For the liquid$-$level control system in Fig $11\mathrm{.}22,$ determine the numerical values of Kc and tau$1$ that result in a stable closed$-$loop system. The level transmitter has negligible dynamics, while the control valve has a time constant of $10$s$.$ The following numerical values are available:

A $=3$ft$^2$

q$3=10$ gal$/$min

Kv $=-1\mathrm{.}3$ gal$/$min$/$mA

Km $=4$ mA$/$ftFigure $11\mathrm{.}22$ Liquid$-$level control system with pump in

exit line.