"
W (s) = 3 + 8s + s2 + 2s3 = 0
"
s3 2 8
s2 1 3
s1 2·3-8·1 = 2 0
-1
s0 1·0-3·2 = 3
-2
"
>>
s3
s2
s1
s0
s3
s2
s1
s0
"
W (s) = 48+28s-56s2-35s3+7s4+7s5+s6 = 0
"
s6 1 7 -56 48
s5 7 -35 28
s4 12 -60 48
s3 48 0 -120 0
s2 -30 48
s1 -43.2 0
s0 48
"
s
"
P (s)
"
P (s) = 48 - 60s2 + 12s4,
dP (s)
= -120s + 48s3.
ds
"
"
W (s) = 0
"
P (s)
s
W (s)
"
>>
s6
s5
s4
s3
s2
s1
s0
s6
s5
s4
s3
s2
s1
s0
"
W (s) = 2+5s+9s2+10s3+3s4+3s5 = 0.
"
"
s5 3 10 5
s4 3 9 2
s3 1 3
s2 µ 0 2
s1 -2/µ
s0 2
"
s
"
µ
µ)
"
W (s) = 0
W (s) = 0
"
>>
s5
s4
s3
s2
s1
s0
s5
s4
s3
s2
s1
s0
"
"
1
Gp(s) =
(2-s)(3+s)
2-s
Gc(s) =
1+s
1
Gs(s) =
1+s
"
"
4 + 7s + 5s2 + s3
1+Gp(s)Gc(s)Gs(s) =
(1 + s)2(3 + s)
(3.20557 + s)[0.6654572 + (0.897215 + s)2]
= .
(1 + s)2(3 + s)
"
Gp(s)Gc(s)Gs(s)|s" = -1

Gc(s)Gp(s)
p = 2
z = 2
"
(1 + s)2(3 + s)
Gry1(s) =
4 + 7s + 5s2 + s3
1 + s
Gdy1(s) =
(2 - s)(4 + 7s + 5s2 + s3)
-(1 + s)(3 + s)
Gny1(s) = ;
4 + 7s + 5s2 + s3
(2 - s)(1 + s)(3 + s)
Gry2(s) =
4 + 7s + 5s2 + s3
(1 + s)2(3 + s)
Gdy2(s) =
4 + 7s + 5s2 + s3
(-2 + s)(3 + s)
Gny2(s) = ;
4 + 7s + 5s2 + s3
1 + s
Gry3(s) =
4 + 7s + 5s2 + s3
(1 + s)2
Gdy3(s) =
(2 - s)(4 + 7s + 5s2 + s3)
(1 + s)2(3 + s)
Gny3(s) = .
4 + 7s + 5s2 + s3
"
Gdy1(s) Gdy3(s)
p = 2
"
R(s) N(s)
C(s)
C(s)
Grc(s) = = Gry2(s)Gp(s)
R(s)
1 + s
=
4 + 7s + 5s2 + s3
C(s)
Gnc(s) = = Gny2(s)Gp(s)
N(s)
-1
= .
4 + 7s + 5s2 + s3
"
"
10
Gp(s) =
0.1+s
ki
Gc(s) = kc +
s
-0.5
Gd(s) =
0.1+s
"
kc ki
"
e(t) = r(t) - c(t) = er(t) + ed(t)
er(t)
ed(t)
"
C(s) = Grc(s)R(s) + Gdc(s)D(s)
Grc(s) Gdc(s)
" er(")
e(")
kc ki; dlaczego?)
er(") = lim sR(s)( - Grc(s ,
s0
C(s) Gc(s)Gp(s)
Grc(s) = = .
R(s) 1 + Gc(s)Gp(s)
 er(")
sR(s)
er(") = .
s0
1 + Gc(s)Gp(s)
10(ki + kcs)
Gc(s)Gp(s) = .
s(0.1 + s)
"
R(s) = 1/s)
R(s) = 1/s2)
1
er(") =
kv
kv = lim sGc(s)Gp(s) = 100ki
s0
"
ed(") = - lim sD(s)Gdc(s).
s0
"
C(s) Gd(s)
Gdc(s) = =
D(s) 1 + Gc(s)Gp(s)
0.5s
= -
ki + (10kc + 0.1)s + s2
0.5s2
ed(") = lim D(s) .
s0
10ki + (10kc + 0.1)s + s2
"
0.05
ed(") = .
ki
"
"
15
Gp(s) = .
(1 + 0.5s)(1 + s)(1 + 2s)
"
Gc(s) = kc.
"
r(t) = 1(t)
|e(")| d" 0.05.
"
W (s) = 15kc + (1 + 0.5s)(1 + s)(1 + 2s)
= 1 + 15kc + 3.5s + 3.5s2 + s3.
"
-0.0667 < kc < 0.75.
"
kp = Gc(0)Gp(0) = 15kc.
"
1
d" 0.05.
|1 + kp|
"
19
kc e" = 1.267.
15
"
"
"
" k kt
º% = 20%
Tº = 1
"
Ts2% Ts5%
"
G(s) = C(s)/R(s).
"
C(s) k
G(s) = =
R(s) k + (1 + kkt)s + s2
C(s) 1
G(s) = =
R(s) 1 + 2Å›Äs + Ä2s2
1 1
Ä2 = 2Å›Ä = + kt
k k
" º%
Tº
0 < Å› < 1
-śĄ
º% = º · 100% = exp · 100%
1 - ś2
Ä„
Tº = Ä.
1 - ś2
"
| ln º|
Å› = = 0.456
Ä„2 + ln2 º
Tº 1 - Å›2
Ä = = 0.283 .
Ä„
"
1
k = = 12.46
Ä2
1
kt = Å›Ä - = 0.178.
k
"
4Ä
Ts2% H" = 2.485
Å›
3Ä
Ts5% H" = 1.86 .
Å›
"
Ts2% = 2.359 Ts5% = 1.488
>>
>>
>>
>>
>>
"
u(t)
U(s) = Gru(s)R(s)
U(s)
Gru(s) =
R(s)
k k · s(1 + s)
= = .
k(1+kts)
k + (1 + kkt)s + s2
1 +
s(1+s)
u(t)
u0 = lim sGru(s)R(s)
s"
k · s(1 + s)
= = k.
k + (1 + kkt)s + s2 s"
1
k =
Ä2
|u0| d" u0 max
Ä
u0
u0 = k = 12.46.
 u(t)
>>
>>
>>
>>
>>
>>
"
k
kt
" k
kt
Ts2% d" 0.25
"
C(s) 2k
G(s) = = .
R(s) 2k + (1 + 2kt)s + s2
1
G(s) =
1 + 2Å›Äs + Ä2s2
1 1 kt
Ä2 = 2Å›Ä = + .
2k 2k k
"
Å› = 1
Ó!
1
G(s) = .
(1 + Äs)2
"
t e" 0
G(s) t
h(t) = L-1 = 1- 1 + e-t/T.
T
" Ts"
Ä…"
Ts"
Ts"
1 + e- Ä = ".
Ä
" = 0.02 " = 0.05
Ts2% H" 5.834 · Ä Ts5% H" 4.744 · Ä
" Å› = 1
Ts"
4Ä 3Ä
Ts2% H" Ts5% H" .
Å› Å›
Å› 1)
"
Ts2% H" 5.834 · Ä
Ä = 0.04285
k = 272.284 kt = 22.8347.
"
Ts2% H" 4Ä/Å›
k = 128.0 kt = 15.5
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
 k0 > 0 T0 > 0
kt > 0
k0 T0
k1 = T1 = .
1 + k0kt 1 + k0kt
k1 < k0 T1 < T0.
 kt < 1
 d(t)
 k
kt
d(t)
|e(")| d" 0.005
Ts2% d" 0.5 .
º%
"
C(s) k
Grc(s) = = .
R(s) k + (3 + kkt)s + s2
"
E(s) -1
Gde(s) = = .
D(s) k + (3 + kkt)s + s2
"
1
D(s) =
s
k > 0
1
|e(")| = .
k
"
k e" k = 200.
" Grc(s)
1
Grc(s) =
1 + 2Å›Äs + Ä2s2
1 3
Ä2 = 2Å›Ä = + kt.
k k
" Ts2%
4Ä
Ts2% H"
Å›
Å›
Ä = .
8
"
k = kmin = 200.
64
ś2 =
k
Å› = 0.566.
-śĄ
º% = exp ·100 % = 11.59 %.
1 - ś2
" Ä
1
Ä = = 0.0707
k
" kt
3
kt = 2Å›Ä - = 0.065.
k
"
>>
>>
>>
>>
"
Ts2% = 0.415
 T = 2
T0 = 0.3
" k
Tv
Mr = 1.4,
-1
É3dB = 15 · .
º
Tº
Ts5%
"
C(s) k
G(s) = = .
R(s) k + (T0 + kTv)s + T0T s2
1
G(s) =
1 + 2Å›Äs + Ä2s2
T0T Tv T0
Ä = Å› = + .
k 2Ä 2kÄ
"
-2
1 - 1 - MR
Å› = , Mr e" 1
2
Mr
Å›
" Ä
É3dB
- ś2 + ( - ś2)2 + 1
Ä = .
É3dB
"
Å› = 0.3874 Ä = 0.0924 .
"
T0T
k = = 70.2969
Ä 2
Ä
Tv = Ä 2Å› - = 0.0673 .
T
"
Å»
º% = 26.7%, Tº = 0.315 , Ts5% = 0.734 .
"
=
Ts5%0.712 .
"
>>
>>
>>
>>
>>
>>
>>
"
>>
 [100, 102]
>>
>>
>>
>>
>>
>>
>>
"
1
Gp(s) =
s(1+0.5s)
0.5(1+3s)
Gc(s) =
s
1
Gs(s) =
1+0.05s
"
e(t) = r(t) - c(t).
"
"
Gc(s)Gp(s)
Grc(s) =
1 + Gc(s)Gp(s)Gs(s)
0.5 + 1.525s + 0.075s2
=
0.5 + 1.5s + s2 + 0.55s3 + 0.025s4
l0 + l1s + l2s2
= .
m0 + m1s + m2s2 + m3s3 + m4s4
"
"
f&
r(t) = 1(t)
m0 - l0
e(") = = 0,
m0
f&
r(t) = t · 1(t)
m1 - l1
e(") = = -0.05.
m0
"
"
1
Gp(s) =
s-1
s-1
Gc(s) =
s+1
"
"
s - 1 s + 1 - 2 2
Gc(s) = = = 1- .
s + 1 s + 1 s + 1
"
‹1(t) = x1(t) - 2x2(t) - x1(t) + r(t) + d(t)
= -2x2(t) + r(t) + d(t)
‹2(t) = -x1(t) - x2(t) + r(t)
c(t) = x1(t).
"
0 -2 1 1
A = , B = , C = 1 0 .
-1 -1 1 0
"
r(t) d(t)
‹1(t) x1(t) r(t)
= A + B
‹2(t) x2(t) d(t)
x1(t)
c(t) = C .
x2(t)
"
A = {1, 2}
1 2
det (I2-A) = 2+-2 = (-1)(+2) = 0.
" 1 = 1 2 = -2
"
Grc(s) Gdc(s) = C (sI2 - A)-1B
-1
s 2 1 1
= 1 0
1 s + 1 1 0
s + 1 -2 1 1
1 0
-1 s 1 0
=
(s - 1)(s + 2)
1 s+1
= .
s+2 (s-1)(s+2)
"
Ó!
"