Process Dynamics and Control A conical tank, of maximal radius R and maximal hei

Question

Process Dynamics and Control

A conical tank, of maximal radius R and maximal height H, has a manipulated inlet flow rate F(t) and a gravity-driven outlet flow rate. The variable of interest is the tank liquid height h(t) and a mass balance results in the continuous model dh(t) aF,(t) _ h(t)--1.5 h(t)2 where both and are constants. Note that neither F(t) nor h(t) are measured or known quantities. Answer the following questions: A) What is the order of this dynamical model (0.25 point)? And on what basis/argument is your answer founded (0.25 point)? B) Is this model linear or nonlinear (0.25 point)? Explain your rationale (0.25 point)

Explanation / Answer

A) The order of the dynamical model: 1. Order of a ordinary differential equation is the order of the highest order derivative present in the system. Here, the highest order derivative present is one (dh/dt).

B) The model is non-linear. If the power of the dependent variable (here h) is any value other than 1 (here there is a h^-2 and h^-1.5 terms. Hence the system is non linear.

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