Exercicio no Matlab Fourrier Resposta ao Degrau e Etc

Considere um sistema com função de transferência Gs de terceira ordem com um polo real e um par de polos complexos e conjugados Com base nos diagramas de Bode parciais apresentados abaixo defina a função de transferência Gs 2 Obtenha a série Trigonométrica de Fourier do sinal apresentado na Figura 2 3 Obtenha a série exponencial de Fourier da corrente senoidal retificada de meia onda mostrada na Figura 3 4 Encontre a resposta ao degrau para o seguinte sistema Gs 1s2 2s 1 5 O sistema a seguir quando sujeito a uma entrada do tipo degrau unitário tem resposta forçada ou resposta em regime permanente igual a 2 Assim pedese obtenha o valor de a que garanta essa resposta Fs sas2s4 1 G1s K1 s α jωcs α jωc s α jωcs α jωc s α2 ωc2 s2 2sα α2 ωc2 s2 2sα α2 ωc2 s2 2s ξ ωn ωn2 ωn2 α2 ωc2 ξ αωn ωn 398 rads G1s K1 s2 2 ξ ωn s ωn2 K1 ωn2 1 sωn2 2ξ sωn 1 G1jω K1 ωn2 1 ωωn2 j2 ωωn ξ 1 G1jωn K1 ωn2 1 j2 j ξ 1 K1 ωn2 2 ξ G1jωn dB 14 20 log10 K1 3982 2 ξ log10 K1 3982 2 ξ 07 K1 3982 1007 794 G10 dB 0 20log K1 ωn2 1 0 j2 ξ 0 1 0 K1 ωn2 1 K1 ωn2 ξ 1 1007 02 G11 1 13982 04 1398 1 G21 K2 s ωn 3 G20 dB 0 K2 1 G2jω dB 20 log 1 j jω ωn 20 log 1 j ω ωn 20 log 1 ω2 ωn2 G2j 2 301 log 1 4 ωn2 01505 1 4 ωn2 141 ωn 2 rads G21 1 1 12 G11 1 1 12 13982 04 1398 1 2 gt 5 x 0 t 1 10 x 1 t 2 0 se 2 t 4 gt gt 4 T 4 L 2 gt a0 Σ an cos mnπt L bn sen mnπt L m1 a0 1L gt dt from c to c2L 12 gt dt from 0 to 4 12 5 dt from 0 to 1 10 dt from 1 to 2 0 dt from 2 to 4 12 51 101 02 152 an 1L gt cosmnπt L dt from c to c2L 12 gt cosmnπt 2 dt from 0 to 4 12 5 cosmnπt 2 dt from 0 to 1 10 cosmnπt 2 dt from 1 to 2 0 cosmnπt 2 dt from 2 to 4 12 5 mnπ2 sen mnπt 2 from 0 to 1 10 mnπ2 sen mnπt 2 from 1 to 2 0 12 10 mnπ sen mnπ2 20mnπ sen mnπ sen mnπ2 12 10mnπ sen mnπ2 20mnπ sen mnπ2 5mnπ sen mnπ2 bn 1L gt senmnπt L dt from c to c2L 12 04 gt senm π t2 dt 12 01 5 senm π t2 dt 12 0 senm π t2 dt 24 0 senm π t2 dt 12 5 cosm π t201 10 cosm π t212 12 5 cosm π 2 1 10 cosm π cosm π 2 12 5 cosm π 2 5 10 1m 52 cosm π 2 1 2 1m gt 154 Σm1 5m π senm π t2 cosm π t2 52 cosm π 2 1 2 1m senm π t2 3 it sent se a ε 0π 0 se i ε π2π it it 2π it Σm Cm ejmω0 t T0 2π ω0 1 Cm 1T0 ccT0 it ejmω0 t dt 12π 02π it ej m t dt 12π 0π sent ej m t dt sent ej n t dt sent u du cost dt dv ej n t dt v ej n t j n sent ej n t cost ej n t dt j n cost ej n t dt cost u du sent dt dv ej n t dt v ej n t j n cost ej n t sent ej n t dt j n sent ej n t sent ej n t cost ej n t j n sent ej n t dt n2 r 1 n2 sent ej n t ej n t cost n2 sent j n sent ej n t n2 ej n t n2 1 cost n2 sent j n ej n t n2 1 cost n sent j Cm 1 2π 0π ej n t cost n sent j n2 1 0π 1 2π n2 1 ej n π cosπ n senπ j ej n 0 cos0 n sen0 j 1 2π n2 1 1n 1 1n 1 2π n2 1 1 1n 2π 1 n2 n 1 C1 sent ej t dt 7 i π 2 it Σm 1m 1 2π 1 n2 ej n t j i π 2 ej t j i π 2 ej t it π ej t j 2 π ej t j 2 Σm m 1 1m 1 2π 1 n2 ej n t j 2 π ej t ej t j 2 Σm m 1 1m 1 2π 1 n2 ej n t π 2 sent j 2 Σm m 1 1m 1 2π 1 n2 ej n t π sent Σm m 1 1m 1 2π 1 n2 ej n t 4 Gs 1 s2 2 s 1 1 s 222 12 1 s 222 122 12 1 s 222 122 L sena t eb t a s b2 a2 gt 2 sent 2 et 2 ut 5 Regime permanente t limt ft lims0 Fs 2 lims0 a s 2s 4 a 2 4 a 8 2 a 16