Hello, I am at my final year of MSc in Electrical engineering and my thesis is about control in a pH neutralization process.
The aim is to control the pH of the system and the chemical equation which occurs in the CSTR is: HCl + NaOH->H + OH + Na + Cl
The input variables of the system are:
-F1 ( HCL flow rate ) [500 lt/min]
-F2(t) ( NaOH flow rate )
-C1 ( inlet concentration of HCl ) [0.01mol/lt]
-C2 (inlet concentration of NaOH ) [0.1mol/lt]
The output variables are:
-F=F1+F2(t) (total flow rate at the exit)
-Ccl(t) (outlet concentration of Cl ions )
-Cna(t) (outlet concentration of Na ions)
-Ch(t) (outlet concentration of Hydrogen ions)
-Coh(t) (outlet concentration of OH ions)
The constants are:
V : volume of CSTR [20000lt]
Kw : water dissociation constant [1e-14 mol^2/lt^2]
The equations that take place here are:
i)Electroneutrality: Ccl+Coh=Cna+Ch
ii)pH definition: pH=-log10(Ch)
iii)Coh*Ch=Kw
iv)mass balances: V*dCcl/dt=F1*C1-(F1+F2)*Ccl V*dCna/dt=F2*C2-(F1+F2)*Cna
The pH of the system is considered to be the output of the system and F2 is considered to be the input (u).Everything else is considered to be constant.
I have managed to represent this in state space form and perform successfully I/O feedback linearization.Specifically:
if x1=Ccl and x2=Cna and x=x1-x2=Ccl -Cna=Ch-Coh
then the system is : V*dx/dt=F1*C1-F2*C2-(F1+F2)*x or in terms of y,x,u: V*dx/dt=F1*C1-u*C2-(F1+u)*x
Also, Ch=[x+sqrt(x^2+Kw)]/2 and the output y=pH=-log10(Ch)
But I have noticed that a lot of papers obtain a transfer function of the system even though it is nonlinear.
Does anyone have any idea how to accomplish that?
I have failed to linearize it around an operating point and obtain the desirable transfer function-> pH(s)/Fb(s)
Some papers use a method called First Order plus Time Delay Model (or FOPTD) but I have found zero theory over that method.
Any ideas or suggestions would be highly appreciated.Thank you in advance!
The aim is to control the pH of the system and the chemical equation which occurs in the CSTR is: HCl + NaOH->H + OH + Na + Cl
The input variables of the system are:
-F1 ( HCL flow rate ) [500 lt/min]
-F2(t) ( NaOH flow rate )
-C1 ( inlet concentration of HCl ) [0.01mol/lt]
-C2 (inlet concentration of NaOH ) [0.1mol/lt]
The output variables are:
-F=F1+F2(t) (total flow rate at the exit)
-Ccl(t) (outlet concentration of Cl ions )
-Cna(t) (outlet concentration of Na ions)
-Ch(t) (outlet concentration of Hydrogen ions)
-Coh(t) (outlet concentration of OH ions)
The constants are:
V : volume of CSTR [20000lt]
Kw : water dissociation constant [1e-14 mol^2/lt^2]
The equations that take place here are:
i)Electroneutrality: Ccl+Coh=Cna+Ch
ii)pH definition: pH=-log10(Ch)
iii)Coh*Ch=Kw
iv)mass balances: V*dCcl/dt=F1*C1-(F1+F2)*Ccl V*dCna/dt=F2*C2-(F1+F2)*Cna
The pH of the system is considered to be the output of the system and F2 is considered to be the input (u).Everything else is considered to be constant.
I have managed to represent this in state space form and perform successfully I/O feedback linearization.Specifically:
if x1=Ccl and x2=Cna and x=x1-x2=Ccl -Cna=Ch-Coh
then the system is : V*dx/dt=F1*C1-F2*C2-(F1+F2)*x or in terms of y,x,u: V*dx/dt=F1*C1-u*C2-(F1+u)*x
Also, Ch=[x+sqrt(x^2+Kw)]/2 and the output y=pH=-log10(Ch)
But I have noticed that a lot of papers obtain a transfer function of the system even though it is nonlinear.
Does anyone have any idea how to accomplish that?
I have failed to linearize it around an operating point and obtain the desirable transfer function-> pH(s)/Fb(s)
Some papers use a method called First Order plus Time Delay Model (or FOPTD) but I have found zero theory over that method.
Any ideas or suggestions would be highly appreciated.Thank you in advance!
