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Aula2_SCII2010 - Sistemas de Controle II Adriano A G...

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Sistemas de Controle II Adriano A. G. Siqueira Aula 2 - Transformada Z Sistemas de Controle II – p. 1/21
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Índice Definição Exemplos Propriedades Transformada Z Inversa Solução de Equações a Diferenças Função de Transferência Discreta Sistemas de Controle II – p. 2/21
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Transformada Z Função discreta x ( kT 0 ) , k = 0 , 1 , · · · , Transformada Z X ( z ) = Z { x ( kT 0 ) } = summationdisplay k =0 x ( kT 0 ) z - k Sistemas de Controle II – p. 3/21
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Exemplos Exemplo 1: x ( kT 0 ) = 1 X ( z ) = summationdisplay k =0 1 z - k = 1 + z - 1 + z - 2 + z - 3 + · · · Série geométrica f ( r ) = a + ar + ar 2 + ar 3 + · · · ... converge para f ( r ) = a 1 - r Sistemas de Controle II – p. 4/21
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Exemplos Exemplo 1: x ( kT 0 ) = 1 X ( z ) = summationdisplay k =0 1 z - k = 1 + z - 1 + z - 2 + z - 3 + · · · Fazendo a = 1 e r = z - 1 X ( z ) = 1 1 - z - 1 = z z - 1 Sistemas de Controle II – p. 5/21
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Exemplos Exemplo 2: x ( kT 0 ) = a kT 0 X ( z ) = summationdisplay k =0 a kT 0 z - k = 1+ a T 0 z - 1 + a 2 T 0 z - 2 + · · · Fazendo a = 1 e r = a T 0 z - 1 X ( z ) = 1 1 - a T 0 z - 1 = z z - a T 0 Sistemas de Controle II – p. 6/21
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