Wavelet Neural Control Of Cascaded
Continuous Stirred Tank Reactors
Tariq Ahamed
AIM
 The main objective of the project is to control the
concentration of reactant in the CSTR.
 The tank is controlled by manipulating the coolant flow rate.
 The system is subjected to step changes and load disturbances
and the responses by different controllers are noted.
CSTR- Model
CA0 Feed
qc
Inputs
States
T1
CA1
T2
CA2
Reaction
A
B
Product
Input= Coolant Flow rate (L/min) : qc = u;
States:
Concentration of A in Reactor #1 (mol/L) : Ca1 = y(1);
Temperature of Reactor #1 (K) : T1 = y(2);
Concentration of A in Reactor #2 (mol/L) : Ca2 = y(3);
Temperature of Reactor #2 (K) : T2 = y(4);
The component balance
Rate of change
of ‘A’ inside the
tank
Rate of change
of ‘A’ caused by
chemical
reaction
Rate of flow of
‘A’ in
dV1C A1
 q C A0  qC A1  V1kC A1
dt
Rate of flow of
‘A’ out
E
dCA1 q
C Af  C A1   C A1e RT1

dt
V1
Where, q= inlet feed rate
Caf= feed concentration of A
V1= volume of reactor 1
 = pre exponential factor for A->B
E/R= Activation energy
The energy balance
Rate of flow of
energy into
CSTR
Rate of change
of liquid energy
dT1C p V
dt
 qCp T f  T1   Q  HV1kCA1
Rate at which
energy is
generated due
to chemical
reaction
Heat removal through energy jacket
dT1 qT f  T1  C pc c qc
U q  C 


1  e A1 c c pc Tcf  T1   He
V1
V1C p 
dt

Where,
Feed Temperature (K) : Tf
Coolant Temperature (K) : Tcf
Overall Heat Transfer Coefficient : UA1
Heat of Reaction: dH
Density of Fluid (g/L): rho
Density of Coolant Fluid (g/L): rhoc
Heat Capacity of Fluid (J/g-K): Cp
Heat Capacity of Coolant Fluid (J/g-K): Cpc

E
RT1
C A1
Cp
Controller Design
 PID controller
 Direct Inverse Controller
 Internal Model Controller
 The neural controllers are also modeled in Wavelet Network.
PID control
 The differential form of PID control is given as:
e= Creq- Ca(t)
And ek-1 and ek-2 are past values of error.
 Steady state initial conditions are given.
 Required concentration of A in reactor 2 is given
Parameters
 Cohen Coon method was used to arrive at the following
values of Kp, Ki and Kd.
 Ki= 304.9508 sec-1
 Kp= 10.628 mol/L/sec
 Kd= 0.0005907 sec
Graph for multiple set point tracking.
-3
x 10
Concentration of A
(mol/L)
6.5
6
5.5
5
4.5
4
3.5
0
100
200
300
400
500
600
Time(sec)
Values
Rise Time (sec)
Peak Overshoot
Settling Time (sec)
Offset
23
0
74
0
Neural Network Training
 A chirp signal (coolant flow rate) is given as input to the
Continuous Stirred Tank Reactor and output (concentration
of A) is taken.
 This pattern is divided in the columns of past inputs, past
outputs, present output and required output.
 The training of the network is done by feeding the feed
forward net with the pattern and adjusting the weights until
the error is reduced.
 The training uses Levenberg Marquardt algorithm.
ANN based DIC
u f
1
u(1),u(2), y(1), y, y(1)
The neural network consisted of 3 layers with 9 sigmoidal neurons in the hidden layer.
The learning rate was 0.3.
Activation function- tansig
-3
x 10
5
Coolant Flow Rate
(L/min)
Concentration of A
(mol/L)
6.5
6
5.5
5
4.5
4
3.5
0
100
200
300
400
500
3
2
1
0
600
Time(sec)
Rise Time (sec)
4
0
50
100
150
200
250
300
350
Time(sec)
Peak Overshoot
Settling Time (sec)
Offset
Load disturbance settling
(Load given for 150 sec)
Values
5
0.00004
25
0
171
400
ANN based IMC
The inverse network was same as the Direct Inverse Controller network.
The forward network had 1 input, 1 hidden layer with 4 neurons and 1 output.
The learning rate was 0.01.
Activation function- tansig
-3
x 10
5
Coolant Flow Rate
(L/min)
Concentration of A
(mol/L)
6.5
6
5.5
5
4.5
4
3.5
0
100
200
300
400
500
3
2
1
0
600
Time(sec)
Rise Time (sec)
4
0
50
100
150
200
250
300
350
Time(sec)
Peak Overshoot
Settling Time (sec)
Offset
Load disturbance settling
(Load given for 150 sec)
Values
14
0
24
0
16
400
Training the neural controllers using
Wavelet Neural Network
Shannon Filter

sin 2  sin  
h( ) 

where
  t  b a
WNN based DIC
 The inverse neural model here consisted of 5 inputs, 1 hidden layer with 7 shannon
neurons and 1 output. The learning rate was 0.064.
-3
x 10
5
Coolant Flow Rate
(L/min)
Concentration of A
(mol/L)
6.5
6
5.5
5
4.5
4
3.5
0
100
200
-3
300
400
500
3
2
1
0
600
Time(sec)
x 10
4
0
50
100
150
200
250
300
350
Time(sec)
Concentration of A
(mol/L)
6.5
6
5.5
5
4.5
4
3.5
0
100
200
300
400
500
Time(sec)
Rise Time (sec)
Peak Overshoot
600
Settling Time (sec)
Offset
Load disturbance settling
(Load given for 150 sec)
Values
3
0.000136
24
0
167
400
WNN based IMC
 The forward model had 3 inputs, 1 output and 1 hidden layer with 5 shannon
neurons with the learning rate of 0.01.
-3
x 10
5
Coolant Flow Rate
(L/min)
Concentration of A
(mol/L)
6.5
6
5.5
5
4.5
4
3.5
0
100
200
300
400
500
3
2
1
0
600
Time(sec)
Rise Time (sec)
4
0
50
100
150
200
250
300
350
Time(sec)
Peak Overshoot
Settling Time (sec)
Offset
Load disturbance settling
(Load given for 150 sec)
Values
14
0
22
0
14
400
Results
Controller
Rise Time
(sec)
Peak
Overshoot
Settling
time (sec)
Offset
(mol/L)
Load
disturbance
settling
(Load given
for 150 sec)
PID
23
0
74
0
-
DIC
5
0.00004
25
0
171
IMC
14
0
24
0
16
DIC-WNN
3
0.000136
24
0
167
IMC-WNN
14
0
22
0
14
ANN- DIC
WNN- DIC
ANN- IMC
WNN- IMC