Description of the Firmware
IP244
C79000–B8576–C860–02
4–6
1.1.1 Closed-Loop Control
The following equation of a PID controller for manipulated variable y (t) as a function of the system
deviation x (t) applies:
1 dx(t)
Y
PID
(t) = K
p
{ x(t) + –––– x(t)dt + T
D
–––––––––– }
T
N
dt
Implementation as a sampling controller allows the representation in the parallel arrangement
shown below:
Fig. 1.1.1/1 Basic structure of the controller
The system deviation at instant k * T
A
is processed in the three parallel branches:
P-branch: p
k
= e
k
T
A
I-branch: i
k
= i
k–1
+ –––––– (e
k
+ e
k–1
)
2T
N
2T
D
T
A
– 2T
Z
D-branch: d
k
= ––––––––––––––– (e
k
– e
k–1
) – ––––––––––––––––– d
k–1
T
A
+ 2T
Z
T
A
+ 2T
Z
Where:
T
A
= sampling time
T
N
= integral action time
T
D
= derivative action time
T
Z
= filter time constant for damping the derivative
influence, selected: T
Z
= 2T
A
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