Hi !

I'm trying to solve a problem concerning a RST regulator. In this context, I need to solve a Diophant Equation.

this equation is :

A(z)*R(z) + B(z)*S(z) = C(z)

where :

A(z) = (z-1)*(z-0.513)

B(z) = 0.648*(z+0.801)

R(z) = r0*z + r1

S(z) = (z-1)*(s0*z + s1)

C(z) = z*(zē-0.7497*z+0.2432)

I need to find r0, r1, s0 and s1 with a minimal solution for S(z)

I have begun with the rewriting of the equation in a matrix :

A*X = C

where (Matlab code) :

Code:

A =
1.0000 0 0.6480 0
-1.5130 1.0000 -0.1290 0.6480
0.5130 -1.5130 -0.5190 -0.1290
0 0.5130 0 -0.5190
C =
1.0000
-0.7497
0.2432
0
X =
r0
r1
s0
s1

For information, A is a Sylvester matrix

I don't know how to do. can you help me ?

(if it is easyer for you, I have Matlab for my disposal)

Thanks !