Convert transfer function from s domain to z^-1 domain

I've tried to convert transfer function from s domain to z^-1 domain. I'm following one research paper and I can't get the same result. I've attached a screenshot of research paper and the code I've run to obtain transfer function.

The numerator should be 1.365 z^-1. It's a typo in the equation but in the simulink model it says 1.365 z^1.

>> Ts = 0.001

Ts =

   1.0000e-03

>> num = [910]

num =

   910

>> den = [0.0665e-2 1]

den =

    0.0007    1.0000

>> sys = tf(num, den)

sys =
 
       910
  --------------
  0.000665 s + 1
 
Continuous-time transfer function.

>> sys_z = c2d(sys, Ts)

sys_z =
 
    707.7
  ----------
  z - 0.2223
 
Sample time: 0.001 seconds
Discrete-time transfer function.

>> sys_DSP = filt(sys_z.Numerator, sys_z.Denominator, Ts)

sys_DSP =
 
    707.7 z^-1
  ---------------
  1 - 0.2223 z^-1
 
Sample time: 0.001 seconds
Discrete-time transfer function.

>> 

Answer 1

[Paul]

c2d supports different methods. The "pole-zero mapping" is what c2d calls "matched." However the result using "matched" does not give the expected result:

Ts = 0.001;
hc = tf(910,[0.065e-2 1]);
hd = c2d(hc,Ts,'matched')

hd =
 
    714.6
  ----------
  z - 0.2147
 
Sample time: 0.001 seconds
Discrete-time transfer function.

But this result appears to be correct insofar as pole zero mapping uses the relationhip z = exp(s*T)

[z,p,k] = zpkdata(hc);
exp(p{1}*Ts)

ans = 0.2147

Maybe the authors were really using a much smaller sample time?

Ts = log(.9985)/p{1}

Ts = 9.7573e-07

hd = c2d(hc,Ts,'matched');
hd.Variable = 'z^-1'

hd =
 
    1.365 z^-1
  ---------------
  1 - 0.9985 z^-1
 
Sample time: 9.7573e-07 seconds
Discrete-time transfer function.

Answer 2

[mmbaka douglas]

how to convert z dormain to s dormain F = 1/(Z -5)^2