Question

fix this code for me in math lab and get it to produce a graph and send me the new code and picture of the graph. I defined all the equations and constants already, I just can't get it to work and I need help.

code :

clear;clc;

t0=0;tf=100;

y0=[1;2]; % input spec ((y(1)- F_1; y(2)-H_1; y(3)- H_3;

soln=ode45(@f,[t0,tf],y0); %Solve the set of ODEs

t=linspace(t0,tf,100); %create x axis spacing

y1=deval(soln,t,1); %get value for y1 @ all t

y2=deval(soln,t,2); %get value for y2 @ all t

plot(t,y1,'k-',t,y2,'k--'); %plot it. y2 is dashed

xlabel('t(s)');

ylabel('tank level(m)');

end

%NOTE: Matlab fundamentally works with matrices, so lines 8-10 work on the

%entire solution set as soon as they're executed. (ie. no loops needed)

function dYdt= f(t,y)

tauv = 3;

F_outspec=0.06684028; %ft3/s

H_1 = 5;

H_2 = 5;

H_d = 2;

A_1 = 15;

A_2 = 20;

K_1 = 1 ;

K_2 = 1 ;

if t>= 400; F_outspec = 0.07352431 ;

end

dYdt(1) = ( F_outspec - y(1))/tauv;

dYdt(2) = ((y(1)/A_1) - (K_1*((H_1 +H_d + H_2)^0.5)/A_1));

dYdt(3) = ((K_2*(H_1 +H_d - H_2)^0.5) - (K_2 * (H_2)^0.5))/A_2 ;

dYdt=dYdt'; %return dYdt as column vector

end

Answer 1

There are two issues with the code:

1) An extra "end" after the ylabel as:

ylabel('tank level(m)');

end ------------> Remove this!!

2) You initial condition set is having only two values for y0 written as:

y0=[1;2]; --------> add one more entry as per the given details for your question, the program works fine!!

For example see the following execution: (Note: we have added a third entry (3) randomly, you need to update the same as per given in original question!)

%===================================================

clc;
clear all;
format long

clear;clc;

t0=0;
tf=100;

y0=[1;2;3]; % input spec ((y(1)- F_1; y(2)-H_1; y(3)- H_3;

soln=ode45(@f,[t0,tf],y0); %Solve the set of ODEs

t=linspace(t0,tf,100); %create x axis spacing

y1=deval(soln,t,1); %get value for y1 @ all t

y2=deval(soln,t,2); %get value for y2 @ all t

plot(t,y1,'k-',t,y2,'k--'); %plot it. y2 is dashed

xlabel('t(s)');

ylabel('tank level(m)');

%NOTE: Matlab fundamentally works with matrices, so lines 8-10 work on the

%entire solution set as soon as they're executed. (ie. no loops needed)

function dYdt= f(t,y)

tauv = 3;

F_outspec=0.06684028; %ft3/s

H_1 = 5;

H_2 = 5;

H_d = 2;

A_1 = 15;

A_2 = 20;

K_1 = 1 ;

K_2 = 1 ;

if t>= 400; F_outspec = 0.07352431 ;

end

dYdt(1) = ( F_outspec - y(1))/tauv;

dYdt(2) = ((y(1)/A_1) - (K_1*((H_1 +H_d + H_2)^0.5)/A_1));

dYdt(3) = ((K_2*(H_1 +H_d - H_2)^0.5) - (K_2 * (H_2)^0.5))/A_2 ;

dYdt=dYdt'; %return dYdt as column vector

end

%==============================================

output plot: