Solve equation that has a complex subexpression
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Bill Tubbs
il 30 Lug 2020
Commentato: Star Strider
il 2 Dic 2020
I want to solve the following equation for omega:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/338971/image.png)
where
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/338974/image.png)
So I tried this:
syms s omega G(s)
G(s) = 10/(s*(1+s)*(1+0.2*s));
% Try to find omega that satisfies the equation:
solve(angle(subs(G(s),s,omega*j))-deg2rad(-135),omega,'Real',true)
Result:
Error using mupadengine/feval_internal (line 172)
No complex subexpressions allowed in real mode.
Error in solve (line 293)
sol = eng.feval_internal('solve', eqns, vars, solveOptions);
Although there is an imaginary number in the expression, the decision variable is real and the expression evaluates to a real number (due to angle) so I don't see why it should have a problem solving this.
Obviously, I can think of other ways to solve the problem, but it would be nice to just use angle on the whole transfer function.
% Get solution a different way:
omega_sol = solve(-pi/2-atan2(omega,1)-atan2(omega,5)-deg2rad(-135),omega)
% Confirm solution:
subs(angle(subs(G(s),s,omega*j))-deg2rad(-135),omega,omega_sol)
omega_sol =
0.7417
ans =
-1.8367e-40
In summary, is there any way to solve the original expression for omega directly:
angle(subs(G(s),s,omega*j)) == deg2rad(-135)
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Risposta accettata
Star Strider
il 30 Lug 2020
Solving for the tangent of the phase angle, rather than using the arctangent of the transfer function, appears to produce the correct result:
syms s omega G(s)
assume(omega > 0)
G(s) = 10/(s*(1+s)*(1+0.2*s));
G = subs(G, s, 1j*omega)
OMG = solve(imag(G)/real(G) == tan(deg2rad(-135)), omega)
vpaOMG = vpa(OMG)
producing:
vpaOMG =
0.74165738677394138558374873231655
.
2 Commenti
Star Strider
il 30 Lug 2020
As always, my pleasure!
I thought about using ‘1j*omega’ as a function argument, however went with subs because that was in your original code, and there was some reason you specifically used it.
Più risposte (1)
Bill Tubbs
il 2 Dic 2020
Modificato: Bill Tubbs
il 2 Dic 2020
4 Commenti
Star Strider
il 2 Dic 2020
I’m not certain what you’re plotting.
Experiment with something like this:
ad = -180:20:180;
ad360 = mod(ad+360,360);
ar = -pi:0.31:pi;
ar2pi = mod(ar+2*pi,2*pi);
.
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