ΣΑΕ Ασκήσεις και...
date post
15-Apr-2016Category
Documents
view
150download
9
Embed Size (px)
description
ΣΑΕ ΑΣΚΗΣΕΙΣ
Transcript of ΣΑΕ Ασκήσεις και...
pi & pi
&
..
2010
user : 1.2,1.52.6,2.73.3,3.64.3,4.55.5,5.66.5,6.6,6.77.2,7.58.5,8.69.3,9.410.2
11
1.1
.
1.2
. pipi : , pi pi. pi- pi pipi;
1.3
- . ;
1.4
() Watt .
1.5
pipi pi ( ) (NC) - -pi.
22
2.1
pi . v1 v2 .
C
R
R1
L
R2
R1
C
R2
+
-
+
-
u
1
2
+
2
-
1 2
1
u
u
u
u
u
2.2
pi . pi . ;
C1
R2C2
L1
R1
i2
i i
2.3
k1, k2 ,pi .
k1
k2
2.4
pi . pipi ;
3 2.5
pi pi pi .
2.6
. ;
4I
1
k
1 n
1
n
2
c
1
2
2
k
2
3
3
c
2
T
1
I
=n /n
1
2
n
1
: . . 1
n : . . 2
2
2.7
. pi.
R
L
+
-
+
-
1
1
2
2
C
b
53
3.1
pi pi pi pi pi . ;
m,I
.
.
l
l/2
K.M.
g
F
m
3.2
pi pi - pi pi pipi : () R2 , () R2 . pipi - pi pi .
h
R
1
R
2
()
ANT
pi
P
g
1
A
3.3
pi pi pi pi . h1 h2 , . pi ;
userHighlight
userHighlight
6m
1
R
1
m
2
R
2
A
1
h
2
A
2
g
h
1
q
q
3.4
pi pi pi m1 m2 - cp1 cp2, . , -.
R
2
R
1
1
2
3.5
pi , (pi qm1) T1. h T2, pi (pi ). cp pi %. pi ;
g
m
1
,
T
1
g
R
T
2
h
A
()
7 3.6
C1 T1. C2 T2, , pi T3. T3 i , T1 T2.
C
1
,
T
1
C
2
,
T
2
T
3
R
2
R
1
i
R
84
4.1
pi pi pi :
C
y
k
2
m
k
1
y(0)=1 ,
2
m= 1 kg
k = 0.3 N/m
k =0.7 N/m
c = 2 N s/m
2
1
4.2
pi pi pi :
(0)=0 ,
c
I
4.3
pi pi pi :
T (t) = 1 + t (t 0) pi t = 0
:
(0) = 0 rad, (0) = 2 rad/sec
9pi , , - pi .
4.4
pi pi pi - . pi , , pi.
x()
1
C
1
m
y(E)
2
C
2
4.5
pi pi pi 4.4 pi . pi , pi.x
1
0
1
3
t
10
5
5.1
pi Laplace pi :
f(t) = sin(t) (t 0)
5.2
pi Laplace :
F (s) =5(s+ 2)
s2(s+ 1)(s+ 3)
5.3
pi pi pi pi pi :
y + ay = x
pi Laplace pi - pi :
x(t) = sin(t) (t 0) y(0) = b
5.4
pi Laplace pi pi pi :
k
y
C
m
11
5.5
pi Laplace pi pi pi :
qm(t) =
{4t
4t+ 160
0 t 22 t 44 t
t
q
m
0 2 4
8
. pi , , pi.
g
h
()
R
()
q ()
m
5.6
pi Laplace pi pi pi :
f(t) = 2u(t) y(0) = 0 (m) y(0) = 1 (m/sec)
pi u(t) pi . pi , pi.y
C
m
k
f
12
6
6.1
pi 2(m) pi pi 1(kg/sec). ;
6.2
pi pi t = 0 q(0) = 0(Q) v(t) = 1(V ) . pi pi pi ( 2% ) ;
pi q(0) = 0.001(Q) v(t) = 10(V ).
u(t)
+
-
C
R
13
6.3
pi pi pi pi- q(0) = 0(Q) v(t) = t2(V ) .
6.4
pi pi pi x(0)=0 (m) v(0)=1 (m/sec) pi pipi :
() m = 1 (kg), c = 4 (Nsec/m), k = 8(N/m)() m = 1 (kg), c = 4 (Nsec/m), k = 4(N/m)() m = 1 (kg), c = 4 (Nsec/m), k = 2(N/m)pi pi , pi,
pi pipi.
k
C
x
m
6.5
pi pi c pi pi pi pi :() pi pi , pi pi 20%.() , pi pi 3 secs() pi ( 2%) , pi pi3 secs
k
C
14
6.6
() .() pi qm(t) = 2(kg/sec) .() pi , pi, pi .
q
m
h
R
A
R
1
1
2
2
h
2
A
1
g
6.7
pipi pi :
s = 2,3 j,5 2j , pi,
pi ;
userHighlight
15
7
7.1
pi pi pi pipi pi :
G
2
G
1
G
3
+
+
+
-
X
()
Y
X
Y
G
1
+
-
G
2
G
6
G
7
G
3
+ +
-
G
4
G
8
G
5
()
7.2
pi :() pi .() pi pi;() .
16
+
--
-
1/s 1/s
1/s b
3
b
2
b
1
1
2
3
++
1
2
3
7.3
pi Routh-Hurwitz - pi:
() s4 + 10s3 + 32s2 + 50s+ 100
() s5 + 10s4 + 30s3 + 80s2 + 344s+ 480
() s4 + 3s3 + 8s2 3s+ 9() 2s4 + 12s2 + 50
() s3 + s+ 1
pipi , pi pi pi pi ;
7.4
pi pi () pi .
+
-
R
K
1
s+4
Y
17
7.5
pi pi pi ( / , ) pi pi pi b1secs.
R +
-
K
Y
1
s(Ts+1)
18
8
8.1
pi , pi pi :
() pi pi ; , pi;() pi .() pi pi ;() pi ( pi ) ,
, pi.
R
K
+
-
K
I
s
+ +
-
s
b
K
D:
,b
K,K
I
8.2 ( - )
R
-
+
____
K
I
S
1 Y R
K
I
KAT.1
+
-
K
2
KAT.2
1
E.
.
.
pipi pi . pi pi , pi pi . pipi - 2 (pi ). pi pi :
() pi pi ;
19
pi pi, pi pi , - pipi.
() pi pi .pi pi , pi.. pi, , pi. pi;
() pi pi 10 % pi , pi pi pi pi . pi ;
pi pipi pi pi;
() pi pi pi pi pi;
8.3 ()
pi -pi (pi..). pi- J = 0.10(kg.m2), pi c = 1(N.m.sec). . pi pi, pi - pi pi 0.50(secs) 10(Nm/volt). pi -, pi, pi, . pi , pi .
pi :
(i) pi pi 0.001(rads/sec)
(ii) pi pi 1(N.m) pi0.01(rads/sec)
(iii) pi pi 0.1(secs)
(iv) pi pi 5%.
() pi pi pi- pi pi (i).
() pi pi (ii);
20
() pi pi pi . pi pi;
pipi pi pi pi pi- (iii) (iv);
() pipi (2 ) pi pi pi. pi (iii) (iv);
pi pi (i) (ii);
() pipi pi pi pi pi (i) (ii);
8.4
q
m1
R
1
q
md
R
2
A
2
g
A
1
h
.
h
2
2d
.
1
h
2
:
() pi 2 pi pi - pi h2d qmd. pi pi 2 , pi pi 1 .
21
() pi pi pi - ( 1);
pi pi pi;
8.5 pi :
pi pi :
M L (M +m) g = f pi
pi ( ) f . pi :
(i) pi 0.707.(ii) pi ( 2%) 8(secs).
8.6
.
A : ,C
2
2
C
1
T
1
R
I
.
i
i
R
2
A
22
pi pi R. C1 T1. pi R1. pi pi C2 T2. R2, pi To. : R = 1(k), R1 = R2 = 1(K.sec/Joule), C1 =C2 = 100(Joule/K)
pi - T2 i pi R. pi :
(i) T2 pi 0.01(K).
(ii) T2 T0 pi 0.01().
(iii) pi pi10%.
(iv) pi 20(secs)
(v) T2 ( ) pi C2 pi 0.1.
pi pi :
() pi , pi - .
() pi pi . pi -.
() ( 2) :
(two-position control) T2 . pi ( T2)
() pi PID ( T2):
(1) pi pi (pi (PID) pi pi pi (i) (ii)
(2) pi pi pi pi pi pi (iii),(iv) (v)
(3) pi , pi 1(sec) DC ( ) 1. pi (1) pi pi pi (i) (ii).
23
() pi PID ( T0, T2):
pi pi (1) T2 T0;
.
() ( T0, T1, T2):
pi T0, T1, T2, pi pi .
(1) pi - pi T0 , pi pipi T2 . pi pi pipi T1 ;
(2) pi pi pi pi - (1) T2, , .
() /.
pi pi (MATLAB,MATRIXx, pipi) pi pi .
pi / , - (pi.. , pi pi T0), pi pipi pi .
pi pi . pi pi pi pipi /.
24
9
9.1 pi
pi pi pipi :
() G(s) = 10/s(s2 + 3s+ 9)2
() G(s) = (s2 + 1)
