Consider the two noninteracting tanks of system $1$ in Figure PII$\mathrm{.}1.$ We want to control the liquid level $h_2$ of tank $2$ by manipulating flow rate $F_1$ through a proportional controller. Assume that the cross$-$sectional areas of the two tanks are equal to $5f{t}^2.$ Initially, the system is at steady state with $F_1=1f\frac{t^3}{m}in$ and $h_1=h_2=3ft.$

describe the dynamic response of liquid level $h_1$ in tank $1,$ for a unit step change in the set point of $h_2.$ Sketch qualitatively these two responses.