Курсов проект- Теория на Управлението
DESCRIPTION
Регулиране температурата в химически реакторTRANSCRIPT
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: 3. 4. 3. . . . . 086105
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1-; 2-; 3,4- U-I; 5,6-; 7,8-
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1. .
1.1. .1.2. .1.2.1. kpk =s.A -.1.2.2. -.1.2.3. , ( ) .1.3. .1.3.1. - ( ).1.3.2. - (kpk,) .1.3.3. ( ) - ( ) kpk.1.4. .
2. ().2.1. .2.2. MATLAB .2.3. , .
3. .3.1. - -.3.2. .3.3. .3.4. . 3.5. .5.[oC]koTokkTkkpckfTffs[]
6750.87001.96001.580.03758502003
1. .
1.1. .
[oC]koTokkTkkpckfTffs[]
750.87001.96001.580.03758502003
k
Matlab
A=75 % - =75Ko=0.8 % To=700 % Kk=1.9 % Tk=600 % Kpc=1.58 % Kf=0.0375 % Tf=850 % B=200 %-fKb=0.7501 % Tb=149.925 % s=31.2. .
1.2.1. kpk =s.A -.
A = B = f
- Matlab KregP=(100*A-100*B*Kf-s*A)/(s*A*Kb*Ko)
=2.25 - Matlab EstP=(s*A)/1002.25
1.2.2 -.
-
1.2.3 , ( ) .
- ().
Matlab
YustP=(A*KregP*Kb*Ko+B*Kf)/(1+KregP*Kb*Ko)
- ().
.Kff Kf . - T , . T , B .
X F X 0 10 0.0001. F F1=0 F2=200
atlab
KxP=(KregP*Kb*Ko)/(1+KregP*Kb*Ko)KffP=Kf/(1+KregP*Kb*Ko)X=[0:0.0001:10]F1=0 F2=200YstP1=KxP*X+KffP*F1 YstP2=KxP*X+KffP*F2hold onplot(X, YstP1)plot(X, YstP2)
-
- , .
= 0
atlab
KxPI=1KffPI=0X=[0:0.0001:10]F1=0 F2=200YstPI1=KxPI*X+KffPI*F1 YstPI2=KxPI*X+KffPI*F2hold onfigure(2)plot(X, YstPI1)plot(X, YstPI2)
, F1=0 F2=200. - .1.3. .1.3.1. - ( ).
- .
atlab
Hp=[(To*Tb) (To+Tb) (1+KregP*Kb*Ko)]roots(Hp)
-0.0040 + 0.0164i -0.0040 - 0.0164i
. .
1.3.2. - (kpk,) .
*
- , , , - , - .
KrepPI PI .
atlab
KregPI=0:100; for i=1:101 TregPI(i)=(Tb*To*KregPI(i)*Kb*Ko)/((Tb+To)*(1+KregPI(i)*Kb*Ko)); end figure(3)plot(KregPI,TregPI)grid on;
MATLAB KregPI TregPI . - regPI TregPI . 20% . (regPI regPI) . SIMULINK - ( ) 20%, Krepi=10 Trepi=860s 19.69% ( ).
- SIMULINK
( t-, Ypi-)
( t-, Ypi-)1.3.3. ( ) - ( ) kpk.
KregPI=10TregPI=860
atlab
KregPI=10TregPI=860Hpi=[TregPI*Tb*To TregPI*(Tb+To) TregPI*(1+KregPI*Kb*Ko) KregPI *Kb*Ko]roots(Hpi)
-0.0035 + 0.0068i -0.0035 - 0.0068i -0.0011
KregPI=10TregPI=860
.
atlab
NumFyxPI=[KregPI*Kb*Ko*TregPI KregPI*Kb*Ko]DenFyxPI=[TregPI*Tb*To (Tb+To)*TregPI TregPI 0][re,im]=nyquist(NumFyxPI,DenFyxPI)figure(4)plot(re,im)grid on
.
- .
atlab
NumFyxPI=[KregPI*Kb*Ko*TregPI KregPI*Kb*Ko] DenFyxPI=[TregPI*Tb*To (Tb+To)*TregPI TregPI 0] figure(5) bode(NumFyxPI, DenFyxPI) margin(NumFyxPI,DenFyxPI) [Gm,Pm,Wg,Wp]=margin(NumFyxPI,DenFyxPI)
, W< .
a - - - .
1.3.2 () TregPI a - =860.
atlab KregPIgr=((TregPI*(Tb+To)/(To*Tb*Kb*Ko-((Tb+To)*TregPI*Kb*Ko))))
KregPIgr = -1.9458 - .
1.4. .
-
atlab
peakp=max(yp)
ans= 105.7759
-
Yp= Peak
- - , 5% , .. .
atlab
ypgg=77.25*ones(size(t))dd=72.75*ones(size(t))plot(t,yp,t,gg,t,dd)[t yp-dd][t yp] t Yp-dd 473.8 -0.0034 547.6 0.0063 -
5%.
( t-, Yp-)
, [sec].
.
[%] [%]
m ; - - . - - .
-0.0040 + 0.0164i -0.0040 - 0.0164i
-, - .
-
peakpi=Max(ypi)
ans= 88.6033
-
Yp= Peak
( t-, Yp-)
atlab
ypigg=77.25*ones(size(t))dd=72.75*ones(size(t)) plot(t,ypi,t,gg,t,dd)[t ypi-gg][t ypi] t Ypi-dd 681.8 0.0009 761.8 -0.0030 -
5%.
( t-, Yp-)
, [sec].
.
[%] [%]
m ; - - . - - .
-0.0035 + 0.0068i -0.0035 - 0.0068i -0.0011
-, - .
2. ().2.1. .
-
IN OUT A,B,C,D
- . :
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*+ *
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+
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, u f 3 (. -. -.
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-
IN OUT A,B,C,D
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+
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, u f 4 (. -. -
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2.2. MATLAB .
MATLAB
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[Apm,Bpm,Cpm,Dpm]=linmod('dveednop')
Apm = -0.0012 0 0 0 -0.0014 0.0050 -0.0021 -0.0552 -0.0067Bpm = 0 1.0000 0 0 48.3269 0Cpm =
0.0000 0.0011 0Dpm =
0 0
-
[Apim,Bpim,Cpim,Dpim]=linmod('dveednopi')
Apim =
-0.0012 0 0 0 0 -0.0014 0.0050 0 -0.0004 -0.0114 -0.0067 0.0116 -0.0000 -0.0011 0 0Bpim =
0 1 0 0 10 0 1 0
Cpim = 0.0000 0.0011 0 0Dpim =
0 0
. -
Matlab
Ap=[-1/850 0 0;0 -1/700 0.8/700;(-(0.7501*48.3269)/149.925) (-(0.7501*48.3269)/149.925) -1/149.925]
eig(Ap)
ans =
-0.0040 + 0.0164i -0.0040 - 0.0164i -0.0012
eig(Apm)
ans =
-0.0040 + 0.0164i -0.0040 - 0.0164i -0.0012 = -
Api=[-1/850 0 0 0;0 -1/700 0.8/700 0; (-(0.7501*10)/149.925) (-(0.7501*10)/149.925) -1/149.925 0.7501/119.925; -10/860 -10/860 0 0]eig(Api)
ans =
-0.0011 -0.0035 + 0.0068i -0.0035 - 0.0068i -0.0012eig(Apim)
ans =
-0.0011 -0.0035 + 0.0068i -0.0035 - 0.0068i -0.0012 ( impulse(A,B,C,D) ) -(Ap,Bp,Cp,Dp - - Api,Bpi,Cpi,Dpi- -) linmod Matlab - (Apm,Bpm,Cpm,Dpm- - Apim,Bpim,Cpim,Dpim - -). .
Matlab
Ap=[-1/Tf 0 0; 0 -1/To Ko/To; (-Kb*KregP)/Tb (-Kb*KregP)/Tb -1/Tb]Bp=[0 Kf/Tf; 0 0; (Kb*KregP)/Tb 0]Cp=[1 1 0]Dp=[0]Api=[-1/Tf 0 0 0; 0 -1/To Ko/To 0; (-Kb*KregPI)/Tb (-Kb*KregPI)/Tb -1/Tb Kb/Tb; -KregPI/TregPI -KregPI/TregPI 0 0]Bpi=[0 Kf/Tf; 0 0; (Kb*KregPI)/Tb 0; KregPI/TregPI 0]Cpi=[1 1 0 0]Dpi=[0][Apm,Bpm,Cpm,Dpm]=linmod('dveednop')[Apim,Bpim,Cpim,Dpim]=linmod('dveednopi')
-
impulse(Ap,Bp,Cp,Dp)
impulse(Apm,Bpm,Cpm,Dpm)
-
impulse(Api,Bpi,Cpi,Dpi)
impulse(Apim,Bpim,Cpim,Dpim)
, .2.3. , .
-
. - , . eig(Ap) ans=
-0.0040 + 0.0164i -0.0040 - 0.0164i , - -0.0012
(,) .n-
rank[B A.B
Matlab
UprP=ctrb(Ap,Bp)rank(UprP)
UprP =
0 0.0000 0 -0.0000 0 0.0000 0 0 0.0003 0 -0.0000 -0.0000 0.2418 0 -0.0016 -0.0000 -0.0001 0.0000ans =
3 .
.n-
rank[ .
Matlab
NablP=obsv(Ap,Cp)rank(NablP)
NablP =
1.0000 1.0000 0 -0.0012 -0.0014 0.0011 -0.0003 -0.0003 -0.0000
ans =
3
.
-
. - , . eig(Api) ans=
-0.0011 -0.0035 + 0.0068i , - -0.0035 - 0.0068i-0.0012
(,) .n- rank[B A.B
Matlab
UprPi=ctrb(Api,Bpi)rank(UprPi)
UprPi =
0 0.0000 0 -0.0000 0 0.0000 0 -0.0000 0 0 0.0001 0 -0.0000 -0.0000 -0.0000 0.0000 0.0500 0 -0.0003 -0.0000 -0.0000 0.0000 0.0000 0.0000 0.0116 0 0 -0.0000 -0.0000 0.0000 0.0000 0.0000ans =
4 .
.n-
rank[ .
Matlab
NablPI=obsv(Api,Cpi)rank(NablPI)
NablPI =
1.0000 1.0000 0 0 -0.0012 -0.0014 0.0011 0 -0.0001 -0.0001 -0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000ans =
4
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3. .3.1. - -.
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3.2. .
==
Matlab
Td=76.1K=Ko*KbT1=TbT2=Tod1=exp(-Td/T1)d2=exp(-Td/T2)A=KregPIB=-KregPI*(1-Td/TregPI)D=((K*T2/(T1-T2))*d2)-(K*T1/(T1-T2))*d1+KF=((K*T2/(T1-T2))*d1)-(K*T1/(T1-T2))*d2+K*d1*d2NumOs=[A*D (A*F+B*D) B*F]DenOs=[1 -(d1+d2+1) (d1*d2+d1+d2) -d1*d2]printsys(NumOs,DenOs)NumZs=[A*D (A*F+B*D) B*F]DenZs=[1 -(d1+d2+1-A*D) (A*F+B*D+d1*d2+d1+d2) (B*F-d1*d2)]printsys(NumZs,DenZs)roots(DenZs)
Td = 76.1K = 0.6001T1 = 149.9250T2 = 700d1 = 0.6257d2 = 0.9044A = 10B = -9.1826D = 0.0117F = 0.0097
NumOs = 0.1175 -0.0107 -0.0892
DenOs = 1.0000 -2.5301 2.0960 -0.5659 0.11745 s^2 - 0.010686 s - 0.089224num/den = ------------------------------------------- s^3 - 2.5301 s^2 + 2.096 s - 0.5659NumZs = 0.1175 -0.0107 -0.0892
DenZs =1.0000 -2.4127 2.0854 -0.6551
0.11745 s^2 - 0.010686 s - 0.089224num/den = ------------------------------------------- s^3 - 2.4127 s^2 + 2.0854 s - 0.65513
3.3. .