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7/24/2019 Statements+Solutions
1/9
g h
g
g
g
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7/24/2019 Statements+Solutions
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0
CL CL CMAC qS qSC e
K CMAC= 0
CH
CH
qSHcH K
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7/24/2019 Statements+Solutions
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qSe (CL+CL) +qScCMACK= 0 CMAC
qSHcH(CH+CH ) K( 0) = 0
0
qSHcH(CH+CH )
0
K( 0)
qSeCL K qSe
CL+
c
eCMAC
qSHcHCH qSHcHCH
K
=
0
K0
=
0 qSeCL+
c
eCMAC
K0 qSHcHCHK
qSeCL K qSeCL+
c
eCMAC
qSHcHCH qSHcHCHK
qD
qDSeCL K qDSe CL+c
eCMAC
qDSHcHCH qDSHcHCHK = 0
qD
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7/24/2019 Statements+Solutions
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3/4
Kh K T T 0
Qh Q
T
0
T
0
UF/b
a =0,1
x = 0,20 r = 0,50 = 10. h/ = 0,50 T/mb= 1. 0 = 1rad/s
d{x}/dt = [A]{x} +[B]{u}
x1 = h x2 = x3 = h x4 =
dx = [A]x + [B](T/mb)
x = [x1x2x3x4]T
T/mb
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7/24/2019 Statements+Solutions
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mh+S+Khh= Qh+T sinSh+I+K= Q+T b (1 a) sin
Qh = 2U2b+ h
U
Q = 2U
2b2a+
1
2
+
h
U
+h/U
mb
mb2
h
b +x+2
h
h
b = 2U
2b
mb+
h
b
+
T
mbsin = 2 1
mb2
U2
b2+
h
b
+
T
mbsin = 2
U2
b2+
h
b
+
T
mbsin
xh
b +r2+r
2
2=
2U2b2
mb2
a+
1
2
+
h
U
+
T
mb(1 a)sin =
= 2m
b2
U2
b2
a+
1
2
+
h
U
+
T
mb(1 a) sin = 2
U2
b2
a+
1
2
+
h
U
+
T
mb(1 a)sin
0 T
20h
b x20+2hh
b + 2
U2
b2+i
0b
U
h
b
=T
mbsin
x20h
b r220+r22
2
U2
b2
a+
1
2
+i
0b
U
h
b
=
T
mb(1 a)sin
1 x
x r2
+
0
2 h
20
0 r2
2
k20
ik0 1
ik0
2
a+
1
2
h/b
=
sin
(1 a)sin T
mb
1 xx r
2
+
2 h
20
0 r2
2
k2
ik 1
ik
2
a+
1
2
= 0
k= b/U
T
0
1 xx r2
+
2 h
2
0
0 r2
2k2 ik 1
ik
2
a+12 = 0
1 +h
2
2+
2
k2ik x+ 2
k2
x 2k2
ik
1
2
r2+r2
2 2
k2
1
2
= 0
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7/24/2019 Statements+Solutions
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1 + 0,52
2+
2
10 k2 ik 0,20 + 2
10 k20,20 2
10 k2 ik0,1 +1
2
0,502 + 0,502
2 2
10 k20,10 +1
2
= 0
1 + 0,52
2 + 2
10 k2ik 0,502 + 0,502
2
2
10 k2 0,10 +1
2
0,20 2
10 k2 ik0,1 +1
2
0,20 + 2
10 k2
= 0
1 + 0,52
2 0,502 + 0,502
2 2
10 k20,10 +1
2
+ 0,20
0,20 + 2
10 k2
= 0
0,502 + 0,502
2 1
5k2
0,10 +1
2
+
0,1 +1
2
0,20 + 1
5k2
= 0
2= +
1
5
8
5
+
25
25 =
33
25
2=
33
25
=
335 1,1489
1 + 0,52 1,32 0,502 + 0,502 1,32 210 k2
0,10 +1
2
+ 0,20
0,20 + 2
10 k2
= 0
1,33
0,08 0,45k2
0,04 + 0,2
5k2 = 0
0,1464 + 0,1464/k2 = 0
k= 1
UFb
=UFb
=
1
k
1
= 1
1 1
1,1489 = 0,8704
x
x =
x1x2x3x4
=
h
h
dx/dt x
T
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7/24/2019 Statements+Solutions
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UF/b I/(b
4)
K = 0
b +b 0,8b b 0,8b
0,006
M = b2
1
U2
(T5 T4T10) 12
UbT4T11 1T3b
2
b2UT12C(k)
1
T10U+b
1
2T11
20
60
I/b4
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7/24/2019 Statements+Solutions
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I +gI
2
+K= I +g
I2
= Q
K Q
Q = b2
1U2(T5 T4T10) 1
2UbT4T11 1
T3b
2
Ub2T12C(k)
1
T10U+
b
2T11
Q = U2b2
1
(T5 T4T10) 1
2ib
UT4T11+
1
T3
2b2
U2
U2b2T12C(k)
1
T10+
1
2ib
UT11
=
=U2
b2 1
(T5 T4T10) + 12
ikT4T11 1T3k
2 T12C(k)
1
T10+
1
2ikT11
= U
2
b2q
2I+igI2 U2b2q = 0 b
42 = I/b4
1 +ig
2 1
k2q
= 0
1 + 1
k2
(q) = 0[1]
g
2 1
k2 (q) = 0[2]
k /
UFb
=UFb
=
1
k
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7/24/2019 Statements+Solutions
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