Consider the liquid-level, PI control system shown in Fig. 11.16 with the following parameter values: A = 3 ft?, R = 1.0 min/ft?, Ky = 0.2 fm/psi, Km = 4 mA/ft, K. = 4, and tr = 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?