S-shaped curve planning method for minimizing maximum speed and maximum acceleration

Abstract

The invention belongs to the technical field of magnetic suspension motion control methods, and particularly relates to an S-shaped curve planning method for minimizing the maximum speed and the maximum acceleration. A displacement stroke threshold value is solved according to the parameters, whether the displacement stroke threshold value is smaller than a given total stroke or not is judged to determine whether a first T-shaped curve or a triangular curve is used, and the shortest time of each curve under the acceleration threshold value and the speed threshold value is solved; respectively judging the relationship between the shortest time and the given total time; under the first T-shaped curve, the maximum acceleration is selectively reduced or the maximum speed is firstly reduced and then the maximum acceleration is reduced according to the relation between the first difference value and the duration time of the first maximum speed; if the shortest time under the triangular curve is smaller than the given total time, the maximum speed is reduced, the triangular curve is changed into a second T-shaped curve, then the maximum acceleration is reduced, and a four-section mode or a six-section mode is adopted; and a distribution coefficient alpha is input, a speed curve which meets the requirement and is more stable is determined according to whether the alpha is smaller than a threshold value under each condition, and the energy consumption of the system is lower.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of magnetic suspension motion control method, and particularly relates to an S-shaped curve planning method for minimizing maximum speed and maximum acceleration. BACKGROUND

[0002] In the prior art, there are mainly two ways for path planning by using the S-shaped curve planning algorithm. One is to plan a curve by using maximum speed and acceleration, and the other is to divide the acceleration into 100 or even more parts and try to reach the displacement of each part of acceleration by iteration. The first way can complete the displacement faster, but causes problems such as too large impact of the mover, too large local heating of the motor and increased energy consumption. The second way needs to be iterated repeatedly, consumes a large amount of computing resources and time, and can only reduce the maximum acceleration but cannot reduce the maximum speed.

[0003] The two ways above cannot meet the conditions of given time and displacement for the planning of the motion curve of the mover, and therefore, under the conditions of given time and displacement, how to plan the S-shaped speed curve of the mover to minimize the maximum speed and the maximum acceleration is a problem to be solved in order to solve the problems such as too large impact of the mover and heating of the motor caused by too large maximum speed and acceleration of the curve by using the existing algorithm. SUMMARY

[0004] The problem to be solved by the application is to provide a S-shaped speed curve planning method of a mover under the conditions of given time and displacement in order to minimize the maximum speed and the maximum acceleration.

[0005] In view of the deficiencies of the prior art, the technical scheme adopted by the application to solve the technical problem is as follows: an S-shaped curve planning method for minimizing maximum speed and maximum acceleration, comprising the following steps, S1: obtaining process parameter requirements, wherein the process parameters include a given speed threshold, a given acceleration threshold, a given total time and a given total displacement; and solving a displacement threshold based on the process parameters; S2: when the displacement threshold is less than the given total displacement, planning a first T-shaped speed curve and determining a first shortest time of the first T-shaped speed curve and a first maximum speed duration, wherein the first shortest time is the shortest time required for completing the given total displacement when the displacement threshold is less than the given total displacement; and when the displacement threshold is greater than or equal to the given total displacement, using a triangular speed curve and determining a triangular shortest time, wherein the triangular shortest time is the shortest time required for completing the given total displacement when the displacement threshold is greater than or equal to the given total displacement, and the first shortest time and the triangular shortest time are determined based on the given acceleration threshold and the given speed threshold; S3: the first shortest time ≥ the given total time, a three-segment T-shaped curve is adopted; the first shortest time < the given total time, S4 is entered; the triangular shortest time ≥ the given total time, a two-segment curve is adopted; the triangular shortest time < the given total time, S5 is entered; S4: the first shortest time < the given total time, the size of the first maximum speed duration and the first difference value determined by the given total time minus the first shortest time is judged, the first difference value < the first maximum speed duration, the S-shaped curve has a uniform speed segment, the first difference value is distributed, the maximum acceleration is reduced, a five-segment or seven-segment S-shaped curve is adopted; the first difference value ≥ the first maximum speed duration, the maximum speed is reduced first, the S-shaped curve has no uniform speed segment, then the maximum acceleration is reduced, a four-segment or six-segment S-shaped curve is adopted. S5: the triangular shortest time < the given total time, the maximum speed is reduced, the triangular speed curve is changed to a second T-shaped speed curve, then the maximum acceleration is reduced, a four-segment or six-segment S-shaped curve is adopted.

[0006] Preferably, in S4, the first difference value is distributed by using an artificially input time distribution coefficient α, the threshold value corresponding to the distribution coefficient under the condition of the first difference value is α1; if the distribution coefficient α is less than the threshold value α1, the S-shaped curve has a uniform acceleration segment and a seven-segment S-shaped curve is adopted; otherwise, the distribution coefficient α is assigned to the threshold value α1, the S-shaped curve has no uniform acceleration segment and a five-segment S-shaped curve is adopted.

[0007] Preferably, in S4, when the first difference value ≥ the first maximum speed duration, the first T-shaped speed curve is changed to a third T-shaped speed curve by keeping the acceleration unchanged, and the third shortest time and the third maximum speed duration of the third T-shaped speed curve satisfy: the third maximum speed duration is equal to the difference between the given total time and the third shortest time, and the difference between the given total time and the third shortest time is a third difference value.

[0008] Preferably, the maximum acceleration of the S-shaped curve is determined after the third difference value is distributed, and the distribution of the third difference value is performed by using an artificially input time distribution coefficient α, the threshold value corresponding to the distribution coefficient under the condition of the third difference value is α3; if the distribution coefficient α is less than α3, the S-shaped curve has a uniform acceleration segment and a six-segment S-shaped curve is adopted; otherwise, the distribution coefficient α is assigned to α3, the S-shaped curve has no uniform acceleration segment and a four-segment S-shaped curve is adopted.

[0009] Preferably, in S5, the second shortest time and the second maximum speed duration under the second T-shaped speed curve satisfy: the second maximum speed duration is equal to the difference between the given total time and the second shortest time, and the difference between the given total time and the second shortest time is a second difference value.

[0010] Preferably, the maximum acceleration of the S-shaped curve is determined after the second difference value is allocated, and the second difference value is allocated by manually inputting a time allocation coefficient a, and the threshold value corresponding to the allocation coefficient under the second difference value is a2; if the allocation coefficient a is less than a2, the S-shaped curve has a uniform acceleration segment, and a six-segment S-shaped curve is used; otherwise, the allocation coefficient a is assigned a2, and the S-shaped curve has no uniform acceleration segment, and a four-segment S-shaped curve is used.

[0011] Preferably, the first minimum time is ; the first maximum speed duration is ; the triangular minimum time is ; is a given speed threshold, is a given acceleration threshold, is a given total time, is a given total distance, is the first minimum time, is the first maximum speed duration, is the triangular minimum time.

[0012] Preferably, the maximum speed of the five-segment or seven-segment S-shaped curve is , ; ; the maximum acceleration is ; , and the allocation coefficient a is selected when the allocation coefficient a is less than its threshold value a1, and the allocation coefficient a is not less than its threshold value a1, and in the formula, a=a1.

[0013] Preferably, the maximum speed of the third T-shaped speed curve is ; the maximum acceleration is ; , where a of the six-segment S-shaped curve is an input allocation coefficient, and a of the four-segment S-shaped curve is , where is the maximum speed of the third T-shaped speed curve, is the maximum acceleration of the third T-shaped speed curve, is the third minimum time.

[0014] Preferably, the maximum speed under the second T-shaped speed curve is : ; the maximum acceleration under the second T-shaped speed curve is : , where a of the six-segment is an input allocation coefficient, and a of the four-segment is , where is the second minimum time The beneficial effects of the present application are as follows: the present application classifies the given total time, the given total stroke, the given speed threshold and the given acceleration threshold by improving the motion curve planning, compares the actual value with the given value, divides it into seven sections from two sections, and minimizes the maximum acceleration and speed under the condition of sufficient given total time. By minimizing the speed and acceleration, the speed curve is optimized, thereby reducing the conveying time, improving the overall conveying efficiency, reducing the motor heating amount, and prolonging the service life of the motor. The smooth acceleration transition reduces the vibration and impact of the system during operation, and enhances the stability of the system. The system can flexibly adjust the motion curve according to different working conditions and requirements, improving the adaptability and flexibility. The motion curve planning of the present application simplifies the calculation process, reduces the design difficulty and implementation complexity of the control system. The mover motion in the magnetic suspension conveying system is smooth and the energy consumption is lower, so as to meet the demand of modern industry and transportation field for high-performance conveying system. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 is a schematic diagram of the planning process of the method of the present application; Figure 2 is a schematic diagram of the two-section speed curve involved in the present application; Figure 3 is a schematic diagram of the three-section speed curve involved in the present application; Figure 4 is a schematic diagram of the distribution coefficient a involved in the present application; Figure 5 is a schematic diagram of the four-section S-shaped speed curve change involved in the present application; Figure 6 is a schematic diagram of the five-section S-shaped speed curve involved in the present application; Figure 7 is a schematic diagram of the six-section S-shaped speed curve involved in the present application; Figure 8 is a schematic diagram of the seven-section S-shaped speed curve involved in the present application; Figure 9 is a schematic diagram of the four-section evolution process when the displacement stroke threshold is less than the given total stroke. DETAILED DESCRIPTION

[0016] The present application will be further described in detail below in conjunction with the drawings and specific embodiments. The embodiments of the present application are given for the purpose of illustration and description, and are not exhaustive or limit the present application to the disclosed forms. Many modifications and variations will be apparent to those of ordinary skill in the art. The embodiments are chosen and described in order to better illustrate the principles and practical application of the present application, and to enable those of ordinary skill in the art to understand the present application in order to design various embodiments with various modifications suitable for specific purposes.

[0017] In the magnetic suspension conveying system, the requirements for the mover are maximum speed, maximum acceleration, total time and total stroke, after knowing the requirements of the process on the maximum speed, maximum acceleration, total time and total stroke of the mover, the appropriate motion curve of the mover needs to be planned; in order to make the motion of the mover more stable, the application provides an S-shaped curve planning method for minimizing the maximum speed and the maximum acceleration, comprising the following steps, S1: obtaining process parameter requirements, the process parameters including a given speed threshold, a given acceleration threshold, a given total time and a given total stroke; solving a displacement stroke threshold based on the process parameters; S2: when the displacement stroke threshold is less than the given total stroke, planning a first T-shaped speed curve and determining a first shortest time of the first T-shaped speed curve and a first maximum speed duration, the first shortest time being the shortest time required to complete the given total stroke when the displacement stroke threshold is less than the given total stroke; when the displacement stroke threshold is greater than or equal to the given total stroke, using a triangular speed curve and determining a triangular shortest time, the triangular shortest time being the shortest time required to complete the given total stroke when the displacement stroke threshold is greater than or equal to the given total stroke, the first shortest time and the triangular shortest time being determined based on the given acceleration threshold and the given speed threshold; S3: when the first shortest time is greater than or equal to the given total time, adopting a three-section T-shaped curve; when the first shortest time is less than the given total time, entering S4; when the triangular shortest time is greater than or equal to the given total time, adopting a two-section curve; when the triangular shortest time is less than the given total time, entering S5; S4: when the first shortest time is less than the given total time, judging the size of the first maximum speed duration and a first difference, the first difference being determined by subtracting the first shortest time from the given total time, and when the first difference is less than the first maximum speed duration, the S-shaped curve has a uniform speed section, the maximum acceleration is reduced after the first difference is allocated, and a five-section or seven-section S-shaped curve is adopted; when the first difference is greater than or equal to the first maximum speed duration, the maximum speed is first reduced, the S-shaped curve has no uniform speed section, the maximum acceleration is then reduced, and a four-section or six-section S-shaped curve is adopted; The first difference is allocated in S4 by manually inputting a time allocation coefficient a, and the allocation coefficient corresponds to a threshold value a1 under the condition of the first difference. If the allocation coefficient a is less than the threshold value a1, the S-shaped curve has a uniform acceleration segment and adopts a seven-segment S-shaped curve. Otherwise, the allocation coefficient a is assigned to the threshold value a1, and the S-shaped curve has no uniform acceleration segment and adopts a five-segment S-shaped curve. In S4, when the first difference is greater than or equal to the first maximum speed duration, the first T-shaped speed curve is changed to a third T-shaped speed curve by keeping the acceleration unchanged, and the third shortest time and the third maximum speed duration of the third T-shaped speed curve satisfy: the third maximum speed duration is equal to the difference between the given total time and the third shortest time, and the difference between the given total time and the third shortest time is the third difference. After allocating the third difference, the maximum acceleration of the S-shaped curve is determined. The third difference is allocated by manually inputting a time allocation coefficient a, and the allocation coefficient corresponds to a threshold value a3 under the condition of the third difference. If the allocation coefficient a is less than a3, the S-shaped curve has a uniform acceleration segment and adopts a six-segment S-shaped curve. Otherwise, the allocation coefficient a is assigned to a3, and the S-shaped curve has no uniform acceleration segment and adopts a four-segment S-shaped curve.

[0018] S5: When the triangular shortest time is less than the given total time, the maximum speed is reduced, the triangular speed curve is changed to a second T-shaped speed curve, and the maximum acceleration is further reduced, adopting a four-segment or six-segment S-shaped curve.

[0019] The second shortest time and the second maximum speed duration under the second T-shaped speed curve in S5 satisfy: the second maximum speed duration is equal to the difference between the given total time and the second shortest time, and the difference between the given total time and the second shortest time is the second difference. After allocating the second difference, the maximum acceleration of the S-shaped curve is determined. The second difference is allocated by manually inputting a time allocation coefficient a, and the allocation coefficient corresponds to a threshold value a2 under the condition of the second difference. If the allocation coefficient a is less than a2, the S-shaped curve has a uniform acceleration segment and adopts a six-segment S-shaped curve. Otherwise, the allocation coefficient a is assigned to a2, and the S-shaped curve has no uniform acceleration segment and adopts a four-segment S-shaped curve.

[0020] That is, given the speed threshold value , the given acceleration threshold value , the given total time , and the given total distance , the S-shaped speed curve of the mover is solved. First, the shortest distance that can be accelerated to the given speed threshold value is solved as the displacement distance threshold value , and it is determined whether the displacement distance threshold value is less than . The solution of the displacement distance threshold value is that after accelerating to the given acceleration threshold value , the maximum speed is reduced, and the time for maintaining the maximum speed is 0. The time required to accelerate to the given acceleration threshold value is The total displacement is The average speed is The displacement threshold value of T-shaped velocity curve and triangular velocity curve is .

[0021] Then the shortest time required to complete is solved , which is divided into two cases, one is the first shortest time solved, and the other is triangular shortest time solved, the shortest time required to complete is solved The values in the above two cases are , .

[0022] 1.1: The first shortest time is solved If , the given total displacement can make the mover accelerate to the given speed threshold , the total displacement S total can make the mover speed reach the given acceleration threshold V thero , in which case, with T-shaped velocity curve planning, set the flag ; The physical meaning of is whether the given total displacement can make the mover accelerate to the given acceleration threshold ; The time of acceleration and deceleration process , the first maximum speed duration is , then the first shortest time .

[0023] 1.2: The triangular shortest time is solved If , the given total displacement cannot make the mover accelerate to the given speed threshold ; then use the triangular velocity curve, select the given acceleration threshold A thero when accelerating, and clear the flag ; Using the displacement of uniform acceleration under the initial speed of 0 , the time threshold of triangular velocity curve is the triangular shortest time , is expressed as .

[0024] 1.3 flag processing If , given total time is enough, set flag ; If , given total time is not enough, clear flag and assign value .

[0025] Case 1: If and , i.e. S thero ≥ S total and , the shortest time of triangle ≥ given total time, then the velocity curve of the moving object is two-section type; set , i.e. ; and , the case of , represents the section number, as shown in Figure 2 is the velocity curve of two-section type, which includes acceleration section and deceleration section, define the time length of acceleration section as and the time length of deceleration section as , then there exists , and can be obtained: , , , , in the formulas of two-section type .

[0026] Case 2: If and , i.e. S thero < S total and , the first shortest time ≥ given total time, then the velocity curve of the moving object is three-section type; set and assign value ; in case 2 and , the case of , as shown in Figure 3 is the velocity curve of three-section type, the moving object accelerates to V thero at point A and ends acceleration, moves uniformly between A and B, and moves decelerately between B and C, define the time length of acceleration section as , the time length of uniform motion section as , and the time length of deceleration section as , then there exists , and can be obtained: , , , various types in the three-stage .

[0027] Scenario 3: If and , that is, S thero total and , reduce the maximum acceleration A max The rear mover speed curve adopts a five-stage or seven-stage S-shaped speed curve; or first reduce the maximum speed V max Then reduce the maximum acceleration A max , mover speed curve or six-segment or four-segment S-shaped speed curve; and situation, : 3.1 Determine the duration of the first maximum speed under the first T-shaped speed curve The relationship with the first difference, the first difference is given by the total time Subtract the shortest time Sure, , that is, compare the first maximum speed duration and The size of is the first difference, and the first maximum speed duration is determined based on whether the first difference is less than the first maximum speed duration. To determine whether there is a uniform speed segment in the curve, the details are as follows: The first difference is less than the first maximum speed duration ,Right now When, define , Characterize the speed curve has a uniform speed segment; can be assigned to a seven-segment or five-segment S-shaped speed curve, the first difference The allocation is performed by using the allocation coefficient ɑ and its corresponding threshold ɑ1 to determine whether to select a seven-segment or five-segment S-shaped speed curve; the first difference is not less than the first maximum speed duration ,Right now When, define , If there is no uniform speed section in the velocity curve, the maximum speed of the first T-shaped velocity curve is reduced to become the third T-shaped velocity curve while keeping the acceleration unchanged; and the third shortest time under the third T-shaped velocity curve is made , Third maximum speed duration Satisfied: Third maximum speed duration Equal to the given total time and the third shortest time The difference, given the total time With the third shortest time ​The difference between the two is the third difference. Distribution is performed to reduce the maximum acceleration, and the selection of a six-stage or four-stage S-shaped speed curve is determined based on the size of ɑ and its corresponding threshold ɑ3.

[0028] 3.2 Regarding the allocation of the difference, for the sake of convenience, this paragraph expresses the difference to be allocated as The distribution coefficient ɑ is defined as Figure 4 As shown in the figure, when the time period from t0 to t1 / 2 is too long, when the T-shaped curve turns into an S-shaped curve, the intersection point of the arc segment and the T-shaped uniform acceleration straight line segment will exceed (t1+t2) / 2, which will cause problems such as curve discontinuity and acceleration mutation. Therefore, the distribution coefficient ɑ is defined, and the method ɑ×(T total -T thero ) / 2 is used to constrain the acceleration period to ensure that the S-shaped curve is continuously tangent and its derivative can be calculated continuously; the distribution coefficient ɑ is defined to constrain the acceleration period; for example, the first T-shaped velocity curve ɑ corresponds to a threshold value ɑ1. If ɑ<ɑ1, then ɑ can ensure that the S-shaped curve is continuously tangent. The point of tangency between the arc segment and the T-shaped uniform acceleration straight line segment is at (t1+t2) / 2, which is the threshold value corresponding to the distribution coefficient ɑ. If ɑ≥ɑ1, the S-shaped curve cannot be continuously tangent. In this case, ɑ is assigned to its threshold value ɑ1 to constrain the acceleration period. Figure 4 The time of the acceleration section under the S-shaped velocity curve shown .like Figure 4 Where L1 is the T-shaped curve before reducing the maximum speed, L2 is the T-shaped curve after reducing the maximum speed, and L3 is the T-shaped curve after reducing the maximum acceleration. After defining the distribution coefficient, the acceleration section length of the trapezoidal speed curve L3 is The length of the uniform speed segment is The length of the deceleration period is . Can be obtained The maximum acceleration after distribution satisfies: , it can be deduced that .

[0029] (1) The value is When, if ,definition , The velocity curve has a uniform acceleration section, and the uniform acceleration section time is not 0. ; (2) The value is When, if ,definition , That is, the velocity curve has no uniform acceleration segment, and ɑ is assigned a value of ɑ1 instead of the input value of ɑ. The uniform acceleration segment time in the S-shaped velocity curve is 0. When a four-segment or six-segment S-shaped velocity curve is used, the following is satisfied: The threshold corresponding to ɑ can be derived when ; The value is When ɑ corresponds to the threshold , .

[0030] 3.3 and In the case of segment=7: Figure 8 The figure shows the seven-segment S-shaped speed curve of the first T-shaped speed curve planning. , maximum acceleration ,definition , using the input The duration of each segment of the seven-segment S-shaped speed curve is: acceleration segment , uniform acceleration section , deceleration and acceleration stage , uniform speed section , acceleration and deceleration sections , uniform deceleration section , deceleration section , the specific durations are: ,definition , , we can get: , , .

[0031] 3.4 and In the case of segment=6: Figure 7 The figure shows the six-stage S-shaped speed curve after the third T-shaped speed curve is planned. Before planning, the maximum speed Reduce the maximum speed to Get the third T-shaped speed curve and the third maximum speed duration Equal to the given total time With the third shortest time The difference, that is, The time of uniform movement of the planned T-shaped speed curve Assigned to By analogy with the first maximum speed duration, , , we can get: where we can get by area method: , the maximum acceleration of the third T-shaped velocity curve is: , the value of the input . The six-segment S-shaped velocity curve is composed of jerk acceleration segment , uniform acceleration segment , deceleration segment , acceleration-deceleration segment , uniform deceleration segment and deceleration-deceleration segment , and the specific time length is: , the maximum acceleration of the third T-shaped velocity curve , , , the maximum acceleration of the third T-shaped velocity curve , , , 3.5 and , segment=5: as shown in Figure 6 , the five-segment S-shaped velocity curve is planned after the first T-shaped velocity curve, and the maximum acceleration of the third T-shaped velocity curve , , the maximum acceleration of the third T-shaped velocity curve , . The five-segment S-shaped velocity curve is composed of jerk acceleration segment , deceleration segment , uniform velocity segment , acceleration-deceleration segment and deceleration-deceleration segment , and the specific time length is: , the maximum acceleration of the third T-shaped velocity curve , , , the maximum acceleration of the third T-shaped velocity curve , , .

[0032] 3.6 and , segment=4: as shown in Figure 9 , the four-segment evolution process when the displacement threshold is less than the given total displacement, first decreases the maximum velocity by the first T-shaped velocity curve S1, then becomes the third T-shaped velocity curve S3, and finally evolves into the four-segment S-shaped curve S 31 under the third T-shaped velocity curve S3, which reduces the maximum acceleration to S 14 , and the maximum velocity : ; the maximum acceleration is , wherein , the maximum acceleration of the third T-shaped velocity curve Each period of the four-stage S-shaped speed curve is the acceleration period. , deceleration and acceleration stage , acceleration and deceleration sections and deceleration section , the specific durations are .

[0033] Definable , . We can obtain: , , .

[0034] Scenario 4: If and , that is, S thero ≥S total and , change the triangular speed curve into the second T-shaped speed curve, and then reduce the maximum acceleration, and adopt a four-stage or six-stage type. Figure 5 As shown, S2 is the triangular speed curve when the displacement stroke threshold ≥ the given total stroke, and after the maximum speed is reduced from S2, it becomes the second T-shaped speed curve S 21 ,S 21 After reducing the maximum acceleration, it becomes S 22 ,S 22 The final change is a four-stage S-shaped curve S4. The second T-shaped speed curve S 21 The second shortest time , Second maximum speed duration Satisfied: Second maximum speed duration Equal to the given total time With the second shortest time The difference, given the total time With the second shortest time The difference is the second difference; and situation, :The triangular speed curve changes to the second T-shaped speed curve so that the second maximum speed duration Equal in size to the second difference, which is , the second shortest time is As described in Section 3.4, we can obtain: the maximum speed under the second T-shaped speed curve is : .

[0035] 4.1 If ,definition , the uniform acceleration period is not 0, ; After the second difference distribution, the maximum acceleration becomes , , using the input values. Refer to section 3.4 for the method to solve the acceleration, velocity and displacement curves.

[0036] 4.2 If , define , the uniform acceleration segment time is 0, ; as described in section 3.6, the maximum velocity : ; take , , define . Refer to section 3.6 for the method to solve the acceleration, velocity and displacement curves. The intervals of ɑ1, ɑ2, ɑ3 are all (0.5, 1).

[0037] From the above process, the flag bits , , and and the true value table of the final velocity curve segment number Segment are as follows:

[0038] The implementation is as follows: design a magnetic levitation conveying system for fast and smooth conveying of parts within a factory. The process requirements of the system are: given the speed threshold V thero = 2 m / s, given the acceleration threshold A thero = 20 m / s², given the total time T total = 1s, given the total stroke S total = 240 mm.

[0039] Equipment and materials: the magnetic levitation conveying system includes a magnetic levitation track, a driving system, a control system and sensors. The control system includes a microprocessor, programming software and interface circuit, and the control system is used to realize the motion curve planning algorithm. The sensors include a speed sensor and an acceleration sensor, which are used to monitor and feedback the system state in real time. The implementation steps are as follows: System initialization: set the given speed threshold V thero = 2 m / s, the given acceleration threshold A thero = 20 m / s². Set the given total time T total = 1s, the given total stroke S total = 240 mm = 0.24 m.

[0040] Motion curve planning: use the algorithm described in the invention to plan the optimal S-shaped motion curve. First, calculate the displacement stroke threshold : , then , the first T-shaped speed curve is reduced to a third T-shaped speed curve with a reduced speed; V , then the first minimum time is determined: , T thero1 = 0.22 s < T total , then ; Secondly, the first maximum speed duration T V1 is calculated: , the first difference = T total -T thero1 = 1-0.22=0.78 s > T V1 , , the first T-shaped speed curve is reduced to a third T-shaped speed curve with a reduced speed; V thero * (T V1 +T thero1 ) / 2=V max * (T V3 +T thero3 ) / 2=V max *T total / 2, V max =0.24* V thero =0.48 m / s; manually input ɑ=0.6, , , ɑ>ɑ3, then ; finally , , and , belongs to the four-segment S-shaped speed curve, which can be substituted into the four-segment curve formula. System debugging: upload the planned motion curve through the control system. Test the performance of the system under given load conditions, including speed, acceleration, energy consumption, and stability. Adjust parameters to optimize system performance. This embodiment provides a specific example to demonstrate how to apply the invention to optimize the motion curve planning of a magnetic levitation conveying system, and is not a limitation of the method of the invention.

[0041] The present application is aimed at dividing the curve planning into 6 categories under the condition of given displacement and time, subdividing 4 categories of curves according to velocity and acceleration, comparing the maximum velocity running time and the total time minus the maximum velocity running time to determine the maximum acceleration reduction amplitude, or reducing the maximum velocity first and then reducing the maximum acceleration. In this way, the maximum velocity and maximum acceleration are minimized to reduce the impact of the mover movement, while avoiding excessive local heating of the motor. Through the implementation of the method of the present application, the magnetic levitation conveying system can realize stable and efficient operation of the mover under the given conditions, avoid excessive impact, significantly improve the conveying efficiency, reduce energy consumption, and prolong the service life of the equipment.

Claims

1. A S-shaped curve planning method for minimizing maximum velocity and maximum acceleration, characterized in that : including the following steps, S1: Obtaining process parameter requirements, wherein the process parameters include a given speed threshold, a given acceleration threshold, a given total time, and a given total stroke; Determine the displacement stroke threshold based on process parameters; S2: When the displacement stroke threshold is less than the given total stroke, a first T-shaped speed curve is planned and a first minimum time and a first maximum speed duration of the first T-shaped speed curve are determined, wherein the first shortest time is the shortest time required to complete the given total stroke when the displacement stroke threshold is less than the given total stroke; When the displacement stroke threshold is ≥ the given total stroke, the triangle speed curve is used to determine the triangle shortest time. The triangle shortest time is the shortest time required to complete the given total stroke when the displacement stroke threshold is ≥ the given total stroke. The first shortest time and the triangle shortest time are both determined based on the given acceleration threshold and the given speed threshold. S3: When the first shortest time is greater than or equal to the given total time, a three-segment T-shaped curve is used; when the first shortest time is less than the given total time, enter S4; when the triangle shortest time is greater than or equal to the given total time, a two-segment curve is used; when the triangle shortest time is less than the given total time, enter S5; S4: When the first shortest time is less than the given total time, the first maximum speed duration and the first difference are determined. The first difference is determined by subtracting the first shortest time from the given total time. If the first difference is less than the first maximum speed duration, the S-shaped curve has a uniform speed segment. The first difference is allocated and the maximum acceleration is reduced, using a five-segment or seven-segment S-shaped curve. If the first difference is greater than or equal to the first maximum speed duration, the maximum speed is first reduced, the S-shaped curve has no uniform speed segment, and then the maximum acceleration is reduced using a four-segment or six-segment S-shaped curve. S5: When the shortest triangle time is less than the given total time, the maximum speed is reduced, and the triangle speed curve is changed to the second T-shaped speed curve. The maximum acceleration is then reduced, and a four-segment or six-segment S-shaped curve is adopted.

2. The S-shaped curve planning method for minimizing maximum speed and maximum acceleration according to claim 1, characterized in that : In S4, the first difference is distributed by manually inputting the time distribution coefficient ɑ. Under the first difference condition, the corresponding threshold of the distribution coefficient is ɑ1; if the distribution coefficient ɑ is less than its threshold ɑ1, the S-shaped curve has a uniform acceleration segment and a seven-segment S-shaped curve is used; otherwise, the distribution coefficient ɑ is assigned to the threshold ɑ1, and the S-shaped curve has no uniform acceleration segment and a five-segment S-shaped curve is used.

3. The S-shaped curve planning method for minimizing maximum speed and maximum acceleration according to claim 2, characterized in that : When the first difference in S4 is ≥ the first maximum speed duration, the first T-shaped speed curve is changed to a third T-shaped speed curve while keeping the acceleration unchanged, and the third shortest time and the third maximum speed duration of the third T-shaped speed curve satisfy: the third maximum speed duration is equal to the difference between the given total time and the third shortest time, and the difference between the given total time and the third shortest time is the third difference.

4. The S-shaped curve planning method for minimizing maximum speed and maximum acceleration according to claim 3, characterized in that : After allocating the third difference, the maximum acceleration of the S-shaped curve is determined. The third difference is allocated by manually inputting the time allocation coefficient ɑ. The corresponding threshold of the allocation coefficient under the third difference condition is ɑ3; if the allocation coefficient ɑ is less than ɑ3, the S-shaped curve has a uniform acceleration segment and a six-segment S-shaped curve is used; otherwise, if the allocation coefficient ɑ is assigned to ɑ3, the S-shaped curve has no uniform acceleration segment and a four-segment S-shaped curve is used.

5. The S-shaped curve planning method for minimizing maximum speed and maximum acceleration according to claim 1, characterized in that : The second shortest time and the second maximum speed duration under the second T-shaped speed curve in S5 satisfy: the second maximum speed duration is equal to the difference between the given total time and the second shortest time, and the difference between the given total time and the second shortest time is the second difference.

6. The S-shaped curve planning method for minimizing maximum speed and maximum acceleration according to claim 5, characterized in that : After allocating the second difference, the maximum acceleration of the S-shaped curve is determined. The second difference is allocated by manually inputting the time allocation coefficient ɑ. The threshold value corresponding to the allocation coefficient under the second difference condition is ɑ2; if the allocation coefficient ɑ is less than ɑ2, the S-shaped curve has a uniform acceleration segment and a six-segment S-shaped curve is used; otherwise, if the allocation coefficient ɑ is assigned to ɑ2, the S-shaped curve has no uniform acceleration segment and a four-segment S-shaped curve is used.

7. The S-shaped curve planning method for minimizing maximum speed and maximum acceleration according to claim 2, characterized in that :The first shortest time is ; The duration of the first maximum speed is: ; The shortest time for a triangle is ; For a given speed threshold, For a given acceleration threshold, For a given total time, For a given total travel distance, The first shortest time, is the first maximum speed duration, The shortest time for a triangle.

8. The S-shaped curve planning method for minimizing maximum speed and maximum acceleration according to claim 7, characterized in that : The maximum speed for a five-segment or seven-segment S-shaped curve is , ; ;The maximum acceleration is ; , when the distribution coefficient ɑ is less than its threshold ɑ1, the distribution coefficient ɑ is selected, and when the distribution coefficient ɑ is not less than its threshold ɑ1, ɑ=ɑ1.

9. The S-shaped curve planning method for minimizing maximum speed and maximum acceleration according to claim 4, characterized in that : Maximum speed of the third T-shaped speed curve ;The maximum acceleration is , where ɑ of the six-segment S-shaped curve is the input distribution coefficient, and ,in is the maximum speed of the third T-shaped speed curve, is the maximum acceleration of the third T-shaped velocity curve, The third shortest time.

10. The S-shaped curve planning method for minimizing maximum speed and maximum acceleration according to claim 6, characterized in that :The maximum speed under the second T-shaped speed curve is : ; The maximum acceleration under the second T-shaped velocity curve is : , where ɑ for the six-stage type is the input distribution coefficient, and ,in The second shortest time.

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