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

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. .. _________________________________________________________________________ ___________________________________________________________________________ .. . .. _________________________________________________________________________ ___________________________________________________________________________ ... (.1), Matlab [1]. .1. [2]: , (.2). .2. (.3). .3. , (.4). .4. [10]. 1. . .. _________________________________________________________________________ ___________________________________________________________________________ [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 TttTk))()(210+ , x (t) - . tk . W(s) . , , .8.5.1 [4] . , [4], x (0) u (0), T Q. tk tk. (.5) lqr Matlab, , , . . .. _________________________________________________________________________ ___________________________________________________________________________ .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& . .. _________________________________________________________________________ ___________________________________________________________________________ .6. u(t)= , .. P(t) u(t), t=tm&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 . .. _________________________________________________________________________ ___________________________________________________________________________ [7], (.5.7): =],[....],[....min0maxktttmtttmm&&& , t=200. .7. , 2-3 4 [8]. 3. [2]: 21=dtd xVK cos - ( HRVVg + ) cos , 21=dtdV xV2 - gsin , dtdH =Vsin . - , V , H , =0e-H , 0 , - , x = mScx - , K=yxcc - , u=Kcos - ( ), g=g0 2)( HRR+ - , g0 , R . , V tk [9]. . .. _________________________________________________________________________ ___________________________________________________________________________ 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= . >+ . .. _________________________________________________________________________ ___________________________________________________________________________ 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)) ( + ); 2y2zC 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), , : . .. _________________________________________________________________________ ___________________________________________________________________________ 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 . .. _________________________________________________________________________ ___________________________________________________________________________ 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.