Difference in discretization of transfer function

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Whynot2 2016-10-13

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https://ww2.mathworks.cn/matlabcentral/answers/307106-difference-in-discretization-of-transfer-function

回答： Swarooph 2016-10-13

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Hey,

I’ve been trying to find the differences in between the following transfer functions:

         T=0.001;% sampling time
         G_c = tf(1,[1 .1  0])
         G_e = tf(1,[1 .1  0], T)
         G_d = c2d(G_c,T,'zoh')

G_d is the exact same as as G_c just in the z-domain. However, I don’t see what happens to G_e? It seems that there is an additional term included which I cannot find any information about and how it looks like. Is it the transfer function of the ZOH? Thanks in advance for every single hint.

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Answer 1

Swarooph 2016-10-13

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/307106-difference-in-discretization-of-transfer-function#answer_238799

Good question. Technically, all 3 are DIFFERENT. G_c and G_d are equivalent in terms of how close their responses might be.

G_c is a continuous time transfer function (so, defined in the 's' domain).

-- This takes numerator and denominator coefficients and add its to a polynomial in 's' in descending powers.

G_e is a discrete time transfer function (so, defined in the 'z' domain).

-- This takes numerator and denominator coefficients and add its to a polynomial in 'z' in descending powers. (There is no conversion from continuous to discrete happening. You are basically just constructing a discrete tf with coefficients)

G_d is a discrete time transfer function (also defined in the 'z' domain).

-- c2d function takes a continuous time transfer function and then discretizes it (using the user chosen method such as 'zoh', 'tustin' etc). This is what you should use to convert a transfer function in the 's' domain to a 'z' domain.