سﻼﭘﻻ ﻞﻳﺪﺒﺗ
لﺎﺜﻣ 1 :
ﻲﻤﻧ ﻪﺒﺳﺎﺤﻣ ﻲﻳاﺮﮕﻤﻫ ﻪﻴﺣﺎﻧ راﺪﻣ سرد رد ار نآ ﺖﻠﻋ و دﻮﺷ
ﻞﻴﻠﺤﺗ و ﻪﻳﺰﺠﺗ سرد رد ﻲﻳاﺮﮕﻤﻫ ﻪﻴﺣﺎﻧ مﻮﻬﻔﻣ رد ﺪﻳﺎﺑ ﺖﻓﺎﻳ ﺎﻬﻤﺘﺴﻴﺳ .
لﺎﺜﻣ 2 : ﺪﺣاو ﻪﻠﭘ ﻊﺑﺎﺗ
لﺎﺜﻣ 3 : ﺪﺣاو ﻪﺑﺮﺿ ﻊﺑﺎﺗ
لﺎﺜﻣ 4 : ﻲﺳﻮﻨﻴﺴﻛ و ﻲﺳﻮﻨﻴﺳ ﻊﺑﺎﺗ
لﺎﺜﻣ 5 : ﺑﺮﭙﻴﻫ ﻊﺑاﻮﺗ ﻲﺳﻮﻨﻴﺴﻛ و ﻲﺳﻮﻨﻴﺳ ﻚﻴﻟﻮ
سﻼﭘﻻ ﻞﻳﺪﺒﺗ صاﻮﺧ
لﺎﺜﻣ 6 :
ﺖﺳا ﻦﻴﻨﭼ دﻮﻳﺮﭘ ﻚﻳ جﻮﻣ ﻞﻜﺷ :
T 2
T
[ ]
f(t) =∫
0∞f(t)e dt = F(s)-st Lf(t) = u(t) F(s) =1
→ s
f(t) = (t)δ →F(s) = 1
2 2
2 2
f(t) sin(at)u(t) F(s) a
s + a f(t) = cos(at)u(t) F(s) = s
s + a
= → =
→
2 2
2 2
f(t) sinh(at)u(t) F(s) a s - a f(t) cosh(at)u(t) F(s) s
s - a
= → =
= → =
T 2
T 2T
لﺎﺜﻣ 7 : لاﺮﮕﺘﻧا ﺖﻴﺻﺎﺧ و ﺪﺣاو ﺐﻴﺷ ﻊﺑﺎﺗ
لﺎﺜﻣ 8 :
ﻌﻣ
سﻼﭘﻻ ﻞﻳﺪﺒﺗ سﻮﻜ
ﺖﻟﺎﺣ 1 : ﺖﺴﻴﻧ يراﺮﻜﺗ جﺮﺨﻣ يﺎﻬﺸﻳر .
ﺐﻳاﺮﺿ ﻪﺑ
k1
ﺪﻨﻳﻮﮔ ﻊﺑﺎﺗ هﺪﻧﺎﻣ .
ﺖﻟﺎﺣ 2 : ﻪﺸﻳر زا ﻲﻜﻳ ﻞﻗاﺪﺣ ﺖﺳا يراﺮﻜﺗ جﺮﺨﻣ يﺎﻫ
.
لﺎﺜﻣ 9 :
لﺎﺜﻣ 10 :
( )
T T
2 2
T 2
- s -Ts - s 2
f(t) = Ku(t) - 2Ku(t - ) + Ku(t - T)
K 2K K K
F(s) = - e + e F(s) = 1- e
s s s → s
( ) ( )
( )
( )
( )
T T
2 2
T 2
T T
4 4
T T
4 4
- s 2 - s
T -Ts - s
s - s
s - s
K K
1- e 1- e
s s
[f (t)] = =
1- e 1+ e
K e - e
K T
= s = tgh( s)
s 4
e + e L
1 s
2
1 f(t) = r(t) = tu(t) F(s) =
s s
→ =
2 +
s s 2
2 2
2 2 +
s s 2
-36s - 24s + 2
v(0 ) lim sV(s) lim = -3
12s +17s + 6 -36s - 24s + 2 [v (t)] = sV(s) - v(0 ) = + 3
12s +17s + 6 27s + 20 =
12s +17s + 6 27s + 20s 9 v (0 ) = lim s [v (t)] lim
12s +17s + 6 4
→∞ →∞
+
→∞ →∞
= =
′
′ ′ = =
L
L
F(s) = N(s) D(s)
1
1 2
1 2
1 2 1 2
2 1
1 1
2 2
1 1
s s
D(s) = (s - s )(s - s )...
k k
F(s) = N(s) + + ...
(s - s )(s - s )... s - s s - s k (s - s ) (s - s )F(s) = N(s) k + + ...
(s - s )... s - s k lim(s - s )F(s)
→
=
=
=
r
D(s) = (s - a) (s - s )...2 r
2
1 1 r 2
1 2 r
2 r
2
r
r-1 r-2 2
1 2 r
2
F(s) = N(s)
(s - a) (s - s )...
A A A k
= + + ... + + ...
(s - a) (s - a) (s - a) s - s (s - a) F(s) = N(s)
(s - s )...
k (s - a) =A (s - a) + A (s - a) + ... + A + + ...
s - s +
r
r s a
r
r
r-2 2
1 r-1
2 1
r
r-1 s a 1
k
r
r-k s a k
A lim(s - a) F(s) d (s - a) F(s) = ds
k (s - a) A (r -1)(s - a) + ... + A + 0 + d + ...
ds s - s
1 d
A lim (s - a) F(s)
1! ds
1 d
A lim (s - a) F(s)
k! ds
→
→
→
=
⎡ ⎤
⎣ ⎦
⎡ ⎤
⎢ ⎥
⎣ ⎦
⎡ ⎤
= ⎣ ⎦
⎡ ⎤
= ⎣ ⎦
2
s + 4 F(s) =
s (s +1)
1 2 1
2
1 s -1 s -1 2
2
2 s 0 s 0
2
1 s 0 s 0
s 0 2
A A k
F(s) = + +
s s s +1
s + 4
k lim(s +1)F(s) lim 3
s s + 4
A lim[s F(s)] lim 4
s +1
d d s + 4
A lim [s F(s)] lim
ds ds s +1
lim -3 = -3 (s +1)
→ →
→ →
→ →
→
= = =
= = =
⎡ ⎤
= = ⎢⎣ ⎥⎦
=
2
-t
-3 4 3
F(s) = + +
s s s +1
f(t) = -3u(t) + 4tu(t) + 3e u(t)
3 2
2
s + s + s + 4 F(s) =
s (s +1)
2
-t
s + 4 F(s) = 1+
s (s +1)
f(t) = (t) - 3u(t) + 4tu(t) + 3e u(t)δ
ﺪﻳﺎﺳ يﻮﻫ ﻂﺴﺑ يرﻮﺌﺗ
ﺒﺛا تﺎ :
لﺎﺜﻣ 11 :
ﺐﻳاﺮﺿ ﻪﻛ ﺖﺳا ﻦﻳا ،ﻲﻠﺒﻗ شور ﻪﺑ ﺖﺒﺴﻧ شور ﻦﻳا ﺖﻳﺰﻣ ﺪﻨﺘﺴﻫ ﻊﺑﺎﺗ ﻚﻳ ﺪﺣ ﻲﮕﻤﻫ .
لﺎﺜﻣ 12 :
ﻢﻬﻣ ﻪﺘﻜﻧ :
F(s) = N(s) D(s)
1
1
1 1
1
1 s s d
ds
D(s) = (s - s )D (s) F(s) k + ...
s - s k lim N(s)
[D(s)]
→
=
=
1 1
1 1
1 1
s s d s s
1 1 1
ds
s s d s s
1 ds
1 1
s s d s s
ds
N(s) N(s)
lim lim
[D(s)] D (s) + (s - s )D (s)
N(s) N(s)
lim lim
[D(s)] D (s)
lim N(s) lim(s - s )F(s) = k [D(s)]
→ →
→ →
→ →
= ′
=
=
2
s + 3 s + 3
F(s) =
(s +1)(s + 2)=s + 3s + 2
1 2
1 s -1
2 s -2
k k
F(s) = +
(s +1) (s + 2) s + 3
k lim 2
2s + 3 s + 3
k lim = -1
2s + 3
→
→
= =
=
-t -2t
2 -1
F(s) = + f(t) = 2e - e
(s +1) (s + 2)⇒
2
(s -1)(s + 2) F(s) =
(s + 3)(s + 2s + 2)
s -3 2 s -1+j
A B C
F(s) =
(s + 3) (s +1- j) (s +1+ j)
(s -1)(s + 2) (s -1)(s + 2)
A lim 0.8 B lim
s + 2s + 2 (s + 3)(s +1+ j)
→ →
+ +
= = =
(-2 + j)(1+ j) 5 153.43 2 45
B (2 + j)(2j) 5 26.57 2 90
2 81.87 2
∠ × ∠
= =
∠ × ∠
= ∠
D D
D D
D s -1-j
(s -1)(s + 2) (-2 - j)(1- j)
C lim
(s + 3)(s +1- j) (2 - j)(-2j)
5 206.57 2 -45 2
C -81.87
5 -26.57 2 -90 2 C = B
= → =
∠ × ∠
= = ∠
∠ × ∠
⇒
D D
D
D D
2 2
81.87 -81.87
0.8 2 2
F(s) =
(s + 3) (s +1- j) (s +1+ j)
∠ ∠
+ +
D D
o o
-3t 2 j81.87 (-1+ j)t 2 j-81.87 (-1- j)t
2 2
f(t)=0.8e + e e + e e
o o
-3t 2 -t j81.87 jt -j81.87 -jt
2
-3t 2 -t
2
f(t) 0.8e + e e e + e e
f(t) 0.8e + e 2 cos(t 81.87 )
⎡ ⎤
= ⎣ ⎦
= + D
