Consider the two liquid storage tanks shown in Figure P4.1. The volumetric flowrate of the stream...

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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. 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.