PMA KS 98 - Page 76

Step response:
After a step change of input variable x1 by {x
=xt-x(t-ts), the output changes to maximum value y
max.
yCaxy
max
=×× +D 0
and decays to 0 according to function
ynts C x y ymax C
n
n
(. ) .
()
=× += ×
-
D 0
1
Thereby, n is the number of calculation cycles ts
after the input step change. Number n of required
calculation cycles ts until output variable decaying
to y(n*Ts) is
n
lg
yn ts
ymax
lgC
=
×
+
()
1
Surface area A under the decaying function is
Ay T ts=×+
max
()
Ramp response:
After ramp starting, output variable y runs towards the fi-
nal value of differentiation quotient
ymaT
max
=××
according to function
yn ts m a T C
n
() ( )×=×××-1
Thereby, m =
m
dx
dt
=
is the gradient factor of the input
function. Relative error F after n calculating cycles Ts re
-
ferred to the final value is calculated as follows:
F=C
n
and the number of required calculating cycles, according
to which function
yn ts()×
approaches final value
y= y
max
to error F is
n
F
C
=
×
lg
lg2
Time functions 9499 040 50611
LEAD ( differentiator ) 76