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Problem 10.01PP
Of the three components of the PID controller (proportional, integral, or derivative), which one is 
the most effective in reducing the error resulting from a constant disturbance? Explain.
Step-by-step solution
step 1 of 3
Integral control is he most effectiTe n reducing the error due to constant disturbances.
Step 2 of 3
Block diagram for showing integral control is the most effective means o f reducing 
steady errors.
Using the above block diagram.
Y^O {W -\-BDc)
E = R - Y = R - 0 { W + EDc) 
1 « OE * - ■W
\+ D c O \ - D ( D
, = 1« , M = l i SB(s) = l i p s f — !— , 
• ̂ ̂ ̂ s-»o^ ll+ £ )p O
O
\+ D fP
Step 3 of 3
Writing G'(-S') = and using a step input R {S )= — and a step disturbance
' ' dO{s) ̂ ' S
0)(^) = ^ we can show that integral control leads to zero steady state error. While
proportional and derivative control in general, do not
Bitegral control, (̂ S) = —
= U E[S)=
i-*0 S+0 dgS + ng )
If
Proportional control, Dq (S) = ^ 0
Derivative control (s) = s , ^ 0 i f i^ p (0 )^ 0
This analysis assumes that there are no pole zero cancellations between the plant G
and the con^ensator, D ,, in general, proportional or derivative control will not have
zero steady state error