Find optimized solution of linear system of equations

I have this system of equations and I am willing to find the value of kp, ki, kp

0.1*kd +0.49 = 18;

0.04*kd +0.1*kp +21.6 = 121;

0.04*kd +0.1*ki +0.98 = 438;

1.96*(kd +kp)+ 0.04*ki = 1030;

1.96*ki = 1200;

and kp, ki, kd > 0

Using linsolve of the system, the answer was Inf for all.

Answer 1

[Star Strider]

Try this:

syms kd kp ki 
Eq1 =  0.1*kd +0.49 == 18;
Eq2 =  0.04*kd +0.1*kp +21.6 == 121;
Eq3 =   0.04*kd +0.1*ki +0.98 == 438;
Eq4 =   1.96*(kd +kp)+ 0.04*ki == 1030;
Eq5 =   1.96*ki == 1200; 

[A,b] = equationsToMatrix(Eq1,Eq2,Eq3,Eq4,Eq5);

Coeffs = lsqr(double(A), double(b));
kd = Coeffs(1)
ki = Coeffs(2)
kp = Coeffs(3)

producing:

kd =
           912.95079751536

ki =
          620.999261482952

kp =
         -397.442602821135

The Symbolic Math Toolbox sorts the variables in lexicographical order, so kd>ki>kp, thus the ordering in the results.

Experiment to get the result you want.