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c2d is used to convert a model from continuous to discrete time. The official doc states:

sysd = c2d(sysc,Ts) discretizes the continuous-time dynamic system model sysc using zero-order hold on the inputs and a sample time of Ts.

Why is it that when I do:

>> c2d(1/s, 1)

I get:

ans =

    1
  -----
  z - 1

Sample time: 1 seconds
Discrete-time transfer function.

but according to Z-transform tables the z transform of 1/s is

ans =

    z
  -----
  z - 1

Why this discrepancy?

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  • 1
    \$\begingroup\$ Probably the integration method. c2d uses the zero order hold by default. Z transform table might use another method. \$\endgroup\$ – Jaywalk Feb 6 at 15:18
  • \$\begingroup\$ The Z-transform table is the result of the backward rectangular rule. \$\endgroup\$ – Suba Thomas Feb 6 at 15:36
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sys = c2d (sys, tsam, method)

If you do not include the method it will use zero-order hold

c2d(G,1,'zoh')

resulting in $$ \frac{1}{z-1} $$

If you pick a different conversion method it gives you different results, but notice that the poles stability will be "conserved"

c2d(G,1,'tustin')

results in $$ \frac{0.5z+0.5}{z-1} $$

c2d(G,1,'impulse')

results in $$ \frac{z}{z-1} $$

c2d(G,1,'matched')

results in $$ \frac{1.052}{z-1} $$

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