CN106168790B

CN106168790B - S-shaped acceleration and deceleration control method for changing target speed and position on line

Info

Publication number: CN106168790B
Application number: CN201610116683.6A
Authority: CN
Inventors: 李迪; 吴杰文; 李松
Original assignee: South China University of Technology SCUT
Current assignee: South China University of Technology SCUT
Priority date: 2016-02-29
Filing date: 2016-02-29
Publication date: 2020-08-18
Anticipated expiration: 2036-02-29
Also published as: CN106168790A

Abstract

The invention provides an on-line eye changing methodS-shaped acceleration and deceleration control method for marking speed and position. The method comprises the following steps: speed planning in an acceleration stage; planning the speed in the deceleration stage; planning the speed at a constant speed stage; predicting an actual deceleration point; processing the maximum speed; compensating for the residual distance; changing the target speed algorithm on line; the target location algorithm is changed online. And respectively calculating the running time of the seven-stage speed planning stage by adopting an acceleration/deceleration discretization speed planning method and combining with user input parameters. According to the condition whether the maximum acceleration and the maximum speed can reach the criterion or not, and considering the acceleration/deceleration, the deceleration and the end point position after discretizationLFor the sampling periodT _sRounding off the problem, correcting for the actual maximum acceleration/deceleration, acceleration/deceleration and feed rate that can be achieved. The invention greatly simplifies the original calculation formula and saves a large amount of computer operation time, and the one-time compensation method is adopted for the residual distance in the deceleration process.

Description

S-shaped acceleration and deceleration control method for changing target speed and position on line

Technical Field

The invention belongs to the field of motion control, and particularly relates to an implementation method of an S-shaped curve acceleration and deceleration control method of a motion control system.

Background

Motion control is a key technology for realizing a numerical control system, and a good acceleration and deceleration control method can effectively avoid the phenomena of impact, step loss or vibration and the like in the motion process of numerical control equipment. The high-speed high-precision machining is an important development direction of numerical control machining, and the numerical control machine tool is required to react quickly and reach a specified speed in a short time; meanwhile, the machining process is required to move as stably as possible and have small impact. Therefore, on the basis of ensuring the stable motion of the machine tool, how to realize the optimal acceleration and deceleration control rule with the shortest machining transition time as the target so that the numerical control machine tool has the acceleration and deceleration characteristic meeting the high-speed and high-precision machining requirements is one of the key problems in the research of the motion control field.

The common acceleration and deceleration control method in the numerical control system comprises the following steps: t-type acceleration and deceleration (also called linear acceleration and deceleration), exponential acceleration and deceleration, trigonometric function acceleration and deceleration, and S-shaped acceleration and deceleration. The T-type acceleration and deceleration algorithm has the advantages of simple algorithm, short consumed time, easiness in implementation and the like, but an acceleration curve is discontinuous, speed abrupt change exists, various vibrations and noises are easy to occur, flexible impact exists in machine tool movement, and the method is suitable for a low-speed and low-cost numerical control system with low requirements on movement precision. The exponential acceleration and deceleration algorithm has better smoothness than T-shaped acceleration and deceleration and high motion precision, but the algorithm is complex, the operation is long in time consumption, the acceleration of the acceleration and deceleration starting point and the acceleration of the deceleration finishing point are sudden, and flexible impact also exists. The acceleration and deceleration rules of the trigonometric function can realize smooth motion, but the trigonometric function is complex in calculation and cannot meet the real-time requirement of a numerical control system, and the trigonometric function must be processed in advance, stored in a memory as a table form and realized in a table look-up mode; in addition, the acceleration and deceleration of the current trigonometric function cannot fully utilize the advantages of the acceleration and the maximum allowable value of the acceleration in order to ensure the velocity profile, so that the velocity cannot reach the expected value within a short time and distance. The S-shaped curve acceleration and deceleration control method has the advantages of stable and impact-free motion, continuous acceleration curve, smooth speed curve and the like, and is particularly suitable for high-speed and high-precision machining occasions, such as a robot control system, a semiconductor chip packaging control system and the like. Meanwhile, the S-shaped curve acceleration and deceleration control method has quite complicated planning process and long operation time, and how to simplify the calculation formula of the planning process and reduce the operation time of the algorithm is the focus of long-term attention of experts and scholars at home and abroad.

At present, few data and documents are used for researching and discussing the function expansion of changing the target speed and the position on line by an S-shaped acceleration and deceleration algorithm, but the function of changing the target speed and the position on line is particularly important in certain application occasions, such as the semiconductor chip packaging industry, the idle running time of equipment can be greatly saved by changing the target speed and the position expansion function on line, the flexibility of a numerical control system is enhanced, and the application requirements of more user groups can be met.

The discretization processing of acceleration/deceleration of the S-shaped acceleration and deceleration control method brings many problems, and the operation time (n) of each stage must be ensured₁，n₂，n₃，n₄，n₅，n₆，n₇) And a sampling period T_sThe integral multiple relationship of the acceleration and deceleration, the actual acceleration and deceleration needs to be recalculated and corrected to ensure that the position of the moving target can be accurately reached after the acceleration and deceleration control operation. The traditional S-shaped acceleration and deceleration algorithm has the defects of complex calculation formula, time consumption for predicting and calculating actual deceleration points and more residual distancesPeriodic compensation and the like.

Disclosure of Invention

Aiming at the defects in the prior art, the invention aims to provide the S-shaped acceleration and deceleration control method for changing the target speed and position on line in real time. The S-shaped acceleration and deceleration control method is subjected to function expansion of changing the target speed and position on line, so that the functions of the numerical control system are enhanced, the flexibility of the numerical control system is improved, and the application requirements of more user groups can be met; the S-shaped acceleration and deceleration control method realizes the discretization of the acceleration/deceleration curve in the process, deduces a simplified recursive calculation formula of speed and displacement according to the integral relation among acceleration/deceleration, speed and displacement, and saves the arithmetic operation time; and a one-time compensation method is adopted for the residual distance brought by discretization, so that the operand is reduced, and the number of interpolation cycles is saved.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows.

A S-shaped acceleration and deceleration control method for changing target speed and position on line aims at user input parameters: total displacement L and initial speed f of movement_sMaximum speed F, end speed F_eMaximum acceleration A, maximum deceleration D, jerk J_accDeceleration rate J_decAnd interpolating the sampling period T_sThe following operations are performed:

(1) firstly, initialization and stage division processing are carried out:

the S-shaped curve is subjected to acceleration/deceleration discretization processing by adopting a three-stage type stage division processing mode of an acceleration region I, a constant speed region II and a deceleration region III, and the method specifically comprises the following steps:

1) in the acceleration region I acceleration discretization processing process, the actual interpolation periods of an acceleration adding section ①, a uniform acceleration section ② and an acceleration reducing section ③ are respectively n according to the condition that whether the maximum acceleration A can reach the criterion or not₁、n₂、n₃；

2) Deceleration zoneIII, calculating according to the condition whether the maximum deceleration D can reach the criterion to obtain the actual interpolation periods of the acceleration and deceleration section ⑤, the uniform deceleration section ⑥ and the deceleration section ⑦ which are respectively n₅、n₆、n₇；

3) The maximum speed value V which can be reached after passing through the deceleration and acceleration section ③ from the current speed and the current acceleration is calculated in advance in real time according to the acceleration adding section ① and the uniform acceleration section ②_mWhile calculating the remaining distance L in real time_rOnce it is predicted that V is satisfied at the same time_m> F and L_r>V_mIf the conditions are met, the next cycle enters the uniform speed segment ④, and the cycle number n of the uniform speed segment ④ follows₄For each additional cycle, the current displacement L_curWith a consequent increase in maximum speed V_mA distance of (1), a remaining distance L_rContinuously reducing; when L is_r<V_mThen entering a deceleration area III for deceleration treatment, and the period number n of the uniform speed segment ④₄Determining;

(2) and then, predicting an actual deceleration point, and judging the actual deceleration point by calculating a deceleration distance and a path residual distance in real time, wherein when the current acceleration and deceleration process is in an acceleration section ① or a uniform acceleration section ②, in order to ensure the continuity of the acceleration, the deceleration distance comprises the distance traveled by a deceleration area III, namely the displacement L of the acceleration and deceleration section ⑤₅Displacement L of uniform deceleration section ⑥₆And displacement L of the deceleration section ⑦₇In addition, the displacement L of the acceleration reducing section ③ is also included₃；

(3) According to the integral relation among the acceleration/deceleration j (t), the acceleration/deceleration a (t), the speed f (t) and the displacement s (t), carrying out real-time interpolation calculation of each section, and updating the current displacement value, the speed value, the acceleration value and the residual distance value in real time; and simultaneously, performing terminal discrimination processing before real-time interpolation calculation so as to ensure that the terminal position is accurately reached.

The invention expands the function of changing the speed and the position of the target on line, can meet the requirement of a user on changing the speed and the position of the target in real time in the movement process, and allows the speed and the position of the target to be changed for many times.

The technical solution of the present invention will be further described in detail below.

Speed planning principle of S-shaped curve acceleration and deceleration control method

On the premise of long enough movement displacement, the process of the S-shaped acceleration and deceleration control method provided by the invention can be divided into an acceleration area I, a constant speed area II and a deceleration area III, wherein the acceleration area I can be further divided into an acceleration section ①, a uniform acceleration section ② and a deceleration section ③, similarly, the deceleration area III can be further divided into an acceleration section ⑤, a uniform deceleration section ⑥ and a deceleration section ⑦, the whole constant speed area II is composed of a constant speed section ④, and input parameters of the S-shaped acceleration and deceleration control method provided by the invention comprise the total movement displacement L and the initial speed f_sMaximum speed F, end speed F_eMaximum acceleration A, maximum deceleration D, jerk J_accDeceleration rate J_decAnd interpolating the sampling period T_s. According to the S curve acceleration and deceleration kinematic equation, the following relations exist between the acceleration/deceleration a (t), the speed f (t) and the displacement S (t) and the time:

in the formula (1), t is a time coordinate, t_iThe method comprises the steps of representing transition point time of each motion stage, wherein i represents each motion stage in a speed planning process, i is 1-7, and i is an integer; tau is_iRepresenting local time coordinates, i.e. τ, with the start of each motion phase as a time zero_i＝t-t_i-1I represents each motion stage in the speed planning process, i is 1-7, and i is an integer; acceleration/deceleration j (t)_i) Is a piecewise function with time as a variable:

in the formula (2), J_iRepresenting the acceleration/deceleration of each motion phase, i represents each motion phase of the velocity planning process, i is 1-7, i is an integer, wherein J₂＝J₄＝J ₆0. Integrating equation (2) to obtainAn acceleration/deceleration a (t) is obtained_i) The equation:

in the formula (3), a and D represent the maximum acceleration and the maximum deceleration, respectively. The velocity f (t) can be derived by integrating equation (3) over time_i) The equation:

in the formula (4), f_iThe method comprises the steps of representing speed values reached by end points of all motion phases, wherein i represents all the motion phases in a speed planning process, i is 1-7, and i is an integer; f represents the maximum speed value which can be reached after the movement process is accelerated by the acceleration area, wherein the maximum speed value is equal to the maximum speed input by the user; t is_iRepresenting the movement time (T) of each movement phase_iIs required to be a sampling period T_sIntegral multiple of the number of the motion phases, i represents each motion phase in the speed planning process, i is 1-7, and i is an integer. Equation of displacement s (t)_i) Can be obtained by integrating equation (4) over time:

in the formula (5), s_iRepresenting the movement displacement amount when each movement stage is finished, wherein i represents each movement stage in the speed planning process, i is 1-7, and i is an integer; l represents the total displacement of motion. For the convenience of subsequent calculation, the calculation formula of the motion displacement in each stage can be calculated by the following equation system:

l in the formula (6)_iAnd the motion planning method comprises the steps of representing the displacement amount of motion in each motion stage, wherein i represents each motion stage in the speed planning process, i is 1-7, and i is an integer.

(II) speed planning staging

Maximum acceleration/deceleration limitThe maximum torque and force limit of a driving motor are obtained generally, and the maximum acceleration and deceleration capacity of a numerical control servo system is reflected; the maximum acceleration/deceleration reflects the flexibility and acceleration time (T) of the numerical control servo system₁、T₃、T₅And T₇) In inverse proportion. If a larger acceleration/deceleration speed is adopted, the impact is large; if infinite acceleration/deceleration is taken under the limit condition, the S-shaped curve acceleration and deceleration is degenerated into T-shaped acceleration and deceleration; if the acceleration and deceleration time is short, the acceleration and deceleration process time of the system is long. So the user can select according to the actual needs of the system. Generally, the acceleration and deceleration capabilities of the motor are the same, and for the sake of simplifying the calculation, it is assumed that the time required for the acceleration/deceleration to increase from 0 to the maximum and the time required for the acceleration/deceleration to decrease from the maximum to 0 are equal, while taking into account the boundary condition f₇＝f_eAnd s₇If L, then the following set of equations holds:

in the formula (7), J_accAnd J_decRespectively representing the acceleration value of an acceleration area I and the deceleration value of a deceleration area III, and setting the discretized interpolation period number of 7 motion phases of the S-shaped curve speed plan to be ① plus acceleration segments n ₁② acceleration homogenizing segment n ₂③ deceleration and acceleration section n ₃④ uniform speed segment n ₄⑤ acceleration and deceleration segment n ₅⑥ uniform deceleration section n₆And ⑦ deceleration section n₇. The discretization process of each region and the derivation process of the corresponding formula are given as follows:

(1) accelerated region I discretization

The acceleration region I comprises an acceleration adding section ①, a uniform acceleration section ② and an acceleration reducing section ③, and the interpolation period number n of the acceleration adding section ① is set₁And the number n of interpolation periods of the deceleration acceleration section ③₃The following relationships exist:

n₃＝n₁-1 (8)

from formula (7):

in the formula (9), ceil (x) represents rounding up of the calculation result of x. Since n is₁Is an integer, when A cannot be substituted by J_accIn order to ensure that the corrected actual jerk and acceleration do not exceed the original set values of the user, rounding up the calculation result of equation (9) is required in the integer division, and as can be seen from equation (3), the accelerations of the i-th cycle jerk ① and jerk ③ after discretization can be calculated by equations (10) and (11), respectively:

a_ai＝i×J_acci∈[0,n₁](10)

a_di＝A-i×J_acci∈[0,n₃](11)

in the formula (10), a_aiRepresents the acceleration of the jerk ①, wherein a is represented by equation (11)_diThe acceleration of the deceleration segment ③ is shown, then the sum of the velocity increments of the jerk segment ① and jerk segment ③ is calculated by equation (12):

in the formula (12), Δ V_accRepresenting the sum of the velocity increments for the plus acceleration segment ① and the minus acceleration segment ③ equations (10) and (11) are substituted for equation (12) and are simplified to yield:

assuming that the speed of movement during movement can reach a given maximum speed F, the speed F is set from the beginning_sThe maximum allowable speed increment to F can be calculated by equation (14):

ΔV_amax＝F-f_s(14)

in the formula (14), Δ V_amaxDenotes F and F_sI.e. the maximum speed increase allowed in the acceleration region i. The criterion whether the maximum acceleration A can be reached can be obtained by the calculation results of the equations (13) and (14):

if Δ V_acc≥ΔV_amaxThen, thenThe maximum acceleration A in the acceleration and deceleration process can not be reached; otherwise the maximum acceleration a is reached. The following is discussed separately in two cases:

a)ΔV_acc≥ΔV_amaxa is not reachable

Since the maximum acceleration A is not reachable, it means that the even acceleration segment ② is missing, i.e., n ₂0, the actual number of interpolation cycles of the acceleration segment ① is added, taking into account equations (13) and (14)

Can be calculated as:

to ensure the actual number of interpolation cycles after quantization

For a sampling period T_sIntegral multiple of (d), the actual jerk and actual acceleration must be corrected and recalculated, i.e.:

and A^realEquation (8) shows that the number of interpolation cycles of the uniform acceleration segment ② and the deceleration segment ③ after discretization of the acceleration region i is:

b)ΔV_acc<ΔV_amaxa can reach

In this case, the maximum acceleration a is reached and the uniform acceleration section is present. From the equation (3), the speed increment of the discretized uniform acceleration section (ii) is:

n₂×A (18)

the sum of the velocity increments DeltaV after the acceleration region I can be obtained according to equation (13)_amaxCan be calculated from the following formula:

ΔV_amax＝(n₁+n₂)×A (19)

let n_a＝n₁+n₂Then equation (19) can be rewritten as:

ΔV_amax＝n_a×A (20)

then n is_aThe actual value of (d) may be calculated as:

the actual acceleration A can be obtained from the equations (20) and (7)^realActual number of interpolation cycles of the acceleration section ①

And actual jerk value

Comprises the following steps:

therefore, the actual interpolation period number of the actual uniform acceleration section ② can be obtained

And actual number of interpolation cycles of the deceleration acceleration section ③

Comprises the following steps:

in summary, the discretization process of the acceleration area i is completed, the actual running interpolation cycles of the acceleration adding section (i), the uniform acceleration section (ii), and the acceleration reducing section (iii) under two different conditions (a, b) are calculated according to the criterion whether the maximum acceleration a can be reached, and the actually reachable acceleration and the jerk are corrected, so as to ensure that the actually reachable acceleration and the jerk do not exceed the original setting value of the user.

(2) Discretization processing of deceleration area III

Similarly, the deceleration zone iii includes an acceleration/deceleration section ⑤, a uniform deceleration section ⑥ and a deceleration section ⑦, and the number n of interpolation cycles of the acceleration/deceleration section ⑤ is set₅And the number n of interpolation periods of the deceleration section ⑦₇The following relationship is satisfied:

n₇＝n₅-1 (25)

considering n₅Must be a sampling period T_sWhile in order to ensure that the actual reachable deceleration value and deceleration-acceleration value do not exceed the original set value of the user, similarly, when the deceleration D can not be decelerated and the acceleration J can not be reduced_decWhen dividing, n is needed₅The rounding-up process is performed according to equation (7):

similarly, as can be seen from equations (3) and (7), the sum Δ V of the speed increments of the acceleration/deceleration section ⑤ and the deceleration/deceleration section ⑦ in the deceleration region iii_decCan be calculated from the following formula:

considering that the speed reached after the movement process is accelerated by the acceleration area I is the maximum speed F, and the speed after the deceleration by the deceleration area III is the end speed F_eThen the maximum speed increment delta V allowed in the deceleration region III can be obtained_{d max}Comprises the following steps:

ΔV_{d max}＝F-f_e(28)

similarly, the criterion whether the maximum deceleration D is reachable can be obtained by the calculation results of equations (27) and (28):

if Δ V_dec≥ΔV_{d max}Then the maximum deceleration D in the acceleration and deceleration process can not be reached; otherwise the maximum deceleration D is achievable.

The following is discussed separately in two cases:

a)ΔV_dec≥ΔV_{d max}d is unreachable

In this case, the deceleration region iii includes only the acceleration/deceleration section ⑤ and the deceleration reduction section ⑦, and the uniform deceleration section ⑥ is not present, so that there is

Using the calculation result of equation (27), equation (28) can be rewritten as:

therefore, the actual interpolation period number of the acceleration/deceleration section ⑤

Comprises the following steps:

by using

The sum formula (29) can obtain the corrected actual deceleration-acceleration value

Comprises the following steps:

so that the actually achievable deceleration value D^realComprises the following steps:

the actual number of interpolation cycles of the deceleration section ⑦ can be obtained from the above-mentioned hypothetical relation (25)

Comprises the following steps:

b)ΔV_dec<ΔV_{d max}and D can reach

In this case, the deceleration region iii includes an acceleration/deceleration section, a uniform deceleration section, and a deceleration section. The velocity increment of the uniform deceleration section after discretization is as follows according to the formula (3):

n₆×D

from the equation (27), the sum of the velocity increments Δ V in the deceleration region III_{d max}Can be calculated by the following equation:

ΔV_{d max}＝(n₅+n₆)×D (33)

let n_d＝n₅+n₆Equation (33) may be rewritten as:

ΔV_{d max}＝n_d×D (34)

from formula (34):

so that the actual achievable deceleration value D^realAnd the actual number of interpolation cycles of the acceleration/deceleration section ⑤

Comprises the following steps:

in the same way, the actual deceleration and acceleration value

The recalculation can be:

from n to_d＝n₅+n₆The actual number of interpolation cycles of the uniform deceleration section ⑥ can be obtained from the sum equation (25)

And actual number of interpolation cycles of the deceleration section ⑦

Comprises the following steps:

in conclusion, the discretization process of the deceleration area iii is completed, the actual running interpolation cycles of the acceleration/deceleration section (the fifth step), the uniform deceleration section (the fourth step) and the deceleration section (the seventh step) under two different conditions (the above a and b) are respectively calculated according to the criterion whether the maximum deceleration D can be reached, and the actual deceleration and deceleration values are corrected to ensure that the actually reachable deceleration and deceleration cannot exceed the original set values of the user.

(3) Discretizing uniform region II

The whole uniform velocity region II is composed of the uniform velocity section ④, and the maximum velocity V reached at the end of the deceleration acceleration section ③ must be ensured_mLess than or equal to the user-given maximum speed F, i.e. the inequality holds:

V_m≤F (39)

v is in the uniform speed area II or the deceleration area III after the deceleration and acceleration section ③ is finished_mRepresenting the maximum speed value that can be reached during the deceleration process starting from the current speed and current acceleration based on the above analysis, the interpolation period number n is interpolated once the jerk segment ① is over₁If it is determined that the number n of interpolation periods in the acceleration section ③ is reduced as shown in equation (8)₃It is determined from equation (13) that the sum of the speed increments Δ V for the acceleration-plus segment ① and the acceleration-minus segment ③_accIt is also known that to ensure that the inequality (39) holds, the next cycle speed value must be calculated in advance in real time in the acceleration segment ① and the jerk segment ②, and once the calculated next cycle speed value is greater than the maximum speed F, the acceleration and deceleration process will proceed to the deceleration segment ③ in the next cycle.

Assume that during a certain current period of the jerk ① or jerk ②, the acceleration is a_curAt a velocity of V_curBegins to enter the deceleration and acceleration section ③, and passes through the i-th period, the acceleration a_iVelocity V_iThe following relationships are associated with period i:

in the formula (40), the reaction mixture is,

representing actual jerk value, i representing current cycle number, i ∈ [0,n₃]I is an integer, so the maximum speed value reached after the end of the deceleration acceleration segment ③ is:

therefore, the maximum speed that can be achieved can be calculated in any period of the acceleration segment ① or the uniform acceleration segment ② in the acceleration region i, and after entering the deceleration segment ③, the maximum speed V of the whole S-shaped speed planning process_mConstant in the plus acceleration section ① or the even acceleration section ②, the maximum velocity V that is possible to reach once the next cycle_mWhen the maximum speed F is exceeded, the next period enters the deceleration and acceleration section ③. because the calculated amount of the equation (42) is larger, a simpler calculation method is given as follows:

(1) setting the maximum speed which can be calculated in the last period as V_m', then there are:

in formula (43), V'_curRepresents the current speed value of the previous cycle, and V'_cur＝V_m-a_cur。

(2) Equation (43) is subtracted from equation (42) and reduced to V in the acceleration section ①_mThe calculation formula of (2) is as follows:

(3) similarly, V in the uniform acceleration section ②_mThe calculation formula of (2) is as follows:

V_m＝V_m'+a_cur(45)

in comparison with equation (42), V is calculated using equations in the form of recursions of equations (44) and (45)_mThe amount of calculation can be reduced.

As can be seen from equations (3) and (4), the calculation formulas of the current acceleration and speed values of the acceleration segment (i) and the uniform acceleration segment (ii) are respectively shown as equations (46) and (47):

(III) actual deceleration Point prediction

The S-shaped curve acceleration and deceleration control method provided by the invention adopts a pre-interpolation acceleration and deceleration control mode suitable for high-speed high-precision machining, simultaneously considers the defect that the actual deceleration point and the theoretical deceleration point after discretization are often not coincident, and how to accurately calculate the actual deceleration point becomes the key point of success of the control method. In order to ensure that the final motion can accurately reach the set target position, the actual deceleration point is judged by calculating the deceleration distance and the path remaining distance in real time, and once the fact that the remaining distance of the next interpolation period is smaller than the deceleration distance is known, the next interpolation period is shifted to the deceleration area III. The current acceleration and deceleration process is in different stages, and the meaning of the deceleration distance is different, so the following regulation is carried out on the deceleration distance:

a) when the current acceleration and deceleration process is in the acceleration section ① or the uniform acceleration section ②, in order to ensure the continuity of the acceleration, the deceleration distance referred to at this time includes the distance traveled by the deceleration region iii (the displacement L of the acceleration and deceleration section ⑤)₅+ displacement L of uniform deceleration section ⑥₆Displacement L of + deceleration section ⑦₇) In addition, the displacement L of the acceleration reducing section ③ is also included₃。

b) In the case other than a), the deceleration distance means the distance traveled by the deceleration region iii (the displacement L of the acceleration/deceleration section ⑤)₅+ displacement L of uniform deceleration section ⑥₆Displacement L of + deceleration section ⑦₇)。

Therefore, the calculation of the deceleration distance can be divided into two parts:

(1) distance traveled by deceleration zone III

The distance covered by the deceleration region III comprises the displacement L of the acceleration and deceleration section ⑤₅Displacement L of uniform deceleration section ⑥₆And displacement L of the deceleration section ⑦₇The calculation is carried out in three steps one by one as follows:

1) calculating the displacement L of the acceleration and deceleration section ⑤₅

From the expressions (3), (4) and (6), the deceleration a of the acceleration/deceleration section ⑤_iVelocity V_iAnd a displacement L_iThe calculation formula is as follows:

the interpolation period number n of the acceleration and deceleration section ⑤₅Substituting the above formula, one can obtain:

2) calculating the displacement L of the uniform deceleration section ⑥₆

Similarly, the deceleration a of the uniform deceleration section ⑥ can be found from the expressions (3), (4) and (6)_iVelocity V_iAnd a displacement L_iThe calculation formula is as follows:

the interpolation period number n of the uniform deceleration section ⑥₆Substituting the above formula, one can obtain:

3) calculating the displacement L of the deceleration section ⑦₇

Similarly, as can be seen from equations (3), (4) and (6), the deceleration a of the deceleration section ⑦ is reduced_iVelocity V_iAnd a displacement L_iThe calculation formula is as follows:

the interpolation period number n of the deceleration section ⑦ is reduced₇Substituting the above formula, one can obtain:

so the deceleration distance L_decCan be calculated from the following formula:

respectively converting L in the formulae (49), (51) and (53)₅、L₆And L₇Substituting, equation (54) can be rewritten as:

as can be seen from equation (55), the deceleration distance L_decIs computationally intensive. The speed of the first period of the deceleration stage is found to be the speed of the deceleration section III through speed analysis of the deceleration section III

The second cycle has a speed of

The third cycle has a speed of

The penultimate cycle speed is

The speed of the third last cycle is

The speed of the fourth last cycle is

Therefore, the 1 st, 2 nd, … … th and n th of the deceleration stage are controlled₇Period and 2 nd, 3 rd, … … th, n th of last₇+1) periods are added separately, the sum of each addition being equal to f_e+V_mThus for L_decThere may be a simpler method for calculating (c), and the derivation process is given below:

and (3) subdividing each motion phase of the deceleration area III: front n₇One period is an acceleration and deceleration section ⑤, (n)₇+1 to (n)₇+n₆) The period is a uniform deceleration section ⑥, (n)₇+n₆+1 to (2 x n)₇+n₆) To reduce the deceleration section ⑦, the last cycle is the ending speed f_e. The first n is obtained from the formula (49)₇Deceleration of one-cycle acceleration/deceleration segment ⑤

Speed of rotation

And displacement of

The calculation formula is as follows:

from equations (49) and (56):

similarly, the deceleration a of the uniform deceleration section ⑥_iVelocity V_iAnd a displacement L_iThe calculation formula is as follows:

the interpolation period number n of the uniform deceleration section ⑥₆By substituting equation (58) for the deceleration of the uniform deceleration section ⑥

Speed of rotation

And displacement of

Comprises the following steps:

will be provided with

Substituted into formula (59) while taking into account formula (56)

Thus, it can be obtained

In the formula (49)

And

while taking into consideration the formula (51)

The following can be obtained:

from formulae (51), (59), and (57):

finally, the deceleration a of the deceleration section ⑦ is reduced_iVelocity V_iAnd a displacement L_iThe calculation formula is as follows:

the interpolation period number n of the deceleration section ⑦ is reduced₇In the substitution of equation (63), the displacement of the deceleration stage ⑦ can be found as:

from formulas (61), (62) and (64):

in view of

Also obtained from formula (53):

from formula (66) to formula (56)

Substituted into the formula (59)

Comprises the following steps:

from formulae (64), (66) and (56)

The following can be obtained:

the deceleration distance L can be obtained from the equations (65), (67) and (68)_decComprises the following steps:

comparing equations (55) and (69), it can be seen that calculating the deceleration distance of the deceleration area iii using equation (69) will greatly reduce the amount of calculation, saving the computation time of the processor.

(2) Displacement L of the deceleration acceleration section ③₃

Considering the acceleration continuity, when the acceleration and deceleration process is in the acceleration section ① or the uniform acceleration section ②, the deceleration distance should include the displacement L of the deceleration section ③ in addition to the distance of the deceleration region iii₃So L is calculated by giving the acceleration segment ① and the uniform acceleration segment ② as follows₃The derivation process of (1):

1) from equation (3), the acceleration value a of the i-th cycle of the deceleration section ③ is calculated_iComprises the following steps:

2) the integral sphere summation of equation (70) yields the velocity value V for the i-th cycle of the deceleration section ③_iComprises the following steps:

3) the displacement L of the i-th cycle of the acceleration section ③ can be reduced by integrating the sum of the equations (71)_iComprises the following steps:

4) n is to be₃Substitution of equation (72) may result in a displacement L of the entire deceleration section ③₃Comprises the following steps:

5) calculating L from equation (73)₃The calculation amount is relatively large, and the derivation process of a simplified calculation formula is given as follows:

let L be obtained from the previous acceleration period₃Comprises the following steps:

the acceleration section includes:

therefore, L in the acceleration section ① can be obtained by subtracting the formula (74) from the formula (73) and substituting the formula (75)₃The calculation formula of (2) is simplified as:

in a similar way, the uniform acceleration section II comprises:

therefore, the L in the acceleration homogenizing section ② can be obtained by subtracting the formula (74) from the formula (73) and substituting the formula (77)₃Is simple in calculation formula

The method comprises the following steps:

L₃＝L'₃+a_cur×n₃(78)

compared with the equation (73), the recursion equations of the equations (76) and (78) are adopted to calculate the L of the acceleration segment ① and the uniform acceleration segment ② respectively₃The amount of calculation will be greatly reduced.

(IV) Compensation of residual distance

In the speed planning of the S-shaped curve acceleration and deceleration control method provided by the invention, through the division of the speed planning stages, the calculation of the reachable maximum speed and the prediction of the deceleration point, a basic prototype of the speed planning of an acceleration and deceleration algorithm is established, and the actual interpolation period number n of six different stages, namely an acceleration adding stage ①, a uniform acceleration stage ②, an acceleration and deceleration stage ③, an acceleration and deceleration stage ⑤, a uniform deceleration stage ⑥ and a deceleration and deceleration stage ⑦, is calculated_iAnd the real-time judgment of the actual deceleration through the calculation of the deceleration distance is realizedThe point is that the actual deceleration point is advanced from the theoretical deceleration point, which artificially advances the actual deceleration point such that the velocity plan will be after the end of the deceleration segment, the remaining distance will not be equal to 0, and the remaining distance needs to be compensated for in deceleration zone iii.

Let the remaining distance be L_rThe current running distance is L_curThen for a period of any phase, the following relationship exists:

L_r＝L-L_cur-L_dec(79)

in equation (79), L represents the total displacement amount of the movement, and the current travel distance can be calculated by the following equation:

in the formula (80), n_iThe interpolation period number of each motion stage is represented, i represents each motion stage in the speed planning process, i is 1-7, and i is an integer; v_jRepresenting each motion phase n_iJ represents all values of the interpolation period number in each motion phase, j is 1 to n_iAnd j is an integer.

From the above analysis, it can be known that the speed planning process of the proposed S-shaped curve acceleration and deceleration control method has the problem that the theoretical deceleration point is not coincident with the actual deceleration point, and the residual L needs to be processed_rTo a problem of (a).

From the equation (79), if the total movement displacement L is large, the calculated L is calculated_rPossibly very large (L)_r>V_m) In order to minimize the compensation period of the remaining distance, the number n of interpolation periods of the uniform velocity segment ④ is also reduced during the segmentation process₄Is not specified and can therefore be compensated with a constant velocity segment. Interpolating the number of cycles n along with the uniform speed section₄Every additional cycle, L_curWith a consequent increase in maximum speed V_mThus leaving a distance L_rIs compensated and continuously reduced. When the remaining distance is less than the maximum velocity value V_mEntering a deceleration area III, and interpolating the number n of cycles of the uniform speed section ④₄And is finally determined.

In deceleration region III L_rCannot be greater than V_mAs can be seen from formula (69), if n is₇Increase by 1 (n)₅Will also increase by 1) and the deceleration distance will increase (V) accordingly_m+f_e) Therefore, it is impossible to increase one acceleration/deceleration period and one deceleration/deceleration period at the same time to realize the L pair_rIf a uniform deceleration period is added, the residual quantity is uniformly inserted into the uniform deceleration process, and the deceleration value of the uniform deceleration section ③ is adjusted correspondingly, but the actual calculation does not necessarily just meet the requirement, the formula (69) is obtained under the condition that the acceleration and deceleration section ⑤ and the deceleration stage ⑦ are symmetrical, if one period is inserted into one of the acceleration and deceleration section ⑤ or the deceleration section ⑦, the formula (69) is not established, the whole operation process becomes complicated, the calculation amount is increased, and the invention integrates the reasons_rAnd (4) a processing method for performing one-time insertion compensation. From the above analysis, L is 0. ltoreq. L_r≤V_mIf the remaining distance L is_rAt maximum speed V_mWith the lowest operating speed f_eIn the deceleration section, compensation is then performed. If the remaining distance L_rIs less than the end speed f_eThen L will be_rSuperimposed on the last motion cycle for compensation.

(V) Online target position changing algorithm

Changing the target location online is implemented based on the idea of a finite state machine, all states including: the method comprises four types of acceleration area I, uniform speed area II, deceleration area III and reverse motion compensation, and the online target position changing mode is as follows: the target position is increased and decreased (if the target position is not changed, the planning is performed according to the original plan, and no processing is needed). According to the different forms of the trigger stage and the target position change, the corresponding processing modes are different, and the processing procedures of various conditions are given as follows:

(1) in the first case: the target position becomes larger

1) When the acceleration area I triggers a position change signal, directly assigning a new target position to the current target position and keeping the current state;

2) when the position signal is triggered to change in the uniform speed area II, a new target position is directly assigned to the current target position, and if the current speed is lower than the target speed, the acceleration area I is skipped to accelerate; if the current speed is equal to the target speed, keeping the current state;

3) when the deceleration area III triggers a position change signal, a new target position is directly assigned to the current target position, and the current target position jumps to the acceleration area I for acceleration.

(2) In the second case: the target position becomes small

When the target position becomes small and reverse movement may occur, the path residual distance L is calculated according to the following formula_remain：

L_remain＝L_r+(L_new×D-L_s)-L_e(81)

In the formula (81), L_rThe remaining distance before the end point position is changed is represented by formula (79); l is_newRepresenting the new endpoint coordinates; d represents the direction of target displacement before changing the target position, if the direction is positive, the value is 1, and if the direction is reverse, the value is-1; l is_sIn-situ shift of point coordinates, L_eThe end point coordinates of the original displacement.

1)L_remain<0

No matter the current state, uniformly jumping to a deceleration area III for deceleration, and when the speed is reduced to 0, jumping to reverse compensation if a new target position is not reached;

2)L_remain>0

if the position signals are triggered to change in the acceleration area I and the uniform speed area II, jumping to a deceleration area III for deceleration processing; if a change of position signal is triggered in the deceleration zone III, a reversal of the compensation is initiated.

(VI) Online Change target speed Algorithm

Changing the target speed online is also realized based on the idea of a finite state machine, and all the states include: the online speed change method comprises three types of acceleration areas I, constant speed areas II and deceleration areas III, and the online speed change target speed change form is as follows: the target speed is increased and decreased (if the target speed is not changed, the planning is performed according to the original plan, and no processing is needed). Changing the target speed online must ensure accurate arrival of the end position, otherwise the shift request is ignored and it is conditional to respond to the shift request. According to the different forms of the trigger stage and the target speed, the corresponding processing modes are different, and the processing procedures of various conditions are given as follows:

(1) in the first case: the target speed becomes large

1) When a speed change signal is triggered in the acceleration region I, a new target speed is directly set as a target speed, and the original state is kept unchanged;

2) when the position signal is triggered to change in the uniform speed area II or the deceleration area III, the distance from the current speed to the new target speed and the distance from the new target speed to the original ending speed need to be calculated, if the remaining distance is enough, the vehicle jumps into the acceleration area I to accelerate, and otherwise, the speed change request is ignored.

(2) In the second case: the target speed becomes smaller

When the speed signal is triggered to change in the acceleration area I, the constant speed area II or the deceleration area III, the deceleration distance needs to be recalculated, the deceleration distance at this moment comprises the distance from the current speed to the new target speed and the distance from the new target speed to the original ending speed, if the remaining distance is enough, the speed is reduced in the deceleration area III, and otherwise, the speed change request is ignored.

Compared with the prior art, the invention has the following beneficial effects and advantages

(1) The acceleration curve obtained by the S-shaped curve acceleration and deceleration control method provided by the invention is continuous, has no sudden change, is smooth in speed curve, is stable in movement, has small impact, and can meet the requirements of high-speed and high-precision processing on acceleration and deceleration characteristics such as short operation time, stable movement, smooth speed, no impact, high precision and the like.

(2) The S-shaped curve acceleration and deceleration control method provided by the invention can set asymmetric acceleration value J_accAnd a deceleration acceleration value J_dec(ii) a Asymmetric acceleration A values and decelerations may also be setA value D; an asymmetrical starting speed f can also be set_sAnd end speed f_eAnd f is_sAnd f_eMay take a non-zero value. The user can set according to different lathe, also can carry out parameter configuration according to the law that provides in order to obtain the best effect, has good flexibility and flexibility.

(3) The S-shaped curve acceleration and deceleration control method provided by the invention has less calculation amount. Simple and feasible deceleration distance L is respectively deduced_decRecursive formula, maximum velocity V_mRecursive formula and acceleration distance reduction L₃And the calculation formula is recurred, so that the time consumption of algorithm operation is greatly reduced.

(4) The invention carries out the function expansion of changing the target speed on line and changing the end point position on line to the S-shaped curve acceleration and deceleration control method, so that the machine tool can move to the target position at a higher speed and then accurately position to the target position at a lower speed, thereby greatly saving the idle running time of equipment, enhancing the function of a numerical control system and improving the flexibility of the numerical control system, and meeting the application requirements of more user groups.

(5) The S-shaped curve acceleration and deceleration control method for changing the target speed and the end point position on line in real time is successfully applied to numerical control systems of SMT chip mounters, die attach machines, dispensing machines and other equipment, and achieves good economic benefits.

Drawings

FIG. 1 is a schematic diagram of a speed plan of an S-shaped curve acceleration and deceleration control method;

FIG. 2 is a schematic diagram illustrating discretization of acceleration in an acceleration region I;

FIG. 3 is a schematic diagram of deceleration discretization of deceleration zone III;

FIG. 4 is a schematic diagram of the actual deceleration point prediction of the S-shaped curve acceleration and deceleration control method;

FIG. 5 is a schematic diagram of compensation of remaining distance in the S-shaped curve acceleration/deceleration control method;

FIG. 6 is a flow chart of an implementation of a S-shaped curve acceleration and deceleration control method;

FIG. 7 is a flow chart of initialization and phase division of the S-shaped curve acceleration/deceleration control method;

FIG. 8 is a diagram of a finite state machine for an on-line change target location algorithm;

FIG. 9 is a diagram of a finite state machine for an on-line change target speed algorithm;

FIG. 10 is a simulation diagram of a displacement curve, a velocity curve and an acceleration curve of the proposed S-shaped curve acceleration/deceleration control method;

FIG. 11 is a simulation diagram of a displacement curve, a velocity curve and an acceleration curve of the proposed S-shaped curve acceleration/deceleration control method;

FIG. 12 is a simulation diagram of a displacement curve, a velocity curve and an acceleration curve of the proposed S-shaped curve acceleration/deceleration control method;

FIG. 13 is a simulation diagram of a displacement curve, a velocity curve and an acceleration curve of the proposed S-shaped curve acceleration/deceleration control method;

FIG. 14 is a simulation diagram of the algorithm displacement curve, velocity curve and acceleration curve for changing the endpoint position on line by the proposed S-shaped curve acceleration and deceleration control method;

FIG. 15 is a simulation diagram of the S-shaped curve acceleration/deceleration control method for changing the displacement curve, velocity curve and acceleration curve of the target velocity algorithm on line.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without any creative effort belong to the protection scope of the present invention.

FIG. 1 is a schematic diagram of a speed plan of an S-shaped curve acceleration and deceleration control method, the process of the S-shaped acceleration and deceleration control method provided by the invention can be divided into an acceleration area I, a uniform speed area II and a deceleration area III, the acceleration area I comprises an acceleration section ①, a uniform acceleration section ② and a deceleration section ③, the deceleration area III can be divided into an acceleration section ⑤, a uniform deceleration section ⑥ and a deceleration section ⑦, the whole uniform speed area is composed of a uniform speed section ④, and input parameters of the control method are divided intoThe number includes total displacement L and initial speed f_sMaximum speed F, end speed F_eMaximum acceleration A, maximum deceleration D, jerk J_accDeceleration rate J_decAnd a sampling period T_s。

In fig. 1, (a), (b), (c) and (d) are respectively a displacement curve diagram, a velocity curve diagram, an acceleration curve diagram and an acceleration curve diagram. In FIG. 1, the ordinate units of (a), (b), (c), and (d) are pulse (pulse), pulse/T_s(pulse/sampling period),

(pulse/sampling period)²) And

(pulse/sampling period)³). t is a time coordinate, t_iRepresenting the transition point moments of the various motion phases; tau is_iRepresenting local time coordinates with the start of each motion phase as a time zero, i.e. τ_i＝t-t_i-1；J_iRepresenting an acceleration/deceleration amplitude; f. of_iRepresenting the velocity values reached at the end points of the respective phases; f represents the maximum speed value that can be reached after the movement process passes through the acceleration zone, T_iRepresenting the run time (for the sampling period T) of each motion phase_sInteger multiples of); s_iDisplacement representing movement at the end of each movement phase; l represents the total displacement amount of the movement path; l is_iDisplacement representing movement in each movement phase; and i represents each motion stage of the speed planning process, i is 1-7, and i is an integer.

According to the S curve acceleration and deceleration kinematic equation, the acceleration/deceleration a (t), the speed f (t) and the displacement S (t) satisfy the formula (1) with time:

in the formula (1), the acceleration j (t) is increased/decreased_i) Is a piecewise function with time as a variable:

by integrating equation (2), the acceleration/deceleration a (t) can be obtained_i) Piecewise function with respect to time:

the velocity f (t) can be derived by integrating equation (3) over time_i)：

Similarly, the displacement equation s (t)_i) Can be obtained by integrating equation (4) over time:

the motion displacement calculation formula in each motion phase can be calculated by the following equation system:

in the formula, L_iAnd the motion displacement amount in each motion stage is shown, i represents each motion stage in the speed planning process, i is 1-7, and i is an integer.

Fig. 2 is a schematic diagram illustrating discretization of acceleration in the acceleration region i. Before performing the acceleration-deceleration phase division, to simplify the calculation, we assume that the time required for the acceleration/deceleration to increase from 0 to the maximum and the time required for the acceleration/deceleration to decrease from the maximum to 0 are equal, that is:

in the acceleration discretization process of the acceleration region i, we may assume the interpolation period number n of the acceleration segment ① without considering the limitation of the maximum speed F₁And subtractInterpolation period number n of acceleration segment ③₃Satisfies the following conditions:

n₃＝n₁-1 (8)

due to the number of interpolation cycles (n) of each motion phase of the acceleration region I₁、n₂、n₃) Must be a sampling period T_sIs calculated, and n is calculated to ensure that the actual jerk and jerk values do not exceed the user's original set point₁Upward rounding is required:

and then calculating the sum of the speed increment of the acceleration adding section (i) and the acceleration reducing section (iii):

reconsidering the influence of the maximum speed F from the starting speed F_sMaximum speed increment allowed to increase to F:

ΔV_amax＝F-f_s(14)

the criterion whether the maximum acceleration A can be reached can be obtained by using the calculation results of the equations (13) and (14):

if Δ V_acc≥ΔV_amaxThe interpolation period number of the acceleration adding section ①, the interpolation period number of the uniform acceleration section ② and the interpolation period number of the deceleration section ③ are calculated according to 2 cases whether A can reach.

a)ΔV_acc≥ΔV_amaxA is not reachable

Actual number of interpolation cycles of the acceleration section ①

To ensure the quantized number of interpolation cycles

For a sampling period T_sThe integral multiple of the actual jerk and the actual reachable acceleration value are recalculated:

for the case of A being unreachable, the calculation result of the actual interpolation period number of each stage is as follows:

b)ΔV_acc<ΔV_amaxa can reach

The speed increment of the uniform acceleration section II is as follows:

n₂×A (18)

sum of velocity increments after acceleration zone i:

ΔV_amax＝(n₁+n₂)×A (19)

let n_a＝n₁+n₂Then equation (19) can be rewritten as:

ΔV_amax＝n_a×A (20)

n_athe actual values of (c) are:

for the actual acceleration A^realPlus the number of cycles of the acceleration section ①

And jerk value

Rounding and correcting to obtain:

for the case of a reachable number, the calculation result of the actual interpolation period number of each stage is:

FIG. 3 is a schematic diagram of the discretization of deceleration in deceleration zone III. similarly, let us say that the number n of cycles of the acceleration/deceleration section ⑤₅And decreasing the number n of cycles of the speed reduction section ⑦₇Satisfies the following conditions:

n₇＝n₅-1 (25)

number n of interpolation cycles for acceleration/deceleration section ⑤₅Getting the whole upward as:

similarly, the sum Δ V of the speed increments of the acceleration/deceleration section ⑤ and the deceleration/deceleration section ⑦ in the deceleration region iii_decComprises the following steps:

taking into account the maximum speed F and the end speed F_eOf the maximum speed increase DeltaV allowed in the deceleration region III_{d max}Comprises the following steps:

ΔV_{d max}＝F-f_e(28)

if Δ V_dec≥ΔV_{d max}Then the maximum acceleration D in the acceleration and deceleration process is not reachable; otherwise the maximum acceleration D is reachable. The following two cases are discussed separately:

a)ΔV_dec≥ΔV_{d max}d is unreachable

therefore, the actual number of interpolation cycles of the acceleration section ⑤ is reduced

Comprises the following steps:

actual deceleration acceleration value

And the actually achievable deceleration value D^realThe correction is as follows:

therefore, for the case of unreachable D, the calculation result of the actual interpolation cycle number at each stage is:

b)ΔV_dec<ΔV_{d max}and D can reach

The speed increment of the uniform deceleration section ⑥ is n₆×D

From equation (27), the sum of the speed increments in the deceleration region iii is:

ΔV_{d max}＝(n₅+n₆)×D (33)

let n_d＝n₅+n₆Equation (33) may be rewritten as:

ΔV_{d max}＝n_d×D (34)

to practice

Getting the whole upward to obtain:

then respectively aiming at the actual achievable deceleration value D^realAnd the number of cycles of the acceleration/deceleration section ⑤

Correcting and rounding as follows:

in the same way, the actual deceleration and acceleration value

The recalculation can be:

so far, for the case of D reachable, the calculation result of the actual interpolation cycle number at each stage is:

fig. 4 is a schematic diagram illustrating the actual deceleration point prediction of the S-shaped curve acceleration and deceleration control method. The S-shaped curve acceleration and deceleration control method provided by the invention has the problem that the actual deceleration point D ' and the theoretical deceleration point D do not coincide after discretization, the curve DE in figure 4 is a theoretical deceleration curve, but because the current speed and the total movement displacement L after quantization cannot be exactly integral multiple, the current residual distance of a certain period is always larger than 0 and smaller than the current speed value, if the next period is to interpolate the current speed value for one period, namely D is reached, the speed is reduced according to the D ' E ' curve, if the acceleration and deceleration is still executed according to the originally planned interpolation period number of each stage, the finally reached end point position of the movement is larger than the original set value of the user. It is necessary to take a method of entering the deceleration region in advance, and as shown in fig. 4, the actual deceleration point is D ', and the D ' E ' curve is the actual deceleration curve. Based on the above analysis, the real-time calculation of the actual deceleration point D' will be one of the key factors for the success or failure of the whole algorithm.

The current acceleration and deceleration process is in different stages, and the meaning of the deceleration distance is different, so the deceleration distance is regulated as follows:

b) In the case other than a), the deceleration distance means the distance traveled by the deceleration region III (displacement L of the acceleration/deceleration section ⑤)₅+ displacement L of uniform deceleration section ⑥₆Displacement L of + deceleration section ⑦₇)。

(1) distance traveled by deceleration zone III

The number n of the periods of the acceleration and deceleration section ⑤ is divided by (3), (4) and (6)₅Substitution can obtain:

2) calculating the displacement L of the uniform deceleration section ⑥₆

Similarly, the number n of the periods of the uniform deceleration section ⑥ is expressed by the formulas (3), (4) and (6)₆Substitution can obtain:

3) calculating the displacement L of the deceleration section ⑦₇

Similarly, the number n of the periods of the deceleration section ⑦ is reduced by equations (3), (4) and (6)₇Substitution can obtain:

the deceleration distance L can be obtained from the equations (49), (51) and (53)_dec：

As can be seen from equation (55), the deceleration distance L_decIs computationally intensive. The speed of the first period of the deceleration area III is found to be

The second cycle has a speed of

The third cycle has a speed of

The penultimate cycle speed is

The speed of the third last cycle is

The speed of the fourth last cycle is

Therefore, the 1 st, 2 nd, … … th and n th speed reduction regions III are set₇Period and 2 nd, 3 rd, … … th, n th of last₇+1) periods are added up separately, the result obtained is f_e+V_mThus for L_decThere may be a simpler method for calculating (c), and the derivation process is given below:

the motion stages of the deceleration area III are divided again, the first n₇One period is an acceleration and deceleration section ⑤, (n)₇+1 to (n)₇+n₆) The period is a uniform deceleration section ⑥, (n)₇+n₆+1 to (2 x n)₇+n₆) To reduce the deceleration section ⑦, the last cycle is the ending speed f_e. The first n is obtained from the formula (49)₇Acceleration of acceleration/deceleration segment ⑤ of one cycle

Speed of rotation

And displacement of

The calculation formula is as follows:

from equations (49) and (56):

similarly, the deceleration a of the uniform deceleration section_iVelocity V_iAnd a displacement L_iThe calculation formula is as follows:

number n of periods of the uniform deceleration section ⑥₆By substituting equation (58) for the deceleration of the uniform deceleration section ⑥

Speed of rotation

And displacement of

Comprises the following steps:

will be provided with

Substituted into formula (59) while taking into account formula (56)

Thus, it can be obtained

In the formula (49)

And

while taking into consideration the formula (51)

The following can be obtained:

from formulae (51), (59), and (57):

will decrease the number n of cycles of the speed reduction section ⑦₇In the substitution of equation (63), the displacement of the deceleration stage ⑦ can be found as:

from formulas (61), (62) and (64):

in view of

Also obtained from formula (53):

from formula (66) to formula (56)

Substituted into the formula (59)

Comprises the following steps:

from formulae (64), (66) and (56)

The following can be obtained:

(2) displacement L of the deceleration acceleration section ③₃

Considering the continuity of the acceleration, when the acceleration and deceleration process is inAdding acceleration section ① or even acceleration section ②, the deceleration distance L_decIncluding the distance traveled by deceleration region III, and also the displacement L of deceleration section ③₃So L is calculated by the procedure of adding acceleration segment ① and homogenizing acceleration segment ② given below respectively₃The derivation process of (1):

2) the integral summation of equation (70) can obtain the velocity value V of the i-th cycle of the deceleration acceleration section ③_iComprises the following steps:

3) the integral summation of equation (71) results in the displacement L of the acceleration segment ③ for the i-th cycle_iComprises the following steps:

the acceleration section includes:

therefore, the L of the acceleration section ① can be obtained by subtracting the formula (74) from the formula (73) and substituting the formula (75)₃The calculation formula of (2) is simplified as:

in a similar way, the uniform acceleration section II comprises:

therefore, by subtracting the formula (74) from the formula (73) and substituting the formula (77), L of the acceleration uniforming section ② can be obtained₃The calculation formula of (2) is simplified as:

L₃＝L'₃+a_cur×n₃(78)

fig. 5 shows a schematic diagram of the remaining distance compensation of the S-shaped curve acceleration and deceleration control method. Based on the above analysis, it is known that entering the deceleration region III in advance will inevitably result in the remaining distance L_rThe compensation is needed during the deceleration process, and the residual distance L needs to be compensated_rSatisfies the following conditions:

0≤L_r<V_m

L_r＝L-L_cur-L_dec(79)

current travel distance L_curComprises the following steps:

from the equation (79), if the total displacement L of motion is large, L obtained by calculation is calculated_rPossibly very large (L)_r>V_m) In order to minimize the compensation period of the remaining distance, and also because of the period number n of the uniform velocity segment ④ during the stage division process₄Is not specified and therefore can be compensated for using the constant velocity segment ④Number n of cycles of constant velocity segment ④₄Every additional cycle, L_curWith a consequent increase in maximum speed V_mThus leaving a distance L_rIs compensated and continuously reduced. When the remaining distance is less than the maximum velocity value V_mEntering a deceleration area III for deceleration processing, and the number n of the periods of the uniform speed segment ④₄And is finally determined.

With appropriate pairs of positions L at any stage of the deceleration zone III_rAnd (4) a processing method for performing one-time insertion compensation. From the above analysis, L is 0. ltoreq. L_r≤V_mIf the remaining distance L is_rAt maximum speed V_mWith the lowest operating speed f_eIn the deceleration section, compensation is then performed. If the remaining distance L_rIs less than the end speed f_eThen L will be_rSuperimposed on the last motion cycle for compensation.

An implementation flow chart of the S-shaped curve acceleration and deceleration control method shown in FIG. 6. The implemented process and steps include:

(1) initializing and dividing stages of the algorithm according to parameters input by a user;

(2) judgment of L_remain

1) If L is_remain>0

a) If V_m>F

i) If n is₃>0, jumping to an acceleration reducing section (5);

ii) otherwise, jumping to the uniform speed segment (6).

b) Otherwise, the current acceleration A needs to be adjusted_curAnd comparing the maximum acceleration A:

i) if A_cur>A, jumping to a uniform acceleration section (4);

ii) otherwise jumping to the acceleration section (3).

2) Otherwise, it is necessary to n₅、n₆、n₇The value of (a):

a) if n is₅>0, entering an acceleration and deceleration section; otherwise, judging n₆Whether greater than 0;

b) if n is₆>0, entering a uniform deceleration section; otherwise, judging n₇Whether greater than 0;

c) if n is₇>0, entering a deceleration reducing section; otherwise, entering an end segment plan (13);

(3) add acceleration segment ① update the current acceleration value A_curCurrent velocity value V_cur、n₁、n₃Calculating L₃And V_mJumping to (10);

(4) uniform acceleration segment ② updating current jerk value J_accCurrent acceleration value A_curCurrent velocity value V_cur、n₂Calculating L₃And V_mJumping to (10);

(5) deceleration acceleration segment ③ updating current acceleration value A_curCurrent velocity value V_cur、n₁、n₃Jumping to (10);

(6) uniform velocity segment ④ updating current jerk value J_accCurrent acceleration value A_curCurrent velocity value V_cur、n₄Calculating L_remainJumping to (12);

(7) acceleration and deceleration section ⑤ for updating current acceleration value A_curCurrent velocity value V_cur、n₅Jumping to (11);

(8) uniform deceleration segment ⑥ updating current jerk value J_decCurrent acceleration value A_curCurrent velocity value V_cur、n₆Jumping to (11);

(9) deceleration segment ⑦ updating current acceleration value A_curCurrent velocity value V_cur、n₇Jumping to (11);

(10) calculating the deceleration distance L_decThe remaining distance L_remain、n₅、n₆、n₇And J_decJumping to (12);

(11) judgment V_cur>L_remainWhether the condition is met or not, if so, performing residual amount compensation; otherwise, jumping to (12);

(12) updating the current location L_curJumping to (1);

(13) and (4) planning an end section: recalculating residual distanceIs far from L_remainAnd further judging:

1) if L is_remain>f_eUpdate the current velocity value V_curRecalculating residual distance L_remainThen updates the current position value L_curJumping to (13);

2) otherwise, compensating the residual distance at one time, and jumping to (14);

(14) the algorithm ends.

Fig. 7 is a flowchart illustrating initialization and phase division of the S-shaped curve acceleration/deceleration control method. The implemented process and steps include:

(1) initializing user input parameters;

(2) judging the remaining distance L_remainAnd starting speed f_sSize:

1) if L is_remain>f_sUpdate V_cur、V_m、L_remainJumping to (3);

2) otherwise, L is updated_curAnd V_curJumping to (6);

(3) for maximum feed speed F and initial speed F_sAnd (3) carrying out size comparison:

1) if F is less than or equal to F_sFor the remaining distance L_remainAnd the current speed V_curAnd (3) comparing the sizes:

i) if L is_remain>V_curRecalculating correction

D^real、

L_decn₅、n₆、n₇And J_dec、L_dec、L_r；

(i) If Lr <0, enter the end segment plan, jump to (6).

(ii) Otherwise, reassign the remaining distance L_remain、n₅、n₆、n₇And J_decJumping to (4);

ii) otherwise, jumping to the end segment plan.

2) Otherwise, recalculating correction

D^real、

L_decn₅、n₆、n₇And J_dec、L_dec、L_r；

i) If Lr <0, jump to the end segment plan.

ii) if not, reassign the remaining distance L_remain、n₅、n₆、n₇And J_decJumping to (5);

(4) need to keep the remaining distance L_remainAnd the current speed V_curAnd (3) comparing the sizes:

1) if L is_remain>V_curEntering a uniform speed area II and jumping to (6);

2) otherwise, entering a deceleration area III and jumping to the step (6);

(5) recalculating A^realAnd

and update A and J_accEntering an acceleration area I and jumping to (6);

(6) the initialization and phase division are ended.

Fig. 8 is a diagram of a finite state machine of an online target location change algorithm. The algorithm is realized based on the idea of a finite-state machine, and as shown in fig. 8, there are 4 states: an acceleration area I, a uniform speed area II, a deceleration area III and reverse motion compensation. According to the different forms of the trigger stage and the target position change, the corresponding processing modes are different, and the specific trigger stage and the processing mode comprise:

(1) when the acceleration area I triggers a request for changing the target position, the processing steps are as follows:

calculate the Path according to equation (81)Total remaining distance L_remain：

1) The target position becomes small:

i) if L is_remain<0, updating the current target position and recalculating the deceleration distance L_decRecalculating residual distance L_r＝L_remain-L_decRecalculating n₅、n₆、n₇、J_decThe current state jumps to reverse motion compensation;

ii) if not, updating the current target position, and jumping to a deceleration area III in the current state;

2) and (5) directly updating the current target position and keeping the current state unchanged when the target position is increased.

(2) When the uniform velocity area II triggers a request for changing the target position, the processing steps are as follows:

the total remaining distance L of the path is calculated by the equation (81)_remain：

1) The target position becomes small:

i) if L is_remain<0, updating the current target position, and skipping to the reverse motion compensation in the current state;

ii) otherwise, updating the current target position and recalculating the deceleration distance L_decRecalculating residual distance L_r＝L_remain-L_decRecalculating n₅、n₆、n₇、J_decSkipping to a deceleration area III from the current state;

2) the target position becomes large:

i) if V_curAnd F, updating the current target position, and keeping the current state unchanged.

ii) otherwise, updating the current target position and recalculating L_r＝L_remain-V_curRecalculating J_accThe current state jumps to a deceleration area I;

(3) when the deceleration area III triggers the request for changing the target position, the processing steps are as follows:

1) The target position becomes small:

i) if L is_remain<0, moreThe new current target position and the current state jumps to the reverse motion compensation.

ii) ignoring the change target location request.

2) The target position is increased, the current target position is updated, and L is recalculated_r＝L_remain-V_curRecalculating J_accThe current state jumps to the deceleration zone i.

Fig. 9 is a schematic diagram of a finite state machine of an online target speed changing algorithm. Changing the target speed online is also realized based on the idea of a finite state machine, and all the states include: an acceleration area I, a uniform speed area II and a deceleration area III. According to the different forms of the trigger stage and the target speed, the corresponding processing modes are different, and the processing procedures of various conditions are given as follows:

(1) the target speed becomes large:

1) if the current state is in the acceleration area I, updating the target speed, and keeping the current state unchanged;

2) if the current speed is in the uniform speed area II, calculating the distance L of the current speed accelerated to the new target speed₁Then, the deceleration from the new target speed to the end speed f is calculated_eDistance L of₂Finally, the current remaining distance L is calculated_r＝L-L_cur-L₁-L₂

i) If L is_r>0, recalculating the deceleration distance L_decRecalculating n₅、n₆、n₇、J_decJumping to an acceleration area I;

ii) if not, ignoring the request for changing the target speed, and keeping the current state unchanged;

3) if the current speed is in the deceleration area III, calculating the distance L of the current speed accelerated to the new target speed₁Then, the deceleration from the new target speed to the end speed f is calculated_eDistance L of₂Finally, the current remaining distance L is calculated_r＝L-L_cur-L₁-L₂

i) If L is_r>0, recalculating the deceleration distance L_decRecalculating n₅、n₆、n₇、J_decJumping to a deceleration area III;

(2) the target speed becomes small:

calculating the distance L of the current speed to the new target speed₁Then, the deceleration from the new target speed to the end speed f is calculated_eDistance L of₂Finally, the current remaining distance L is calculated_r＝L-L_cur-L₁-L₂

ii) otherwise, ignoring the change target speed request, the current state is unchanged.

Fig. 10 is a simulation diagram of a displacement curve, a velocity curve and an acceleration curve of the proposed S-shaped curve acceleration and deceleration control method. The control method input parameters are set as follows: l2000 pulses, F100 pulses/sampling period, F_s0 pulses/sampling period, f_e0 pulses/sampling period, and a 10 pulses/sampling period²D10 pulses/sampling period²，J_acc2 pulses/sampling period³，J_dec2 pulses/sampling period³Sampling period T_sAs can be seen from FIG. 10, the maximum acceleration (deceleration) A (D) and the maximum speed F set by the user can be achieved due to the fact that the total movement L is long enough, the symmetrical acceleration A and deceleration D are set, and the symmetrical acceleration value and deceleration value are set at the same time, the S-shaped curve acceleration and deceleration shown by the simulation diagram comprises a complete 7-segment S-shaped curve acceleration and deceleration process, namely an acceleration segment ①, a uniform acceleration segment ②, a deceleration segment ③, a uniform velocity segment ④, an acceleration and deceleration segment ⑤, a uniform deceleration segment ⑥ and a deceleration segment ⑦, and the acceleration curve obtained by the S-shaped curve acceleration and deceleration control method is continuous and free of sudden change, smooth in speed curve, smooth in movement and small in impact, and can meet the requirements of high-speed and high-precision processing on acceleration and deceleration characteristics such as short running time, smooth in movement, no impact, high precision and the like。

Fig. 11 is a simulation diagram of a displacement curve, a velocity curve and an acceleration curve of the proposed S-shaped curve acceleration and deceleration control method. The control method input parameters are set as follows: 1000 pulses L, 100 pulses/sampling period F _s0 pulses/sampling period, f _e0 pulses/sampling period, and a 10 pulses/sampling period²D10 pulses/sampling period²，J _acc2 pulses/sampling period³，J _dec2 pulses/sampling period³

Sampling period T

_s1 millisecond. As can be seen from fig. 11, since the total movement displacement L is moderate, the maximum acceleration (deceleration) speed a (D) is reachable, while the maximum target speed F is not reachable, and symmetric acceleration a and deceleration D are set, and symmetric acceleration and deceleration values are set; the simulation graph shows that the acceleration curve obtained by the S-shaped curve acceleration and deceleration control method is continuous, has no sudden change and has a smooth speed curve.

Fig. 12 is a simulation diagram of a displacement curve, a velocity curve and an acceleration curve of the proposed S-shaped curve acceleration and deceleration control method. The input parameters of the manufacturing method are set as follows: 400 pulses L, 100 pulses/sampling period F _s0 pulses/sampling period, f _e0 pulses/sampling period, and a 10 pulses/sampling period²D10 pulses/sampling period²，J _acc2 pulses/sampling period³，J _dec2 pulses/sampling period³

Sampling period T

_s1 millisecond. As can be seen from fig. 12, since the total movement displacement L is small, neither the maximum acceleration (deceleration) a (D) nor the maximum target velocity F is reachable, and symmetrical acceleration a and deceleration D are set, and symmetrical jerk and jerk are set; the simulation graph shows that the acceleration curve obtained by the S-shaped curve acceleration and deceleration control method is continuous, has no sudden change and has a smooth speed curve.

Fig. 13 is a simulation diagram of a displacement curve, a velocity curve and an acceleration curve of the proposed S-shaped curve acceleration and deceleration control method. The input parameters of the manufacturing method are set as follows: l3000 pulses, F100 pulses/sampling period, F _s1 pulse/sampling period, f _e2 pulses/sampling period, a ═20 pulses/sampling period²D10 pulses/sampling period²，J _acc5 pulses/sampling period³，J _dec2 pulses/sampling period³

Sampling period T

_s1 millisecond. As can be seen from the simulation diagram of fig. 13, since the total movement displacement L is long enough, the maximum plus (minus) speed a (D) and the maximum target speed F set by the user can be achieved, and the control method input adopts asymmetric a and D and asymmetric J_accAnd J_dec(ii) a Additional starting speed f_sAnd end speed f_eAll are not zero, the user can set according to different machine tools, and can also carry out parameter configuration according to the provided rule to obtain the best effect, and the device has good flexibility and flexibility. The simulated acceleration curve is continuous, has no sudden change, and the speed curve is smooth.

FIG. 14 is a simulation diagram of the algorithm displacement curve, velocity curve and acceleration curve of the proposed S-shaped curve acceleration and deceleration control method for changing the endpoint position on line. The input parameters of the manufacturing method are set as follows: original end position L is 3000 pulses, F is 50 pulses/sampling period, F _s0 pulses/sampling period, f _e0 pulse/sampling period, and a 5 pulse/sampling period²D5 pulses/sampling period²，J _acc1 pulse/sampling period³，J _dec1 pulse/sampling period³

Sampling period T

_s1 millisecond, when the change of the end position is triggered at the uniform speed stage, the new end position L ₁2000 pulses. As shown in fig. 14, the end point position L originally set by the user is 3000 pulses, and then when the current motion is in the uniform motion stage, the user triggers the end point position change request to change the new end point position L₁When the current position at this time exceeds 2000 pulses, the control system receives a request for changing the end position from the user, and the process is as follows: first, the speed is instantly reduced to 0 from the current speed, then the reverse compensation processing is carried out, and finally the speed is accelerated reversely to a new end position. The displacement curve, the speed curve and the acceleration curve graph in the graph can be known, the obtained acceleration curve is continuous and has no abrupt change and the speed curve is smooth from the simulation graph,namely, the algorithm for changing the end point position on line by the S-shaped curve acceleration and deceleration control method is feasible; the algorithm can meet the requirement of a user on the change of the end point position of the numerical control equipment in the motion process, expand the functions of the numerical control system, improve the flexibility of the numerical control system and meet the application requirements of more user groups.

FIG. 15 is a simulation diagram of the S-shaped curve acceleration/deceleration control method for changing the displacement curve, velocity curve and acceleration curve of the target velocity algorithm on line. The input parameters of the manufacturing method are set as follows: end position L3000 pulses, F100 pulses/sampling period, F _s0 pulses/sampling period, f _e0 pulses/sampling period, and a 10 pulses/sampling period²D10 pulses/sampling period²，J _acc2 pulses/sampling period³，J _dec2 pulses/sampling period³Sampling period T_sFor the first time, 1 ms triggers a change of the target speed to f in the acceleration phase ₁60, the second time in the uniform speed stage triggers the change of the target speed f ₂40. As can be seen from fig. 15, the target speed F originally set by the user is 100 pulses/sampling period, and the user triggers 2 requests to change the target speed at different stages in the current process of the movement. Since the current movement is in the acceleration phase when the first change target speed request is triggered, the new target speed can be directly assigned, so that the maximum target speed reached is 60 instead of 100 as originally set, as can be seen from the speed curve in the figure; the second request to change the target speed is that the current motion is in a constant speed phase (f)₁60) is triggered, and the response continues to the request to change the target speed again, since the remaining distance is still sufficient and the distance required to decelerate from the current speed (60) to the new target speed (40) and from the new target speed (40) to the end speed.

The simulation graph shows that the obtained acceleration curve is continuous, has no sudden change, and the speed curve is smooth, the S-shaped curve acceleration and deceleration control method is feasible for changing the target speed algorithm on line, and can realize the requirement of changing the speed for many times; the algorithm can meet the requirement of a user on the change of the target speed of the numerical control equipment in the motion process, expand the functions of the numerical control system, improve the flexibility of the numerical control system and meet the application requirements of more user groups.

Claims

1. A S-shaped acceleration and deceleration control method for changing target speed and position on line is characterized in that aiming at user input parameters: total displacement L and initial speed f of movement_sMaximum speed F, end speed F_eMaximum acceleration A, maximum deceleration D, jerk J_accDeceleration rate J_decAnd interpolating the sampling period T_sThe following operations are performed:

(1) firstly, initialization and stage division processing are carried out:

2) In the process of discretization processing of deceleration in the deceleration area III, the actual interpolation periods of the acceleration and deceleration section ⑤, the uniform deceleration section ⑥ and the deceleration section ⑦ are respectively n according to the condition that whether the maximum deceleration D can reach the criterion or not₅、n₆、n₇；

2. The S-shaped acceleration and deceleration control method for changing the target speed and position online according to claim 1, characterized in that: the acceleration/deceleration a (t), the speed f (t) and the displacement s (t) have the following relations with time:

in the formula (1), t is a time coordinate, t_iThe method comprises the steps of representing transition point time of each motion stage, representing each motion stage in a speed planning process by i, wherein i is 1-7, i is an integer, dividing the motion process into 7 motion stages, namely an acceleration adding section ①, a uniform acceleration section ②, an acceleration reducing section ③, a uniform speed section ④, an acceleration and deceleration section ⑤, a uniform deceleration section ⑥ and a deceleration reducing section ⑦, and enabling tau to be zero_iRepresenting local time coordinates, i.e. τ, with the start of each motion phase as a time zero_i＝t-t_i-1I represents each motion stage in the speed planning process, i is 1-7, and i is an integer;

acceleration/deceleration j (t)_i) Is a piecewise function with time as a variable:

in the formula (2), J_iRepresenting the acceleration/deceleration of each motion phase, i represents each motion phase of the velocity planning process, i is 1-7, i is an integer, wherein J₂＝J₄＝J₆＝0；

Acceleration/deceleration a (t)_i) Is a piecewise function with time as a variable, satisfying equation (3):

in the formula (3), a and D represent the maximum acceleration and the maximum deceleration input by the user, respectively;

the speed f (t)_i) Is a piecewise function with time as a variable, satisfying equation (4):

in the formula (4), f_iThe method comprises the steps of representing speed values reached by end points of all motion phases, wherein i represents all the motion phases in a speed planning process, i is 1-7, and i is an integer; f represents the maximum speed value which can be reached after the movement process is accelerated by the acceleration area, wherein the maximum speed value is equal to the input maximum speed; t is_iRepresenting the movement time, T, of each movement phase_iFor a sampling period T_sI represents each motion stage in the speed planning process, i is 1-7, and i is an integer;

the displacement s (t)_i) Is a piecewise function with time as a variable, satisfying equation (5):

in the formula (5), s_iRepresenting the movement displacement amount when each movement stage is finished, wherein i represents each movement stage in the speed planning process, i is 1-7, and i is an integer;l represents the total displacement of motion; for the convenience of subsequent calculation, the calculation formula of the motion displacement in each stage can be calculated by the following equation system:

3. the S-shaped acceleration and deceleration control method for changing the target speed and position online according to claim 2, characterized in that: the maximum acceleration/deceleration limit is obtained from the maximum moment and force limit of the driving motor, and reflects the maximum acceleration and deceleration capacity of the numerical control servo system; the maximum acceleration/deceleration reflects the flexibility of the numerical control servo system and the acceleration time T₁、T₃、T₅And T₇In inverse proportion; assuming that the time required for the acceleration/deceleration to increase from 0 to the maximum and the time required for the acceleration/deceleration to decrease from the maximum to 0 are equal, the following equation sets:

in the formula (7), J_accAnd J_decRespectively representing the jerk value of the acceleration region i and the jerk value of the deceleration region iii.

4. The S-shaped acceleration and deceleration control method for changing the target speed and position online according to claim 3, characterized in that: the input of the S-shaped acceleration and deceleration control method allows setting asymmetric maximum acceleration A and maximum deceleration D; or inputting asymmetrical jerk J_accAnd deceleration J_dec(ii) a Or to set an asymmetrical starting speed f_sAnd f_eAnd f is_sAnd f_eMay take a non-zero value.

5. The S-shaped acceleration and deceleration control method for changing the target speed and position online according to claim 4, characterized in that: the discretization processing process of the accelerating area I is as follows:

the acceleration region I comprises an acceleration adding section ①, a uniform acceleration section ② and an acceleration reducing section ③, and the interpolation period number n of the acceleration adding section ① is set₁And the number n of interpolation periods of the deceleration acceleration section ③₃The following relationships exist: n is₃＝n₁-1 (8)

From formula (7) to n₁Getting the whole upward:

the sum of the speed increments for the plus acceleration segment ① and the minus acceleration segment ③ is calculated:

calculating the velocity f from the start_sMaximum allowable speed increment to F: Δ V_amax＝F-f_s(14)

Thereby deducing the criterion whether the maximum acceleration A can be reached: if Δ V_acc≥ΔV_amaxThen the maximum acceleration A in the acceleration and deceleration process can not be reached; otherwise, the maximum acceleration A can be reached;

a)ΔV_acc≥ΔV_amaxa is not reachable

Calculating the actual number of interpolation cycles of the acceleration segment ①

And (3) correcting and recalculating the actual acceleration and the actual acceleration:

is calculated toNumber of interpolation cycles to smooth acceleration segment ② and deceleration segment ③:

b)ΔV_acc＜ΔV_amaxa can reach

Calculating the velocity increment n of the even acceleration segment ②₂×A (18)

The sum of the velocity increments DeltaV after passing through the acceleration region I can be obtained from the formula (13)_amax：ΔV_amax＝(n₁+n₂)×A (19)

Let n_a＝n₁+n₂Then equation (19) can be rewritten as: Δ V_amax＝n_a×A (20)

Then n is_aThe actual value of (d) may be calculated as:

actual acceleration A^realActual number of interpolation cycles of the acceleration section ①

And actual jerk value

6. The S-shaped acceleration and deceleration control method for changing the target speed and position online according to claim 5, characterized in that: the discretization processing process of the deceleration area III is as follows:

the deceleration zone III comprises an acceleration and deceleration section ⑤, a uniform deceleration section ⑥ and a deceleration and deceleration section ⑦, and the number n of interpolation cycles of the acceleration and deceleration section ⑤ is set₅And the number n of interpolation periods of the deceleration section ⑦₇The following relationship is satisfied: n is₇＝n₅-1 (25)

According to formula (7) to n₅Getting the whole upward:

calculating the speed increment sum delta V of the acceleration and deceleration section ⑤ and the deceleration and deceleration section ⑦_dec：

Calculating the deceleration from the maximum speed F to the end speed F_eMaximum allowable speed increment Δ V_dmax：ΔV_dmax＝F-f_e(28)

The criterion whether the maximum deceleration D can be reached is obtained by the calculation results of the equations (27) and (28): if Δ V_dec≥ΔV_dmaxThen the maximum deceleration D in the acceleration and deceleration process can not be reached; otherwise, the maximum deceleration D can be reached;

a)ΔV_dec≥ΔV_dmaxd is unreachable

calculating the reality of the acceleration and deceleration segment ⑤Number of interpolation cycles

By using

And equation (29) corrects the actual deceleration-acceleration value

Correcting the actually achievable deceleration value D^real：

Calculating the actual number of interpolation cycles of the uniform deceleration section ⑥ and the deceleration section ⑦:

b)ΔV_dec＜ΔV_dmaxand D can reach

Calculating the speed increment n of the uniform deceleration section ⑥₆×D

The sum of the velocity increments Δ V after passing through the deceleration region III can be obtained from the equation (27)_dmax：ΔV_dmax＝(n₅+n₆)×D (33)

Let n_d＝n₅+n₆Equation (33) may be rewritten as: Δ V_dmax＝n_d×D (34)

Then n is_dThe actual value of (d) may be calculated as:

actual decelerationDegree D^realActual number of interpolation cycles in acceleration/deceleration section ⑤

And actual deceleration-acceleration value

For the case of D reachable numbers, the actual interpolation period number calculation result at each stage is:

7. the S-shaped acceleration/deceleration control method of changing the target speed and position online according to claim 6, characterized in that: said maximum achievable speed V_mThe calculation is specifically as follows:

to ensure that the maximum velocity V is reached at the end of the deceleration acceleration section ③_mLess than or equal to the user-given maximum speed F, i.e. the inequality holds: v_m≤F (39)，

V in formula (39)_mRepresenting the maximum speed value which can be reached in the process of reducing and accelerating from the current speed and the current acceleration; in order to ensure that the inequality (39) is true, it is necessary to add in advanceThe acceleration section ① and the uniform acceleration section ② calculate the speed value of the next period in real time, and once the calculated speed value of the next period is greater than the maximum speed F, the acceleration and deceleration process is switched to the deceleration and acceleration section ③ in the next period;

in the formula (40), the reaction mixture is,

representing actual jerk value, i representing current cycle number, i ∈ [1, n₃]I is an integer, so the maximum speed value reached after the end of the deceleration acceleration segment ③ is:

since the amount of calculation of equation (42) is relatively large, a simpler calculation method is derived:

1) plus acceleration section ① V_mThe calculation formula of (2) is as follows:

in formula (44), V'_mIndicating the maximum speed value that was achievable in the last cycle calculation.

2) V in uniform acceleration section ②_mThe calculation formula of (2) is as follows: v_m＝V′_m+a_cur(45)。

8. The S-shaped acceleration and deceleration control method for changing the target speed and position online according to claim 7, characterized in that: the actual deceleration point prediction judges the actual deceleration point by calculating the deceleration distance and the path remaining distance in real time, and once the fact that the remaining distance of the next interpolation period is smaller than the deceleration distance is known, the next interpolation period is shifted to a deceleration area III, which is specifically as follows:

when the current acceleration and deceleration process is in the acceleration section ① or the uniform acceleration section ②, in order to ensure the continuity of the acceleration, the deceleration distance includes the distance traveled by the deceleration region iii, i.e., the displacement L of the acceleration and deceleration section ⑤_n5Displacement L of uniform deceleration section ⑥_n6And displacement L of the deceleration section ⑦_n7In addition, the displacement L of the acceleration reducing section ③ is also included_n3；

1) Deceleration distance L_decCan be calculated from the following formula:

finally obtaining the simplified deceleration distance L_decThe iterative calculation formula is:

in the formula (69), L_n5Indicating the displacement, L, of the acceleration-deceleration section ⑤_n6Indicating the displacement, L, of the uniform deceleration section ⑥_n7Indicating the displacement, V, of the deceleration section ⑦_mRepresents the maximum speed value reached after the end of the deceleration section ③;

2) displacement L of the deceleration acceleration section ③₃Simplifying the calculation formula:

a) l plus acceleration section ①₃The iterative calculation formula of (2):

l 'in formula (76)'₃Value L representing the last cycle₃，V_curSpeed value representing the current cycle, a_curIndicates the acceleration value of the current cycle,

representing an actual jerk value;

b) l of uniform acceleration section ②₃The iterative calculation formula of (2): l is₃＝L'₃+a_cur×n₃(78)

L 'in formula (78)'₃Value L representing the last cycle₃。

9. The S-shaped acceleration/deceleration control method of changing the target speed and position online according to claim 8, characterized in that: the residual distance compensation mode is realized by adopting a mode of one-time compensation at a proper position at any stage of the deceleration area III, and specifically comprises the following steps:

the actual deceleration point is judged in real time through calculation of the deceleration distance, the actual deceleration point is advanced from the theoretical deceleration point, the speed planning is finished after the deceleration section is finished due to the fact that the actual deceleration point is artificially advanced, the residual distance is not equal to 0, and the residual distance needs to be compensated in a deceleration area III; let the remaining distance be L_rThe current running distance is L_curThen for a period of any phase, the following relationship exists: l is_r＝L-L_cur-L_dec(79)

In the formula (79), L represents the total displacement of the movement, L_decRepresenting a deceleration distance; and the current travel distance may be calculated by:

in the formula (80), n_iThe interpolation period number of each motion stage is represented, i represents each motion stage in the speed planning process, i is 1-7, and i is an integer; v_jRepresenting each motion phase n_iJ represents all values of the interpolation period number in each motion phase, j is 1 to n_iJ is an integer; if the total movement displacement L is large, calculating the obtained L_rGreater than the actual maximum speed V achievable_mIn order to minimize the compensation period of the remaining distance, and due to the phaseIn the dividing process, the interpolation period number n of the uniform speed segment ④₄Is not specified, so the constant speed section can be used for compensation; interpolating the number of cycles n along with the uniform speed section₄Every additional cycle, L_curWith a consequent increase in maximum speed V_mThus leaving a distance L_rIs compensated and continuously reduced; when the remaining distance is less than the maximum velocity value V_mEntering a deceleration area III; from the above analysis, L is 0. ltoreq. L_r≤V_mIf the remaining distance L is_rAt maximum speed V_mAnd end speed f_eThen compensation is performed in the deceleration section; if the remaining distance L_rIs less than the end speed f_eThen L will be_rSuperimposed on the last motion cycle for compensation.

10. The S-shaped acceleration and deceleration control method for changing the target speed and position online according to claim 2, characterized in that: the online target position changing is realized based on the idea of a finite state machine, and all the states comprise: an acceleration area I, a uniform speed area II, a deceleration area III and reverse motion compensation; the request for changing the target position for multiple times can be realized;

the online change target speed is realized based on a finite state machine, and all the states comprise: an acceleration area I, a uniform speed area II and a deceleration area III; changing the target speed on-line must ensure accurate arrival of the target position, otherwise ignoring the shift request, so responding to the shift request is conditional; a request to change the target speed a plurality of times in succession may be implemented.