section_5_p_2 Моделирование в simulink.pdf
TRANSCRIPT
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5. Simulink
2.
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5. Simulink
1553
. ., . .
.............................................................. 1554
. . MATLAB/SIMULINK ................................................................................. 1561
. ., . ., . . MATLAB/SIMULINK .................... 1573
. . PSPICE SIMULINK...................................................... 1583
. ., . . MATLAB SIMULINK...................................................................... 1589
. . SIMULINK............................ 1596
. . SIMULINK-STATEFLOW ............................................................................ 1603
. ., . ., . ., . ., . . SIMULINK.............................................................. 1608
. ., . . SIMULINK ( )............................................ 1611
. ., . . MATLAB/SIMULINK ............... 1634
. ., . ., . . SIMULINK......................................... 1653
. ., . . SIMULINK ..................................................................................................... 1661
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II MATLAB
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chard Publications., 2003. 501 p. 2. Attia, John Okyere. MATLAB Fundamentals. Electronics and Circuit Analy-
sis using MATLAB / Ed. John Okyere. Attia Boca Raton: CRC Press LLC, 1999. 399p.
3. Steven M. Sandler. The SPICE Handbook of 50 Basic Circuits http://www.pcbcafe.com/BOOKS/SpiceHandBook/.
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. 17. [11] .
FH , -
F (FH-F ), 0 (- ) , , b , , . - .
[11] - . :
FH+=1,79 H, F+=0,97 H, 0+=0,003915 /c, b+=0 Hc/, FH-=-1,63 H, F-=-0,84 H, 0-=-0,003915 /c, b-=0 / .
. 15 . . 18.
. 18. [11] .
, , , , sgn, - [12]. -
-
5. Simulink
1623
-
( ) ( )( ) ( )2/ 2sgnSSS C S CF F F F e = + + , FC , FS , 2 - , S ( ). , . - .
3. ( )
(), - , .
- , - , . - [12].
, [9], (Dahl, 1968). [13] , Bo Pavelescu (1982), Armstrong-Helouvry (1991), Harnoy Friedland (1994), Canudas de Wit, Olsson, Astrm Lischinsky (1995).
Bo Pavelescu , - (dxS /dt ) (. . 25 [13]): ( )
. .. .
( )Sx x
C S CF x F F F e F x
= + + . FC, FS, Sx
. ,
. 3.1.
-
[14] (o [9] (K.J. strm) (C. Canudas de Wit P. Lischinsky), LuGre Lund-Grenoble):
-
II MATLAB
1624
0 1 2 ,dzF zdt
= + + (4)
,( )
dz zdt g
= (5) ( )20 ( ) ( ) .sC S Cg F F F e
= + (6) : F , , z , - , - , 0 - , - -, 1 , , 2 , FC , FS , S . , -.
(4)(6) , . 19.
. 19. .
1/g(v) . 20.
. 20. 1/g(v).
-
5. Simulink
1625
, - [9]. [9] , , (4) (6), , , , - - . - .
[9] . , 1.425 , 95% FS. 1.425 , 1.425 , 1.425 . -. , . 19. , - , . 21. - . 22.
. 21. .
F(x) , [9]. , , , . F() , , . (Dahl, 1968). Fa > F, - .
, . , . . . . 23, ) , - . 23, ).
-
II MATLAB
1626
=0.0007 / , 0.001 /. , . : 1 = 1 /, 2 = 10 / 3 = 25 /, , - [5].
. 22. .
) )
. 23. .
-
, . . . , =0.08 /, 1 = 10 / 2 = 20 /. 24.
-
5. Simulink
1627
. 24.
: , , . . - .
- - , - [9]: . - , - ( ) , -. , . 25, ). - Fa: 1 /c, 5 /c, 15 /c 50 /c. , - , . 25, )
, - , , (. . ) . ; FC = 1 .
-
II MATLAB
1628
) )
. 25. .
3.2. -
-
, . - ( , - Leuven).
- [16] , - , . . , , -, , , - . , - .
- , . 26. , , Fa, - FS, , (. 26, ). - (. 26, ), (. 26, ) - (. 26, ). , , , - , - , .
, , , - . [17] , - , , - -
-
5. Simulink
1629
. , - - - , .
) )
) ) . 26. .
4.
-
[18] - [12], [19]. - (ISW), (. 27). ISW, G. Pritschow, - , , [20], [21]. - dSPACE RTW MATLAB/Simulink Td = 125 s.
-
II MATLAB
1630
. 27. (ISW).
- - , fft. . 28. . 28, - - (f1 = 117 Hz, D1 = 0.055, f2 = 349 Hz, - D2 = 0.05) . - - . 29.
- . , .
. 30 , - -: l lC CF F+ = = 1.6 , l lS SF F+ = = 1.85 , S+ = 0.004 /,
S = 0.005 /, 2+ = 17 /, 2 = 8 /.
( ) . 31.
-
5. Simulink
1631
. 28. .
. 29. ().
. 30. ().
. 31.
( ).
-
II MATLAB
1632
- . , , . -, - . , - . . 1. Armstrong-Hlouvry B., Dupont P., Canudas De Wit C. A survey of models,
analysis tools and compensation methods for the control of machines with friction // Automatica. 1994. V.30. N.7. P.10831138.
2. . . - // . 2000. 7. .4454.
3. . . - // . 2000. 7. .1113.
4. Hess D. P., Soom A. Friction at a lubricated line contact operating at oscillat-ing sliding velocities // J. Tribology. 1990. V.112. P.147152.
5. . . . .: . . -, 1979. 246 .
6. . ., . . . . -, 1987. 183 .
7. . . . --: , 2000. 293 .
8. Kozlowski K. R., Dutkiewicz P. Experimental identification of robot and load dynamics // IFAC 13th Triennial World Congress. San Francisco, 1996. P.397402.
9. Canudas De Wit ., Olsson H., strm K. J., Lischinsky P. A new model for control of systems with friction // IEEE Transactions on Automatic Con-trol. 1995. V.40. N.3. P.419424.
10. / . .. , . 3. .: , 1967. 770 .
11. Kern R. H., Gao C.-T., Nitsche R. Reibkraftkompensation mittels Fuzzy-Logik // Automatisierungstechnischepraxis. 1995. V.37. P.5060.
12. . ., . . // . -. . SICPRO2003. .: , 2003. . 18211849 (CD ISBN 5-201-14948-0).
-
5. Simulink
1633
13. Armstrong B. Challendges to Systematically Engineered Friction Compensa-tion // Proc. of IFAC Workshop on Motion Control. Munich. 1995. P.2130.
14. Canudas-De-Wit . Comments on A New Model for Control of Systems with Friction // IEEE Transactions on Automatic Control. 1998. V.43. N.8. P.11891190.
15. . . // - ( . .). 1999. 2. .226228.
16. Dupont P., Hayward V., Armstrong B., Altpeter F. Single state elasto-plastic friction models // IEEE Transactions on Automatic Control. V.47. N.5. May 2002. P.787792.
17. Swevers J., Al-Bender F., Ganseman C.G., Prajogo T. An integrated friction model structure with improved presliding behavior for accurate friction com-pensation // IEEE Transactions on Automatic Control. V.45. N.4. April 2000. P.675686.
18. . , .. - // . . . SICPRO2004. .: , 2004. .571588 (CD ISBN 5-201-14966-9).
19. . . - // . . . SICPRO2000. .: ..16961709(CD ISBN 5-201-09605-0).
20. Pritschow G., Ketterer G. Rechnergestuetzte Identifikation von Reibkennlinien an elastisch gekoppelten Bewegungsachsen // Antriebstechnik. 1993. V.32. N.9. P.6772.
21. Augsten G., Schmid D. Einfluss von Spiel und Reibung auf die Konturfehler bahngesteuerter Werkzeugmaschinen // Steuerungstechnik. 1969. V.2. N.3. P.103108.
-
II MATLAB
1634
004
MATLAB/SIMULINK
. ., . . , ,
e-mail:[email protected]
Excel , , . , -. , .
MATLAB. - (Toolboxes) . - FinancialToolbox, Excel ExcelLink, Word Notebook.
Simulink, . - . . - , . , - .
Simulink. - . 1. ,
. , - . , - . , - , .
: . : . : - ,
-
5. Simulink
1635
. - , .
- .
. - , . .
(, , ).
. , - , . - - . , . - : , -.
.
: t=tf BDt = PRFt * TXRT, t=tb
BDt , - t, .; PRFt (profit), t, /.; TXRT (tax rate); t , . , ; tb (begin) - ; tf (final) .
t=tf CPt = PRFt * (1TXRT), t=tb
t PRFt = CPt * RN,
RN . , .
Simulink. Simulink- -, . , - .
-
II MATLAB
1636
. . 1.1.
. 1.1. .
, . CapF. , . , . CapS.
( ) PrfF Rntb.
- Rntb. [0.2:0.2:0:8]. MATLAB , - 20% 20% 80%. - MATLAB.
Scope1 - CapS.
( ) - TaxRate. - TxF.
-
5. Simulink
1637
TaxRate. [0:0.1:1:0]. , - 0% 10% 100%. - MATLAB.
. - TxF BdjS. Scope . Display BdjS.
- , - .
, . : - , , -.
. - Scope Display.
--: . . , . %Optimal profit tax rate simulation %File: C:\Csr_MtLb\TxRt\TaxRate_DscM.m and TaxRate_Dsc.mdl %================================================= path(path,'C:\Csr_MtLb\TxRt') %Set model Path %================================================= open_system('TaxRate_Dsc') %Load TaxRate_Dsc.mdl TaxRate=[0:0.05:0.7] %- for Rntb = 0.2:0.2:1 % - sim('TaxRate_Dsc') %Run model plot(TaxRate, ScopeData(end,2:end)) % hold on % grid % end hold off % %======= end TaxRate_DscM.m program =============== m- -. .
-
II MATLAB
1638
-. .m- - Simulink - Simulink .mdl.
. open_system
. TaxRate -
. 8 14 for -
. sim -
, -.
plot . 1.3, (work space) MATLAB, - Scope. hold on - , - .
. . 1.2.
. 1.2. -.
-
5. Simulink
1639
- m- . Simulink . Scope - () . - , - plot MATLAB.
1. . - .
Simulation, Scope - : , - . .
, . , . . - . - : -, - .
2. . - - . -, . . .
MATLAB TaxRate_DscM.m. . . Tools > Run. MATLAB - - , . 1.3.
. , . - ( ), , , , 23%.
-
II MATLAB
1640
. 1.3. - .
,
, - . , - . . , , - . , - .
2.
.
(18421924) , . - . , 80 - OPEC, , .
. , , . -
-
5. Simulink
1641
, , . , , MATLAB_Simulink.
. - . : , -, .
. : , , , . . - , . . -. , . : .
. - : , , , .
Dmd=D0 Kd*Prc, Dmd (demand) ; D0 ; Kd ; Prc (price) .
Spl=S0+Ks*Prc,
Spl (supply) ; S0 - ; Ks ; Prc (price) .
Simulink. - - . 2.1.
. 2.1. - .
-
II MATLAB
1642
-, . DmdFn. , . :
u = Prc, D0 = 100, Kd = 10. . -
SplFn. - , .
: u = Prc, S0 = 10, Ks = 7.
. Spl, .
SplFn1 - . , - . Prc, Spl . DmdFn.
. . -
. - Scope. - . , - . , - .
. , . - MATLAB - . - . - , . . -.
MATLAB. - MATLAB. %Market equlibrim price simulation %File: C:\Csr_MtLb\DmdSplEquM.m %1.Simulate static functions, plot its %2.Simulate price dynamic, plot price Web graphics
-
5. Simulink
1643
%================================================= %Set model Path path(path,'C:\Csr_MtLb\MrktEqlPrc') %================================================= %1.Simulate static functions, plot its %Load and Run DmdSplEqu.mdl open_system('DmdSplEqu') sim('DmdSplEqu')%Write Vars into WS from Scope %Plot Static features plot(ScopeData(:,2),ScopeData(:,3:4)) hold on grid pause(5)% % %================================================= %2.Simulate price dynamic sim('DmdSplEqu') %================================================= %3. plot price Web graphics for i = 2:11 % line([ScopeData(i-1,2) ScopeData(i,2)],[ScopeData(i,4) ScopeData(i,4)]) line([ScopeData(i,2) ScopeData(i,2)],[ScopeData(i,4) ScopeData(i+1,4)]) end hold off %=================================================
. % - . path - . open system - - Simulink.
sim . Plot . Hold on . Grid . -. pause 5 - .
. Sim . . Scopes MATLAB workspace.
for, , - .
. 2.2.
-
II MATLAB
1644
. 2.2. - .
/ MATLAB c -
. Simulink. Scope, Scope1 , - . - , MATLAB.
1. -. MATLAB m- DmdSplEquM.m. . Tools>Run. . Simulink . Scope Figure. Scope1 . 2.3.
Scope . 2.4.
-
5. Simulink
1645
. 2.3. , - .
. 2.4. , Scope.
- . 2.5.
-
II MATLAB
1646
. 2.5. .
2. - . D0 DmdFn SplFn1 .
S0 SplFn .
3. - . - Kd DmdFn SplFn1 .
- Ks SplFn .
Ks . Ks = Kd . . - , . . . Ks > Kd , , - . -, .
-
5. Simulink
1647
3.
. - . . , , .
- , - . , . - - .
, 1962 -, . - . , . , 300 , 10 . : , , -, , , .
. .
. - - .
. Simulink - , . - Simulink . 3.1.
. 3.1. .
-
II MATLAB
1648
70 , , - 5-10 . , - .
. (-) NeedPrk ( ). - , : - ( Prdct), c InPrk ( ). OutPrk ( , ).
- , RealPrk ( -, ). - - urDmd. Saturation () , - : urDmd >= 0.
- . , - , ( ).
. - Scope , . - , -, . . 3.2.
. .
. 3.3.
-
5. Simulink
1649
. 3.2. Simulink Scope.
. 3.3. .
-
II MATLAB
1650
Simulink. . Scope1. MATLAB. Scope.
1. . - MATLAB . Simulink ParkPrdct.mdl.
Simulation>start. Scope - , - . 3.4 3.5.
. 3.4. , , Scope1.
-
5. Simulink
1651
. 3.5. , , Scope.
- . , , -. , . . , - , . . , -, .
2. - . , , -. - , . . -, , . , - . , , . . .
3. - . - - .
- , -
-
II MATLAB
1652
. , . - , . . , -, .
-, - , -, . . .
1. . . .
.: -,1996. 2. ., . . .: , 1992. 3. . . . MATLAB_Simulink -
. .: , 2001. 4. . . .
.: , 2002. 5. . . . .
.: -, 2002. 6. . . . . .: , 1997.
-
5. Simulink
1653
613.314
SIMULINK
. ., . .,
, , e-mail:[email protected], [email protected]
. . (), ,
e-mail: [email protected] -
: OrCad, Micro Cap, Electronic Work Bench . . , , , - - . - , , . , -, , , ( - -, . .). , . , -. - , - .
Simulink MATLAB Sim Power System (SPS) - . SPS - , - . , . Sim Power System, ( -) Simulink.
-
II MATLAB
1654
- -. , ( ) , ( ). , - , , , - - . , - 1000 50, 210-5 . , - 10100 , , - : 0.010.001 c. - , 50-500 , .
- . - :
1. . 2. - . -.
3. , .
4. - . .
5. - .
6. - .
7. .
8. . 2 .
-
5. Simulink
1655
, - . ( ) .
. 1.
.1. .
Electro, Teplo. Pulse Generator , . - ( Electro), ( Teplo). Step Control Subsystem - - . - . 2.
.2. .
-
II MATLAB
1656
Product - . , , , -. , , - . Timer , , - . ( ) Step Switch. Step Switch (. 3) Constant , S-function - . . 3 - .
.3. .
S-function - : set_param(_,'maxstep',num2str(u) ), set_param - , _ Simulink-, maxstep ( ), u .
S- : function [sys,x0,str,ts]=Set_Max_Step_Size(t,x,u,flag,m_name) % switch flag, case 0, [sys,x0,str,ts]=mdlInitializeSizes(m_name); case 3, sys=mdlOutputs(t,x,u,m_name); case {1,2,4,9} sys=[]; otherwise error(['Unhandled flag = ',num2str(flag)]); end % function [sys,x0,str,ts]=mdlInitializeSizes(m_name) %
-
5. Simulink
1657
sizes = simsizes; sizes.NumContStates = 0; sizes.NumDiscStates = 0; sizes.NumOutputs = 0; sizes.NumInputs = 1; sizes.DirFeedthrough = 1; sizes.NumSampleTimes = 1; sys = simsizes(sizes); % x0 = []; str = []; ts = [-1]; % function sys=mdlOutputs(t,x,u,m_name) % set_param( m_name,'maxstep',num2str(u) ); % sys=[];
S- m_name - . S- [1].
, - . , , .
. 4.
, . , - R_variable, , - . - (. 5).
-: ( - ), - . T_In . - - . , .
-
II MATLAB
1658
. 4. .
. 5. .
(. 6) - , - . , - .
-
5. Simulink
1659
. 6. .
. 7 - .
. 7. .
. 7, , , . . ,
-
II MATLAB
1660
- . - .
1. . . Simulink. .
M.: -, 2004. 496 .
-
5. Simulink
1661
621.878.25
SIMULINK
. ., . . - ,
e-mail: [email protected]
() () . , , - , . - , , [6].
[2] - (. 1): - , , - , , (), , () .
P10
P1 P2 P3 P4
P5
P6 P7
P8 P9 P11
P12
P13 P14 P15
P16 P17 P18
. 1. - .
Pi. (P1), (P2),
-
II MATLAB
1662
(P11), ( -, ). , -, (P6), , - (P5) (). , - (3), - (4) (7). (8) (14) (15), (10) , , , . - (11) (16).
() - (17) (10). - (18), (12) (13), - [7].
, -, , - .
, [1]:
+= ll ll sineAeA)(R ||2||12y 21 , (1)
-; 1, 2 ; 1, 2 - ; .
(1) [1]: y(n) = a01x(n) + b11y(n-1) + a02x(n) + a12x(n-1) + b12y(n-1) + b22y(n-2), (2) 01, 02, 12, b11, b12, b22 [1].
:
+=
=km
kmnc
)n(yM1)m(y , (3)
k = 0,5(Mc 1); Mc ; y(n) - .
, -, , : ;
1pTpTkpk
)p(y)p(yW
y22
y1
y2y1
1
yy
1
+++==
(4)
-
5. Simulink
1663
;1pTpT
kpk)p(y)p(yW
y22
y1
y4y3
2
yy
2
+++==
(5)
,1pTpT
k)p(F)p(yW
y22
y1
y5
Fy
++== (6)
y1, y2 ; F ; kiy, Tiy - , .
:
;1pTpT
kpk)p(y)p(W
22
1
21
1
y1
+++==
(7)
;1pTpT
kpk)p(y)p(W
22
1
43
2
y2
+++==
(8)
,1pTpT
k)p(M
)p(W2
21
5
F
M F
++==
(9)
F , , - .
, - :
( ) ,eke1p
kk
)p(y)p(y
)p(W p3p2
1
y
+== (10)
y - ; y - ; ki , - ; . ( ),tankyy += (11) k . k = L / 2, (12) L .
h, , y.
( F F ) , - , - [6].
-
II MATLAB
1664
, [4]:
,MMdt
dJ f23 +++= (13)
; J3 ; f ; , - ; , ; 2 - . f = k Pf (v); (14) = k F; (15) = k sin (); (16) v = k 1, (17) Pf(v) - ; ; ; , ; 1 . k = r / i, (18) r ; i -.
[6]:
,kdt
dJ 112 += (19) , ; J2 ; k , - .
, - [7]:
( ) ( )( )
>+
+==,
1pC
;1p
C
pppW
1
(20)
, , ; , - ; .
() [5]:
( ) ( ) ( ) ;p1pek
)p(UpLpW
p1
1
+== (21)
-
5. Simulink
1665
( ) ( ) ,1p
ek)p(UpMpW
p2
2
+== (22)
L ; - , ; U ; k1 , - ; k2 , ; , ; .
- (. 2), (2) (22), - .
- , - , ( , - .), -. , - , - . ( ), , , [3, 7].
. - , - ( - ). - , - , . , .
: ( ) - ( ), - , , .
-
II MATLAB
1666
d dt
k1yp + k2y
1 T1yp2 + T2yp + 1
?y1
?y2
F
y k3yp + k4y
k5y
-
v
k1p + ky
1 T1yp2 + T2yp + 1
k3p + k4
k5 MF t
MF
h F
k1
k2
e-p
k3 e-p
?y
tan
k
y
y t
F
h
F
F
v
h
k
k
Pf =f(v)
v
f
k
J3
2
k v 2
2
1
C Tp + 1
d dt J2
k
1
e-p 1 Tp + 1
k1 p
U
L
h h
h k2
h
sin
M
C Tp + 1
. 2. .
-
, . 3. - b1 b2 ( ) (b1 b2), . - c - , .
U
1
1
b1 b2
. 3. : b1 ; b2 -
; .
-
5. Simulink
1667
, , h , - .
- Simulink. - , , .
, -, .
1. . . -
- / . . . , -. : , 2004. . 1. .1. .152158.
2. . . // - , , , : . .-. . . 2. : - , 2003. .250253.
3. . ., . . . .: , 1979. 280 .
4. . . . .: , 1980. 215 .
5. . . - : . . . . , , 1997. 172 .
6. . ., . . - // . . . 4. . : - , 2003. .7275.
7. . ., . . - // , : . .-. . : - , 2004. .219220.