A unity-feedback system has closed-loop transfer function $C(s)/R(s)=(s+90)/(s^2+10s+90)$. Find steady-state error to a unit ramp, to one decimal place.
For unity feedback, E/R=1−T=(s²+9s)/(s²+10s+90). A unit ramp has R=1/s². The final-value theorem gives ess=lim sE=lim (s+9)/(s²+10s+90)=9/90=.1. The closed-loop poles are stable, so the steady-state limit is valid.
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