-spectrum optimal motion command generation model is established using linear programming. By solving for the control vertices of the time B-spline, motion commands are designed for the flexible feed system, specifically including: Motion commands are represented by time-B-spline curves, where the control vertex P of the time-B-spline is the variable to be solved. The motion command generation model with optimal time-spectrum is as follows: ； 。

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