Wavelet Neural Control Of Cascaded Continuous Stirred Tank Reactors 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 ID: 358101
Download Presentation The PPT/PDF document "Tariq Ahamed" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Tariq Ahamed
Wavelet Neural Control Of Cascaded Continuous Stirred Tank ReactorsSlide2
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.Slide3
CSTR- Model
C
A0
Input= Coolant Flow rate (L/min) : q
c
= u;
States: Concentration of A in Reactor #1 (mol/L) : C
a1
= y(1);
Temperature of Reactor #1 (K) : T
1
= y(2);
Concentration of A in Reactor #2 (mol/L) : C
a2
= y(3);
Temperature of Reactor #2 (K) : T
2
= y(4);Slide4
The component balance
Rate of flow of
‘A’ in
Rate of flow of
‘A’ out
Rate of change
of ‘A’ caused by
chemical
reaction
Rate of change
of ‘A’ inside the
tank
Where, q= inlet feed rate
C
af
= feed concentration of A
V
1
= volume of reactor 1
= pre exponential factor for A->B
E/R= Activation energy Slide5
The energy balance
Rate of flow of
energy into
CSTR
Heat removal through energy jacket
Rate at which
energy is
generated due
to chemical
reaction
Rate of change
of liquid energy
Where, Feed Temperature (K) :
T
f
Coolant Temperature (K) :
T
cf
Overall Heat Transfer Coefficient : U
A1
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): C
pcSlide6
Controller Design
PID controller
Direct Inverse Controller
Internal Model Controller
The neural controllers are also modeled in Wavelet Network.Slide7
PID control
The differential form of PID control is given as:
e= C
req
- C
a
(t)
And e
k-1
and e
k-2 are past values of error.
Steady state initial conditions are given.Required concentration of A in reactor 2 is givenSlide8
Parameters
Cohen Coon method was used to arrive at the following values of
K
p
,
K
i and Kd
.
K
i
= 304.9508 sec-1Kp= 10.628
mol/L/secKd= 0.0005907 secSlide9
Graph for multiple set point tracking.
Rise Time (sec)
Peak Overshoot
Settling Time (sec)
Offset
Values
23
0
74
0Slide10
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.Slide11
ANN based DIC
The neural network consisted of 3 layers with 9 sigmoidal neurons in the hidden layer. The learning rate was 0.3.
Activation function- tansigSlide12
Rise Time (sec)
Peak Overshoot
Settling Time (sec)
Offset
Load disturbance settling (Load given for 150 sec)
Values
5
0.00004
25
0
171Slide13
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- tansigSlide14
Rise Time (sec)
Peak Overshoot
Settling Time (sec)
Offset
Load disturbance settling (Load given for 150 sec)
Values
14
0
24
0
16Slide15
Training the neural controllers using Wavelet Neural Network
Shannon Filter
whereSlide16
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.
Rise Time (sec)
Peak Overshoot
Settling Time (sec)
Offset
Load disturbance settling (Load given for 150 sec)
Values
3
0.000136
24
0
167Slide17
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.
Rise Time (sec)
Peak Overshoot
Settling Time (sec)
Offset
Load disturbance settling (Load given for 150 sec)
Values
14
0
22
0
14Slide18
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
-
DIC50.00004
250171
IMC140240
16DIC-WNN3
0.000136240167
IMC-WNN140
22014Slide19
ANN- DIC
WNN- DIC
ANN- IMC
WNN- IMC