How do I solve multivariable equation system?

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Krzysztof Lakomy
Krzysztof Lakomy 2015-10-16
评论： Krzysztof Lakomy 2015-10-16
Hello,
I'm trying to solve 3 equation system with 3 variables. I have implemented code presented below:
syms kp Ti Td
lambda = 5;
ksi = sqrt(2)/2;
omega = 50;
Eqs = [((0.8*Ti+0.4*kp*Ti+Td*Ti*kp)/(0.3*Ti+0.4*Td*Ti*kp) == (lambda*omega*ksi + 2*ksi*omega)),
((+1.5*Ti+0.4*kp+kp*Ti)/(0.3*Ti+0.4*Td*Ti*kp) == (omega^2 + 2*ksi^2*omega^2*lambda)),
(kp/(0.3*Ti+0.4*Td*Ti*kp) == lambda*omega^3*ksi)];
[sol_kp, sol_Td, sol_Ti] = solve(Eqs,kp,Td,Ti);
sol_kp = double(sol_kp)
sol_Ti = double(sol_Ti)
sol_Td = double(sol_Td)
ogr1 = 0.3*sol_Ti+0.4*sol_Td*sol_Ti*sol_kp;
ogr2 = 0.8*sol_Ti+0.4*sol_Ti*sol_kp+sol_Td*sol_Ti*sol_kp;
ogr3 = 1.5*sol_Ti+0.4*sol_kp+sol_Ti*sol_kp;
ogr4 = sol_kp;
s1 = ogr2/ogr1 - lambda*omega*ksi - 2*ksi*omega
s2 = ogr3/ogr1 - omega^2 + 2*ksi^2*omega^2*lambda
s3 = ogr4/ogr1 - lambda*omega^3*ksi
I obtained a solution (sol_kp, sol_Td, sol_Ti). To check whether solution is appropriate, I have computed values of s1-3 (they should be zero if the solution is correct, unfortunately they are not). I double checked equations and they seems to be right. Could you tell me if I made a mistake using the solve () function ?

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采纳的回答

Torsten
Torsten 2015-10-16
s2 = ogr3/ogr1 - omega^2 - 2*ksi^2*omega^2*Lambda
instead of
s2 = ogr3/ogr1 - omega^2 + 2*ksi^2*omega^2*Lambda
Best wishes
Torsten.
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Torsten
Torsten 2015-10-16
Is this also the case if you call solve as
[sol_kp, sol_Td, sol_Ti] = solve(Eqs,[kp,Td,Ti]);
?
Best wishes
Torsten.
Krzysztof Lakomy
Krzysztof Lakomy 2015-10-16
Unfortunately, when I'm calling like this, I obtain empty variables and matlab returns warning:
Warning: 6 equations in 3 variables.
> In C:\Program Files\MATLAB\R2012a\toolbox\symbolic\symbolic\symengine.p>symengine at 54
In mupadengine.mupadengine>mupadengine.evalin at 97
In mupadengine.mupadengine>mupadengine.feval at 150
In solve at 160
In ED_PID_synt at 20
Warning: Explicit solution could not be found.
> In solve at 169
In ED_PID_synt at 20

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