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controller gain<br />

set-point u 0<br />

error<br />

integral time<br />

constant<br />

e<br />

K p<br />

Industrial Automation<br />

PI (Proportional-Integral) Controller<br />

1<br />

T i<br />

process value y 0<br />

PI<br />

dt<br />

t<br />

∫<br />

t 0<br />

command<br />

variable<br />

1<br />

m = K p ( e(<br />

t)<br />

+ e(<br />

τ ) dτ<br />

)<br />

T<br />

1<br />

s<br />

i<br />

m<br />

plant<br />

measurement<br />

The integral factor Ki produces a non-zero control variable even when the error is zero.<br />

27/40 2.2 Continuous plants and regulation

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