Why am I getting the following errors

For the following code, I am getting an error and I am unable to figure out why. Any help would be handy.

%MATLAB     SYMBOL              DESCRIPTION                             IC                  Units
%x(1)               X                   Cell Concentration              0.5                 kmol/m3
%x(2)               S                   Substrate  Concentration        0.38                kmol/m3
%x(3)               P                   Product Concentration              0                kmol/m3
%x(4)               G                   Glycerol Concentration         0                kmol/m3
%x(5)               V                   Volume                             0                m3
 
ic = [0.5; 0.38; 0; 0; 0];
 
%MATLAB     PARAMETER       DESCRIPTION                                 Value           UNITS 
%mumax      mu_{max}            Maximum Growth Rate                     0.2             1/hour
%Ks         K_s                 Monod Constant                          2               kg/m3
%Yxs        Y_{X/S}             Cell Yield                              0.58            kg/kg
%Ypx        Y_{P/X}             Product Yield                           0.2             kg/kg
%Yxo        Y_{X/O}             Glycerol Yield 
%Sf         S_f                 Feed Substrate Concentration            0.37            kmol/m3
%Kp         K_p                 Product Inhibition                      97.9            kg/m3
 
mumax = 0.20;
Ks = 2;
Yxs = 0.58;
Ypx = 0.2; 
Yxo = 2.46;
Sf = 0.37;
Kp = 97.9;
 
mu = @(S,P) (mumax*S./(Ks + S))*(1 - (P/Kp))^0.5; % Monod Equation
rg = @(X,S,P) mu(S,P)*X; % Rate of cell growth
rp = @(X,S,P) Ypx*rg(X,S,P); % Rate of ethanol formation
rpg = @(X,S,P,G) Yxo*rg(X,S,P); % Rate of glycerol formation 
 
F = @(t) 2;
 
dXV = @(t, x) x(5) *rg(x(1),x(2),x(3));
dPV = @(t, x) x(5) *rp(x(1),x(2),x(3));
dSV = @(t, x) F(t)*Sf - x(5)*rg(x(1),x(2),x(3),x(4))/Yxs;
dGV = @(t, x) x(5) *rpg(x(1),x(2),x(3));
dV = @(t, x) F(t); 
 
dX = @(t, x) (dXV(t,x) - x(1)*dV(t,x))/x(5);
dS = @(t, x, s) (dSV(t,x) - x(2)*dV(t,x))/x(5);
dP = @(t, x, p) (dPV(t,x) - x(3)*dV(t,x))/x(5);
dG = @(t, x, g) (dGV(t,x) - x(4)*dV(t,x))/x(5);
 
f = @(t,x) [dX(t,x); dS(t,x,s); dP(t,x,p); dG(t,x,g); dV(t,x)];
 
tspan = [0 100];
[t,x] = ode45(f,tspan,ic);
 
subplot(2,2,1);
plot(t,x(:,1));
xlabel('Time (hr)');
ylabel('X (kmol/m3)');
title('Cell Concentration');
 
subplot(2,2,2);
plot(t,x,s(:,3));
xlabel('Time (hr)');
ylabel('P (kmol/m3 )');
title('Product Concentration');
 
 
subplot(2,2,3);
plot(t,x,p(:,2));
xlabel('Time (hr)');
ylabel('S (kmol/m3)');
title('Substrate Concentration');
 
subplot(2,2,4);
plot(t,x,g(:,4));
xlabel('Time (hr)');
ylabel('V (m3)');
title('Volume');
subplot(2,2,5);
plot(t,x,g,p(:,5));
xlabel('Time (hr)');
ylabel('Glycerol Concentration (kmol/m3)');
title('Glycerol');

The error is:

Undefined function or variable 's'.

Error in @(t,x)[dX(t,x);dS(t,x,s);dP(t,x,p);dG(t,x,g);dV(t,x)]

Error in odearguments (line 90)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options,

varargin);

[Stephen23]

"I am getting an error and I am unable to figure out why. Any help would be handy."

First read the error message:

Undefined function or variable 's'.
Error in @(t,x)[dX(t,x);dS(t,x,s);dP(t,x,p);dG(t,x,g);dV(t,x)]

Then look at that line of code:

f = @(t,x) [dX(t,x); dS(t,x,s); dP(t,x,p); dG(t,x,g); dV(t,x)];

Where is s defined?

[Jan]

I've formatted your code today to improve the readability. Do you see the bar on top of the field to edit your message? Please use it.

Answer 1

[Torsten]

dS = @(t, x) (dSV(t,x) - x(2)*dV(t,x))/x(5);
dP = @(t, x) (dPV(t,x) - x(3)*dV(t,x))/x(5);
dG = @(t, x) (dGV(t,x) - x(4)*dV(t,x))/x(5);
 
f = @(t,x) [dX(t,x); dS(t,x); dP(t,x); dG(t,x); dV(t,x)];

Answer 2

[Jan]

This is strange:

dS = @(t, x, s) (dSV(t,x) - x(2)*dV(t,x))/x(5);
dP = @(t, x, p) (dPV(t,x) - x(3)*dV(t,x))/x(5);
dG = @(t, x, g) (dGV(t,x) - x(4)*dV(t,x))/x(5);

You do not use s, p, g inside the functions, so why do you provide them?

f = @(t,x) [dX(t,x); dS(t,x,s); dP(t,x,p); dG(t,x,g); dV(t,x)];

Or, better: You do not provide them. Here the variabels s,p,g are not defined. Although they are not used later, Matlab must assign a value to them, when the anonymous function is evaluated.

The exhaustive use of nested anonymous function is hard to debug. I prefer to use standard functions and to use anonymous functions only to provide the parameters. Then I can simply set a breakpoint in the debugger to see what's going on.

A hint: ^0.5 is more expensive than sqrt.

Answer 3

[Jesús Zambrano]

Hi,

One thing I saw is that you define rg with three variables, but then you say:

dSV = @(t, x) F(t)*Sf - x(5)*rg(x(1),x(2),x(3),x(4))/Yxs;

where it uses 4 variables. This still cannot explain your error message but is something that would be good to look at.

[em246]

I had noticed earlier and corrected that, thank you!

Now the code is working however only 4 plots appear not 5. My adjusted code is below, and the 'volume' subplot is not coming up. Is it something in the code thats wrong? Thanks in advance.

%MATLAB     SYMBOL           DESCRIPTION                     IC                  Units
%x(1)               X        Cell Concentration              0.5                 kmol/m3
%x(2)               S        Substrate  Concentration        0.38                kmol/m3
%x(3)               P        Product Concentration              0                kmol/m3
%x(4)               G        Glycerol Concentration             0                kmol/m3
%x(5)               V        Volume                             1                m3
ic = [0.5; 0.38; 0; 0; 5];
 
%MATLAB     PARAMETER    DESCRIPTION                    Value       UNITS 
%mumax      mu_{max}     Maximum Growth Rate            0.2         1/hour
%Ks         K_s          Monod Constant                 2           kg/m3
%Yxs        Y_{X/S}      Cell Yield                     0.58        kg/kg
%Ypx        Y_{P/X}      Product Yield                  0.2         kg/kg
%Yxo        Y_{X/O}      Glycerol Yield                 2.46        kg/kg
%Sf         S_f          Feed Substrate Concentration   0.37        kmol/m3
%Kp         K_p          Product Inhibition             97.9        kg/m3
 
mumax = 0.20;
Ks = 2;
Yxs = 0.58;
Ypx = 0.2; 
Yxo = 2.46;
Sf = 0.37;
Kp = 97.9;
 
mu = @(S,P) (mumax*S./(Ks + S))*sqrt(1 - (P/Kp)); % Monod Equation
rg = @(X,S,P) mu(S,P)*X; % Rate of cell growth
rp = @(X,S,P) Ypx*rg(X,S,P); % Rate of ethanol formation
rpg = @(X,S,P) Yxo*rg(X,S,P); % Rate of glycerol formation
F = @(t) 5;
 
dXV = @(t,x) x(5)*rg(x(1),x(2),x(3));
dPV = @(t,x) x(5)*rp(x(1),x(2),x(3));
dSV = @(t,x) F(t)*Sf - x(5)*rg(x(1),x(2),x(4))/Yxs;
dGV = @(t,x) x(5)*rpg(x(1),x(2),x(3));
dV = @(t,x) F(t); 
 
dX = @(t,x) (dXV(t,x) - x(1)*dV(t,x))/x(5);
dS = @(t,x) (dSV(t,x) - x(2)*dV(t,x))/x(5);
dP = @(t,x) (dPV(t,x) - x(3)*dV(t,x))/x(5);
dG = @(t,x) (dGV(t,x) - x(4)*dV(t,x))/x(5);
 
f = @(t,x) [dX(t,x); dS(t,x); dP(t,x); dG(t,x); dV(t,x)];
 
tspan = [0 100];
[t,x] = ode45(f,tspan,ic);
 
subplot(2,2,1);
plot(t,x(:,1));
xlabel('Time (hr)');
ylabel('X (kmol/m3)');
title('Cell Concentration');
subplot(2,2,2);
plot(t,x(:,3));
xlabel('Time (hr)');
ylabel('P (kmol/m3 )');
title('Product Concentration');
subplot(2,2,3);
plot(t,x(:,2));
xlabel('Time (hr)');
ylabel('S (kmol/m3)');
title('Substrate Concentration');
subplot(2,2,4);
plot(t,x(:,4));
xlabel('Time (hr)');
ylabel('Glycerol Concentration (kmol/m3)');
title('Glycerol');
subplot(2,2,5);
plot(t,x(:,5));
xlabel('Time (hr)');
ylabel('V (m3)');
title('Volume');

[Jesús Zambrano]

Hi!,

Since you want to show 5 plots using the subplot command, then try subplot(3,2,1), ..., subplot(3,2,5). In other words:

subplot(3,2,1);
plot(t,x(:,1));
xlabel('Time (hr)');
ylabel('X (kmol/m3)');
title('Cell Concentration');
subplot(3,2,2);
plot(t,x(:,3));
xlabel('Time (hr)');
ylabel('P (kmol/m3 )');
title('Product Concentration');
subplot(3,2,3);
plot(t,x(:,2));
xlabel('Time (hr)');
ylabel('S (kmol/m3)');
title('Substrate Concentration');
subplot(3,2,4);
plot(t,x(:,4));
xlabel('Time (hr)');
ylabel('Glycerol Concentration (kmol/m3)');
title('Glycerol');
subplot(3,2,5);
plot(t,x(:,5));
xlabel('Time (hr)');
ylabel('V (m3)');
title('Volume');