solving system of 2 equations with complex components

Hello,

I'm trying to solve a complex equation which it is proposed in two, separately, taking the module (1) and the angle (2). The solution must be ki=242.1123 and kp=5.7424, but unfortunatelly it is not be able to solve it. Can somebody help me?

Thanks!

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% Original complex equation, Open Loop Transfer Function, OLTF(s)=Gpi(s)*G(s)=(kp·s+ki)/s · Kt/(J·s+Bv), 
% -> s=jw for frequency domain (Bode)-->OLTF(jw)=OLTF(w*1i)=Kt*(kp*w*1i+ki)/(Bv*w*1i-J*w^2)
syms ki kp
J=0.057;Bv=0.015;w=300;PM=82*pi/180;Kt=2.9489;
eqns=[abs(Kt*(kp*w*1i+ki)/(Bv*w*1i-J*w^2))==1,angle(Kt*(kp*w*1i+ki)/(Bv*w*1i-J*w^2))==PM-pi]; % eq(1),eq(2)
S=vpasolve(eqns,[ki kp])

% no solution

S.ki

ans =

Empty sym: 0-by-1

S.kp

ans =

Empty sym: 0-by-1

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Answer 1

[Alan Stevens]

Here's a non-symbolic way to solve your equations

ki0 = 200; kp0 = 10;
k0 = [ki0, kp0];

k = fminsearch(@search,k0);

ki = k(1); kp = k(2);
disp(k)

function F = search(k)

        J=0.057;Bv=0.015;w=300;PM=82*pi/180;Kt=2.9489;
        ki = k(1); kp = k(2);
        
        d1 = abs(Kt*(kp*w*1i+ki)/(Bv*w*1i-J*w^2))-1;
        d2 = angle(Kt*(kp*w*1i+ki)/(Bv*w*1i-J*w^2))-(PM-pi);
        
        F = norm(d1)+norm(d2);
end

[Patxi]

Hello Alan Stevens,

thank you very much for your help. I'm very grateful for that!

Regards,

Patxi