Consider the two liquid storage tanks shown in Figure P4.1. The volumetric flowrate of the stream that connects the two tanks is proportional to the difference between the two levels F = (h-h)/R, which is considered positive when liquid flows from the second to the first tank. The volumetric flow rate of the exit stream is F = h/R2. (a) Write down a state-space model for this system of tanks. (b) Derive the transfer function between F, and h. (c) If A = 1 m, 4 = 2 m, R = 1 min m and R = 1/2 min m, calculate the response of h to a step increase in F.,, by 1 m/min. Fin(t) h(1) h(1) F(1) F(1) A A R R Figure P4.1 Interacting tanks, with feed and exit line in the same tank.