Question $5(20$ marks$)$

A PID controller had $K_P=2\mathrm{.}0,K_{\text{I}}=2\mathrm{.}2se{c}^{-1},K_D=2sec$ and $P_{\text{I}}(0)=40\%$

From the graph provided in figure $7$

Figure $7$

Determine:

i$.$ The offset error for the intervals provided in graph $(9$ marks$)$

ii$.$ The controller output for the intervals provided as well as beyond $6$ secs$.(12$ marks$)$