CN103076759A - Method and device for acquiring S-shaped curve of numerical control system - Google Patents

Abstract

The embodiment of the invention discloses a method for acquiring an S-shaped curve of a numerical control system. The method comprises the following steps of: rounding the original time span of each time interval of the S-shaped curve of the numerical control system to obtain a corresponding rounded time span of each time interval; obtaining the maximum acceleration, maximum deceleration, maximum jerk and target speed of the S-shaped curve according to the rounded time span of each time interval; obtaining a curve length which corresponds to each time interval according to the rounded time span of each time interval, the maximum acceleration, the maximum deceleration, the maximum jerk and the target speed; and obtaining the displacement of the S-shaped curve which corresponds to the time point of the S-shaped curve according to the curve length which corresponds to each time interval to complete planning of the S-shaped curve. The embodiment of the invention further discloses a device for acquiring the S-shaped curve of the numerical control system. Through the way, the calculation accuracy of acceleration and deceleration planning can be increased, and the problem of shaking in a machining process is solved.

Description

A kind of method and device thereof that obtains the S type curve of digital control system

Technical field

The present invention relates to the digital control system field, particularly relate to a kind of method and device thereof that obtains the S type curve of digital control system.

Background technology

In the digital control system, for guarantee lathe startup stop or two segment of curve between do not produce impact, step-out, the excess of stroke or concussion during transition, need to carry out curve acceleration and deceleration system, namely adopt special acceleration and deceleration control planning algorithm, so that the input of motor changes according to certain rule, in various processing situations, can both locate fast and accurately.Prior art is divided into seven time periods with S type curve in the deceleration planning of S type curve, according to the time spans of each time periods of calculation of parameter such as system's peak acceleration to finish the planning of S type curve.The time span of above-mentioned each time period that calculates can not guarantee it just in time is the integral multiple of interpolation cycle, and the input of motor is carried out take interpolation cycle as chronomere, can cause the velocity jump of last interpolation cycle like this, thereby the jitter problem in the process occur.A kind of solution is to adjust the time span value at the joining place of each time period in the prior art, for example use the time of the second time period with last interpolation cycle compensation of very first time section, by that analogy, carry out the planning of curve according to the time span of adjusting again.

The present application people finds in long-term R ﹠ D, although the solution of prior art has been carried out compensation at each time period joining place, still exists error, this error will affect the time period afterwards within the cycle of joining place.As in last interpolation cycle of first time period, be to add accelerated motion in the time at first half; Uniformly accelerated motion in time at latter half.When calculating corresponding during this period of time length of curve, actually carry out according to accelerating, speed and the length of calculating all can be bigger than normal like this, and speed and the length computation of follow-up time section caused error effect.

Summary of the invention

The technical matters that the present invention mainly solves provides a kind of method and device thereof that obtains the S type curve of digital control system, can improve the computational accuracy of deceleration planning, solves the jitter problem in the process.

For solving the problems of the technologies described above, an aspect of of the present present invention is: a kind of method of obtaining the S type curve of digital control system is provided, comprises: the original time length to each time period of the S type curve of digital control system is carried out the rounding time span that rounding obtains each corresponding time period; Obtain peak acceleration, maximum deceleration, maximum acceleration and the target velocity of S type curve according to the rounding time span of each time period; Rounding time span, peak acceleration, maximum deceleration, maximum acceleration and target velocity according to each time period obtain length of curve corresponding to each time period; According to the displacement of S type curve corresponding to the time point of length of curve acquisition S type curve corresponding to each time period, to finish the planning of described S type curve.

Wherein, the original time length of each time period of the S type curve of digital control system being carried out the step that rounding obtains the rounding time span of each corresponding time period specifically comprises: each time period A that obtains S type curve _iThe original time length T _i, wherein, each time period A _iBe specially: add boost phase A ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆And subtract decelerating phase A ₇, each time period A _iOriginal time length be shown below:

T _i=n _i·T+Δt _i

Wherein, T _iExpression original time length, n _iBe integer, T is interpolation cycle, Δ t _iExpression is less than the time span of an interpolation cycle T, 0＜Δ t _i＜T, i=1,2 ..., 7;

To each time period A _iThe original time length T _iIn the time span Δ t less than an interpolation cycle T _iRounding is that an interpolation cycle T obtains each time period A _iThe rounding time span, wherein, each time period A _iThe rounding time span be shown below:

T _i′=(n _i+1)·T

Wherein, T _i' expression rounding time span.

Wherein, the step that obtains peak acceleration, maximum deceleration, maximum acceleration and the target velocity of S type curve according to the rounding time span of each time period specifically comprises: according to each time period A _iRounding time span T _i', peak acceleration, maximum deceleration, maximum acceleration, target velocity and each time period A _iSpeed and the relation between the length of curve of corresponding section end point obtain respectively following system of equations:

Each time period A _iThe rate equation group (1) of corresponding section end point:

$\left\{\begin{array}{c}{f}_1=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\′2}\\ f_2=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\′2}+{\mathrm{AT}}_2^{\′}\\ f_3=f\\ f_4=f\\ f_5=f-\frac{1}{2}{\mathrm{JT}}_5^{\′2}\\ f_6=f-\frac{1}{2}{\mathrm{JT}}_5^{\′2}-{\mathrm{DT}}_6^{\′}\end{array}\right.---\left(1\right)$

The length of curve system of equations (2) that each time period is corresponding:

$\left\{\begin{array}{c}{l}_1=f_s{T}_1^{\′}+\frac{1}{6}{\mathrm{JT}}_1^{\′3}\\ l_2=f_1{T}_2^{\′}+\frac{1}{2}{\mathrm{AT}}_2^{\′2}\\ l_3=f_2{T}_3^{\′}+\frac{1}{2}{\mathrm{AT}}_3^{\′2}-\frac{1}{6}{\mathrm{JT}}_3^{\′3}\\ l_4=f_3{T}_4^{\′}\\ l_5=f_4{T}_5^{\′}-\frac{1}{6}{\mathrm{JT}}_5^{\′2}\\ l_6=f_5{T}_6^{\′}-\frac{1}{2}{\mathrm{DT}}_6^{\′2}\\ l_7=l_6{T}_7^{\′}-\frac{1}{2}{\mathrm{DT}}_7^{\′2}+\frac{1}{6}{\mathrm{JT}}_7^{\′3}\end{array}\right.---\left(2\right)$

Wherein, f ₁, f ₂, f ₃, f ₄, f ₅, f ₆Expression adds boost phase A respectively ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆The speed of corresponding section end point, f _sThe initial velocity of expression S type curve, f represents the target velocity of S type curve, l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇Expression adds boost phase A respectively ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆, subtract decelerating phase A ₇Corresponding length of curve, A represents peak acceleration, and D represents maximum deceleration, and J represents maximum acceleration;

According to each time period A _iCorresponding length of curve and the relation of S type curve total length obtain following formula:

L=l ₁+l ₂+l ₃+l ₄+l ₅+l ₆+l ₇ （3）

Wherein, L represents S type curve total length;

System of equations (1), (2) substitution formula (3) are obtained following formula:

$L=(T_1^{\′}+T_2^{\′}+T_3^{\′})(\frac{f}{2}+f_s)+{\mathrm{fT}}_4^{\′}+(T_5^{\′}+T_6^{\′}+T_7^{\′})(\frac{f}{2}+f_e)---\left(4\right)$

Further obtain target velocity f according to formula (4), shown in the formula specific as follows:

$f=\frac{L-(T_1^{\′}+T_2^{\′}+T_3^{\′})f_s-(T_5^{\′}+T_6^{\′}+T_7^{\′})f_e}{\frac{T_1^{\′}+T_2^{\′}+T_3^{\′}+T_5^{\′}+T_6^{\′}+T_7^{\′}}{2}+T_4^{\′}}---\left(5\right)$

According to each time period A _iRounding time span T _i' and peak acceleration A, maximum deceleration D, maximum acceleration J, target velocity f between relation obtain following system of equations:

$\left\{\begin{array}{c}{T}_1^{\′}=T_3^{\′}=\frac{A}{J}\\ T_5^{\′}=T_7^{\′}=\frac{D}{J}\\ T_2^{\′}=\frac{f-f_s}{A}-\frac{A}{J}\\ T_6^{\′}=\frac{f-f_e}{D}-\frac{D}{J}\end{array}\right.---\left(6\right)$

Wherein, f _eThe terminal velocity of expression S type curve;

Further obtain peak acceleration A, maximum deceleration D, maximum acceleration J according to system of equations (6), respectively as following various shown in:

$A=\frac{f-f_s}{T_1^{\′}+T_2^{\′}}---\left(7\right),$ $D=\frac{f-f_e}{T_5^{\′}+T_6^{\′}}---\left(8\right)$

$J=\frac{f-f_s}{(T_1^{\′}+T_2^{\′})T_1^{\′}}=\frac{f-f_e}{(T_5^{\′}+T_6^{\′})T_5^{\′}}---\left(9\right).$

Wherein, the step that obtains length of curve corresponding to each time period according to rounding time span, peak acceleration, maximum deceleration, maximum acceleration and the target velocity of each time period specifically comprises: with each time period A _iRounding time span T _i', formula (5), (7), (8), (9) target velocity f, the peak acceleration A, maximum deceleration D and the maximum acceleration J substitution system of equations (1) that obtain respectively obtain each time period A _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆With each time period A _iRounding time span T _i', target velocity f, peak acceleration A, maximum deceleration D, maximum acceleration J and each time period A _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆Substitution system of equations (2) obtains each time period A _iCorresponding length of curve l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇

Wherein, the step that obtains the displacement of S type curve corresponding to the time point of S type curve according to length of curve corresponding to each time period specifically comprises: obtain the time point of S type curve and the time period A at time point place according to system of equations (2) _iCorresponding starting point is t constantly _I-1Between curve distance, specific as follows shown in:

$\left\{\begin{array}{cc}{l}_1^{\&prime;}=f_{s}t+\frac{1}{6}{\mathrm{Jt}}^3& (0\&le;t<t_1)\\ l_2^{\&prime;}=f_1(t-t_1)+\frac{1}{2}A{(t-t_1)}^2& (t_1\&le;t<t_2)\\ l_3^{\&prime;}=f_2(t-t_2)+\frac{1}{2}A{(t-t_2)}^2-\frac{1}{6}J{(t-t_2)}^3& (t_2\&le;t<t_3)\\ l_4^{\&prime;}=f_3(t-t_3)& (t_3\&le;t<t_4)\\ l_5^{\&prime;}=f_4(t-t_4)-\frac{1}{6}J{(t-t_4)}^3& (t_4\&le;t<t_5)\\ l_6^{\&prime;}=f_5(t-t_5)-\frac{1}{2}D{(t-t_5)}^2& (t_5\&le;t<t_6)\\ l_7^{\&prime;}=f_6(t-t_6)-\frac{1}{2}D{(t-t_6)}^2+\frac{1}{6}J{(t-t_6)}^3& (t_6\&le;t<t_7)\end{array}\right.---\left(10\right)$

Wherein, t represents the time point of S type curve, l _iThe time point t of ' expression S type curve and the time period A at time point t place _iCorresponding starting point is t constantly _I-1Between curve distance, t _iRepresent each time period A _iTerminal point constantly, i=1,2 ..., 7;

According to each time period A _iCorresponding length of curve, the time point t of S type curve and the time period A at time point t place _iCorresponding starting point is t constantly _I-1Between curve distance l (t) obtain the displacement of S type curve corresponding to time point t, specific as follows shown in:

$L\left(t\right)=\left\{\begin{array}{cc}{l}_1^{\&prime;}& (0\&le;t<t_1)\\ l_1+l_2^{\&prime;}& (t_1\&le;t<t_2)\\ l_1+l_2+l_3^{\&prime;}& (t_2\&le;t<t_3)\\ l_1+l_2+l_3+l_4^{\&prime;}& (t_3\&le;t<t_4)\\ l_1+l_2+l_3+l_4+l_5^{\&prime;}& (t_4\&le;t<t_5)\\ l_1+l_2+l_3+l_4+l_5+l_6^{\&prime;}& (t_5\&le;t<t_6)\\ l_1+l_2+l_3+l_4+l_5+l_6+l_7^{\&prime;}& (t_6\&le;t<t_7)\end{array}\right.---\left(11\right)$

The displacement of the S type curve that wherein, the time point t of L (t) expression S type curve is corresponding.

For solving the problems of the technologies described above, another aspect of the present invention is: a kind of device that obtains the S type curve of digital control system is provided, comprise: time span rounding module is used for the original time length of each time period of the S type curve of digital control system is carried out rounding and obtained the rounding time span of each corresponding time period; The parameter of curve acquisition module is used for peak acceleration, maximum deceleration, maximum acceleration and target velocity according to the rounding time span acquisition S type curve of each time period; The length of curve acquisition module is used for obtaining length of curve corresponding to each time period according to rounding time span, peak acceleration, maximum deceleration, maximum acceleration and the target velocity of each time period; The curve displacement acquisition module is used for the displacement according to S type curve corresponding to the time point of length of curve acquisition S type curve corresponding to each time period.

Wherein, time span rounding module specifically comprises: original time length acquiring unit, and for each time period A that obtains S type curve _iThe original time length T _i, wherein, each time period A _iBe specially: add boost phase A ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆And subtract decelerating phase A ₇, each time period A _iOriginal time length be shown below:

T _i=n _i·T+Δt _i

Wherein, T _iExpression original time length, n _iBe integer, T is interpolation cycle, Δ t _iExpression is less than the time span of an interpolation cycle T, 0＜Δ t _i＜T, i=1,2 ..., 7;

Rounding time span acquiring unit is used for each time period A _iThe original time length T _iIn the time span Δ t less than an interpolation cycle T _iRounding is that an interpolation cycle T obtains each time period A _iThe rounding time span, wherein, each time period A _iThe rounding time span be shown below:

T _i′=(n _i+1)·T

Wherein, T _i' expression rounding time span.

Wherein, the parameter of curve acquisition module specifically comprises: the target velocity acquiring unit is used for according to each time period A _iRounding time span T _i', peak acceleration, maximum deceleration, maximum acceleration, target velocity and each time period A _iSpeed and the relation between the length of curve of corresponding section end point obtain respectively following system of equations:

Each time period A _iThe rate equation group (1) of corresponding section end point:

$\left\{\begin{array}{c}{f}_1=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\&prime;2}\\ f_2=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\&prime;2}+{\mathrm{AT}}_2^{\&prime;}\\ f_3=f\\ f_4=f\\ f_5=f-\frac{1}{2}{\mathrm{JT}}_5^{\&prime;2}\\ f_6=f-\frac{1}{2}{\mathrm{JT}}_5^{\&prime;2}-{\mathrm{DT}}_6^{\&prime;}\end{array}\right.---\left(1\right)$

The length of curve system of equations (2) that each time period is corresponding:

$\left\{\begin{array}{c}{l}_1=f_s{T}_1^{\&prime;}+\frac{1}{6}{\mathrm{JT}}_1^{\&prime;3}\\ l_2=f_1{T}_2^{\&prime;}+\frac{1}{2}{\mathrm{AT}}_2^{\&prime;2}\\ l_3=f_2{T}_3^{\&prime;}+\frac{1}{2}{\mathrm{AT}}_3^{\&prime;2}-\frac{1}{6}{\mathrm{JT}}_3^{\&prime;3}\\ l_4=f_3{T}_4^{\&prime;}\\ l_5=f_4{T}_5^{\&prime;}-\frac{1}{6}{\mathrm{JT}}_5^{\&prime;2}\\ l_6=f_5{T}_6^{\&prime;}-\frac{1}{2}{\mathrm{DT}}_6^{\&prime;2}\\ l_7=l_6{T}_7^{\&prime;}-\frac{1}{2}{\mathrm{DT}}_7^{\&prime;2}+\frac{1}{6}{\mathrm{JT}}_7^{\&prime;3}\end{array}\right.---\left(2\right)$

Wherein, f ₁, f ₂, f ₃, f ₄, f ₅, f ₆Expression adds boost phase A respectively ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆The speed of corresponding section end point, f _sThe initial velocity of expression S type curve, f represents the target velocity of S type curve, l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇Expression adds boost phase A respectively ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆, subtract decelerating phase A ₇Corresponding length of curve, A represents peak acceleration, and D represents maximum deceleration, and J represents maximum acceleration;

The target velocity acquiring unit also is used for according to each time period A _iCorresponding length of curve and the relation of S type curve total length obtain following formula:

L=l ₁+l ₂+l ₃+l ₄+l ₅+l ₆+l ₇ （3）

Wherein, L represents S type curve total length;

The target velocity acquiring unit also is used for described system of equations (1), (2) substitution formula (3) are obtained following formula:

$L=(T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;})(\frac{f}{2}+f_s)+{\mathrm{fT}}_4^{\&prime;}+(T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;})(\frac{f}{2}+f_e)---\left(4\right)$

The target velocity acquiring unit also is used for obtaining target velocity f according to formula (4), shown in the formula specific as follows:

$f=\frac{L-(T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;})f_s-(T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;})f_e}{\frac{T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;}+T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;}}{2}+T_4^{\&prime;}}---\left(5\right)$

Acceleration obtainment unit is used for according to each time period A _iRounding time span T _i' and peak acceleration A, maximum deceleration D, maximum acceleration J, target velocity f between relation obtain following system of equations:

$\left\{\begin{array}{c}{T}_1^{\&prime;}=T_3^{\&prime;}=\frac{A}{J}\\ T_5^{\&prime;}=T_7^{\&prime;}=\frac{D}{J}\\ T_2^{\&prime;}=\frac{f-f_s}{A}-\frac{A}{J}\\ T_6^{\&prime;}=\frac{f-f_e}{D}-\frac{D}{J}\end{array}\right.---\left(6\right)$

Wherein, f _eThe terminal velocity of expression S type curve;

Acceleration obtainment unit also is used for obtaining peak acceleration A, maximum deceleration D, maximum acceleration J according to system of equations (6), respectively as following various shown in:

$A=\frac{f-f_s}{T_1^{\&prime;}+T_2^{\&prime;}}---\left(7\right),$ $D=\frac{f-f_e}{T_5^{\&prime;}+T_6^{\&prime;}}---\left(8\right)$

$J=\frac{f-f_s}{(T_1^{\&prime;}+T_2^{\&prime;})T_1^{\&prime;}}=\frac{f-f_e}{(T_5^{\&prime;}+T_6^{\&prime;})T_5^{\&prime;}}---\left(9\right).$

Wherein, the length of curve acquisition module specifically comprises: the last spot speed acquiring unit of section is used for each time period A _iRounding time span T _i', target velocity f, peak acceleration A, maximum deceleration D and maximum acceleration J substitution system of equations (1) obtain each time period A _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆Time step curve length acquiring unit is used for each time period A _iRounding time span T _i', target velocity f, peak acceleration A, maximum deceleration D, maximum acceleration J and each time period A _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆Substitution system of equations (2) obtains each time period A _iCorresponding length of curve l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇

Wherein, the curve displacement acquisition module specifically comprises: the curve distance acquiring unit is used for obtaining the time point of S type curve and the time period A at time point place according to system of equations (2) _iCorresponding starting point is t constantly _I-1Between curve distance, specific as follows shown in:

$\left\{\begin{array}{cc}{l}_1^{\&prime;}=f_{s}t+\frac{1}{6}{\mathrm{Jt}}^3& (0\&le;t<t_1)\\ l_2^{\&prime;}=f_1(t-t_1)+\frac{1}{2}A{(t-t_1)}^2& (t_1\&le;t<t_2)\\ l_3^{\&prime;}=f_2(t-t_2)+\frac{1}{2}A{(t-t_2)}^2-\frac{1}{6}J{(t-t_2)}^3& (t_2\&le;t<t_3)\\ l_4^{\&prime;}=f_3(t-t_3)& (t_3\&le;t<t_4)\\ l_5^{\&prime;}=f_4(t-t_4)-\frac{1}{6}J{(t-t_4)}^3& (t_4\&le;t<t_5)\\ l_6^{\&prime;}=f_5(t-t_5)-\frac{1}{2}D{(t-t_5)}^2& (t_5\&le;t<t_6)\\ l_7^{\&prime;}=f_6(t-t_6)-\frac{1}{2}D{(t-t_6)}^2+\frac{1}{6}J{(t-t_6)}^3& (t_6\&le;t<t_7)\end{array}\right.---\left(10\right)$

Wherein, t represents the time point of S type curve, l _iThe time point t of ' expression S type curve and the time period A at time point t place _iCorresponding starting point is t constantly _I-1Between curve distance, t _iRepresent each time period A _iTerminal point constantly, i=1,2 ..., 7;

The curve displacement acquiring unit is used for according to each time period A _iCorresponding length of curve, the time point t of S type curve and the time period A at time point t place _iThe curve distance l (t) of corresponding starting point between constantly obtains the displacement of S type curve corresponding to time point t, specific as follows shown in:

$L\left(t\right)=\left\{\begin{array}{cc}{l}_1^{\&prime;}& (0\&le;t<t_1)\\ l_1+l_2^{\&prime;}& (t_1\&le;t<t_2)\\ l_1+l_2+l_3^{\&prime;}& (t_2\&le;t<t_3)\\ l_1+l_2+l_3+l_4^{\&prime;}& (t_3\&le;t<t_4)\\ l_1+l_2+l_3+l_4+l_5^{\&prime;}& (t_4\&le;t<t_5)\\ l_1+l_2+l_3+l_4+l_5+l_6^{\&prime;}& (t_5\&le;t<t_6)\\ l_1+l_2+l_3+l_4+l_5+l_6+l_7^{\&prime;}& (t_6\&le;t<t_7)\end{array}\right.---\left(11\right)$

The displacement of the S type curve that wherein, the time point of L (t) expression S type curve is corresponding.

The invention has the beneficial effects as follows: be different from the situation of prior art, embodiment of the present invention is carried out the rounding time span that rounding obtains each corresponding time period by the original time length to each time period of the S type curve of digital control system; Be peak acceleration, maximum deceleration, maximum acceleration and the target velocity that the rounding time span of each time period of interpolation cycle integral multiple obtains S type curve according to time span, improve the degree of accuracy of the parameter value such as peak acceleration; Further rounding time span, peak acceleration, maximum deceleration, maximum acceleration and the target velocity according to each time period obtains length of curve corresponding to each time period; Obtain at last the displacement corresponding to time point of S type curve according to length of curve corresponding to each time period, can improve the computational accuracy of deceleration planning, solve the jitter problem in the process.

Description of drawings

Fig. 1 is the process flow diagram of method one embodiment of the present invention's S type curve of obtaining digital control system;

Fig. 2 carries out the process flow diagram that rounding obtains the rounding time span to original time length in method one embodiment of the present invention's S type curve of obtaining digital control system;

Fig. 3 is the process flow diagram that obtains peak acceleration, maximum deceleration, maximum acceleration and target velocity in method one embodiment of the present invention's S type curve of obtaining digital control system according to the rounding time span;

Fig. 4 is the process flow diagram that obtains length of curve in method one embodiment of the present invention's S type curve of obtaining digital control system according to rounding time span, peak acceleration, maximum deceleration, maximum acceleration and target velocity;

Fig. 5 is the process flow diagram that obtains the displacement of S type curve corresponding to the time point of S type curve in method one embodiment of the present invention's S type curve of obtaining digital control system according to length of curve corresponding to each time period;

Fig. 6 is the theory diagram of device one embodiment of the present invention's S type curve of obtaining digital control system;

Fig. 7 is the theory diagram of time span rounding module in device one embodiment of the present invention's S type curve of obtaining digital control system;

Fig. 8 is the theory diagram of parameter of curve acquisition module in device one embodiment of the present invention's S type curve of obtaining digital control system;

Fig. 9 is the theory diagram of length of curve acquisition module in device one embodiment of the present invention's S type curve of obtaining digital control system;

Figure 10 is the theory diagram of curve displacement acquisition module in device one embodiment of the present invention's S type curve of obtaining digital control system.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described, obviously, described embodiment only is the present invention's part embodiment, rather than whole embodiments.Based on the embodiment among the present invention, those of ordinary skills all belong to the scope of protection of the invention not making the every other embodiment that obtains under the creative work prerequisite.

See also Fig. 1, method one embodiment that the present invention obtains the S type curve of digital control system may further comprise the steps:

Step S101: original time length is carried out rounding obtain the rounding time span;

Original time length to each time period of the S type curve of digital control system is carried out the rounding time span that rounding obtains each corresponding time period.S type curve index control system is S-type in the rate curve shape in acceleration and deceleration stage.S type curve specifically comprises seven continuous time periods, lights respectively to be from S type curve: add boost phase, even boost phase, subtract boost phase, at the uniform velocity stage, acceleration and deceleration stage, even decelerating phase and the decelerating phase of subtracting; Wherein, add boost phase and refer to acceleration and the continuous time period that increases of speed in the S type curve, even boost phase refers to the time period that acceleration remains unchanged, speed constantly increases, subtract the time period that boost phase refers to that acceleration constantly reduces, speed constantly increases, at the uniform velocity the stage refers to the time period that acceleration and speed all remain unchanged, the acceleration and deceleration stage refers to that retarded velocity constantly increases, ever-reduced time period of speed, even decelerating phase refer to that retarded velocity remains unchanged, the ever-reduced time period of speed, subtracts the decelerating phase to refer to retarded velocity and ever-reduced time period of speed.The rounding time span refers to that the time span of each time period is the integral multiple of interpolation cycle.

Step S102: obtain peak acceleration, maximum deceleration, maximum acceleration and target velocity according to the rounding time span;

Further obtain peak acceleration, maximum deceleration, maximum acceleration and the target velocity of S type curve according to the rounding time span that adds seven time periods such as boost phase of step S101 acquisition.Wherein, acceleration is the derivative of acceleration.

Step S103: obtain length of curve according to rounding time span, peak acceleration, maximum deceleration, maximum acceleration and target velocity;

The rounding time span that adds seven time periods such as boost phase according to step S102 acquisition, the peak acceleration of S type curve, maximum deceleration, maximum acceleration and target velocity further obtain to add seven lengths of curve corresponding to time period such as boost phase, be the starting point moment and the curve distance of terminal point between the moment of each time period, for example even length of curve corresponding to boost phase is the starting point moment and the length of curve size of terminal point between the moment of even boost phase, the starting point of even boost phase is the terminal point moment that a time period adds boost phase constantly, and the terminal point of even boost phase is the starting point moment that the next time period subtracts boost phase constantly.

Step S104: according to the displacement of S type curve corresponding to the time point of length of curve acquisition S type curve corresponding to each time period.

Displacement according to S type curve corresponding to step S103 adding of obtaining time point that seven lengths of curve corresponding to time period such as boost phase further obtain S type curve, namely obtain the length of curve size between the starting point corresponding and S type curve of the random time point between the Origin And Destination on the S type curve, to finish the planning of S type curve.

See also Fig. 2, the present invention obtains in method one embodiment of S type curve of digital control system and original time length to be carried out rounding obtains the rounding time span and specifically comprise following substep:

Substep S1011: the original time length that obtains each time period;

Obtain each time period A of S type curve _iThe original time length T _i, namely add boost phase A ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆And subtract decelerating phase A ₇The original time length T that difference is corresponding ₁, T ₂, T ₃, T ₄, T ₅, T ₆, T ₇, the original time length T _iObtain according to digital control system parameters such as original peak acceleration, original maximum deceleration, original maximum accelerations.The original time length T _iValue formula specific as follows shown in:

T _i=n _i·T+Δt _i

Wherein, T _iExpression original time length, T is interpolation cycle, n _iBe integer, Δ t _iExpression is less than the time span of an interpolation cycle T, 0＜Δ t _i＜T, i=1,2 ..., 7.

Substep S1012: be an interpolation cycle to the time span rounding less than an interpolation cycle in the original time length of each time period.

Each time period A to S type curve _iThe original time length T _iIn the time span Δ t less than an interpolation cycle _iRounding is that an interpolation cycle T obtains each time period A _iRounding time span T _i', rounding time span T _i' be the integral multiple of interpolation cycle T time span, rounding time span T _i' value formula specific as follows shown in:

T _i′=(n _i+1)·T

Wherein, T _i' expression rounding time span, n _iBe above-mentioned original time length T _iIn n _iThe below is illustrated the rounding of original time length, for example as even boost phase A ₂Corresponding original time length T ₂=5T+ Δ t ₂(0＜Δ t ₂＜T), n ₂=5, this moment is to the original time length T ₂In the time span Δ t less than an interpolation cycle T ₂Rounding is that an interpolation cycle T obtains even boost phase A ₂Corresponding rounding time span T ₂The T=6T of '=(5+1); As Δ t ₂=0 o'clock, rounding time span T ₂'=5T.

The rounding time span T of above-mentioned acquisition _i' be the integral multiple of interpolation cycle T, meet the rule that motor is inputted take interpolation cycle T as chronomere, utilize rounding time span T _i' further adjust the parameters such as peak acceleration that obtain S type curve, can improve the computational accuracy of S type curve planning.

See also Fig. 3, the present invention obtains and obtains peak acceleration, maximum deceleration, maximum acceleration and target velocity according to the rounding time span in method one embodiment of S type curve of digital control system and specifically comprise following substep:

Substep S1021: speed and length of curve according to rounding time span, peak acceleration, maximum deceleration, maximum acceleration, target velocity and section end point obtain respectively system of equations (1), (2);

According to each time period A _iRounding time span T _i', peak acceleration A, maximum deceleration D, maximum acceleration J, target velocity f and each time period A of S type curve _iThe speed of corresponding section end point and the relation between the length of curve be rate equation group (1), the length of curve system of equations (2) put of the section of acquisition end respectively, shown in system of equations (1), (2) are specific as follows:

Each time period A _iThe rate equation group (1) of corresponding section end point:

$\left\{\begin{array}{c}{f}_1=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\&prime;2}\\ f_2=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\&prime;2}+{\mathrm{AT}}_2^{\&prime;}\\ f_3=f\\ f_4=f\\ f_5=f-\frac{1}{2}{\mathrm{JT}}_5^{\&prime;2}\\ f_6=f-\frac{1}{2}{\mathrm{JT}}_5^{\&prime;2}-{\mathrm{DT}}_6^{\&prime;}\end{array}\right.---\left(1\right)$

Each time period A _iCorresponding length of curve system of equations (2):

$\left\{\begin{array}{c}{l}_1=f_s{T}_1^{\&prime;}+\frac{1}{6}{\mathrm{JT}}_1^{\&prime;3}\\ l_2=f_1{T}_2^{\&prime;}+\frac{1}{2}{\mathrm{AT}}_2^{\&prime;2}\\ l_3=f_2{T}_3^{\&prime;}+\frac{1}{2}{\mathrm{AT}}_3^{\&prime;2}-\frac{1}{6}{\mathrm{JT}}_3^{\&prime;3}\\ l_4=f_3{T}_4^{\&prime;}\\ l_5=f_4{T}_5^{\&prime;}-\frac{1}{6}{\mathrm{JT}}_5^{\&prime;2}\\ l_6=f_5{T}_6^{\&prime;}-\frac{1}{2}{\mathrm{DT}}_6^{\&prime;2}\\ l_7=l_6{T}_7^{\&prime;}-\frac{1}{2}{\mathrm{DT}}_7^{\&prime;2}+\frac{1}{6}{\mathrm{JT}}_7^{\&prime;3}\end{array}\right.---\left(2\right)$

Wherein, f ₁, f ₂, f ₃, f ₄, f ₅, f ₆Expression adds boost phase A respectively ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆The speed of corresponding section end point, f _sThe initial velocity of expression curve, f represents the target velocity of curve, l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇Expression adds boost phase A respectively ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆, subtract decelerating phase A ₇Corresponding length of curve, A represents peak acceleration, and D represents maximum deceleration, and J represents maximum acceleration.

Substep S1022: the relation according to length of curve corresponding to each time period and curve total length obtains formula (3);

According to each time period A _iCorresponding length of curve and the relation of S type curve total length obtain formula (3) as follows:

L=l ₁+l ₂+l ₃+l ₄+l ₅+l ₆+l ₇ （3）

Wherein, L represents S type curve total length.

Substep S1023: obtain target velocity according to system of equations (1), (2) and formula (3);

Above-mentioned system of equations (1), (2) corresponding substitution formula (3) are obtained the relational expression between curve total length and rounding time span, target velocity, initial velocity and the terminal velocity, i.e. formula as follows (4):

$L=(T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;})(\frac{f}{2}+f_s)+{\mathrm{fT}}_4^{\&prime;}+(T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;})(\frac{f}{2}+f_e)---\left(4\right)$

Further obtain target velocity f according to formula (4), shown in the formula specific as follows:

$f=\frac{L-(T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;})f_s-(T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;})f_e}{\frac{T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;}+T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;}}{2}+T_4^{\&prime;}}---\left(5\right)$

With rounding time span T _i, initial velocity f _sAnd terminal velocity f _eThe above-mentioned formula of value substitution (5) can obtain the value of target velocity f.

Substep S1024: obtain peak acceleration, maximum deceleration, maximum acceleration according to the relation equation group between rounding time span and peak acceleration, maximum deceleration, maximum acceleration, the target velocity.

According to each time period A _iRounding time span T _i' and peak acceleration A, maximum deceleration D, maximum acceleration J and target velocity f between relation obtain rounding time span T _i' about the system of equations (3) of peak acceleration A, maximum deceleration D, maximum acceleration J, target velocity f:

$\left\{\begin{array}{c}{T}_1^{\&prime;}=T_3^{\&prime;}=\frac{A}{J}\\ T_5^{\&prime;}=T_7^{\&prime;}=\frac{D}{J}\\ T_2^{\&prime;}=\frac{f-f_s}{A}-\frac{A}{J}\\ T_6^{\&prime;}=\frac{f-f_e}{D}-\frac{D}{J}\end{array}\right.---\left(6\right)$

Wherein, f _eThe terminal velocity of expression S type curve;

Further obtain peak acceleration A, maximum deceleration D, maximum acceleration J according to above-mentioned system of equations (6), respectively as following various shown in:

$A=\frac{f-f_s}{T_1^{\&prime;}+T_2^{\&prime;}}---\left(7\right),$ $D=\frac{f-f_e}{T_5^{\&prime;}+T_6^{\&prime;}}---\left(8\right)$

$J=\frac{f-f_s}{(T_1^{\&prime;}+T_2^{\&prime;})T_1^{\&prime;}}=\frac{f-f_e}{(T_5^{\&prime;}+T_6^{\&prime;})T_5^{\&prime;}}---\left(9\right)$

With target velocity f, rounding time span T _i', initial velocity F _sAnd terminal velocity f _eThe above-mentioned formula of value substitution (7), (8), (9) can obtain respectively the value of peak acceleration A, maximum deceleration D and maximum acceleration J.

Utilize time span to be the rounding time span T of the integral multiple of interpolation cycle T _i' obtain target velocity f, peak acceleration A, maximum deceleration D and maximum acceleration J, can eliminate speed and the sudden change of acceleration of interpolation cycle T final step, solve the jitter problem in the process.

See also Fig. 4, the present invention obtains and obtains length of curve according to rounding time span, peak acceleration, maximum deceleration, maximum acceleration and target velocity in method one embodiment of S type curve of digital control system and specifically comprise following substep:

Substep S1031: the speed that obtains section end point according to rounding time span, target velocity, peak acceleration, maximum deceleration and maximum acceleration;

With each time period A _iRounding time span T _i', the rate equation group (1) among the above-mentioned substep S1021 of target velocity f, peak acceleration A, maximum deceleration D and maximum acceleration J substitution that obtains respectively of above-mentioned formula (5), (7), (8), (9) obtains each time period A _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆

Substep S1032: the speed according to rounding time span, target velocity, peak acceleration, maximum deceleration, maximum acceleration and section end point obtains length of curve.

Further with each time period A _iRounding time span T _i', each time period A of obtaining of target velocity f, peak acceleration A, maximum deceleration D, maximum acceleration J and step S1031 _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆Length of curve system of equations (2) among the above-mentioned substep S1021 of substitution and obtain each time period A _iCorresponding length of curve l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇

See also Fig. 5, the present invention obtains and obtains displacement corresponding to time point according to length of curve corresponding to each time period in method one embodiment of S type curve of digital control system and specifically comprise following substep:

Substep S1041: time point starting point the curve distance moment between corresponding with the time period at time point place that obtains S type curve according to system of equations (2);

With the rounding time span T in the length of curve system of equations (2) among the above-mentioned substep S1021 _i' replace with the time point of S type curve and the time period A at time point place _iCorresponding starting point is t constantly _I-1Between time span, can obtain the time point of S type curve and the time period A at time point place _iCorresponding starting point is t constantly _I-1Between curve distance, shown in the piecewise function formula (10) specific as follows:

$\left\{\begin{array}{cc}{l}_1^{\&prime;}=f_{s}t+\frac{1}{6}{\mathrm{Jt}}^3& (0\&le;t<t_1)\\ l_2^{\&prime;}=f_1(t-t_1)+\frac{1}{2}A{(t-t_1)}^2& (t_1\&le;t<t_2)\\ l_3^{\&prime;}=f_2(t-t_2)+\frac{1}{2}A{(t-t_2)}^2-\frac{1}{6}J{(t-t_2)}^3& (t_2\&le;t<t_3)\\ l_4^{\&prime;}=f_3(t-t_3)& (t_3\&le;t<t_4)\\ l_5^{\&prime;}=f_4(t-t_4)-\frac{1}{6}J{(t-t_4)}^3& (t_4\&le;t<t_5)\\ l_6^{\&prime;}=f_5(t-t_5)-\frac{1}{2}D{(t-t_5)}^2& (t_5\&le;t<t_6)\\ l_7^{\&prime;}=f_6(t-t_6)-\frac{1}{2}D{(t-t_6)}^2+\frac{1}{6}J{(t-t_6)}^3& (t_6\&le;t<t_7)\end{array}\right.---\left(10\right)$

Wherein, t represents the time point of S type curve, l _iThe time point t of ' expression S type curve and the time period A at time point t place _iCorresponding starting point is t constantly _I-1Between curve distance, t _iRepresent each time period A _iTerminal point constantly, i=1,2 ..., 7.The time point t that for example works as S type curve ₁≤ t＜t ₂The time, i.e. the time period A at time point t place _iBe even boost phase A ₂, with in the corresponding above-mentioned piecewise function formula of substitution of the value of t (10)

Obtain l ₂' value, namely obtain t and A ₂Starting point t constantly ₁Between curve distance l ₂'.

Substep S1042: obtain displacement corresponding to time point according to the curve distance of length of curve, the time point starting point corresponding with the time period at time point place between constantly.

According to each time period A _iThe time point t of the S type curve that corresponding length of curve, substep S1041 obtain and the time period A at time point t place _iCorresponding starting point is t constantly _I-1Between curve distance l (t) further obtain the displacement of S type curve corresponding to time point t, shown in the piecewise function formula specific as follows (11):

$L\left(t\right)=\left\{\begin{array}{cc}{l}_1^{\&prime;}& (0\&le;t<t_1)\\ l_1+l_2^{\&prime;}& (t_1\&le;t<t_2)\\ l_1+l_2+l_3^{\&prime;}& (t_2\&le;t<t_3)\\ l_1+l_2+l_3+l_4^{\&prime;}& (t_3\&le;t<t_4)\\ l_1+l_2+l_3+l_4+l_5^{\&prime;}& (t_4\&le;t<t_5)\\ l_1+l_2+l_3+l_4+l_5+l_6^{\&prime;}& (t_5\&le;t<t_6)\\ l_1+l_2+l_3+l_4+l_5+l_6+l_7^{\&prime;}& (t_6\&le;t<t_7)\end{array}\right.---\left(11\right)$

The displacement of the S type curve that wherein, the time point t of L (t) expression S type curve is corresponding.The time point t that for example works as S type curve ₁≤ t＜t ₂The time, will add the length of curve of boost phase and t and the A that substep S1041 obtains ₂Starting point t constantly ₁Between curve distance l ₂L in the above-mentioned piecewise function formula of ' corresponding substitution (11) ₁+ l ₂' obtain the value of L (t), namely obtain the displacement L (t) of S type curve corresponding to time point t, the displacement L (t) of S type curve is the starting point of S type curve and the curve distance between the time point t.

Relation between the displacement of the time point that obtains S type curve and S type curve be above-mentioned piecewise function formula (11) afterwards, namely finish the deceleration planning of the S type curve of digital control system.The follow-up above-mentioned piecewise function formula (11) of can utilizing of digital control system is carried out Interpolation Process, the corresponding coordinate of each step-length that obtains processing, the corresponding coordinate of each step-length is sent to servo-driver with the control servomotor, so that the input of servomotor changes according to certain rule, lathe can both rest on the given position in the situation of various processing operations rapidly and accurately.

Be appreciated that method one embodiment that the present invention obtains the S type curve of digital control system carries out the rounding time span that rounding obtains each corresponding time period by the original time length to each time period of the S type curve of digital control system; Be peak acceleration, maximum deceleration, maximum acceleration and the target velocity that the rounding time span of each time period of interpolation cycle integral multiple obtains S type curve according to time span, improve the degree of accuracy of the parameter value such as peak acceleration; Further rounding time span, peak acceleration, maximum deceleration, maximum acceleration and the target velocity according to each time period obtains length of curve corresponding to each time period; According to the displacement of S type curve corresponding to the time point of length of curve acquisition S type curve corresponding to each time period, by the way, can improve the computational accuracy of deceleration planning at last, solve the jitter problem in the process.

See also Fig. 6, device one embodiment that the present invention obtains the S type curve of digital control system comprises:

Time span rounding module 201 is used for the original time length of each time period of the S type curve of digital control system is carried out rounding and obtained the rounding time span of each corresponding time period.

Parameter of curve acquisition module 202, the rounding time span that is used for each time period of obtaining according to time span rounding module 201 further obtains peak acceleration, maximum deceleration, maximum acceleration and the target velocity of S type curve.

Length of curve acquisition module 203 further obtains length of curve corresponding to each time period for the rounding time span of each time period that obtains according to time span rounding module 201 and peak acceleration, maximum deceleration, maximum acceleration and the target velocity of parameter of curve acquisition module 202 acquisitions.

Curve displacement acquisition module 204 is used for obtaining according to length of curve corresponding to each time period that length of curve acquisition module 203 obtains the displacement of S type curve corresponding to the time point of S type curve.

See also Fig. 7, the present invention obtains that time span rounding module specifically comprises in device one embodiment of S type curve of digital control system:

Original time length acquiring unit 2011 is for each time period A that obtains S type curve _iThe original time length T _i, wherein, each time period A _iBe specially: add boost phase A ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆And subtract decelerating phase A ₇, each time period A _iOriginal time length be shown below:

T _i=n _i·T+Δt _i

Wherein, T _iExpression original time length, n _iBe integer, T is interpolation cycle, Δ t _iExpression is less than the time span of an interpolation cycle T, 0＜Δ t _i＜T, i=1,2 ..., 7;

Rounding time span acquiring unit 2012 is used for each time period A that original time length acquiring unit 2011 is obtained _iThe original time length T _iIn the time span Δ t less than an interpolation cycle T _iRounding is that an interpolation cycle T obtains each time period A _iThe rounding time span, wherein, each time period A _iThe rounding time span be shown below:

T _i′=(n _i+1)·T

Wherein, T _i' expression rounding time span.

See also Fig. 8, the present invention obtains that the parameter of curve acquisition module specifically comprises in device one embodiment of S type curve of digital control system:

Target velocity acquiring unit 2021 is used for each time period A that obtains according to rounding time span acquiring unit 2012 _iRounding time span T _i', peak acceleration, maximum deceleration, maximum acceleration, target velocity and each time period A _iSpeed and the relation between the length of curve of corresponding section end point obtain respectively following system of equations:

Each time period A _iThe rate equation group (1) of corresponding section end point:

$\left\{\begin{array}{c}{f}_1=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\&prime;2}\\ f_2=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\&prime;2}+{\mathrm{AT}}_2^{\&prime;}\\ f_3=f\\ f_4=f\\ f_5=f-\frac{1}{2}{\mathrm{JT}}_5^{\&prime;2}\\ f_6=f-\frac{1}{2}{\mathrm{JT}}_5^{\&prime;2}-{\mathrm{DT}}_6^{\&prime;}\end{array}\right.---\left(1\right)$

The length of curve system of equations (2) that each time period is corresponding:

$\left\{\begin{array}{c}{l}_1=f_s{T}_1^{\&prime;}+\frac{1}{6}{\mathrm{JT}}_1^{\&prime;3}\\ l_2=f_1{T}_2^{\&prime;}+\frac{1}{2}{\mathrm{AT}}_2^{\&prime;2}\\ l_3=f_2{T}_3^{\&prime;}+\frac{1}{2}{\mathrm{AT}}_3^{\&prime;2}-\frac{1}{6}{\mathrm{JT}}_3^{\&prime;3}\\ l_4=f_3{T}_4^{\&prime;}\\ l_5=f_4{T}_5^{\&prime;}-\frac{1}{6}{\mathrm{JT}}_5^{\&prime;2}\\ l_6=f_5{T}_6^{\&prime;}-\frac{1}{2}{\mathrm{DT}}_6^{\&prime;2}\\ l_7=l_6{T}_7^{\&prime;}-\frac{1}{2}{\mathrm{DT}}_7^{\&prime;2}+\frac{1}{6}{\mathrm{JT}}_7^{\&prime;3}\end{array}\right.---\left(2\right)$

Wherein, f ₁, f ₂, f ₃, f ₄, f ₅, f ₆Expression adds boost phase A respectively ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆The speed of corresponding section end point, f _sThe initial velocity of expression S type curve, f represents the target velocity of S type curve, l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇Expression adds boost phase A respectively ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆, subtract decelerating phase A ₇Corresponding length of curve, A represents peak acceleration, and D represents maximum deceleration, and J represents maximum acceleration;

Target velocity acquiring unit 2021 also is used for according to each time period A _iCorresponding length of curve and the relation of S type curve total length obtain following formula:

L=l ₁+l ₂+l ₃+l ₄+l ₅+l ₆+l ₇ （3）

Wherein, L represents S type curve total length;

Target velocity acquiring unit 2021 also is used for system of equations (1), (2) substitution formula (3) are obtained following formula (4):

$L=(T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;})(\frac{f}{2}+f_s)+{\mathrm{fT}}_4^{\&prime;}+(T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;})(\frac{f}{2}+f_e)---\left(4\right)$

Target velocity acquiring unit 2021 also is used for obtaining target velocity f according to formula (4), shown in the formula specific as follows (5):

$f=\frac{L-(T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;})f_s-(T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;})f_e}{\frac{T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;}+T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;}}{2}+T_4^{\&prime;}}---\left(5\right)$

Acceleration obtainment unit 2022 is used for each time period A that obtains according to rounding time span acquiring unit 2012 _iRounding time span T _i' and peak acceleration A, maximum deceleration D, maximum acceleration J, target velocity f between relation obtain following system of equations:

$\left\{\begin{array}{c}{T}_1^{\&prime;}=T_3^{\&prime;}=\frac{A}{J}\\ T_5^{\&prime;}=T_7^{\&prime;}=\frac{D}{J}\\ T_2^{\&prime;}=\frac{f-f_s}{A}-\frac{A}{J}\\ T_6^{\&prime;}=\frac{f-f_e}{D}-\frac{D}{J}\end{array}\right.---\left(6\right)$

Wherein, f _eThe terminal velocity of expression S type curve;

Acceleration obtainment unit 2022 also is used for obtaining peak acceleration A, maximum deceleration D, maximum acceleration J according to system of equations (6), respectively as following various shown in:

$A=\frac{f-f_s}{T_1^{\&prime;}+T_2^{\&prime;}}---\left(7\right),$ $D=\frac{f-f_e}{T_5^{\&prime;}+T_6^{\&prime;}}---\left(8\right)$

$J=\frac{f-f_s}{(T_1^{\&prime;}+T_2^{\&prime;})T_1^{\&prime;}}=\frac{f-f_e}{(T_5^{\&prime;}+T_6^{\&prime;})T_5^{\&prime;}}---\left(9\right)$

Acceleration obtainment unit 2022 is further with target velocity f, rounding time span T _i', initial velocity f _sAnd terminal velocity f _eThe above-mentioned formula of value substitution (7), (8), (9) can obtain respectively the value of peak acceleration A, maximum deceleration D and maximum acceleration J.

See also Fig. 9, the present invention obtains that the length of curve acquisition module specifically comprises in device one embodiment of S type curve of digital control system:

The last spot speed acquiring unit 2031 of section is used for each time period A that rounding time span acquiring unit 2012 is obtained _iRounding time span T _i', the target velocity f that obtains of target velocity acquiring unit 2021, peak acceleration A, maximum deceleration D and the maximum acceleration J substitution system of equations (1) that acceleration obtainment unit 2022 obtains further obtain each time period A _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆

Time step curve length acquiring unit 2032 is used for each time period A that rounding time span acquiring unit 2012 is obtained _iRounding time span T _i', each time period A of obtaining of target velocity f that target velocity acquiring unit 2021 obtains, the last spot speed acquiring unit 2031 of peak acceleration A, maximum deceleration D, maximum acceleration J and section that acceleration obtainment unit 2022 obtains _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆Substitution system of equations (2) further obtains each time period A _iCorresponding length of curve l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇

See also Figure 10, the present invention obtains that the curve displacement acquisition module specifically comprises in device one embodiment of S type curve of digital control system:

Curve distance acquiring unit 2041 is used for obtaining the time point of S type curve and the time period A at time point place according to system of equations (2) _iCorresponding starting point is t constantly _I-1Between curve distance, specific as follows shown in:

$\left\{\begin{array}{cc}{l}_1^{\&prime;}=f_{s}t+\frac{1}{6}{\mathrm{Jt}}^3& (0\&le;t<t_1)\\ l_2^{\&prime;}=f_1(t-t_1)+\frac{1}{2}A{(t-t_1)}^2& (t_1\&le;t<t_2)\\ l_3^{\&prime;}=f_2(t-t_2)+\frac{1}{2}A{(t-t_2)}^2-\frac{1}{6}J{(t-t_2)}^3& (t_2\&le;t<t_3)\\ l_4^{\&prime;}=f_3(t-t_3)& (t_3\&le;t<t_4)\\ l_5^{\&prime;}=f_4(t-t_4)-\frac{1}{6}J{(t-t_4)}^3& (t_4\&le;t<t_5)\\ l_6^{\&prime;}=f_5(t-t_5)-\frac{1}{2}D{(t-t_5)}^2& (t_5\&le;t<t_6)\\ l_7^{\&prime;}=f_6(t-t_6)-\frac{1}{2}D{(t-t_6)}^2+\frac{1}{6}J{(t-t_6)}^3& (t_6\&le;t<t_7)\end{array}\right.---\left(10\right)$

Wherein, t represents the time point of S type curve, l _iThe time point t of ' expression S type curve and the time period A at time point t place _iCorresponding starting point is t constantly _I-1Between curve distance, t _iRepresent each time period A _iTerminal point constantly, i=1,2 ..., 7.The time point t that for example works as S type curve ₁≤ t＜t ₂The time, i.e. the time period A at time point t place _iBe even boost phase A ₂, with in the corresponding above-mentioned piecewise function formula of substitution of the value of t (10)

Obtain l ₂' value, namely obtain t and A ₂Starting point t constantly ₁Between curve distance l ₂'.

Curve displacement acquiring unit 2042 is used for each time period A that obtains according to time step curve length acquiring unit 2032 _iThe time point t of the S type curve that corresponding length of curve, curve distance acquiring unit 2041 obtain and the time period A at time point t place _iThe curve distance l (t) of corresponding starting point between constantly further obtains the displacement of S type curve corresponding to time point t, specific as follows shown in:

$L\left(t\right)=\left\{\begin{array}{cc}{l}_1^{\&prime;}& (0\&le;t<t_1)\\ l_1+l_2^{\&prime;}& (t_1\&le;t<t_2)\\ l_1+l_2+l_3^{\&prime;}& (t_2\&le;t<t_3)\\ l_1+l_2+l_3+l_4^{\&prime;}& (t_3\&le;t<t_4)\\ l_1+l_2+l_3+l_4+l_5^{\&prime;}& (t_4\&le;t<t_5)\\ l_1+l_2+l_3+l_4+l_5+l_6^{\&prime;}& (t_5\&le;t<t_6)\\ l_1+l_2+l_3+l_4+l_5+l_6+l_7^{\&prime;}& (t_6\&le;t<t_7)\end{array}\right.---\left(11\right)$

The displacement of the S type curve that wherein, the time point of L (t) expression S type curve is corresponding.The time point t that for example works as S type curve ₁≤ t＜t ₂The time, will add the length of curve of boost phase and t and the A that substep S1041 obtains ₂Starting point t constantly ₁Between curve distance l ₂L in the above-mentioned piecewise function formula of ' corresponding substitution (11) _i+ l ₂' obtain the value of L (t), namely obtain the displacement L (t) of S type curve corresponding to time point t, the displacement L (t) of S type curve is the starting point of S type curve and the curve distance between the time point t.

Be appreciated that device one embodiment that the present invention obtains the S type curve of digital control system carries out the rounding time span that rounding obtains each corresponding time period by the original time length of each time period of the S type curve of 201 pairs of digital control systems of time span rounding module; Parameter of curve acquisition module 202 is peak acceleration, maximum deceleration, maximum acceleration and the target velocity that the rounding time span of each time period of interpolation cycle integral multiple obtains S type curve according to time span, the degree of accuracy of the parameter values such as raising peak acceleration; Length of curve acquisition module 203 further obtains length of curve corresponding to each time period according to rounding time span, peak acceleration, maximum deceleration, maximum acceleration and the target velocity of each time period; Curve displacement acquisition module 204 according to the displacement of S type curve corresponding to the time point of length of curve acquisition S type curve corresponding to each time period, by the way, can improve the computational accuracy of deceleration planning at last, solves the jitter problem in the process.

The above only is embodiments of the present invention; be not so limit claim of the present invention; every equivalent structure or equivalent flow process conversion that utilizes instructions of the present invention and accompanying drawing content to do; or directly or indirectly be used in other relevant technical fields, all in like manner be included in the scope of patent protection of the present invention.

Claims (10)

1. a method of obtaining the S type curve of digital control system is characterized in that, comprising:

Original time length to each time period of the S type curve of digital control system is carried out the rounding time span that rounding obtains each corresponding time period;

Obtain peak acceleration, maximum deceleration, maximum acceleration and the target velocity of S type curve according to the rounding time span of described each time period;

Rounding time span, peak acceleration, maximum deceleration, maximum acceleration and target velocity according to described each time period obtain length of curve corresponding to each time period;

According to the displacement of S type curve corresponding to the time point of length of curve acquisition S type curve corresponding to described each time period, to finish the planning of described S type curve.

2. method according to claim 1 is characterized in that, the original time length of each time period of described S type curve to digital control system is carried out the step that rounding obtains the rounding time span of each corresponding time period and specifically comprised:

Obtain each time period A of described S type curve _iThe original time length T _i, wherein, described each time period A _iBe specially: add boost phase A ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆And subtract decelerating phase A ₇, described each time period A _iOriginal time length be shown below:

T _i=n _i·T+Δt _i

Wherein, T _iRepresent described original time length, n _iBe integer, T is interpolation cycle, Δ t _iExpression is less than the time span of a described interpolation cycle T, 0＜Δ t _i＜T, i=1,2 ..., 7;

To described each time period A _iThe original time length T _iIn the time span Δ t less than an interpolation cycle T _iRounding is that an interpolation cycle T obtains each time period A _iThe rounding time span, wherein, described each time period A _iThe rounding time span be shown below:

T _i′=(n _i+1)·T

Wherein, T _iThe described rounding time span of ' expression.

3. method according to claim 2 is characterized in that, the step that described rounding time span according to each time period obtains peak acceleration, maximum deceleration, maximum acceleration and the target velocity of S type curve specifically comprises:

According to described each time period A _iRounding time span T _i', peak acceleration, maximum deceleration, maximum acceleration, target velocity and each time period A _iSpeed and the relation between the length of curve of corresponding section end point obtain respectively following system of equations:

Described each time period A _iThe rate equation group (1) of corresponding section end point:

$\left\{\begin{array}{c}{f}_1=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\&prime;2}\\ f_2=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\&prime;2}+{\mathrm{AT}}_2^{\&prime;}\\ f_3=f\\ f_4=f\\ f_5=f-\frac{1}{2}{\mathrm{JT}}_5^{\&prime;2}\\ f_6=f-\frac{1}{2}{\mathrm{JT}}_5^{\&prime;2}-{\mathrm{DT}}_6^{\&prime;}\end{array}\right.---\left(1\right)$

The length of curve system of equations (2) that described each time period is corresponding:

$\left\{\begin{array}{c}{l}_1=f_s{T}_1^{\&prime;}+\frac{1}{6}{\mathrm{JT}}_1^{\&prime;3}\\ l_2=f_1{T}_2^{\&prime;}+\frac{1}{2}{\mathrm{AT}}_2^{\&prime;2}\\ l_3=f_2{T}_3^{\&prime;}+\frac{1}{2}{\mathrm{AT}}_3^{\&prime;2}-\frac{1}{6}{\mathrm{JT}}_3^{\&prime;3}\\ l_4=f_3{T}_4^{\&prime;}\\ l_5=f_4{T}_5^{\&prime;}-\frac{1}{6}{\mathrm{JT}}_5^{\&prime;2}\\ l_6=f_5{T}_6^{\&prime;}-\frac{1}{2}{\mathrm{DT}}_6^{\&prime;2}\\ l_7=l_6{T}_7^{\&prime;}-\frac{1}{2}{\mathrm{DT}}_7^{\&prime;2}+\frac{1}{6}{\mathrm{JT}}_7^{\&prime;3}\end{array}\right.---\left(2\right)$

Wherein, f ₁, f ₂, f ₃, f ₄, f ₅, f ₆Represent respectively the described boost phase A that adds ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆The speed of corresponding section end point, F _sThe initial velocity that represents described S type curve, f represent the target velocity of described S type curve, l ₁, l ₂, l ₃, l ₄, l ₅l ₆, l ₇Represent respectively the described boost phase A that adds ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆, subtract decelerating phase A ₇Corresponding length of curve, A represents described peak acceleration, and D represents described maximum deceleration, and J represents described maximum acceleration;

According to described each time period A _iCorresponding length of curve and the relation of S type curve total length obtain following formula:

L=l ₁+l ₂+l ₃+l ₄+l ₅+l ₆+l ₇ （3）

Wherein, L represents described S type curve total length;

Described system of equations (1), (2) substitution formula (3) are obtained following formula:

$L=(T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;})(\frac{f}{2}+f_s)+{\mathrm{fT}}_4^{\&prime;}+(T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;})(\frac{f}{2}+f_e)---\left(4\right)$

Further obtain target velocity f according to described formula (4), shown in the formula specific as follows:

$f=\frac{L-(T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;})f_s-(T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;})f_e}{\frac{T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;}+T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;}}{2}+T_4^{\&prime;}}---\left(5\right)$

According to described each time period A _iRounding time span T _i' and peak acceleration A, maximum deceleration D, maximum acceleration J, target velocity f between relation obtain following system of equations:

$\left\{\begin{array}{c}{T}_1^{\&prime;}=T_3^{\&prime;}=\frac{A}{J}\\ T_5^{\&prime;}=T_7^{\&prime;}=\frac{D}{J}\\ T_2^{\&prime;}=\frac{f-f_s}{A}-\frac{A}{J}\\ T_6^{\&prime;}=\frac{f-f_e}{D}-\frac{D}{J}\end{array}\right.---\left(6\right)$

Wherein, f _eThe terminal velocity that represents described S type curve;

Further obtain peak acceleration A, maximum deceleration D, maximum acceleration J according to described system of equations (6), respectively as following various shown in:

$A=\frac{f-f_s}{T_1^{\&prime;}+T_2^{\&prime;}}---\left(7\right),$ $D=\frac{f-f_e}{T_5^{\&prime;}+T_6^{\&prime;}}---\left(8\right)$

$J=\frac{f-f_s}{(T_1^{\&prime;}+T_2^{\&prime;})T_1^{\&prime;}}=\frac{f-f_e}{(T_5^{\&prime;}+T_6^{\&prime;})T_5^{\&prime;}}---\left(9\right).$

4. method according to claim 3, it is characterized in that the step that described rounding time span according to each time period, peak acceleration, maximum deceleration, maximum acceleration and target velocity obtain length of curve corresponding to each time period specifically comprises:

With described each time period A _iRounding time span T _i', formula (5), (7), (8), (9) target velocity f, the peak acceleration A, maximum deceleration D and the maximum acceleration J substitution system of equations (1) that obtain respectively obtain each time period A _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆

With described each time period A _iRounding time span T _i', target velocity f, peak acceleration A, maximum deceleration D, maximum acceleration J and each time period A _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆Substitution system of equations (2) obtains each time period A _iCorresponding length of curve l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇

5. method according to claim 4 is characterized in that, the described step that obtains the displacement of S type curve corresponding to the time point of S type curve according to length of curve corresponding to each time period specifically comprises:

Obtain the time point of S type curve and the time period A at time point place according to described system of equations (2) _iCorresponding starting point is t constantly _I-1Between curve distance, specific as follows shown in:

$\left\{\begin{array}{cc}{l}_1^{\&prime;}=f_{s}t+\frac{1}{6}{\mathrm{Jt}}^3& (0\&le;t<t_1)\\ l_2^{\&prime;}=f_1(t-t_1)+\frac{1}{2}A{(t-t_1)}^2& (t_1\&le;t<t_2)\\ l_3^{\&prime;}=f_2(t-t_2)+\frac{1}{2}A{(t-t_2)}^2-\frac{1}{6}J{(t-t_2)}^3& (t_2\&le;t<t_3)\\ l_4^{\&prime;}=f_3(t-t_3)& (t_3\&le;t<t_4)\\ l_5^{\&prime;}=f_4(t-t_4)-\frac{1}{6}J{(t-t_4)}^3& (t_4\&le;t<t_5)\\ l_6^{\&prime;}=f_5(t-t_5)-\frac{1}{2}D{(t-t_5)}^2& (t_5\&le;t<t_6)\\ l_7^{\&prime;}=f_6(t-t_6)-\frac{1}{2}D{(t-t_6)}^2+\frac{1}{6}J{(t-t_6)}^3& (t_6\&le;t<t_7)\end{array}\right.---\left(10\right)$

Wherein, t represents the time point of described S type curve, l _iThe time point t of the described S type curve of ' expression and the time period A at time point t place _iCorresponding starting point is t constantly _I-1Between curve distance, t _iRepresent described each time period A _iTerminal point constantly, i=1,2 ..., 7;

According to described each time period A _iCorresponding length of curve, the time point t of S type curve and the time period A at time point t place _iCorresponding starting point is t constantly _I-1Between curve distance l (t) obtain the displacement of S type curve corresponding to time point t, specific as follows shown in:

$L\left(t\right)=\left\{\begin{array}{cc}{l}_1^{\&prime;}& (0\&le;t<t_1)\\ l_1+l_2^{\&prime;}& (t_1\&le;t<t_2)\\ l_1+l_2+l_3^{\&prime;}& (t_2\&le;t<t_3)\\ l_1+l_2+l_3+l_4^{\&prime;}& (t_3\&le;t<t_4)\\ l_1+l_2+l_3+l_4+l_5^{\&prime;}& (t_4\&le;t<t_5)\\ l_1+l_2+l_3+l_4+l_5+l_6^{\&prime;}& (t_5\&le;t<t_6)\\ l_1+l_2+l_3+l_4+l_5+l_6+l_7^{\&prime;}& (t_6\&le;t<t_7)\end{array}\right.---\left(11\right)$

The displacement of the S type curve that wherein, the time point t of the described S type curve of L (t) expression is corresponding.

6. a device that obtains the S type curve of digital control system is characterized in that, comprising:

Time span rounding module is used for the original time length of each time period of the S type curve of digital control system is carried out rounding and obtained the rounding time span of each corresponding time period;

The parameter of curve acquisition module is used for peak acceleration, maximum deceleration, maximum acceleration and target velocity according to the rounding time span acquisition S type curve of described each time period;

The length of curve acquisition module is used for obtaining length of curve corresponding to each time period according to rounding time span, peak acceleration, maximum deceleration, maximum acceleration and the target velocity of described each time period;

The curve displacement acquisition module is used for the displacement according to S type curve corresponding to the time point of length of curve acquisition S type curve corresponding to described each time period.

7. device according to claim 6 is characterized in that, described time span rounding module specifically comprises:

Original time length acquiring unit is for each time period A that obtains described S type curve _iThe original time length T _i, wherein, described each time period A _iBe specially: add boost phase A ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆And subtract decelerating phase A ₇, described each time period A _iOriginal time length be shown below:

T _i=n _i·T+Δt _i

Wherein, T _iRepresent described original time length, n _iBe integer, T is interpolation cycle, Δ t _iExpression is less than the time span of a described interpolation cycle T, 0＜Δ t _i＜T, i=1,2 ..., 7;

Rounding time span acquiring unit is used for described each time period A _iThe original time length T _iIn the time span Δ t less than an interpolation cycle T _iRounding is that an interpolation cycle T obtains each time period A _iThe rounding time span, wherein, described each time period A _iThe rounding time span be shown below:

T _i′=(n _i+1)·T

Wherein, T _iThe described rounding time span of ' expression.

8. device according to claim 7 is characterized in that, described parameter of curve acquisition module specifically comprises:

The target velocity acquiring unit is used for according to described each time period A _iRounding time span T _i', peak acceleration, maximum deceleration, maximum acceleration, target velocity and each time period A _iSpeed and the relation between the length of curve of corresponding section end point obtain respectively following system of equations:

Described each time period A _iThe rate equation group (1) of corresponding section end point:

$\left\{\begin{array}{c}{f}_1=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\&prime;2}\\ f_2=f_s+\frac{1}{2}{\mathrm{JT}}_1^{\&prime;2}+{\mathrm{AT}}_2^{\&prime;}\\ f_3=f\\ f_4=f\\ f_5=f-\frac{1}{2}{\mathrm{JT}}_5^{\&prime;2}\\ f_6=f-\frac{1}{2}{\mathrm{JT}}_5^{\&prime;2}-{\mathrm{DT}}_6^{\&prime;}\end{array}\right.---\left(1\right)$

The length of curve system of equations (2) that described each time period is corresponding:

$\left\{\begin{array}{c}{l}_1=f_s{T}_1^{\&prime;}+\frac{1}{6}{\mathrm{JT}}_1^{\&prime;3}\\ l_2=f_1{T}_2^{\&prime;}+\frac{1}{2}{\mathrm{AT}}_2^{\&prime;2}\\ l_3=f_2{T}_3^{\&prime;}+\frac{1}{2}{\mathrm{AT}}_3^{\&prime;2}-\frac{1}{6}{\mathrm{JT}}_3^{\&prime;3}\\ l_4=f_3{T}_4^{\&prime;}\\ l_5=f_4{T}_5^{\&prime;}-\frac{1}{6}{\mathrm{JT}}_5^{\&prime;2}\\ l_6=f_5{T}_6^{\&prime;}-\frac{1}{2}{\mathrm{DT}}_6^{\&prime;2}\\ l_7=l_6{T}_7^{\&prime;}-\frac{1}{2}{\mathrm{DT}}_7^{\&prime;2}+\frac{1}{6}{\mathrm{JT}}_7^{\&prime;3}\end{array}\right.---\left(2\right)$

Wherein, f ₁, f ₂, f ₃, f ₄, f ₅, f ₆Represent respectively the described boost phase A that adds ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆The speed of corresponding section end point, f _sThe initial velocity that represents described S type curve, f represent the target velocity of described S type curve, l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇Represent respectively the described boost phase A that adds ₁, even boost phase A ₂, subtract boost phase A ₃, stage A at the uniform velocity ₄, the acceleration and deceleration stage A ₅, even decelerating phase A ₆, subtract decelerating phase A ₇Corresponding length of curve, A represents described peak acceleration, and D represents described maximum deceleration, and J represents described maximum acceleration;

Described target velocity acquiring unit also is used for according to described each time period A _iCorresponding length of curve and the relation of S type curve total length obtain following formula:

L=l ₁+l ₂+l ₃+l ₄+l ₅+l ₆+l ₇ （3）

Wherein, L represents described S type curve total length;

Described target velocity acquiring unit also is used for described system of equations (1), (2) substitution formula (3) are obtained following formula:

$L=(T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;})(\frac{f}{2}+f_s)+{\mathrm{fT}}_4^{\&prime;}+(T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;})(\frac{f}{2}+f_e)---\left(4\right)$

Described target velocity acquiring unit also is used for obtaining target velocity f according to described formula (4), shown in the formula specific as follows:

$f=\frac{L-(T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;})f_s-(T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;})f_e}{\frac{T_1^{\&prime;}+T_2^{\&prime;}+T_3^{\&prime;}+T_5^{\&prime;}+T_6^{\&prime;}+T_7^{\&prime;}}{2}+T_4^{\&prime;}}---\left(5\right)$

Acceleration obtainment unit is used for according to described each time period A _iRounding time span T _i' and peak acceleration A, maximum deceleration D, maximum acceleration J, target velocity f between relation obtain following system of equations:

$\left\{\begin{array}{c}{T}_1^{\&prime;}=T_3^{\&prime;}=\frac{A}{J}\\ T_5^{\&prime;}=T_7^{\&prime;}=\frac{D}{J}\\ T_2^{\&prime;}=\frac{f-f_s}{A}-\frac{A}{J}\\ T_6^{\&prime;}=\frac{f-f_e}{D}-\frac{D}{J}\end{array}\right.---\left(6\right)$

Wherein, f _eThe terminal velocity that represents described S type curve;

Described acceleration obtainment unit also is used for obtaining peak acceleration A, maximum deceleration D, maximum acceleration J according to described system of equations (6), respectively as following various shown in:

$A=\frac{f-f_s}{T_1^{\&prime;}+T_2^{\&prime;}}---\left(7\right),$ $D=\frac{f-f_e}{T_5^{\&prime;}+T_6^{\&prime;}}---\left(8\right)$

$J=\frac{f-f_s}{(T_1^{\&prime;}+T_2^{\&prime;})T_1^{\&prime;}}=\frac{f-f_e}{(T_5^{\&prime;}+T_6^{\&prime;})T_5^{\&prime;}}---\left(9\right).$

9. device according to claim 8 is characterized in that, described length of curve acquisition module specifically comprises:

The last spot speed acquiring unit of section is used for described each time period A _iRounding time span T _i', target velocity f, peak acceleration A, maximum deceleration D and maximum acceleration J substitution system of equations (1) obtain each time period A _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆

Time step curve length acquiring unit is used for described each time period A _iRounding time span T _i', target velocity f, peak acceleration A, maximum deceleration D, maximum acceleration J and each time period A _i(i=1,2 ..., 6) and the corresponding last speed f that puts of section ₁, f ₂, f ₃, f ₄, f ₅, f ₆Substitution system of equations (2) obtains each time period A _iCorresponding length of curve l ₁, l ₂, l ₃, l ₄, l ₅, l ₆, l ₇

10. device according to claim 9 is characterized in that, described curve displacement acquisition module specifically comprises:

The curve distance acquiring unit is used for obtaining the time point of S type curve and the time period A at time point place according to described system of equations (2) _iCorresponding starting point is t constantly _I-1Between curve distance, specific as follows shown in:

$\left\{\begin{array}{cc}{l}_1^{\&prime;}=f_{s}t+\frac{1}{6}{\mathrm{Jt}}^3& (0\&le;t<t_1)\\ l_2^{\&prime;}=f_1(t-t_1)+\frac{1}{2}A{(t-t_1)}^2& (t_1\&le;t<t_2)\\ l_3^{\&prime;}=f_2(t-t_2)+\frac{1}{2}A{(t-t_2)}^2-\frac{1}{6}J{(t-t_2)}^3& (t_2\&le;t<t_3)\\ l_4^{\&prime;}=f_3(t-t_3)& (t_3\&le;t<t_4)\\ l_5^{\&prime;}=f_4(t-t_4)-\frac{1}{6}J{(t-t_4)}^3& (t_4\&le;t<t_5)\\ l_6^{\&prime;}=f_5(t-t_5)-\frac{1}{2}D{(t-t_5)}^2& (t_5\&le;t<t_6)\\ l_7^{\&prime;}=f_6(t-t_6)-\frac{1}{2}D{(t-t_6)}^2+\frac{1}{6}J{(t-t_6)}^3& (t_6\&le;t<t_7)\end{array}\right.---\left(10\right)$

Wherein, t represents the time point of described S type curve, l _iThe time point t of the described S type curve of ' expression and the time period A at time point t place _iCorresponding starting point is t constantly _I-1Between curve distance, t _iRepresent described each time period A _iTerminal point constantly, i=1,2 ..., 7;

The curve displacement acquiring unit is used for according to described each time period A _iCorresponding length of curve, the time point t of S type curve and the time period A at time point t place _iThe curve distance l (t) of corresponding starting point between constantly obtains the displacement of S type curve corresponding to time point t, specific as follows shown in:

$L\left(t\right)=\left\{\begin{array}{cc}{l}_1^{\&prime;}& (0\&le;t<t_1)\\ l_1+l_2^{\&prime;}& (t_1\&le;t<t_2)\\ l_1+l_2+l_3^{\&prime;}& (t_2\&le;t<t_3)\\ l_1+l_2+l_3+l_4^{\&prime;}& (t_3\&le;t<t_4)\\ l_1+l_2+l_3+l_4+l_5^{\&prime;}& (t_4\&le;t<t_5)\\ l_1+l_2+l_3+l_4+l_5+l_6^{\&prime;}& (t_5\&le;t<t_6)\\ l_1+l_2+l_3+l_4+l_5+l_6+l_7^{\&prime;}& (t_6\&le;t<t_7)\end{array}\right.---\left(11\right)$

The displacement of the S type curve that wherein, the time point of the described S type curve of L (t) expression is corresponding.

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