Московский государственный технический университетiu1.bmstu.ru/materials/demenkov/lab.pdfМосковский государственный технический университет им. Н.Э. Баумана

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  • . ..

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    ..

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    ... (.1), Matlab [1].

    .1.

    [2]: , (.2).

    .2.

    (.3).

    .3.

    , (.4).

    .4.

    [10].

    1.

  • . ..

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    [2]. , , . .

    - . , , . , , .

    y1(t)=0,5[1+cost/10]. ,

    . x& =A x + Bu , y = C x . . , , y1(t)

    y1(t) | u2(t)| u2max(t) |y2(t)| y2max(t) .

    - . ,

    () [3] J= dtuRuxxQxx T

    t

    t

    Tk

    ))()(21

    0

    + ,

    x (t) - . tk

    .

    W(s) . ,

    , .8.5.1 [4] .

    , [4], x (0) u (0), T Q.

    tk tk.

    (.5) lqr Matlab, , , .

  • . ..

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    .5.

    y (t) ,

    , () [5].

    2.

    , .. .. [2]. :

    - , - , (g=const), - . OXY

    (.6) [6]:

    dtdVx =

    mP cos ,

    dtdVy =

    mP sin ,

    dtdX =Vx ,

    dtdY =Vy.

    P= c, m& Vx Vy V, P , a, - , - . m&

  • . ..

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    .6.

    u(t)= , ..

    P(t) u(t), t=t

    m&

    k Y(tk)=Y Vx(tk)=Vx max Vy(tk)=0.

    , .

    minm& , =0, m& maxm& minm&

    os2 + sin2 =1. J = - Vx(tk) : 1 = Vy(tk) = 0, 2 = m(tk) - m =0. , ,

    P1(tk) = -1,

    (.1) Y = 450000 .

    1

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    [7], (.5.7):

    =

    ],[....],[....

    min

    0max

    k

    tttmtttm

    m&

    && , t=200.

    .7.

    ,

    2-3 4 [8].

    3.

    [2]:

    21

    =dtd xVK cos - ( HR

    VVg

    + ) cos ,

    21

    =dtdV xV2 - gsin ,

    dtdH =Vsin .

    - , V , H , =0e-H , 0 , -

    , x = mScx - , K=

    y

    x

    cc -

    , u=Kcos - ( ),

    g=g0 2)( HRR

    + - , g0

    , R .

    , V tk [9].

  • . ..

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    t=t0 0=(t0),V0=V(t0),H0=H(t0), 0, ,x, g0, R u(t), - V |u(t)|u0 (.8).

    .8.

    : H=6600 .

    . : J = V.

    , :

    u= .

    >+

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    V = -qV2Cx - sin + P/Mu(1 - 2/2) (1 - 2/2), = qVC& y - cos /V + P/(MuV), & = - (q V Cz + P (1 - 2/2)/(Mu V))/cos, X& = k V cos cos , Y& = k V sin, Z& = - k V cos sin ,

    q = (0a2S/2m0g) Hi(Y)/Mu(Y) = 0.92 Hi(Y)/Mu(Y), k = a2/g* l0 = 9,174, Mu = m(t)/m0 , m0- , P = P(t)/ m0g , Xi = (Y)/0, 0 = 1.29 /3 - . (X,Y,Z) (.9): Y

    , (X,Z) . . (X,Y,Z) . , = (Y)- ( ), V- ; S- ; Cx,Cy,Cz- ; - (X,Z) ( ); - (X,Z) X, a- , Y 300 /.

    .9.

    : Cy = (a0(M) + F(,M) a1(M)) Cz = (d0(M) + F(,M) d1(M)) Cx = Cx0(M) + K(t) Cxd(M) + Cx(M,Y) + (b0(M) - b1(M)) ( + ); 2y

    2zC

    M = V/a - ;

    F(,M) =

    max i=1 i- Ji(S) (

    ), S. i(S) , i- .

    , k- . S, , S k. k- : S, .. Xk(S)=S, Jk(S)=Lk(S).

    S ( ), S Xk(S) Jk(S). .

    , (k-1)- . S. Jk-1(S) : (k-1)- k- ( ).

    (k-1)- (k-1)- , (S-X). :

    Lk-1(X)+Jk(S-X), , :

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    Jk-1(S)= sx

    max {Lk-1(X)+Jk(S-X)}

    sx

    max , X,

    ( , S, ), , . , X, ,- (k-1) .

    (k-2)-, (k-3)- .. . i- :

    Ji(S)= sx

    max {Li(X)+Ji+1(S-X)}

    Xi(S) - X, .

    1, Si, , :

    J*=J1()= Px max

    {L1(X)+L2(-X)}

    , () . . X, , X1* 1- .

    , , -X1*.

    S, : X2*=X2(-X1*), .. .

    , .

    7.

    , (X0,Y0) (Xk,Yk) J (, , ..) [2].

    (X,Y) X Y . . , : U=0, X, U=1, Y. , U={0,1}.

    , , , . L(X,U), . .

    , , . X , . Y. xij

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    X=i Y=j, i+j .

    Xn , n . xij , i+j=n. n=0,1,2,..., X0=x00 ; X1={x10 ,x01}; X2={x20, x11, x02} ..

    . , .

    1. .., .. Control System Toolbox. MATLAB 5 / . ... .: -, 1999. -287.

    2. .. : . . .: - ..., 2007. 171.

    3. .. . .: , 1968. - 368. 4. ., ., . . .

    . .: , 1970. -620. 5. .. : . . .:

    - ..., 2005. 200. 6. ., , .: ,

    1972. 544. 7. .., ..

    / , 1962, .2, 6. .1132-1139. 8. ..

    / , 1982, .22, 1. .79-89. 9. .., .., ..

    / 297. .: - .... 1979. C.35-43.

    10. : . / . ... .: - ..., 2002. -72.

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