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CBE 491 /433

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15 Oct 12 Model of Stirred Tank Heater. CBE 491 /433. Goal: set up models to simulate and see effect of tuning parameters 1 st principles (Chaps 3 – 6); transfer functions (just looked at this a bit) process simulators ( AspenPlus Dynamics; CBE 450/550 class). - PowerPoint PPT Presentation
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1 CBE 491 /433 15 Oct 12 Model of Stirred Tank Heater Goal: set up models to simulate and see effect of tuning parameters 1 st principles (Chaps 3 – 6); transfer functions (just looked at this a bit) process simulators (AspenPlus Dynamics; CBE 450/550 class)
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Page 1: CBE 491 /433

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CBE 491 /433 15 Oct 12Model of Stirred Tank Heater

Goal: set up models to simulate and see effect of tuning parameters

• 1st principles (Chaps 3 – 6); • transfer functions (just looked at this a bit)• process simulators (AspenPlus Dynamics; CBE 450/550 class)

Page 2: CBE 491 /433

2

1sK

L

L

++

si

1sK

P

P

cG-

sE+ sR sC

sKsG

IcC

11)(

energy balance on tank w/o control

Stirred Tank Heater (w/ PI

Controller)

)(1

)(1

sMsKs

sKsC

P

Pi

L

L

)()()()(1 tMKKtKtC

dttdC

TiT

dttEKtEKtM

I

CC )()()(

sM

)(1

)(1

*1 1 sMsKKs

sK T

iT

21 KKK sV

PI controller equation

)()()( tCtRtE

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3

Let:

Stirred Tank Heater (w/ PI Controller)

)()()(1)( 1 tMKKtKtCdttdC T

iT

errsumKtCtRKtMI

CC

)()()(

dttEerrsum )( )(tEdterrsumd

)()( tCtRdterrsumd

)()()()(1 tMKKtKtC

dttdC

TiT

dttEKtEKtM

I

CC )()()(

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4

ODE Solver (POLYMATH; MATLAB; MATHCAD; etc)

)()()(1)( 1 tMKKtKtCdttdC T

iT

errsumKtCtRKtMI

CC

)()()(

Polymath code:step= if (t<1) then (0) else (1)Ti = 0 + step * 10

0@0 ttC

)()( tCtRdterrsumd

0@0 terrsum

CTO

T oK %5.0

min5

0)( tR

COTO

TKK %%

1 8.0

TOCO

CK %%3.1

min10I

Page 5: CBE 491 /433

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ODE Solver: POLYMATHPolymath code (stirred tank heater):d(C) / d(t) = -1/tau*C + KT/tau*Ti + K1KT/tau*MC(0) = 0d(errsum) / d(t) = R – Cerrsum(0) = 0tau = 5 # minKT = 0.5 # %TO/degCK1KT = 0.8 # %TO/%COR = 0 # set point stays sameM = Kc*(R-C) + Kc/tauI*errsumstep = if (t<1) then (0) else (1)Ti = 0 + step * 10 # step change disturbanceKc = 1.3 # %CO/%TOtauI = 10 # mint(0) = 0t(f) = 100 # min

In Class Demo / Exercise:• Polymath Demonstration• Build model in Polymath (ODE solver)• Solve; graph C vs t• Explore:• Try P-only controller• Adjust Kc and tauI to get QAD• Try different Kc/tauI sets• Can you get underdamped response?•What is response to step change in R(t); holding Ti at the SS value?

Page 6: CBE 491 /433

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CBE 491 / 433 Model of Stirred Tank HeaterGoal: set up models to simulate and see effect of tuning parameters

• 1st principles (Chaps 3 – 6); • transfer functions (just looked at this a bit)• process simulators (AspenPlus Dynamics; CBE 450/550 class)

Page 7: CBE 491 /433

7

155.0s

++

si

158.0scG

-

sE+ sR sC

ssEsMsGC 10

113.1)()()(

Stirred Tank Heater (transfer function simulator)

sM

Transfer function simulator: Loop Pro Developer (Control Station) In Class Demo / Exercise:• Build model in Loop Pro Developer (Custom Process)• Turn on PI Controller and set Kc and tauI• Explore:• Change load (Ti) up by 10 to 60%; observe system response• Change back to 50%; observe response• Try P-only controller• Adjust Kc and tauI to get QAD• Try different Kc/tauI settings• Can you get underdamped response?•What is response to step change in R(t) to 60%?

Page 8: CBE 491 /433

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CBE 491 / 433 Model of Stirred Tank HeaterGoal: set up models to simulate and see effect of tuning parameters• 1st principles (Chaps 3 – 6); • transfer functions (just looked at this a bit)• process simulators (AspenPlus Dynamics; CBE 450/550 class)

Page 9: CBE 491 /433

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SAVE your Polymath and Loop Pro Developer Models !!


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