I am fitting these curves in my MATLAB but the y-axis of every curve is not matching with that of the textbook figure. Can someone help in this. I am in real worry.

This is the graph I want to plot-----

And the parameters are------

But I am getting this graph----

I am also attaching the code which I used-------------------------------------------------------------------------

% implement YanoandKoga1 Model as a Matlab anonymous function

YanoandKoga1 = @(S) 0.51*S./(1.413+S+(S.^2/1250)+(S.^3/4.561));

% calculate mu

mu = YanoandKoga1(S);

hold on

% plot result

plot(S,mu,'k --'), xlabel('S (g/l)'), ylabel('\mu (1/h)');

% implement YanoandKoga2 Model as a Matlab anonymous function

YanoandKoga2= @(S) 0.41*S./(5.23+S+(S.^3/2.64));

% calculate mu

mu = YanoandKoga2(S);

hold on

% plot result

plot(S,mu,'k-'), xlabel('S (g/l)'), ylabel('\mu (1/h)');

% implement AlagappanandCowan Model as a Matlab anonymous function

AlagappanandCowan= @(S)(0.82*S./(4.366+S+(S.^2/2.246)))-(0.004379*(S+2.985));

% calculate mu

mu = AlagappanandCowan(S);

hold on

% plot result

plot(S,mu,'k-o'), xlabel('S (g/l)'), ylabel('\mu (1/h)');

% implement WaymanandTseng Model as a Matlab anonymous function

WaymanandTseng= @(S)(0.3164*S./(0.7346+S))-((0.01618)*(S+0.2886));

% calculate mu

mu = WaymanandTseng(S);

hold on

% plot result

plot(S,mu,'k -.'), xlabel('S (g/l)'), ylabel('\mu (1/h)'), legend('YanoandKoga1','YanoandKoga2', 'AlagappanandCowan','WaymanandTseng');

axis([0 20 0 0.3])

set(gca,'YTick',[0 0.05 .1 0.15 0.2 0.25 0.3 ])

set(gca,'YTickLabel',[0 0.05 .1 0.15 0.2 0.25 0.3 ])

set(gca,'XTick',[0 2 4 6 8 10 12 14 16 18 20 ])

set(gca, 'XTicklabel', [0 2 4 6 8 10 12 14 16 18 20 ])

title('\mu vs S')

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Can anyone tell where I am lacking?

Thanks in advance.

[VBBV]

% implement YanoandKoga1 Model as a Matlab anonymous function
YanoandKoga1 = @(S) 0.51*S./(1.413+S+(S.^2/1250)+(S.^3/4.561));
% calculate mu
mu = YanoandKoga1(S);
hold on
% plot result
plot(S,mu,'k --'), xlabel('S (g/l)'), ylabel('\mu (1/h)');
% implement YanoandKoga2 Model as a Matlab anonymous function
YanoandKoga2= @(S) 0.41*S./(5.23+S+(S.^3/2.64));
% calculate mu
mu = YanoandKoga2(S);
hold on
% plot result
plot(S,mu,'k-'), xlabel('S (g/l)'), ylabel('\mu (1/h)');
% implement AlagappanandCowan Model as a Matlab anonymous function
AlagappanandCowan= @(S)(0.82*S./(4.366+S+(S.^2/2.246)))-(0.004379*(S+2.985)); % NOTICE THE CHANGE IN SIGN 
% calculate mu
mu = AlagappanandCowan(S);
hold on
% plot result
plot(S,mu,'k-o'), xlabel('S (g/l)'), ylabel('\mu (1/h)');
% implement WaymanandTseng Model as a Matlab anonymous function
WaymanandTseng= @(S)(0.3164*S./(0.7346+S))-((0.01618)*(S+0.2886)); % NOTICE CHANGE IN THE SIGN 
% calculate mu
mu = WaymanandTseng(S);
hold on
% plot result
plot(S,mu,'k -.'), xlabel('S (g/l)'), ylabel('\mu (1/h)'), legend('YanoandKoga1','YanoandKoga2', 'AlagappanandCowan','WaymanandTseng');
axis([0 20 0 0.3])
set(gca,'YTick',[0 0.05 .1 0.15 0.2 0.25 0.3 ])
set(gca,'YTickLabel',[0 0.05 .1 0.15 0.2 0.25 0.3 ])
set(gca,'XTick',[0 2 4 6 8 10 12 14 16 18 20 ])
set(gca, 'XTicklabel', [0 2 4 6 8 10 12 14 16 18 20 ])
title('\mu vs S')

[VBBV]

Check if the coefficients you are using are correct for the four models than the one shown. for the desired amplitudes you want

[Shubhangi Agrawal]

Where is the change ?

[VBBV]

I mean the desired coefficients for desired amplitudes you want may not be same. The amplitudes you shown in reference figure may require or is using different coefficients than the ones shown.

Answer 1

[Shubham Khatri]

Hello,

You need to define a symbolic variable. You can define it by using syms. For more information on syms please refer to this documentation link. After defining the variable you need to define a range of values for which you need to find the value of the function. I have specified a range from 0 to 20 with an intervel of 0.01 in variable S. Also, I found some typos in the code which I have corrected. Please find the below code.

clc
clear all
syms S
% implement YanoandKoga1 Model as a Matlab anonymous function
YanoandKoga1 = @(S) 0.51*(S./(1.413+S+((S.^2)./1250)+((S.^3)./4.561)));
% calculate mu
S=0:0.01:20;
mu =YanoandKoga1(S);
hold on
% plot result
plot(S,mu,'k --'), xlabel('S (g/l)'), ylabel('\mu (1/h)');
% implement YanoandKoga2 Model as a Matlab anonymous function
YanoandKoga2= @(S) 0.41.*(S./((5.23+S+((S.^3)./2.64))));
% calculate mu
mu = YanoandKoga2(S);
hold on
% plot result
plot(S,mu,'k-'), xlabel('S (g/l)'), ylabel('\mu (1/h)');
% implement AlagappanandCowan Model as a Matlab anonymous function
AlagappanandCowan= @(S)0.82.*(S./(4.366+S+((S.^2)./2.246)))-(0.004379.*(S+2.985)); % NOTICE THE CHANGE IN SIGN 
% calculate mu
mu = AlagappanandCowan(S);
hold on
% plot result
plot(S,mu,'k-o'), xlabel('S (g/l)'), ylabel('\mu (1/h)');
% implement WaymanandTseng Model as a Matlab anonymous function
WaymanandTseng= @(S)(0.3164*(S./(0.7346+S)))-((0.01618)*(S+0.2886)); % NOTICE CHANGE IN THE SIGN 
% calculate mu
mu = WaymanandTseng(S);
hold on
% plot result
plot(S,mu,'k -.'), xlabel('S (g/l)'), ylabel('\mu (1/h)'), legend('YanoandKoga1','YanoandKoga2', 'AlagappanandCowan','WaymanandTseng');
axis([0 20 0 0.3])
set(gca,'YTick',[0 0.05 .1 0.15 0.2 0.25 0.3 ])
set(gca,'YTickLabel',[0 0.05 .1 0.15 0.2 0.25 0.3 ])
set(gca,'XTick',[0 2 4 6 8 10 12 14 16 18 20 ])
set(gca, 'XTicklabel', [0 2 4 6 8 10 12 14 16 18 20 ])
title('\mu vs S')

Hope it helps