Control of Glucose Concentration by Insulin in the Liver

1
Control of Glucose Concentration by Insulin in
the Liver

• 52185 Process Dynamics and Control
• Design Challenge II
• ICE-COLD Inc.
• Aiman M. Alam
• Valerie A. Perrin
• December 16th, 2004

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Outline

• Glucose Regulation
• Model
• Process Variables
• Block Diagrams
• Stability Analysis
• Routh
• Root-locus
• Bode
• Nyquist
• Simulink
• Controller Tuning
• Cohen Coon
• Internal Model Control
• Tyreus-Luyben
• Ziegler-Nichols
• Fine Tuning
• Conclusions

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What is Glucose?

• Monosaccharide commonly found in the human body
• Hexose (six carbon molecule)
• Exists as a pyranose ring
• Molecular formula C6H12O6

C6H12O6 6O2 ? 6CO2 6H2O Energy

• Blood glucose concentrations in a
• healthy adult range from 70-110 mg/dL

Sources
http//www.psrc.usm.edu/macrog/images/glucose.gif,
Retrieved October 5th, 2004
Nelson, D., Cox, M. (2004). Lehninger Principles
of Biochemistry (4th Ed.). W. H.Publishers.
4
How is Glucose Regulated?

• When blood glucose levels are high

• Insulin produced by beta cells in the pancreas
• As blood glucose concentration rises, insulin
  concentration rises to allow for increased
  glucose uptake by the organs
• High blood glucose levels cause the liver to
  convert glucose to glycogen

Insulin
When blood glucose levels are low

• Glucagon produced by alpha cells of the pancreas
• As blood glucose concentration drops, glucagon
  concentration increases
• Low blood glucose levels cause the liver to
  convert glycogen to glucose

Glucagon
Sources
http//www.bodybuilding.com/fun/glycogen.jpg,
Retrieved October 5th, 2004
http//www.cryst.bbk.ac.uk/PPS95/course/8_folds/1g
cn.gif, Retrieved October 5th, 2004
http//www.sickkids.on.ca/HowellLab/images/structu
res/insulin-t6_tmb.gif, Retrieved October 5th,
2004
Nelson, D., Cox, M. (2004). Lehninger Principles
of Biochemistry (4th Ed.). W. H.Publishers.
5
Overview of Blood Glucose Regulation
Sources
http//www.fda.gov/cber/genetherapy/pancislet-img1
.gif, Retrieved October 6th, 2004
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Model
Assumptions

• F1 F2 F 1 L/min
• Perfectly mixed CSTR
• Constant density
• Constant volume 1 L
• k1 0.0005 L/mgmin
• k2 0.05 min-1

Cg f(Ci0, Cg0)
Component Balances
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Process Variables

• Controlled variable Cg
• Manipulated variable Ci0
• Disturbance variable Cg0

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Open Loop System
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Closed Loop System
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Closed Loop Transfer Functions
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Stability Analysis
Routh
Root-locus
Bode Nyquist
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Routh
13
Root-locus
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Bode (Kc -4572)
15
Nyquist (Kc -4572)
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Unit Step in Set Point (Cgsp)
Stable system at Kc gt critical Kc
Sustained oscillatory behavior at Kc
critical Kc
Unstable system at Kc lt critical Kc
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Unit Step in Disturbance (Cg0)
Stable system at Kc gt critical Kc
Sustained oscillatory behavior at Kc
critical Kc
Unstable system at Kc lt critical Kc
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Unit Impulse in Set Point (Cgsp)
Stable system at Kc gt critical Kc
Sustained oscillatory behavior at Kc critical
Kc
Unstable system at Kc lt critical Kc
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Unit Impulse in Disturbance (Cg0)
Stable system at Kc gt critical Kc
Sustained oscillatory behavior at Kc
critical Kc
Unstable system at Kc lt critical Kc
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Controller Tuning
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Cohen Coon
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Unit Step
Set Point (Cgsp)
Disturbance (Cg0)
23
Unit Impulse
Set Point (Cgsp)
Disturbance (Cg0)
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Internal Model Control (IMC)
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Unit Step
Set Point (Cgsp)
Disturbance (Cg0)
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Unit Impulse
Set Point (Cgsp)
Disturbance (Cg0)
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Tyreus-Luyben
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Unit Step
Set Point (Cgsp)
Disturbance (Cg0)
29
Unit Impulse
Set Point (Cgsp)
Disturbance (Cg0)
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Ziegler-Nichols
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Unit Step
Set Point (Cgsp)
Disturbance (Cg0)
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Unit Impulse
Set Point (Cgsp)
Disturbance (Cg0)
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Fine Tuning
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Unit Step
Set Point (Cgsp)
Disturbance (Cg0)
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Unit Impulse
Set Point (Cgsp)
Disturbance (Cg0)
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Ramp
Set Point (Cgsp)
Disturbance (Cg0)
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Tyreus-Luyben PID Controller
Unit Step in Disturbance (Cg0)
Unit Impulse Disturbance (Cg0)
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Conclusions

• Nyquist is the sweetest method for obtaining
  critical Kc values
• System is stable at -4752 lt Kc lt 0
• Best controller is PID using the Tyreus-Luyben
  method
• Fine tuning led to even better results

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Andre 3000
Whats cooler than being cool? ICE-COLD!
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Questions?

• Acknowledgements
• Dr. V.G.J. Rodgers
• The Classes of 04, 05, and 06 Jerry