Fraçoes parciais

Trabalho Professor Chaves
Hugo Sampaio Gomes
18/09/2012

I. G1(s) = 10s+10

V(s) = 1S V(s) 10S + 10 y(s) y(s) = G(s). V(s) y(s) = 10s+10.1s
Y(s) = k1s+k2(s+10)

lim⁡ s→0 s-ri10s+10 = lims→ris-rik1s.k2s+10
Ri= 0, -10 lims→-10(s+10)10s+10.s = lims→-10(s+10)k1s+k2s+10
10-10 = lims→-10s+10.k1s+s+10.k2(s+10)
-1 = k2

lims→0(s)10s+10.s = lims→0(s)k1s+k2s+10
10s+10 = lims→0s.k1s+s.k2(s+10)
100+10 = lims→0s.k1s+0.k2(s+10)
1010=k1
1 = k1 Y(s) = k1s + k2s+10
Y(s) = 1s + -1s+10
Y(t) = 1 - 1e-10t

II. G2(s) = 20s+10

(s) = 1S V(s) 20S + 10 y(s) y(s) = G(s). V(s) y(s) = 20s+10.1s
Y(s) = k1s+k2(s+10)

lims→-10(s+10)20s+10.s = lims→-10(s+10)k1s+k2s+10
20s = lims→-10s+10.k1s+s+10.k2(s+10)
20-10 = lims→-10-10+10.k1s+s+10.k2(s+10)
-2 = k2

lims→0(s)20s+10.s = lims→0(s)k1s+k2s+10
20s+10 = lims→0s.k1s+s.k2(s+10)
200+10 = lims→0s.k1s+0.k2(s+10)
2010=k1
2 = k1 Y(s) = k1s + k2s+10
Y(s) = 2s + -2s+10
Y(t) = 2 - 2e-10t

III. G3(s) = 10s+1

V(s) = 1S V(s) 10S + 1 y(s) y(s) = G(s). V(s) y(s) = 10s+1.1s
Y(s) = k1s+k2(s+1)

lims→-1(s+1)10s+1.s = lims→-1(s+1)k1s+k2s+1
10-1 = lims→-1s+1.k1s+s+1.k2(s+1)
-10 = k2

lims→0(s)10s+1.s = lims→0(s)k1s+k2s+1
10s+1 = lims→0s.k1s+s.k2(s+1)
100+10 = lims→0s.k1s+0.k2(s+10)
1010=k1
1 = k1

Y(s) = k1s + k2s+1
Y(s) = 10s + -10s+1
Y(t) = 10 - 10e-t

IV. G4(s) = 10s+100

V(s) = 1S V(s) 10S + 100 y(s) y(s) = G(s). V(s) y(s) = 10s+100.1s
Y(s) = k1s+k2(s+100)

lims→-100(s+100)10s+100.s = lims→-100(s+100)k1s+k2s+100
10s = lims→-100s+100.k1s+s+100.k2(s+100)
10-100 = lims→-100s+100.k1s+s+100.k2(s+100)
- 0,1= k2

lims→0(s)10s+100.s = lims→0(s)k1s+k2s+100
10s+100 = lims→0s.k1s+s.k2(s+100)
100+100 = lims→0s.k1s+0.k2(s+100)
10100=k1