1

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)

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

sMs

Ks

s

KsC

P

Pi

L

L

)()()()(

1 tMKKtKtCdt

tdCTiT

dttEK

tEKtMI

CC )()()(

sM

)(1

)(1

*1 1 sMs

KKs

s

K Ti

T

21 KKK sV

PI controller equation

)()()( tCtRtE

3

Let:

Stirred Tank Heater (w/ PI Controller)

)()()(1)( 1 tM

KKt

KtC

dt

tdC Ti

T

errsumK

tCtRKtMI

CC

)()()(

dttEerrsum )(

)(tEdt

errsumd

)()( tCtR

dt

errsumd

)()()()(

1 tMKKtKtCdt

tdCTiT

dttEK

tEKtMI

CC )()()(

4

ODE Solver (POLYMATH; MATLAB; MATHCAD; etc)

)()()(1)( 1 tM

KKt

KtC

dt

tdC Ti

T

errsumK

tCtRKtMI

CC

)()()(

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

0@0 ttC

)()( tCtR

dt

errsumd 0@0 terrsum

CTO

T oK %5.0

min5

0)( tR

COTO

TKK %%

1 8.0

TOCO

CK %%3.1

min10I

5

ODE Solver: POLYMATHPolymath code (stirred tank heater):

d(C) / d(t) = -1/tau*C + KT/tau*Ti + K1KT/tau*M

C(0) = 0

d(errsum) / d(t) = R – C

errsum(0) = 0

tau = 5 # min

KT = 0.5 # %TO/degC

K1KT = 0.8 # %TO/%CO

R = 0 # set point stays same

M = Kc*(R-C) + Kc/tauI*errsum

step = if (t<1) then (0) else (1)

Ti = 0 + step * 10 # step change disturbance

Kc = 1.3 # %CO/%TO

tauI = 10 # min

t(0) = 0

t(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?

6

CBE 491 / 433 Model 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)

7

15

5.0

s

++

si

15

8.0

scG-

sE+ sR sC

ssE

sMsGC 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%?

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CBE 491 / 433 Model 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)

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SAVE your Polymath and Loop Pro Developer Models !!