MATLAB: Need help setting up function and graphing

graphintegrationmatlab functionvariables

Im trying to write a code and graph it but i keep getting these following errors:
Error using odearguments (line 87)
The entries in tspan must strictly increase or decrease.
Error in ode45 (line 115)
odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
Error in SEMIBATCH_6_6graph (line 3)
[v,x]=ode45('SEMIBATCH_6_6',vspan,ic);
Im a bit new to Matlab and am slowly but surely figuring this all out. 
% xdot(1)=dV/d(t)
% xdot(2)=d(Nc)/d(t)
% xdot(3)=d(Nb)/d(t)
% xdot(4)=d(Na)/d(t)
function xdot=SEMIBATCH_6_6(v,x)
Cbo = 1.5;
Fbo = 6;
Cao = 0.75;
Nao = 1125;
k = 5.1;
rho =1000;
MWCO2 = 44;
Cc=Nc/V;
X = (Nao-Na)/Nao;
Ca = Na/V;
Cb = Nb/V;
ra = -k*Ca*Cb;
vo = Fbo/Cbo;
FCO2 = -ra*V;
vCO2 = FCO2*MWCO2/rho;
Cd = Cc;
xdot(1,:) = vo-vCO2;
xdot(2,:) = -ra*V;
xdot(3,:) = Fbo+ra*V;
xdot(4,:) = ra*V;
end
Here is the code for the graphing. Any little bit helps 
ic=[1125; 0; 0];
vspan= [1500, 1500, 2450.5, 2450.5];
[v,x]=ode45('SEMIBATCH_6_6',vspan,ic);
plot(v,x);
title('Semibatch with Moles as the Variables');
xlabel('V(Seconds)');
ylabel('Na,Nb,Nc');
ic=[.75; 0; 0];
xspan=[0,0,1,1];
[v,x]=ode45('SEMIBATCH_6_6',xspan,ic);
plot(v,x);
title('Semibatch with Moles as the Variables');
xlabel('V(Seconds)');
ylabel('Ca,Cb,Cc');

Best Answer

Hi
First correction in your subfunction : there was missing code (see comments) : V, Nc, Nb, Na are not defined (how they are linked to x)
function xdot=SEMIBATCH_6_6(v,x)
% xdot(1,:)=dV/d(t)
% xdot(2,:)=d(Nc)/d(t)
% xdot(3,:)=d(Nb)/d(t)
% xdot(4,:)=d(Na)/d(t)
	Cbo = 1.5;
	Fbo = 6;
	Cao = 0.75;
	Nao = 1125;
	k = 5.1;
	rho =1000;
	MWCO2 = 44;
	
	%%%%%%%%%%%%%%%


	% missing code : V, Nc, Nb, Na are not defined (how they are linked to x)
	V = x(1,:);
	Nc = x(2,:);
	Nb = x(3,:);
	Na = x(4,:);
	%%%%%%%%%%%%%%%
    
	Cc=Nc/V;
	X = (Nao-Na)/Nao;
	Ca = Na/V;
	Cb = Nb/V;
	ra = -k*Ca*Cb;
	vo = Fbo/Cbo;
	FCO2 = -ra*V;
	vCO2 = FCO2*MWCO2/rho;
	Cd = Cc;
	xdot(1,:) = vo-vCO2;
	xdot(2,:) = -ra*V;
	xdot(3,:) = Fbo+ra*V;
	xdot(4,:) = ra*V;
end
then there was some issue with time span and ic vector size . I could make the code to work, but I let you double check if it matches your expectations. I let you correct your second ode computation based on the suggestion below :
also I prefer to use t instead of v as time output of the ode45 function. This could lead to some confusion with your V variable
(that's why I was not sure either if you plot the data vs time t or vs V)
% ic=[1125; 0; 0];  % ic vector size (1x3) inconsistent with x vector in the ODE (4x1)
ic=[1125; 0; 0; 0]; % ic vector must be the same size as your x vector in the ODE (4x1)
% 	V, Nc, Nb, Na link to x : 
% 	V = x(1,:);
% 	Nc = x(2,:);
% 	Nb = x(3,:);
% 	Na = x(4,:);
	%%%%%%%%%%%%%%%
% vspan= [1500, 1500, 2450.5, 2450.5];  % twice too much variables 
vspan= [1500, 2450.5];  % this is the time span ( t start , t end) so only 2 variables
[t,x]=ode45('SEMIBATCH_6_6',vspan,ic);
figure(1),
subplot(2,1,1),plot(t,x(:,1)); % only display first column of x (corresponding to V)
title('Plot vs time');
xlabel('time (Seconds)');
ylabel('V');
legend('V');
subplot(2,1,2),plot(t,x(:,2:4)); % only display last 3 columns of x (corresponding to Na,Nb,Nc)
title('Plot vs time');
xlabel('time (Seconds)');
ylabel('Na,Nb,Nc');
legend('Na','Nb','Nc');
figure(2),
plot(x(:,1),x(:,2:4)); 
title('Plot Na,Nb,Nc vs V');
xlabel('V');
ylabel('Na,Nb,Nc');
legend('Na','Nb','Nc');
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