Consider the system presented in Fig. 2.28, consisting in the process of liquid accumulation in series of two tanks. The two vessels operate at atmospheric pressure. Based on the mass balance of...

Consider the system presented in Fig. 2.28, consisting in the process of liquid accumulation in series of two tanks. The two vessels operate at atmospheric pressure.

Based on the mass balance of liquid in each of the tanks, the first order differential equations may be obtained:

where T₁, T₂, k₁
and k₂
have constant values.

Furthermore, the second order differential equation describing the relationship between the level in the second tank and the flow rate entering the first tank is:

(a)    Compute the general solution of equation (2.122), taking into account the constant initial conditions H₂(0) = a and (dH₂/dt)(0) = b.

(b) Verify whether the system is BIBO stable.