How i can convert discrete filter to continuous transfer function?

b0 = 12.575612; b1 = -18.9426445; b2 = 6.4607418;

b = [b0 b1 b2];

a0 = 1.7892133; a1 = -0.7892133; a2 = 0;

a = [a0 a1 a2];

hq = dfilt.df1(b,a,);

How i can convert discrete filter to continuous transf

I need sys = tf(hq);

It not working. Is it possible to convert? If is possible, then how?

Answer 1

[Star Strider]

You need to ‘invert’ the bilinear transform using the Symbolic Math Toolbox, then solve:

syms H(s) T z Z
assume(T > 0)
Eq =  s == 2/T * (z - 1)/(z + 1);
Z = solve(Eq, z)

b0 = 12.575612; 
b1 = -18.9426445; 
b2 = 6.4607418;
b = [b0 b1 b2];
bz = poly2sym(b, z)
bs = subs(bz,z,Z)
bs = vpa(expand(simplify(bs, 'Steps', 10)), 5)

a0 = 1.7892133; 
a1 = -0.7892133; 
a2 = 0;
a = [a0 a1 a2];
az = poly2sym(a, z)
as = subs(az,z,Z)
as = vpa(expand(simplify(as, 'Steps', 10)), 5)

producing:

bs = (176.38*T*s)/(T^2*s^2 - 4.0*T*s + 4.0) - 151.54/(T^2*s^2 - 4.0*T*s + 4.0) + 37.979
as = (17.471*T*s)/(T^2*s^2 - 4.0*T*s + 4.0) - 6.3137/(T^2*s^2 - 4.0*T*s + 4.0) + 2.5784

The ‘T’ variable is the sampling interval (inverse of the sampling frequency). Substitute your actual sampling interval for ‘T’, then use the numden and sym2poly functions (in that order) to create your polynomials to give to the Control System Toolbox tf function.

I leave prewarping and other design decisions to you. Incorporate it as necessary.