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GIVE FULL COMPLETE SOLUTION AND COMPLETE WORKINGOUT OF SOLUTION DONT JUST WRITE SIMPLE ONE LINE EQUATIONS GIVE CONPLMPLETE SOLUTION Consider the cylindrical tank in the

GIVE FULL COMPLETE SOLUTION AND COMPLETE WORKINGOUT OF SOLUTION
DONT JUST WRITE SIMPLE ONE LINE EQUATIONS GIVE CONPLMPLETE SOLUTION
Consider the cylindrical tank in the Fig-
ure mixing a pure component A stream
and an inert solvent S stream. Assume
perfect flow control. A P level controller
with a gain Kc=0.2min-1 manipulates
the outflow with the two inflow streams
being independent. Initially the system
is at steady state with the salient de-
sign and operating conditions noted in
the Figure. The initial hold up is 50%
of full tank capacity. Answer the follow-
ing questions.
(a) Using linearization, derive a linear dynamic ODE model relating the outlet A concentration
cA to the two independent flow rate setpoints, FASP and FSSP.
(b) Present the ODE model above as a block diagram with appropriate transfer functions.
(c) Obtain an analytic expression for cA(t) for the linear ODE clerived in part (a) for a step change
in the solvent flow rate of size FS0.
(d) It is proposed to use a PI controller that manipulates FASP to hold cA. The integral time I
is set to twice the mixing tank residence time at the initial steady state and the controller
gain Kc is chosen for a dominant closed loop pole pair damping coefficient of 0.5. Calculate
Kc and I.
(e) Obtain an analytical expression for the response of cA(t) to a step change in the solvent rate
of size FSO with the composition controller in part (d) on automatic.
(f) What is the maximum deviation from setpoint in the closed loop cA response.
Consider first order reaction that means r = k*c_A
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