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? 

(c) Based on your results for (b) What is the maximum flow change, u_max, that can occur without the tank overflowing?

Transcribed Image Text:

ÿ + 5ỷ + y(t) = 8ù + u(t)