Consider the storage tank shown below. F, = 3 m'/min F, = 2 m/min The cross-sectional area is 1 m2. Suppose that we want to control the liquid level in the tank at the height of 5 m, by manipulating the effluent flow rate F2, given that F3 is constant, according to the following proportional control law: F2 = 10(5 h) + 1 %3D 3.1. Develop the transfer function between h and F, (10) 3.2. Determine the time constant and static gain of the tank under control. (4) 3.3. Determine the dynamic response of the liquid level to a step change in F, by 1m/min (i.e., find how h(t) changes with time). (5) 3.4. Determine the new steady state value for the liquid level.