When I enter the following code in 2017 MATLAB it gives me a nonsense answer, or so it is to me. does some one know how to fix it? i am trying to solve for w and the second one does give the right answer but the first one does not.

Code entered:

format compact
syms w;
y = solve( ( 5 / ( (-1.5*w^2)^2 + ( w - 0.5*w^3 )^2 )^(1/2) ) - 1 );
x = solve( (-pi/2) - atan(w/2) - atan(w) + (pi) );
disp(y);
disp(x);
num = [5];
den = [0.5 1.5 1 0]; 
G = tf(num, den);
bode(G), grid
margin(num, den);

answer given:

 root(z^6 + 5*z^4 + 4*z^2 - 100, z, 1)
 root(z^6 + 5*z^4 + 4*z^2 - 100, z, 2)
 root(z^6 + 5*z^4 + 4*z^2 - 100, z, 3)
 root(z^6 + 5*z^4 + 4*z^2 - 100, z, 4)
 root(z^6 + 5*z^4 + 4*z^2 - 100, z, 5)
 root(z^6 + 5*z^4 + 4*z^2 - 100, z, 6)
2^(1/2)

Answer 1

[Walter Roberson]

I would suggest instead

vpa(y)

There are 6 solutions. vpasolve() would pick one of them, but there is no inherent reason to favour one over another.

If it is known that the solution should be a positive value, then add that as an assumption:

syms w positive
y = solve( ( 5 / ( (-1.5*w^2)^2 + ( w - 0.5*w^3 )^2 )^(1/2) ) - 1 );

This will get you the exact solution, though you may wish to simplify(y), which would give you

(3^(1/2)*((1315 - 6*47973^(1/2))^(1/3) + (6*47973^(1/2) + 1315)^(1/3) - 5)^(1/2))/3

You could vpa() that or you could double() that depending on your needs.

[aldo angulo]

Thanks for the help, really helped me go faster through the problems instead of doing everything by hand on paper.

Answer 2

[Birdman]

y = vpasolve( ( 5 / ( (-1.5*w^2)^2 + ( w - 0.5*w^3 )^2 )^(1/2) ) - 1 );
disp(y)

Solve returns symbolic solutions, vpasolve returns numeric solutions.

[aldo angulo]

Thanks a lot, it solved the issue and you saved me a lot of time. I was using the 2011 version and the command solve would get the job done but I really had no clue about what you stated "Solve returns symbolic solutions, vpasolve returns numeric solutions."

[Birdman]

Walter's answer explains it.