Question $3$

Results of the open$-$loop frequency response of an industrial automation system using PID control are given in Table $2.$

Table $2$

$($a$)$ Plot the results of Table $2$ on a Nichols chart. Determine the bandwidth $($BW$)$ of the closed loop system and use it to estimate the $\backslash (0-95\backslash \%\backslash )$ rise time.

$[6$ marks$]$

$($b$)$ In order to reduce the system response time, the gain parameter is increased by $6$ dB$.$ Show how this increase in gain changes the Nichols chart for the system, and use it to determine the new $\backslash (0-95\backslash \%\backslash )$ rise time.

$[4$ marks$]$

$($c$)$ Using the Nichols chart of part $($b$),$ calculate $($i$)$ the percentage step response overshoot and $($ii$)$ the $\backslash (\backslash$pm $5\backslash \%\backslash )$ settling time.

$[8$ marks$]$

$($d$)$ Suggest an alternative method for reducing the system response time which would have greater stability than that proposed in part $($b$).$

$[2$ marks$]$