Hi Bahadir,
I'm not sure if the code is implementing what it should, but the reason the result is coming back with Ki = bres = 0 is due to the form of the equations.
syms s x s h y z t K_d K_p K_i ares bres;
% symbolic variables are defined to see if function is working correctly
h=12;x=15;y=35;z=45;t=50;
pole = 1-1i;
p_ds = expand((s-pole) * (s-(conj(pole))));
coef2=coeffs(p_ds,s,'All');
p_es = (s^2+ares*s+bres);
coef = coeffs(p_es,s,'All');
Gs = h /(x*s^3+y*s^2+z*s+t);
[numGs,denGs] = numden(Gs);
denGs1 = coeffs(denGs);
denGs2 = double(denGs1);
p = (p_es * p_ds);
p1 =coeffs(p,s,'All');
Fs = (K_d*s^2+K_p*s+K_i )/ s;
Tss = (Gs*Fs)/(1+Gs*Fs);
[numTss,pcs] = numden(Tss);
prob = coeffs(pcs/x,s,'all') == coeffs(p_ds*p_es,s,'all');
%{
for i = 1:length(prob)
disp(vpa(prob(i),4));
end
%}
Here are the equations to be solved.
prob(:),split(string(char(prob(:))),";")
The first equation is extraneous. The last equation is a simple relationship between Ki and bres. Apparently solve can find a soluution to all of the equations with Ki = bres = 0
sol = solve(prob)
If you want to get all solutions parametrically, then use the ReturnConditions flag.
sol = solve(prob,'ReturnConditions',true)
Apparently only ares is fixed and the rest of the unknowns are determined from a single parameter.
