66. In a paint mixing plant, two tanks supply fluids to a mixing cistern. The height,…

66. In a paint mixing plant, two tanks supply fluids to a mixing cistern. The height, h, of the fluid in the cistern is dependent upon the difference between the input mass flow rate, q, and the output flow rate, qe. A nonlinear differential equation describing this depen- dency is given by (Schiop, 2010 dh A pA where A – cross-sectional area of the cistern, Ac – cross-sectional area of the exit pipe, g – acceleration due to gravity, and ρ-liquid density. a. Linearize the nonlinear equation about the equilibrium point (ho, qo) and find the transfer function relating the output cistern fluid level H(s), to the input mass flow rate, Q(s)