z-table - 1 2 3 4 5 Fonction du Temps f (t ), t > 0...

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Unformatted text preview: 1 2 3 4 5 Fonction du Temps f (t ), t > 0 Transformée de Laplace F ( s) Transformée en z F ( z) u s (t ) (échelon) t t2 2 1 s 1 s2 1 s3 e − at te − at t 2 − at e 2 (s + a ) 2 (s + a ) 1 1 s+a 1 6 3 T2 2 (z − e ) z (z + e ) e (z − e ) − aT 2 T 2 z ( z + 1) 2 ( z − 1)3 z z − e − aT Tze − aT z z −1 Tz (z − 1)2 − aT − aT − aT 3 7 8 9 10 11 (− 1)m−1 ∂ m−1 e −at (m − 1)! ∂a m−1 1 − e − at 1 (t − 1 + e −at ) a e − at 1 (s + a ) m a s (s + a ) a 2 s (s + a ) b−a (s + a )(s + b ) s (s + a ) 2 (− 1)m−1 ∂ m−1 (m − 1)! ∂a m−1 z (aT − 1 + e − aT )z + (1 − e − aT − aTe − aT ) − e )z (z − e )(z − e −bT ) − aT − bT − aT [ z (1 − e − aT ) (z − 1)(z − e −aT ) 2 z z − e − aT a( z − 1) (z − e − aT −e − bt (e ) 1 − e − at (1 + at ) sin( wt ) cos( wt ) e − at sin( wt ) e − at cos( wt ) a2 2 z 1 − e − aT − aTe − aT z + e −2 aT − e − aT + aTe − aT [( (z − 1)(z − e ) − aT 2 ) 12 13 14 15 (s + a )2 + w 2 w s + w2 s 2 s + w2 w z sin( wT ) z − 2 cos( wT ) z + 1 z ( z − cos( wT ) ) 2 z − 2 cos( wT ) z + 1 2 ze − aT sin( wT ) z 2 − 2e − aT cos( wT ) z + e − 2 aT z 2 − ze − aT cos( wT ) z 2 − 2e − aT cos( wT ) z + e − 2 aT z ( Az + B ) 2 (z − 1) z − 2e −aT cos(wT ) z + e −2 aT s+a (s + a )2 + w 2 16 1 − e − at ⋅ a (cos(wt ) + w sin( wt ) ) s (s + a ) + w 2 2 [ a 2 + w2 ( ) A = 1− e − aT cos( wT ) − e a w − aT sin( wT ) a B = e −2 aT + w e − aT sin( wT ) − e − aT cos( wT ) ...
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This note was uploaded on 05/08/2011 for the course DEE 785 taught by Professor Table during the Spring '11 term at Presentation.

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