Closed-Loop Control - Siemens SIMATIC S5 Manual

Description of the Firmware

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
Y (t) = K { x(t) + ––––
PID p
T
N
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
P-branch: p = e
k k
T
A
I-branch: i = i + –––––– (e
k k–1
2T
2T
D
D-branch: d = ––––––––––––––– (e
k
T + 2T
A
Where:
T = sampling time
A
T = integral action time
N
T = derivative action time
D
T = filter time constant for damping the derivative
Z
influence, selected: T
4–6
dx(t)
x(t)dt + T –––––––––– }
D
dt
is processed in the three parallel branches:
A
+ e )
k k–1
N
– e ) – ––––––––––––––––– d
k k–1
Z
= 2T
Z A
T – 2T
A Z
k–1
T + 2T
A Z
C79000–B8576–C860–02
IP244