lecture 15

lecture 15 - * * * * z X z Y z G z X z G z Y s X s G s X s...

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1 z-plane analysis Impulse sampling x(t) x(k) x(0) x(1) x(2) t k x(t) x(k)
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2 ........ ) 2 ( ) 1 ( ) 0 ( ) ( )] ( [ ; 1 )] ( [ ........ ) 2 ( ) 2 ( ) 1 ( ) 1 ( ) ( ) 0 ( ) ( 2 * * + + + = = = + + + = Ts Ts nTs e x e x x s X e nT t L t L t x t x t x t x δ ) ( * s X is called the starred Laplace transform of x(t). If we define z e Ts = or T z s ln = ) ( ....... ) 2 ( ) 1 ( ) 0 ( | ) ( 2 1 ln * z X z x z x x s X T z s = + + + = =
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3 Conclusion 1. The z transform can be achieved from the starred Laplace transform by replacing . 2. The relation between the Laplace transform and z transform is: sT e with z z e Ts = Sample and Hold x(t) h(t) x(0) x(1) x(2) t k x(t) x(k) hold h(t)
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4 1 T h(t) t t x(k) 1 ) ( 1 ) ( 1 ) ( T t t t h = s e e s s s H Ts Ts = = 1 1 1 ) ( 1 ) ( = s X s e s X s H s G Ts ho = = 1 ) ( ) ( ) (
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5 z transfer function ) ( s G ) ( * t x ) ( * s X ) ( t y ) ( s Y ) ( * t y ) ( * s Y ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )] ( ) ( [ ) ( ) ( ) ( ) ( * *
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Unformatted text preview: * * * * z X z Y z G z X z G z Y s X s G s X s G s Y s X s G s Y = = = = = ) ( z G is defined as z-transfer function of ) ( s G . z transfer function of cascaded elements ) ( ) ( ) ( z GH z H z G )] ( ) ( [ )] ( [ )] ( [ s H s G Z s H Z s G Z 6 z transfer functions of the closed loop systems In a closed loop system, the existence or non-existence of an output sampler within the loop makes a difference in the behavior of the system....
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This note was uploaded on 06/02/2010 for the course HET 489 taught by Professor Zhenwei during the Three '08 term at Swinburne.

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lecture 15 - * * * * z X z Y z G z X z G z Y s X s G s X s...

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