69
Calculation of the controller parameters
Optimi-
zation
Con
troll
er
Controller parameters
Transfer function on
step change in setpoint
Equivalent
time
constant of
the
optimized
control loop
T
I
Tn Tv Kp
Only lag
Kp
With
integral
t
an
t
aus
o
%
Linear
optimum
I
4V
s
-
-
-
-
-
12
0
P
-
-
-
T
1
/(4V
s
)
T
i
/ 4
PI
4V
s
T
1
-
T
1
/(4V
s
) -
PD -
-
T
2
T
1
/(4V
s
)
T
i
/ 4
PID 4V
s
T
1
T
2
T
1
/(4V
s
) -
Absolute
value
optimum
I
2V
s
-
-
-
-
4.7
8.4
4,3
P
-
-
-
T
1
/(2V
s
)
T
i
/ 2
PI
2V
s
T
1
-
T
1
/(2V
s
) -
PD -
-
T
2
T
1
/(2V
s
)
T
i
/ 2
PID 2V
s
T
1
T
2
T
1
/(2V
s
) -
Only lag
SO
PI
V
s
2
/T
1
4 -
T
1
/(2V
s
) -
>3.1 <16.5 <43,4 2 +0.5t
gs
PID
V
s
2
/T
1
4
T
2
T
1
/(2V
s
) -
<7.6 <13.3 <8,1
SO with
Integral
PI
2
/T
i
-
-
T
i
/
2 3.1 16.5 43,4 4
PID 8
2
/T
i
T
2
-
T
i
/
2 7.6 13.3 8,1
t
rise
: rise time; t
settle
: settling time, o: overshoot as a percentage
T
i
= T
0
/V
s
: integral-action time of the controlled system; T
0
: integral-action time, V
s
: Controlled
system gain
SO: symmetrical optimum
Compensation of disturbance variables
A controlled system is also subject to disturbance variables, such as a load surge on a
variable-speed drive.
This load surge results in a system deviation that is corrected by the controller.
The constancy of the control stated in the Operating Instructions refers to a long period of, for
example, 10 seconds. It therefore does not take a transient system deviation caused by a
disturbance variable into account. This can therefore be greater than the value stated as the
constancy.
We do not intend to look at formal derivation of the response to precontrol here. Suffice it to
say that a controller adjusted according to the symmetrical optimum is more advantageous
than one adjusted according to the absolute value optimum in such cases.
Str
uct
Transfer function on a
step response of the
disturbance variable:
Optimized according to
absolute value optimum
Optimized
according to:
symmetrical
optimum
Symmetrical optimum with
an integral in the
controlled system
