"
N(s) 1
�
k�G0(s) = k� = k� , k e" 0.
D(s) s(2 + s)3
"
" k
" k
s = -0.5
"
m = 0)
n = 4) p1 = 0
p2 = p3 = p4 = -2
"
ą45ć% ą135ć%
"
�ą = (3 � (-2) - 0)/4 = -1.5.
"
"
N(s)D (s) - N (s)D(s) = 0
N(s) = 1 oraz D(s) = s(2 + s)3.
"
(2 + s)2(1 + 2s) = 0.
sd1 = -0.5 oraz sd2 = -2.
sd2 = p2,3,4.
Ż
" k
k+s(2+s)3 = k+8s+12s2+6s3+s4 = 0.
"
s4 1 12 k
s3 6 8
s2 10.6667 k
s1 8 - 0.5625k
s0 k
Ż
0 < k < k = 14.222.
" �n
Ż
k = 14.222
Ż
ks2 + 10.10.6667 = 0.
"
�n = 2/ 3rad � s-1.
"
s = sd1 = -0.5
1
k = = 1.6875.
�
G0(s) s=-0.5
"
N(s) 0.5 + s
�
k�G0(s) = k� = k� .
D(s) s(-1 + s)(9 + 3s + s2)
"
k e" 0
"
p1,2 = -1.5ąj2.59808, p3 = 0, p4 = 1.
 z1 = -0.5
ą60ć%
180ć%
�a = -0.5
(-", z1] *" [p3, p4]
(-", -0.5] *" [0, 1].
N(s)D (s) - N (s)D(s) =
0
-1.5 + 2s + 3s2 + 2s3 + s4 = 0
s1 = -1.41167, s2,3 = -0.5 ą j1.52681
s4 = 0.41167.
 sa = s1
sd = s4
p2
Ńp1 = 90ć%
Ńp3 = 180ć%-arctan(2.598/1.5) = 120ć%
Ńp4 = 180ć%-arctan(2.598/2.5) = 133.9ć%
Ńz1 = 180ć% - arctan 2.598 = 111.05ć%.
p2 = -1.5+j2.59808
Ńp2 = Ńz1-Ńp1-Ńp3-Ńp4+180ć% = -52.85ć%.
0.5k + (k - 9)s + 6s2 + 2s3 + s4 = 0.
k
k " (11.35425, 16.64575)
s4 1 6 0.5k
s3 2 k - 9
s2 -0.5k + 10.5 0.5k
s1 94.5-14k+0.5k2
-10.5+0.5k
s0 0.5k.
P (s) = 0.5k + (-0.5k + 10.5)s2
k = 11.35425 �! ąj1.08495
k = 16.64575 �! ąj1.95522
s =
sa s = sd k
1
ka = = 25.2359
�
G0(s) s=sa
1
kd = = 2.7641.
�
G0(s) s=sd
"
"
Ws(s) = 15+(6+15kt)s+(3+5kt)s2+2s3 = 0.
kt e" 0
"
Ts5% d" 3 s?
"
kt
(15 + 6s + 3s2 + 2s3) + kt � 5s(3 + s) = 0.
"
N(s) 5s(3 + s)
�
kt�G0(s) = kt� = kt� .
D(s) 15 + 6s + 3s2 + 2s3
�
" G0(s)
p1 = -1.94283, p2,3 = 0.22142ąj1.95226
z1 = -3 oraz z2 = 0.
"
[-", -3] *" [-1.94283, 0].
"
z1 z2
-"
"
N(s)D (s) - N (s)D(s) = 0
-45 - 30s + 3s2 + 12s3 + 2s4 = 0.
s1 = -5.3410, s2,3 = -1.22355ąj0.92676
s4 = 1.7881
s1
sa = s1
s1 " [-", -3] *" [-1.94283, 0]
"
Ńd3 = 162.69ć%
p3 = 0.22142 +
j1.95226
Ńd3 = Ńz1 + Ńz2 - Ńp1 - Ńp2 + 180ć%
Ńz1 = arctan(1.952/3.221) = 31.21ć%
Ńz2 = arctan(1.952/0.221) = 83.53ć%
Ńp1 = arctan(1.952/2.164) = 42.05ć%
Ńp2 = 90ć%.
" kt
Ż
kt > kt = 0.14031.
Ż
kt
ąj2.01304
" Ts5%
Ts5% H" -3/�0
�0 < 0
" Ts5% = 3 s
�0 = -1.
Ws
p = s - �0 = s + 1.
"
p
Wp(p) = Ws(s)|s=p-1
= 10 - 10kt + (6 + 5kt)p +
(-3 + 5kt)p2 + 2s3.
" Wp(p)
kt
kt > 0.6, kt < 1
(6 + 5kt)(-3 + 5kt) > 2(10 - 10kt)
(kt - 0.71774)(kt + 2.11774) > 0.
"
kt " (0.71774, 1)
Ws(s) = 0
�0 = -1
"
kt = 0.9
Ts5% = 2.31 s.