CBE 491 /433
15 Oct 12
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)
1
Stirred Tank Heater
i s 
(w/ PI Controller)
Rs  +
E s 
Gc
M s 

1 

GC ( s )  K c 1 
 I s 
KL
 L s 1
KP
 P s 1
+
+
C s 
K1  K V  s K 2
 KL 
 KP 
1* K T 
 K1 K T 
C s   

(
s
)

M
(
s
)


(
s
)

 i


 s  1 i
 s  1 M ( s )

s

1

s

1




 L

 P


dC (t )
 C (t )  K T i (t )  K1 K T M (t )
dt
energy balance on tank w/o control


K
M (t )  K C  E (t )  C  E (t )dt 
I


PI controller equation
E (t )  R(t )  C (t )
2
Stirred Tank Heater

dC (t )
 C (t )  KT i (t )  K1 KT M (t )
dt


K
M (t )  K C  E (t )  C  E (t )dt
I


(w/ PI Controller)
dC (t )
1
K
KK
  C (t )  T i (t )  1 T M (t )
dt



Let: errsum   E (t )dt
d errsum 
 E (t )
dt
d errsum 
 R(t )  C (t )
dt
M (t )  K C R(t )  C (t )  
KC
I
errsum
3
ODE Solver
(POLYMATH; MATLAB; MATHCAD; etc)
C t   0 @ t  0
dC (t )
1
K
KK
  C (t )  T i (t )  1 T M (t )
dt



d errsum 
 R(t )  C (t )
dt
M (t )  K C R(t )  C (t )  
  5 min
K T  0.5 %oTO
C
errsum  0 @ t  0
KC
I
errsum
Polymath code:
step= if (t<1) then (0) else (1)
Ti = 0 + step * 10
TO
K1 KT  0.8 %%CO
R(t )  0
K C  1.3 %%CO
TO
 I  10 min
4
ODE Solver: POLYMATH
Polymath 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)
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?
Ti = 0 + step * 10 # step change disturbance
Kc = 1.3 # %CO/%TO
tauI = 10 # min
t(0) = 0
t(f) = 100 # min
5
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)
6
Stirred Tank Heater
i s 
(transfer function simulator)
Rs  +
E s 
Gc
GC ( s ) 
M s 
0.5
5 s 1
0.8
5 s 1
+
+
C s 

M (s)
1 

 1.31 
E (s)
 10 s 
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%?
7
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)
8
SAVE your Polymath and Loop Pro Developer Models !!
9