Method 1: characteristic a(n) in a polynomial or hyperbolic form

In the range above the limit speed, the current acceleration is optionally specified via a third-degree polynomial or via a hyperbole function. In the case of both characteristics, a constant acceleration aconst is used in the range below nlimit. This corresponds to the acceleration at nominal speed. The characteristics apply to both the speed setup and slowdown phases.

Method 1: characteristic a(n) in a polynomial or hyperbolic form 1:
Figure 1-14: Course of acceleration in accordance with a polynomial or hyperbole

Interpolation points on the drive characteristic a(n) are used to determine the coefficients of the characteristics. Four or three interpolation points are needed to determine them.

One interpolation point P1=(n1, (a(n1)) is already defined by the parameter for constant acceleration aconst and the limit speed nlimit, and the user can define the remaining three or two along the drive characteristic a(n). It is best for the abscissa values to be at a constant distance. The equations for determining the coefficients are listed below.

Method 1: characteristic a(n) in a polynomial or hyperbolic form 2:

Polynomial

Method 1: characteristic a(n) in a polynomial or hyperbolic form 3:

Example of determining characteristics

Interpolation point

Acceleration a [°/s] 2

Speed n [°/s]

1

16000

12000

2

8000

24000

3

4000

36000

4

2000

48000

a_const = 16000[degrees/s2] to nlimi = 12000 [degrees/s]

We arrive at the following for the coefficients:

b3 = -1.92901234E-10 [s/°2]
b2 = 2.08333333E-5 [1/°]
b1 = -0.88888888 [1/s]
b0 = a_konst = 16000 [°/s2]

As from the nominal speed (nlimit) the characteristic profile is as follows: n-n_limit/°/s

Method 1: characteristic a(n) in a polynomial or hyperbolic form 4:

Hyperbole

Method 1: characteristic a(n) in a polynomial or hyperbolic form 5:

Example of determining characteristics

Interpolation point

Acceleration a [°/s] 2

Speed n [°/s]

1

16000

12000

2

8000

24000

3

4000

36000

a_const = 16000[degrees/s2] to nlimit = 12000 [degrees/s]

We arrive at the following for the coefficients:

b2 = 4.166666E-1[]
b3 = 2.857142E-2[]
b1 = 2.285714E4[°/s2]

As from the nominal speed (nlimit) the characteristic profile is as follows:n-n_limit

Method 1: characteristic a(n) in a polynomial or hyperbolic form 6:

Parameters

P-AXIS-00202

Characteristic type: 1 (hyperbole) or 2 (polynomial)

P-AXIS-00130

Limit speed nlimit

P-AXIS-00007

Constant acceleration aconst for n<nlimit

P-AXIS-00010

Minimum acceleration amin

P-AXIS-00026

Coefficient b1

P-AXIS-00027

Coefficient b2

P-AXIS-00028

Coefficient b3

Parameterization examples 

# 
beschl_kennlinie.typ 1 Hyperbole 
beschl_kennlinie.a_min 1400 [ ° /s*s] 
beschl_kennlinie.n_grenz 12000000 [10-3 ° /s] 
beschl_kennlinie.a_konst 16000 [ ° /s*s] 
beschl_kennlinie.b1 2.285714E4 [°/s*s]
beschl_kennlinie.b2 4.166666E-1 [] 
beschl_kennlinie.b3 -2.857142E-2 []
# 
# 
beschl_kennlinie.typ 2 Polynomial 
beschl_kennlinie.a_min 2000 [ ° /s*s] 
beschl_kennlinie.n_grenz 12000000 [10-3 ° /s] 
beschl_kennlinie.a_konst 16000 [ ° /s*s] 
beschl_kennlinie.b1 -0.88888888 [1/s]
beschl_kennlinie.b2 2.08333333E-5 [1/Grad
beschl_kennlinie.b3 -1.92901234E-10 [s/Grad²]
#