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Question

# A conttrol system with a PD controller is shown in the figure. If the velocity error constant Kv=1000 and the damping ratio ζ=0.5, then the values of KP and KD are

A
KP=100,KD=0.09
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B
KP=100,KD=0.9
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C
KP=10,KD=0.09
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D
KP=10,KD=0.9
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Solution

## The correct option is B KP=100,KD=0.9Kv=lims→0sG(s)H(s) 1000=lims→0s×(KP+KDs)100s(s+10) ⇒KP=100 Now characteristics eq. (1+G(s)H(s))=0 1+(KP+KDs)100s(s+10)=0 Putting KP=100 s2+10s+104+100KDs=0 s2+(10+100KD)s+104=0 Comparing with standard second order eq. i.e s2+2ζωns+ω2n=0 So, ωn=100;2ζωn=10+100KD Given,ζ=0.5 2×0.5×100=10+100KD KD=0.9

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