Regler Kp?

Guide behavior is understood to mean the behavior of the control loop to changes and a control loop has good guidance behavior if the desired variable is reached as much as possible at the output (overshooters, on-and-off control time are initially set to this point).

But I have to correct myself, but not because the increase of Kp would not reduce the deviation of the rule and bring the actual size of the desired size closer, but because it was not asked at all.

The posted question is what to do so that the leadership is not changes. That is, the output variable should remain as accurately as possible as before. That is, the previous control deviation should also remain this.

It should be simplified

W: Eingangsgröße
Y: Ausgangsgröße
E: Regelabweichung -> E = W - Y
Kp: Verstärkungsfaktor
Gr: Übertragungsfunktion des P-Reglers -> Kp
Gs: Übertragungsfunktion der Regelstrecke

The transmission function of a simplified control loop with a P controller and a control path G:

Y/W = (Gr*Gs) / ( 1+ Gr*Gs )

We want to see what we get as an initial size. To this end, we introduce a stretch reinforcement Ks. In addition, we convert the equation directly to Y.

Y = W * (Kp*Gs*Ks) / ( 1 + Kp*Gs*Ks )

If we keep the input signal constant with W = 1, Kp = 1, Gs = 1 and Ks = 1, we get

Y=0.5

It’s bad first. Because we want to achieve our desired size = 1 and are still 0.5 away. Does Kp need to be reduced so that we get closer from 0.5 to 1.

For Kp = 0.5 we get Y = 0.33
For Kp = 2.0 we get Y = 0.67

What happens if we double the line reinforcement and halve Kp from 1 to 0.5 or double to 2, while our W remains at W = 1.

For Kp = 0.5 we get Y = 0.5
For Kp = 2.0 we get Y = 0.8

By increasing the amplification, the desired variable is approached, since the control deviation is reduced.

However, since, as I said, it was not necessary to halve Kp here, so that the remaining control deviation from before is actually preserved.