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integral time<br />
proportional factor<br />
set-point u 0<br />
derivative time<br />
process value y 0<br />
dx<br />
=<br />
dt<br />
dx<br />
dt<br />
0 x1<br />
1<br />
error<br />
( x + D + K ( u − x −T<br />
x − x + u )<br />
1 = 2 f 0 0)<br />
TT2<br />
Industrial Automation<br />
PID and Plant Simulation (Excel sheet)<br />
K<br />
K<br />
1<br />
1<br />
0<br />
CL<br />
1<br />
1<br />
T i<br />
PID<br />
dx<br />
dt<br />
dx<br />
dt<br />
1<br />
T d<br />
X 3<br />
K<br />
T<br />
i<br />
1<br />
s<br />
Nf<br />
1<br />
s<br />
close / open loop<br />
2 = ( u0<br />
− y0<br />
⎛<br />
⎞<br />
⎜ 1<br />
= Nf − x + − ⎟<br />
3 K(<br />
u0<br />
0)<br />
⎜ T<br />
⎟<br />
⎝ d<br />
⎠<br />
3 y<br />
)<br />
X2 U1 ( 1<br />
32/40 2.2 Continuous plants and regulation<br />
1<br />
1<br />
+ sT + s<br />
D<br />
f<br />
X 1<br />
(hidden)<br />
1<br />
2<br />
TT<br />
2<br />
)<br />
filtered derivative<br />
X 0<br />
⎛ 1<br />
⎞<br />
= Nf<br />
⎜<br />
⎜−<br />
x + ( − )<br />
⎟<br />
3 K u0<br />
x0<br />
⎝ Td<br />
⎠
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