Real-time vibration suppression method based on input shaping and S-shaped speed planning

Abstract

The invention belongs to the field of high-end logistics equipment control, and relates to a real-time vibration suppression method based on input shaping and S-shaped speed planning, which comprises the following steps of: S1, for a moving object in a mechanism system, dynamically generating an S-shaped speed planning curve based on real-time target displacement and initial and final speeds in the moving process of the object; s2, constructing a zero-vibration input shaper based on system characteristics, and performing convolution operation on the S-shaped speed planning curve by using the shaper to obtain a target demand speed control curve; and S3, according to the target demand speed control curve, calculating an instruction control speed of the current system based on the real-time displacement feedback information, and inputting the instruction control speed to a motion control system to realize residual vibration suppression. According to the method, the vibration of the high-speed moving object can be efficiently suppressed, and meanwhile, the requirement for real-time performance in an open-loop control scene is met.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of high-end logistics equipment control, and particularly relates to a real-time vibration suppression method based on input shaping and S-shaped speed planning. BACKGROUND

[0002] In some motion systems involving large-size or high-elevation structures, due to the flexible characteristics of the mechanism itself and the response differences between multiple drive units, obvious shaking is easily generated during the motion. Such vibration not only limits the design operating speed of the system, but also can cause damage to the carried objects or equipment structures, affecting the operation safety. In addition, when the system needs to frequently start and stop between multiple target positions, the mutation of speed is easy to excite residual vibration, resulting in a decrease in positioning accuracy and operation efficiency. Long-term sustained vibration also accelerates structural fatigue and component wear, increases maintenance costs and brings potential operation risks.

[0003] Currently, in many general motion control scenes, the control method of trapezoidal speed curve combined with displacement feedback is still widely used to realize basic positioning function. This method can still meet the demand in low-speed, light-load or structure with strong rigidity applications, but when facing high-speed, heavy-load or structure with strong flexibility and complex dynamic characteristics, it is difficult to realize high stability and high precision control due to problems such as response lag and insufficient vibration suppression capability. SUMMARY

[0004] In order to solve the above technical problems existing in the prior art, the application proposes a real-time vibration suppression method based on input shaping and S-shaped speed planning, which can efficiently suppress the vibration of high-speed motion systems while meeting the real-time requirements in open-loop control scenarios. The specific technical scheme is as follows: A real-time vibration suppression method based on input shaping and S-shaped speed planning, comprising the following steps: S1: For a moving object in a mechanism system, based on the real-time target displacement and initial and final velocities in the object motion process, an S-shaped speed planning curve is dynamically generated; S2: A zero-vibration input shaper is constructed based on the system characteristics, and the S-shaped speed planning curve is convolved using the shaper to obtain a target demand speed control curve; S3: According to the target demand speed control curve, the current system's instruction control speed is calculated based on real-time displacement feedback information and input to the motion control system to realize residual vibration suppression.

[0005] Further, the S1 specifically includes: S1.1: Set the parameters required for S-shaped speed planning, including the initial velocity , final velocity , maximum speed Initial acceleration Maximum acceleration Initial acceleration Accelerate Target displacement The time required for each stage of S-shaped speed planning Displacement Final velocity of each stage ,and The S-shaped velocity programming is divided into seven motion stages, denoted as... , to These correspond to the acceleration phase, uniform acceleration phase, deceleration phase, constant speed phase, acceleration / deceleration phase, uniform deceleration phase, and deceleration / deceleration phase, respectively. S1.2: Simultaneously based on the initial acceleration Initial acceleration Determine the specific stage of the S-shaped velocity planning curve that the system is currently in in order to determine the displacement planning method; S1.3: Based on the mathematical relationship between jerk, acceleration, velocity and displacement, the displacement values ​​of each segment in the S-shaped velocity planning curve are solved, and the velocity that the current system should maintain is deduced in real time based on the displacement values, thus solving the time and velocity curve.

[0006] Furthermore, in S1.1, for any motion stage in the S-shaped velocity planning, As constants, the formulas for calculating acceleration, velocity, and displacement are as follows: ; ; .

[0007] Furthermore, in S1.2, because the object's initial velocity... It can be in 7 stages: acceleration stage, uniform acceleration stage, deceleration stage, uniform speed stage, acceleration / deceleration stage, uniform deceleration stage, and deceleration / deceleration stage. The current initial acceleration... With initial acceleration The S-shaped velocity planning curve can be divided into seven cases: .

[0008] Furthermore, in S1.2, when the initial velocity of the system... During any acceleration phase, determine when the maximum speed has been reached. minimum distance Deceleration to final speed minimum distance The sum of the target displacements If the relationship, Then the system's speed can reach its maximum speed. ;like If the system cannot reach its maximum speed, then the system's speed will be insufficient. ; When the initial velocity of the system It is in the acceleration phase, and the object has accelerated to its maximum speed. According to the final velocity size, The initial velocity is in the acceleration phase, and the total displacement is divided into... , The initial velocity is in the uniform acceleration phase, and the total displacement is divided into... , The initial velocity is in the deceleration / acceleration phase, and the total displacement is divided into... , The initial velocity is in the uniform phase, and the total displacement is divided into... ; When the initial velocity of the system During the acceleration phase, the system cannot accelerate to its maximum speed. According to the final velocity size, The initial velocity is in the acceleration phase, and the total displacement can be divided into... , The initial velocity is in the uniform acceleration phase, and the total displacement can be divided into... ; When the initial velocity of the system The deceleration phase is independent of the system's maximum speed. , initial velocity During the acceleration / deceleration phase, the total displacement is divided into... , initial velocity During the uniform deceleration phase, the total displacement is , initial velocity During the deceleration phase, the total displacement is .

[0009] Furthermore, S2 specifically includes: S2.1: Apply transient pulse excitation to the system and collect multiple sets of time-domain response signals through sensors. Calculate the system's free oscillation frequency and damping ratio from the response signals using system identification methods. S2.2: Construct a zero-vibration shaper based on the free oscillation frequency and system damping characteristics; S2.3: Perform time-domain convolution between the S-shaped velocity planning curve and the zero-vibration shaper to obtain the shaped S-shaped velocity planning curve.

[0010] Furthermore, S2.1 specifically involves: applying a transient pulse excitation to the top of the system using a standard hammer to induce broadband free vibration. The dynamic response of the system is synchronously acquired by a laser displacement sensor, recording the time history curve of the vibration displacement. By performing parameter identification and analysis on multiple sets of acquired time-domain response signals, the free oscillation frequency in each experiment is extracted. Finally, through statistical averaging, the accurate estimate of the system's natural frequency is determined, as expressed below: ; ; ; ; This is the actual measured damped oscillation frequency. pass. It is the damped oscillation period, the time interval between adjacent peaks or troughs measured in a free decaying signal; It is the amplitude of the nth wave peak. It is the amplitude of the (n+k)th wave crest, where k is the number of period intervals; It is the logarithmic decay rate, which is the logarithmic ratio that characterizes the degree of amplitude decay in each cycle; It is the damped natural frequency, the actual measured damped oscillation frequency; It is the damping ratio, which characterizes the energy dissipation rate of the system, and is the critical damping time. , It is the undamped natural frequency, the inherent angular frequency of the system under ideal undamped conditions.

[0011] Furthermore, in S2.2, the zero-vibration shaper includes two pulses that satisfy the residual oscillation constraint condition. The following conditions are given: time-optimal and pulse amplitude constraints, the simultaneous equations formed by the constraints, and the pulse amplitude and time lag values ​​obtained by solving the constraints. The residual oscillation ratio (PRV) of the input command is as follows: ; ; ; The time-domain expression for eliminating residual oscillations using the ZV shaper is obtained as follows: ; in, , , It is the residual vibration amplitude. It is the cosine component response. It is a sinusoidal component response. It is the residual vibration ratio. It is the amplitude of the i-th pulse. It is the time of the i-th pulse. It was Dirac The function is given by K, where K is the damping coefficient and T is the damped oscillation period. This is the second pulse time.

[0012] Furthermore, S2.3 specifically involves: firstly, dividing the continuous S-shaped velocity planning curve into an array sequence according to the discrete time step; then, converting the time-domain parameters of the zero-vibration shaper into the corresponding discrete delay steps; and finally, by performing a convolution operation, weighting and superimposing the curve array and the shaper coefficient array to generate the shaped S-shaped velocity planning curve.

[0013] Furthermore, S3 specifically involves: the system detecting the actual displacement of the object's motion in real time based on the shaped S-shaped velocity planning curve, resolving the velocity command to be tracked, and sending it to the controller. This velocity command is then sent to the servo driver in real time, forming a closed-loop control, thereby ensuring that the system's motion follows the shaped planned trajectory. Compared with existing methods, the beneficial effects of this invention include:

[0014] (1) The present invention can calculate the S-shaped speed planning curve in real time according to the target distance set by the system in real time. When the object running task encounters a sudden situation and needs to change the target displacement and final velocity in real time, a new target displacement curve can be generated quickly, while ensuring the smooth transition of the speed of the high-speed running object and improving the safety of the system.

[0015] (2) The present invention constructs a zero-vibration input shaper by measuring the free oscillation frequency of the system, and performs convolution operation between the shaper and the control signal output by the S-shaped velocity real-time planning algorithm to generate a new motion control curve, thereby more effectively suppressing residual vibration on the basis of smooth speed transition.

[0016] (3) The velocity motion curve of the input system of the present invention is based on real-time displacement feedback to calculate the speed that the current object should run at in real time, avoiding the problem of not being able to accurately reach the target position due to slippage and loss of steps during operation, making the system run more efficiently. Attached Figure Description

[0017] Figure 1 This is a flowchart of the real-time vibration suppression method based on input shaping and S-shaped velocity planning of the present invention. Figure 2 This is a flowchart of the real-time planning of the S-shaped velocity curve according to the present invention; Figure 3 The flowchart for constructing the zero-vibration shaper of the present invention is shown below; Figure 4 To accelerate the process, the classification graph can be planned at the maximum speed. Figure 5 A classification diagram is used to plan the maximum speed that cannot be accelerated during the acceleration phase; Figure 6 A classification diagram for the deceleration phase; Figure 7 The figure shows the S-shaped velocity planning curve and the results of the shaper convolution calculation. Detailed Implementation

[0018] To make the objectives, technical solutions, and technical effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0019] See Figure 1 This invention discloses a real-time vibration suppression method for a stacker crane system based on input shaping and S-shaped velocity planning, comprising the following steps: S1: For moving objects in the mechanism system, dynamically generate an S-shaped velocity planning curve based on the real-time target displacement and initial and final velocities during the object's motion. This includes the following steps: S1.1: Set the basic parameters required for S-shaped velocity planning, including the initial velocity of the object's motion. Final velocity Maximum speed Initial acceleration Maximum acceleration Initial acceleration Accelerate Target displacement The time required for each stage of S-shaped speed planning Displacement Final velocity of each stage ,and The S-shaped speed planning is divided into seven stages, denoted as... , to These correspond to the acceleration phase, uniform acceleration phase, deceleration phase, constant speed phase, acceleration / deceleration phase, uniform deceleration phase, and deceleration / deceleration phase, respectively.

[0020] For any stage in the S-shaped velocity planning, Since acceleration, velocity, and displacement are constants, the general formulas for calculating them are as follows: ; ; .

[0021] S1.2: Simultaneously based on the initial acceleration Initial acceleration Reference Figure 2The logic shown determines the specific stage of the current S-shaped velocity curve to determine the displacement planning method, specifically including: S1.2.1: Because of the object's initial velocity It can be in 7 stages, and the present invention uses the current initial acceleration With initial acceleration The S-shaped velocity planning curve is divided into seven cases for discussion: .

[0022] S1.2.2: Based on different stage conditions, the algorithm performs corresponding curve planning and calculates the displacement of each segment in the S-shaped velocity planning, as follows: When the initial velocity of the object's system During any acceleration phase, based on the target displacement and final velocity Size can determine whether the system can reach its maximum speed. : Determine if the speed has accelerated to maximum. minimum distance Deceleration to final speed minimum distance The sum of the target displacements If the relationship, Then the system's speed can reach its maximum speed. ;like If the system cannot reach its maximum speed, then the system's speed will be insufficient. .

[0023] The initial velocity can be calculated using the general formulas for acceleration, velocity, and displacement. At any point during the acceleration phase, the acceleration to the maximum speed can be calculated. minimum distance Deceleration to final speed minimum distance The sum, expressed as follows: ; ; Minimum distance during acceleration phase middle Does it depend on the initial velocity? The minimum distance during the deceleration phase depends on which stage you are in. middle Does it exist based on the final velocity? It is determined by the size.

[0024] In one embodiment, when the system initial velocity During the acceleration phase, an object can accelerate to its maximum speed. According to the final velocity size, The initial velocity is in the acceleration phase, and the total displacement can be divided into... ; The initial velocity is in the uniform acceleration phase, and the total displacement can be divided into... ; The initial velocity is in the deceleration / acceleration phase, and the total displacement can be divided into... ; When the initial velocity is in the uniform phase, the total displacement can be divided into... .

[0025] exist Figure 4 The figure shows four categories of situations in which an object can accelerate to its maximum speed during the acceleration, uniform acceleration, deceleration, and constant speed stages. The velocity, acceleration, and displacement curves corresponding to each figure all conform to the S-shaped velocity planning described above.

[0026] In one embodiment, when the system initial velocity During the acceleration phase, the object cannot accelerate to its maximum speed. According to the final velocity The magnitude and initial velocity are in the acceleration phase, and the total displacement of the motion can be divided into... ; The initial velocity is in the uniform acceleration phase, and the total displacement can be divided into... .

[0027] exist Figure 5 The figures show two categories of situations where the system object cannot accelerate to the maximum speed during the acceleration and uniform acceleration phases. The velocity, acceleration and displacement curves corresponding to each figure all conform to the S-shaped curve velocity planning described above. In one embodiment, when the object's initial velocity During deceleration phase and at maximum system speed Irrelevant, initial velocity During the acceleration / deceleration phase, the total displacement can be divided into... Initial velocity During the uniform deceleration phase, the total displacement is Initial velocity During the deceleration phase, the total displacement is .

[0028] exist Figure 6 The figure shows the three types of acceleration / deceleration, uniform deceleration, and deceleration during the deceleration phase of the system. The velocity, acceleration, and displacement curves corresponding to each figure all conform to the described S-shaped velocity planning.

[0029] S1.3: Based on the description of the embodiment in S1.2.2 above, it can be determined how many segments the S-shaped planning curve to the target consists of. Based on the mathematical relationship between acceleration, velocity, and displacement in S1.1, the displacement required for each stage of the S-shaped velocity planning curve can be calculated. The time-displacement curves are obtained, and then the time-velocity curves are solved.

[0030] It should be noted that the residual vibration suppression algorithm involved in this invention is mainly aimed at large-scale industrial high-speed mobile systems. Such systems generally use PLCs to control motors. If speed commands are directly applied to the motor, the actual displacement may deviate due to problems such as transmission slippage. Therefore, the precise speed that should be maintained is solved in reverse by real-time displacement feedback, so as to achieve precise closed-loop control of the running speed. Therefore, it is necessary to solve the time and displacement curves.

[0031] It should be understood that the S-shaped velocity real-time planning curve algorithm strictly follows... Figure 2 The solution is obtained by following the steps outlined in the flowchart shown. The process first involves setting the parameters, and then solving based on the set acceleration. and accelerometer The algorithm determines the current time stage of the system. Based on different stage conditions, it performs corresponding curve planning and calculates the displacement of each segment in the S-shaped velocity planning. Finally, based on the calculated displacement, it infers the current speed to be maintained in real time, thereby achieving real-time planning of the S-shaped velocity.

[0032] Furthermore, the S-shaped velocity real-time planning algorithm supports dynamic parameter setting during the object's movement. This algorithm can set the target final velocity and displacement in real time based on the system's current initial velocity and initial acceleration, thereby effectively responding to possible emergencies during operation, avoiding control failures caused by fixed trajectories, and ultimately achieving online adjustment and optimization of the object's running speed state.

[0033] S2: Construct a zero-vibration input shaper based on system characteristics. Use this shaper to perform convolution operations on the above S-shaped velocity planning curve to obtain the target required velocity control curve, i.e., the vibration suppression curve. The specific steps include the following: S2.1: Apply transient pulse excitation to the system and collect multiple sets of time-domain response signals through sensors. Calculate the system's free oscillation frequency and damping ratio from the response signals using system identification methods.

[0034] Specifically, a transient pulse excitation was applied to the top of the system using a standard hammer to induce its broadband free vibration. The dynamic response of the system was synchronously acquired by a high-precision laser displacement sensor, recording the time history curve of the vibration displacement. By performing parameter identification and analysis on multiple sets of acquired time-domain response signals, the free oscillation frequencies in each experiment were extracted. Finally, through statistical averaging, the accurate estimate of the system's natural frequency was determined.

[0035] ; ; ; ; This is the actual measured damped oscillation frequency. pass. It is the damped oscillation period, the time interval between adjacent peaks or troughs measured in a free decaying signal; It is the amplitude of the nth wave peak. It is the amplitude of the (n+k)th wave crest, where k is the number of period intervals; It is the logarithmic decay rate, which is the logarithmic ratio that characterizes the degree of amplitude decay in each cycle; It is the damped natural frequency, the actual measured damped oscillation frequency; It is the damping ratio, which characterizes the energy dissipation rate of the system, and is the critical damping time. , It is the undamped natural frequency, the inherent angular frequency of the system under ideal undamped conditions.

[0036] S2.2: Construct a zero-vibration shaper based on the free oscillation frequency and system damping characteristics. It contains two pulses and needs to satisfy the residual oscillation constraint condition. And time-optimal and pulse amplitude constraints.

[0037] The simultaneous equations formed by the constraints are as follows. The pulse amplitude and time lag value obtained through the solution of the constraints, and the residual oscillation ratio (PRV) of the input command are also as follows: ; ; ; The time-domain expression for eliminating residual oscillations using the ZV shaper is obtained as follows: ; in, , , It is the residual vibration amplitude. It is the cosine component response. It is a sinusoidal component response. It is the residual vibration ratio. It is the amplitude of the i-th pulse. It is the time of the i-th pulse. It was Dirac The function is given by K, where K is the damping coefficient and T is the damped oscillation period. This is the second pulse time.

[0038] S2.3: Perform time-domain convolution between the S-shaped velocity planning curve and the zero-vibration shaper to obtain the shaped S-shaped velocity planning curve.

[0039] It should be noted that applying a zero-vibration input shaper to the displacement curve is essentially a weighted delay and accumulation process based on the displacement signal. First, the continuous displacement curve is divided into an array sequence according to the discrete time step. Then, the time-domain parameters of the shaper are converted into corresponding discrete delay steps. By performing convolution operations, the displacement curve array and the shaper coefficient array are weighted and superimposed to generate the shaped displacement curve. Finally, based on the shaped displacement curve, the speed command that the current system should have can be deduced in real time and sent to the controller.

[0040] The construction of the aforementioned zero-vibration shaper strictly follows Figure 3 The flowchart shown first applies transient pulse excitation to the stacker crane system and collects multiple sets of time-domain response signals through sensors. Then, based on the system identification method, the system's free oscillation frequency and damping ratio are calculated from the response signals. Based on this frequency and the system's damping characteristics, the time-delay pulse amplitude and action time point required for the zero-vibration shaper can be calculated, thus completing the construction of the shaper. Finally, the original S-shaped velocity planning curve is convolved with the shaper to obtain the shaped velocity planning curve.

[0041] S-shaped velocity real-time planning aims to achieve smooth velocity changes, which helps reduce the amplitude of residual vibrations, but cannot completely eliminate them. By combining the S-shaped velocity real-time planning algorithm with an input shaping algorithm, residual vibrations of the system can be suppressed more effectively while ensuring a smooth velocity transition.

[0042] S3: Based on the target required speed control curve and real-time displacement feedback information, calculate the current system command control speed and input it to the motion control system to achieve residual vibration suppression.

[0043] Based on the shaped velocity planning curve, the system detects the actual displacement of the object in the system in real time, and then deduces the current speed command to be tracked. The speed command is then sent to the servo driver in real time to form a closed-loop control, thereby ensuring that the system can accurately follow the shaped planned trajectory.

[0044] This invention performs a convolution operation between the S-shaped velocity planning curve and the designed shaper to obtain the shaped velocity curve and the corresponding displacement-time relationship. In this relationship, each point on the displacement curve corresponds strictly to a certain velocity value in the velocity-time curve. Therefore, by continuously resolving the corresponding real-time velocity based on the current actual displacement, it can be ensured that the system displacement always follows the preset displacement curve. If the control is executed by directly tracking the original velocity curve, displacement accumulation error may occur due to actual factors such as wheel slippage and step loss. The displacement feedback mechanism described in this invention can effectively overcome this problem and improve the accuracy and robustness of trajectory control.

[0045] In summary, the S-shaped velocity planning algorithm proposed in this invention, based on real-time motion target requirements, dynamically calculates the running velocity curve of the S-shaped velocity planning according to the real-time target displacement and initial and final velocity requirements during the object's motion. This allows for the rapid generation of a new target displacement curve when the object encounters unexpected situations requiring real-time changes to the target displacement and final velocity, ensuring a smooth transition of the high-speed object's velocity. A zero-vibration input shaper is constructed based on the system's free oscillation frequency detected by a laser displacement sensor. This shaper is then convolved with the control signal output from the real-time S-shaped velocity planning algorithm to generate a vibration suppression curve that fuses the input shaping and S-shaped velocity planning. This curve, based on real-time displacement feedback, is used to calculate the current velocity and input it to the motion control system, avoiding the problem of inaccurate target positioning due to slippage and missed steps during operation, ultimately achieving effective suppression of residual vibration. This invention can efficiently suppress the vibration of high-speed moving objects while meeting the real-time requirements of open-loop control scenarios.

[0046] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the implementation process of the present invention has been described in detail above, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A real-time vibration suppression method based on input shaping and S-shaped velocity planning, characterized in that, Includes the following steps: S1: For moving objects in the mechanism system, dynamically generate an S-shaped velocity planning curve based on the real-time target displacement and initial and final velocities during the object's motion. S2: Construct a zero-vibration input shaper based on system characteristics, and use this shaper to perform convolution operation on the above S-shaped velocity planning curve to obtain the target required velocity control curve; S3: Based on the target speed control curve and real-time displacement feedback information, calculate the current system command control speed and input it to the motion control system to achieve residual vibration suppression.

2. The real-time vibration suppression method as described in claim 1, characterized in that, S1 specifically includes: S1.1: Set the parameters required for S-shaped velocity planning, including the initial velocity of the object's motion. Final velocity Maximum speed Initial acceleration Maximum acceleration Initial acceleration Accelerate Target displacement The time required for each stage of S-shaped speed planning Displacement Final velocity of each stage ,and The S-shaped velocity programming is divided into seven motion stages, denoted as... , to These correspond to the acceleration phase, uniform acceleration phase, deceleration phase, constant speed phase, acceleration / deceleration phase, uniform deceleration phase, and deceleration / deceleration phase, respectively. S1.2: Simultaneously based on the initial acceleration Initial acceleration Determine the specific stage of the S-shaped velocity planning curve that the system is currently in in order to determine the displacement planning method; S1.3: Based on the mathematical relationship between jerk, acceleration, velocity and displacement, the displacement values ​​of each segment in the S-shaped velocity planning curve are solved, and the velocity that the current system should maintain is deduced in real time based on the displacement values, thus solving the time and velocity curve.

3. The real-time vibration suppression method as described in claim 2, characterized in that, In S1.1, for any motion stage in the S-shaped velocity programming, As constants, the formulas for calculating acceleration, velocity, and displacement are as follows: ； ； 。 4. The real-time vibration suppression method as described in claim 2, characterized in that, In S1.2, because of the object's initial velocity... It can be in 7 stages: acceleration stage, uniform acceleration stage, deceleration stage, uniform speed stage, acceleration / deceleration stage, uniform deceleration stage, and deceleration / deceleration stage. The current initial acceleration... With initial acceleration The S-shaped velocity planning curve can be divided into seven cases: 。 5. The real-time vibration suppression method as described in claim 4, characterized in that, In S1.2, when the initial velocity of the system... During any acceleration phase, determine when the maximum speed has been reached. minimum distance Deceleration to final speed minimum distance The sum of the target displacements If the relationship, Then the system's speed can reach its maximum speed. ;like If the system cannot reach its maximum speed, then the system's speed will be insufficient. ; When the initial velocity of the system It is in the acceleration phase, and the object has accelerated to its maximum speed. According to the final velocity size, The initial velocity is in the acceleration phase, and the total displacement is divided into... , The initial velocity is in the uniform acceleration phase, and the total displacement is divided into... , The initial velocity is in the deceleration / acceleration phase, and the total displacement is divided into... , The initial velocity is in the uniform phase, and the total displacement is divided into... ; When the initial velocity of the system During the acceleration phase, the system cannot accelerate to its maximum speed. According to the final velocity size, The initial velocity is in the acceleration phase, and the total displacement can be divided into... , The initial velocity is in the uniform acceleration phase, and the total displacement can be divided into... ; When the initial velocity of the system The deceleration phase is independent of the system's maximum speed. , initial velocity During the acceleration / deceleration phase, the total displacement is divided into... , initial velocity During the uniform deceleration phase, the total displacement is , initial velocity During the deceleration phase, the total displacement is .

6. The real-time vibration suppression method as described in claim 2, characterized in that, S2 specifically includes: S2.1: Apply transient pulse excitation to the system and collect multiple sets of time-domain response signals through sensors. Calculate the system's free oscillation frequency and damping ratio from the response signals using system identification methods. S2.2: Construct a zero-vibration shaper based on the free oscillation frequency and system damping characteristics; S2.3: Perform time-domain convolution between the S-shaped velocity planning curve and the zero-vibration shaper to obtain the shaped S-shaped velocity planning curve.

7. The real-time vibration suppression method as described in claim 6, characterized in that, S2.1 specifically involves: applying a transient pulse excitation to the top of the system using a standard hammer to induce broadband free vibration. The dynamic response of the system is synchronously acquired by a laser displacement sensor, recording the time history curve of the vibration displacement. By performing parameter identification and analysis on multiple sets of acquired time-domain response signals, the free oscillation frequency in each experiment is extracted. Finally, through statistical averaging, the accurate estimate of the system's natural frequency is determined, as shown in the following expression: ； ； ； ； This is the actual measured damped oscillation frequency. pass. It is the damped oscillation period, the time interval between adjacent peaks or troughs measured in a free decay signal; It is the amplitude of the nth wave crest. It is the amplitude of the (n+k)th wave crest, where k is the number of period intervals; It is the logarithmic decay rate, which is the logarithmic ratio that characterizes the degree of amplitude decay in each cycle; It is the damped natural frequency, the actual measured damped oscillation frequency; It is the damping ratio, which characterizes the energy dissipation rate of the system, and is the critical damping ratio. , It is the undamped natural frequency, the inherent angular frequency of the system under ideal undamped conditions.

8. The real-time vibration suppression method as described in claim 7, characterized in that, In S2.2, the zero-vibration shaper contains two pulses that satisfy the residual oscillation constraint condition. The following conditions are given: time-optimal and pulse amplitude constraints, the simultaneous equations formed by the constraints, and the pulse amplitude and time lag values ​​obtained by solving the constraints. The residual oscillation ratio (PRV) of the input command is as follows: ； ； ； The time-domain expression for eliminating residual oscillations using the ZV shaper is obtained as follows: ； in, , , It is the residual vibration amplitude. It is the cosine component response. It is a sinusoidal component response. It is the residual vibration ratio. It is the amplitude of the i-th pulse. It is the time of the i-th pulse. It was Dirac The function is given by K, where K is the damping coefficient and T is the damped oscillation period. This is the second pulse time.

9. The real-time vibration suppression method as described in claim 6, characterized in that, Specifically, S2.3 involves: first, dividing the continuous S-shaped velocity planning curve into an array sequence according to the discrete time step; then, converting the time-domain parameters of the zero-vibration shaper into the corresponding discrete delay steps; and finally, performing a convolution operation to weighted superposition of the curve array and the shaper coefficient array to generate the shaped S-shaped velocity planning curve.

10. The real-time vibration suppression method as described in claim 1, characterized in that, Specifically, S3 is as follows: the system detects the actual displacement of the object in the system in real time according to the S-shaped velocity planning curve after shaping, and solves the speed command that should be followed at the moment. The speed command is then sent to the controller and sent to the servo driver in real time to form a closed-loop control, so that the motion of the system follows the planned trajectory after shaping.

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