Protein Digestion: A Dynamic Model

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Protein Digestion A Dynamic Model

• Student Name 1 Student Name 2
• Process Control Design Challenge I

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Our System

• Assumptions
• Well mixed
• Constant V, Xbi, density, flow rates

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Steady State Solution
Given Values
K 5 mlmin/mg
F1 15 ml/min
F2 7 ml/min
V 1000 ml
Xai 150 mg/ml
Xbi 1000 mg/ml
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Steady State Solution
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Mathematical Solution
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Mathematical Solution
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Mathematical Solution Cont.
Inverse Laplace via Maple
Impulse Response
Step Response
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Step Response
Matlab Input
function hdotstomachstep(t,h) hdotzeros(3,1) F1
15 F27 F322 V1000 k5 Xbi1000 if tlt100
Xai100 else Xai150 end hdot(1)(F1Xai-Vkh(
1)h(2)-F3h(1))/V hdot(2)(F2Xbi-Vkh(1)h(2)-
F3h(2))/V hdot(3)(kVh(1)h(2)-F3h(3))/V t0
0 tf400 h00.021 216 102.3 t,hode23(_at_sto
machstep,t0 tf,h0) plot(t,h(,2),t,h(,3))
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Step Response

• Matlab Output

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Step Response
Simulink Diagram
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Step Response

• Simulink Output for Enzyme

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Step Response

• Simulink Output for Tryptophan

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Impulse Response
Matlab Input
function hdotstomachimpulse(t,h) hdotzeros(3,1)
F115 F27 F322 V1000 k5 Xbi1000 if
tlt100 Xai200 elseif tgt105 Xai200 else
Xai500 end hdot(1)(F1Xai-Vkh(1)h(2)-F3h(1
))/V hdot(2)(F2Xbi-Vkh(1)h(2)-F3h(2))/V hd
ot(3)(kVh(1)h(2)-F3h(3))/V t00 tf400
h00.0021 216 102.3 t,hode23(_at_stomachimpulse
,t0 tf,h0) plot(t,h(,2),t,h(,3))
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Impulse Response

• Matlab Output

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Impulse Response
Simulink Diagram
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Impulse Response

• Simulink Output for Enzyme

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Impulse Response
Simulink Output for Tryptophan
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Final Thoughts
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References

• Biglione, N., Yousef, M., Rodgers, V.G.J.,
  (2004). Process Dynamics Control in Design
  52185 Lab 1 Programming and Simulation using
  Matlab and Simulink.
• Seborg, D.E., Edgar, T.F., Millichamp, D.A.
  (2004). Process Dynamics and Control (2nd ed.).
  Hoboken, NJ John Wiley Sons.
• Vander, A., Sherman, J., Luciano, D. (2001).
  Human Physiology The Mechanisms of Body Function
  (8th ed.). Boston McGraw Hill.

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Questions?