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wolfram alpha

Page history last edited by Bill McEachen 3 years, 1 month ago

$$PENDING

 

for A/D stuff, one can do the following (w/o showing scaling)

1. z transform calculator

2.Bode plot of s/(1-s) sampling period 0.02

3. bode plot of (2 z (2 z+1)) / (2 z-1)^3

 

One must match the Initial value of the Analog/Digital.  

Note the modified z-transform would map roots to [ 1 - A*(4w/ws)^B ] with (A,B) a f{specific system}

As 4*wi approaches Ws, of course we see [1 - A]

 

z-root:  ~ exp(aT) *[1-0.85*(4a/Ws)^3.17 ]      ie (a,b) = ( 0.85,3.17 )

 

recall Ws= 2Pi/T   so given t=0.2s, Ws= 31.4.  So, for (s +2.5), converts to (z+ 1.61), where the mult adjust= 0.98

If sampling is slowed to say 10 rad/s (T= 1.26s),  the mult adjust = 0.15, a substantial decrease from the std z-transform

 

Recall FVT s*F(s) as s goes to 0  and   (z-1)F(z)  as z goes to 1

IVT s*F(s) as s goes to infinity  and   F(z)  as z goes to infinity

 

So, from above FVT analog=0.  digital=0.   IVT analog -infinity     digital =0.5

 

 

 

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