
Proportional controller applied to a 1st order system
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G=K0/(1+s.tau)
nKG= K.K0
dKG= 1+s.tau

Gcf= KG/(1 + KG)= nKG / (dKG + nKG) = K.K0 / (1+s.tau + K.K0)

pole= -(1+K.K0)/tau
if K0=1 and K=1 then pole= -2/tau
if K0=1 and K=2 then pole= -3/tau
