Question: A liquid storage facility can be modeled by where y is the liquid level (m) and u is an inlet flow rate (m 3 /s).

A liquid storage facility can be modeled by

where y is the liquid level (m) and u is an inlet flow rate (m³/s). Both are defined as deviations from the nominal steady-state values. Thus, y = u = 0 at the nominal steady state. Also, the initial values of all the derivatives are zero.

(a) If u(t) suddenly changes from 0 to 1 m³ /s at t = 0, deter-mine the liquid level response,y(t).

(b) If the tank height is 2.5 m, will the tank overflow?

+ 5 + y(t) = 8 + u(t)

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