Proiect Sisteme adaptive
Masterand: Nagy Levente - Jozsef
Coordonator: Prof.Dr.Ing. Ioan Nascu
GPC
Figura 1cleartend=400;num=2*[3 1];den=conv([6 1],[4 1]);
%process (continuous)ts=3;te=3; %controller sample perioddd=0;
%discrete delay[numz,denz]=c2dm(num,den,ts); %process
(discrete)np=length(denz)-1; %process
order[A,B,C,D]=tf2ss(num,den);
%estimatorth0=[denz(2:np+1),numz(2:np+1)]; %initial estimatesth0=[1
0.5 0.05 0.1]; th0=[-1 0.5 -0.1 0.1];lam=0.9; %weighting
factordel=1000; %initial gainve=1;%controllerN1=1; N2=3; nn=[N1
N2]; %prediction horizonNu=1; %control horizonro=0; %weight of
umm=[-100 100]; %saturation limits [ucmin,ucma]
Figura 2
cleartend=400;num=2*[3 1];den=conv([6 1],[4 1]); %process
(continuous)ts=3;te=3; %controller sample perioddd=0; %discrete
delay[numz,denz]=c2dm(num,den,ts); %process
(discrete)np=length(denz)-1; %process
order[A,B,C,D]=tf2ss(num,den);
%estimatorth0=[denz(2:np+1),numz(2:np+1)]; %initial estimatesth0=[1
0.5 0.05 0.1]; th0=[-1 0.5 -0.1 0.1];lam=0.9; %weighting
factordel=1000; %initial gainve=1;%controllerN1=1; N2=3; nn=[N1
N2]; %prediction horizonNu=1; %control horizonro=0; %weight of
umm=[-100 100]; %saturation limits [ucmin,ucma]
Figura 3
cleartend=400;num=2*[3 1];den=conv([6 1],[4 1]); %process
(continuous)ts=3;te=3; %controller sample perioddd=0; %discrete
delay[numz,denz]=c2dm(num,den,ts); %process
(discrete)np=length(denz)-1; %process
order[A,B,C,D]=tf2ss(num,den);
%estimatorth0=[denz(2:np+1),numz(2:np+1)]; %initial estimatesth0=[1
0.5 0.05 0.1]; th0=[-1 0.5 -0.1 0.1];lam=0.9; %weighting
factordel=1000; %initial gainve=1;%controllerN1=1; N2=3; nn=[N1
N2]; %prediction horizonNu=1; %control horizonro=0; %weight of
umm=[-100 100]; %saturation limits [ucmin,ucma]
Figura 4
cleartend=400;num=2*[3 1];den=conv([6 1],[4 1]); %process
(continuous)ts=3;te=3; %controller sample perioddd=0; %discrete
delay[numz,denz]=c2dm(num,den,ts); %process
(discrete)np=length(denz)-1; %process
order[A,B,C,D]=tf2ss(num,den);
%estimatorth0=[denz(2:np+1),numz(2:np+1)]; %initial estimatesth0=[1
0.5 0.05 0.1]; th0=[-1 0.5 -0.1 0.1];lam=0.9; %weighting
factordel=1000; %initial gainve=1;%controllerN1=1; N2=3; nn=[N1
N2]; %prediction horizonNu=1; %control horizonro=67; %weight of
umm=[-100 100]; %saturation limits [ucmin,ucma]
Figura 5
cleartend=400;num=2*[3 1];den=conv([6 1],[4 1]); %process
(continuous)ts=3;te=3; %controller sample perioddd=0; %discrete
delay[numz,denz]=c2dm(num,den,ts); %process
(discrete)np=length(denz)-1; %process
order[A,B,C,D]=tf2ss(num,den);
%estimatorth0=[denz(2:np+1),numz(2:np+1)]; %initial estimatesth0=[1
0.5 0.05 0.1]; th0=[-1 0.5 -0.1 0.1];lam=0.9; %weighting
factordel=1000; %initial gainve=1;%controllerN1=1; N2=3; nn=[N1
N2]; %prediction horizonNu=1; %control horizonro=67; %weight of
umm=[-100 100]; %saturation limits [ucmin,ucma]
Figura 6
cleartend=400;num=2*[3 1];den=conv([6 1],[4 1]); %process
(continuous)ts=3;te=3; %controller sample perioddd=0; %discrete
delay[numz,denz]=c2dm(num,den,ts); %process
(discrete)np=length(denz)-1; %process
order[A,B,C,D]=tf2ss(num,den);
%estimatorth0=[denz(2:np+1),numz(2:np+1)]; %initial estimatesth0=[1
0.5 0.05 0.1]; th0=[-1 0.5 -0.1 0.1];lam=0.9; %weighting
factordel=1000; %initial gainve=1;%controllerN1=1; N2=3; nn=[N1
N2]; %prediction horizonNu=1; %control horizonro=67; %weight of
umm=[-100 100]; %saturation limits [ucmin,ucma]
Figura 7
cleartend=400;num=2*[3 1];den=conv([6 1],[4 1]); %process
(continuous)ts=3;te=3; %controller sample perioddd=0; %discrete
delay[numz,denz]=c2dm(num,den,ts); %process
(discrete)np=length(denz)-1; %process
order[A,B,C,D]=tf2ss(num,den);
%estimatorth0=[denz(2:np+1),numz(2:np+1)]; %initial estimatesth0=[1
0.5 0.05 0.1]; th0=[-1 0.5 -0.1 0.1];lam=0.9; %weighting
factordel=1000; %initial gainve=1;%controllerN1=1; N2=4; nn=[N1
N2]; %prediction horizonNu=2; %control horizonro=0; %weight of
umm=[-100 100]; %saturation limits [ucmin,ucma]
Figura 8
cleartend=400;num=2*[3 1];den=conv([6 1],[4 1]); %process
(continuous)ts=3;te=3; %controller sample perioddd=0; %discrete
delay[numz,denz]=c2dm(num,den,ts); %process
(discrete)np=length(denz)-1; %process
order[A,B,C,D]=tf2ss(num,den);
%estimatorth0=[denz(2:np+1),numz(2:np+1)]; %initial estimatesth0=[1
0.5 0.05 0.1]; th0=[-1 0.5 -0.1 0.1];lam=0.9; %weighting
factordel=1000; %initial gainve=1;%controllerN1=1; N2=10; nn=[N1
N2]; %prediction horizonNu=2; %control horizonro=0; %weight of
umm=[-100 100]; %saturation limits [ucmin,ucma]
Reglarea niveluluiSe considera un rezervor a carui sectiune A se
modifica in functie de inaltimea h. Modelul procesului, considernd
ca mrime de ieire (reglat) nlimea h iar ca mrime de intrare debitul
de alimentare qi , se poate scrie sub forma:
(1.1)
unde A(h) reprezint seciunea rezervorului la nlimea h, iar a
seciunea transversal a conductei de ieire.n regim staionar,
corespunztor punctului de funcionare caracterizat de h0, respectiv
qi0 relaia (1) devine: (1.2)
Modelul liniarizat n jurul acestui punct de funcionare este dat
de funcia de transfer:
(1.3)unde (1.4)
Consideram un regulator PI:
(1.5)
in care
(1.6)
Se va obine un sistem n bucl nchis de ordinul doi cu pulsaia
natural i factor de amortizare . nlocuind expresiile obinute pentru
i se obine:
(1.7)
(1.8)
De regul, valorile numerice sunt astfel nct 2. Expresiile de mai
sus se pot n acest caz simplifica rezultnd: k=2A(h0); Ti =2/, caz n
care este suficient s ajustm ctigul k proporional cu seciunea
transversal a rezervorului.Valoarea seciunii transversale poate fi
determinat fie printr-o relaie matematic, n funcie de nlimea h, fie
din tabele. Nici n acest caz nu sunt necesare traductoare
suplimentare.Pentru calculul parametrilor regulatorului 1 se
introduc urmatoarele date initiale:- h=1;- g=10;- =3%;- tr=3;Astfel
modelul liniarizat in jurul acestui punct de functionare este:
(1.9)iar regulatorul Hr1 rezultat: (1.10)
Pentru calculul parametrilor regulatorului 2 se introduc
urmatoarele date initiale:- h=5;- g=10;- =3%;- tr=3;Astfel modelul
liniarizat in jurul acestui punct de functionare este:
(1.11)iar regulatorul Hr2 rezultat: (1.12)In Figura 1.1 pot fi
observate rezultatele simularii celor 2 sisteme in bucla inchisa,
la referinta de tip treapta unitara.
Figura 1.1 Comportamentul sistemului la h=1, h=5
