Consider the liquid-level PI control system shown in Figure with the following parameter values: A = 3 ft2, R = 1.0 min/ft2, Kv = 0.2 cfm/psi, Km = 4 mA/ft, Kc 4, and τ1 = 3 min. Suppose that the system is initially at the nominal steady state with a liquid level of 2 ft. If the set point is suddenly changed from 2 to 3 ft, how long will it take the system to reach
(a) 2.5 ft and
(b) 3 ft?