Prev: Searches vector
Next: Windows 7 file Explorer crashing on encountering Matlab .mat files
From: david on 2 Jan 2010 04:12
"Bruno Luong" <b.luong(a)fogale.findmycountry> wrote in message <hhhjii$spo$1(a)fred.mathworks.com>...
> "david " <david.sabine760(a)gmail.com> wrote in message <hhfkiu$oi6$1(a)fred.mathworks.com>...
> > Hello all,
> > If we have uncontrollable system ,how can we make it controllable in matlab ? What do we do in the matrix A,B to make the system controllable?
> > where my state space system is described by
> > x(k+1) =A*x(k) +B*u(k)
> > y(k)= C*x(k)
> >
>
> Is it just an academic example where you can play with A, B, C or it is from a real-world model? If it is a last case, then you are screwed.
>
> For the first case, you could just select A contractant (l2 norm strictly smaller than 1), B and C full rank, for example.
>
> I assume u is the control (?).
>
> Bruno
Thans Bruno,
It is a model for contrling the traffic on an over-saturated intersection .where u is the control variable (the green time in the traffic light) and :
A=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]
B=[s1-q1;s2-q2;-s3;-s4]
C=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]
D=[0];
s1=0.38; %1368 veh/h
s2=0.27; %972 veh/h
s3=0.19; %684 veh/h
s4=0.20; %720 veh/h
q1=0.5; %2160 veh/h
q2=0.4; %1800 veh/h
In this case how do i do to make my system controllable (the rank of controllability matrix= n )where n= the number of state variables.
BEST REGARDS
david
From: Bruno Luong on 2 Jan 2010 04:54

> It is a model for contrling the traffic on an over-saturated intersection .where u is the control variable (the green time in the traffic light) and :
> A=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]
> B=[s1-q1;s2-q2;-s3;-s4]
> C=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]
> D=[0];
> s1=0.38; %1368 veh/h
> s2=0.27; %972 veh/h
> s3=0.19; %684 veh/h
> s4=0.20; %720 veh/h
> q1=0.5; %2160 veh/h
> q2=0.4; %1800 veh/h
> In this case how do i do to make my system controllable (the rank of controllability matrix= n )where n= the number of state variables.
> BEST REGARDS
> david

So everything are fixed and the system is not controllable. I can't see what else you can do beside praying for a miracle.

I don't understand how you can multiply B (vector) with u (vector) and why the D? Are you sure to formulate the problem correctly?

Bruno
From: david on 2 Jan 2010 05:06
"Bruno Luong" <b.luong(a)fogale.findmycountry> wrote in message <hhn53r$1lb$1(a)fred.mathworks.com>...
>
> > It is a model for contrling the traffic on an over-saturated intersection .where u is the control variable (the green time in the traffic light) and :
> > A=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]
> > B=[s1-q1;s2-q2;-s3;-s4]
> > C=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]
> > D=[0];
> > s1=0.38; %1368 veh/h
> > s2=0.27; %972 veh/h
> > s3=0.19; %684 veh/h
> > s4=0.20; %720 veh/h
> > q1=0.5; %2160 veh/h
> > q2=0.4; %1800 veh/h
> > In this case how do i do to make my system controllable (the rank of controllability matrix= n )where n= the number of state variables.
> > BEST REGARDS
> > david
>
> So everything are fixed and the system is not controllable. I can't see what else you can do beside praying for a miracle.
>
> I don't understand how you can multiply B (vector) with u (vector) and why the D? Are you sure to formulate the problem correctly?
>
> Bruno
For u ,it is a one variable vector so we can do B*u .in the following you find my code

%/////////////////////////////////////////////////////////////
clear
clc
s1=0.38; %1368 veh/h
s2=0.27; %972 veh/h
s3=0.19; %684 veh/h
s4=0.20; %720 veh/h
q1=0.5; %2160 veh/h
q2=0.4; %1800 veh/h
q3=0.4; %1440 veh/h
q4=0.3; %1080 veh/h
%--------------------------------
c=160;
rho=0.2;
%x(k)=[x1(k);x2(k);x3(k);x4(k)]
A=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]
B=[s1-q1;s2-q2;-s3;-s4]
C=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]
D=[0];
L=[q1-s1;q2-s2;q3;q4]
K=[q1;q2;0;0]
e=[1;1;1;1]

poles = eig(A)

%////////////////////////////////////////////////////////////////
%x(k+1)= A*x(k)+B*u(k)+L*c+K*u2(k-1)
%u(k)=u(k-1)+rho*((e'*x(k))/(q1+q2));
%/////////////////////////////////////////////////////////////////

%///////////////// Checking controllability////////////////////////////////
co=ctrb(A,B)
Controllability=rank(co)

%/////////////////////////////////////////////////////////////////////////

%///////////////// Checking observability/////////////////////////////////
ob=obsv(A,C)
Observability=rank(ob)
%////////////////////////////////////////////////////////////////////////

xold=[0;0;0;0];
uold=70;
for k = 1:3000
unew=uold+rho*((e'*xold)/(q1+q2));
xnew= A*xold+B*unew+L*c+K*uold;
Z(:,k)=xnew;
V(k)=unew;
uold=unew;
xold=xnew;

end

plot([1:3000],Z(1,:),'b',[1:3000],Z(2,:),'r',[1:3000],Z(3,:),'g',[1:3000],Z(4,:),'y')
% plot([1:50],Z(1,:))
%////////////////////////////////////////the end /////////////////////////////////


the simulation results show that the system is not stable . For that i did the controlability test and i found that it is not true ?Alors i don't kno how to do for making it controllable by modyfing the matrix or by using a certain matlab commands
Best regards

David
From: david on 3 Jan 2010 09:51
Is there anyone help me please???
From: dpb on 3 Jan 2010 10:20
david wrote:
> Is there anyone help me please???

'Fraid not unless you change the system -- as Bruno says, and your
previous description sounds like, there aren't enough DOF.

--
First  |  Prev  |  Next  |  Last
Pages: 1 2 3
Prev: Searches vector
Next: Windows 7 file Explorer crashing on encountering Matlab .mat files