[PROCESS CONTROL]

We will develop a dynamic model for stirred tank Assumption: CAO,F. 1. The mixture in the tank is well-mixed F 2. Liquid density is constant in every flow rate 3. The cross-sectional area of the tank is A (m) CA. Fo 4. There are 2 pumps to measure the flow rate in and out of the tank, the purpose is to design a control system to control the liquid level at tank, h and concentration A, CA Question: a. Determine the inputs and outputs of the control system b. Prove that the dynamic model for this case is: dh dt (F, +F; - F.) A F. F dea_F, =CAo - ca) - Fi CA dt Ah Ah C. Derivate the equation for the mathematic model in the form of variable deviation for this case d. Is this system linear or non-linear? Why? e. Prove that the second order differential equation using the LAPLACE TRANSFORMATION for the control system is: g(t) =c-1 = 1- 2e-ete-20 s(s + 1)(8 + 2) [ - {: t Where : F Fi = m/s = kg/m = m/s = m/s = kg/m2 = kg/m Fo CA