Liquid flow out of a spherical tank discharging through a valve can be described approximately by the following nonlinear differential equation:

where the variables used arc consistent with other liquid level models we have developed.

(a) Derive a linearized model (in deviation variables) of the form

(b) Develop a transfer function relating the liquid level to the volumetric flow of liquid into the tank. Give the final expression in terms of the state- space model coefficient, a andb.

Transcribed Image Text:

ala-cua) - Crh dh T(D - H)h dt