ΣΑΕ Ασκήσεις και...

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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)