1. Tariq Ahamed Wavelet Neural Control Of Cascaded Continuous Stirred Tank Reactors

2. 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.

3. 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);

4. 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

5. 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): C p Heat Capacity of Coolant Fluid (J/g-K): C pc

6. Controller Design PID controller Direct Inverse Controller Internal Model Controller The neural controllers are also modeled in Wavelet Network.

7. 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 given

8. Parameters Cohen Coon method was used to arrive at the following values of K p, K i and K d. K i = 304.9508 sec -1 K p = 10.628 mol/L/sec K d = 0.0005907 sec

9. Graph for multiple set point tracking. Rise Time (sec)Peak OvershootSettling Time (sec)Offset Values230740

10. 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.

11. 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- tansig

12. Rise Time (sec)Peak OvershootSettling Time (sec)Offset Load disturbance settling (Load given for 150 sec) Values50.00004250171

13. 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

14. Rise Time (sec)Peak OvershootSettling Time (sec)Offset Load disturbance settling (Load given for 150 sec) Values14024016

15. Training the neural controllers using Wavelet Neural Network Shannon Filter where

16. 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 OvershootSettling Time (sec)Offset Load disturbance settling (Load given for 150 sec) Values30.000136240167

17. 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 OvershootSettling Time (sec)Offset Load disturbance settling (Load given for 150 sec) Values14022014

18. Results ControllerRise Time (sec) Peak Overshoot Settling time (sec) Offset (mol/L) Load disturbance settling (Load given for 150 sec) PID230740- DIC50.00004250171 IMC14024016 DIC-WNN30.000136240167 IMC-WNN14022014

19. ANN- DIC WNN- DIC ANN- IMC WNN- IMC