Re: control problem: lsim

[Rudolf Widmer-Schnidrig]

On 25.02.13 07:45, Lukas Reichlin wrote:
> On 24.02.2013, at 23:17, Rudolf Widmer-Schnidrig <address@hidden> wrote:
>
> > Dear Lukas, dear List,
> >
> > What is the best way to evaluate the quality of a LTI model
> > which I have obtained like this
> >
> > octave> dat = iddata(yout,xin);      % yout is observed output to input xin
> > octave> sys = arx (dat,'NA',2,'NB',1')
> >
> >  From the control manual I expected that I could run
> >
> > octave> lsim(sys,xin)
> >
> > to predict the output for input xin given the system sys.
> >
> > but I get the error: lsim: input vector u must have 2 columns
> >
> > what am  missing?
> >
> >        many thanks in advance,             -Ruedi
> Hi Ruedi,
>
> If dat has p outputs and m inputs,
>
> [n, p, m, e] = size (dat)
> [n, p] = size (yout)
> [n, m] = size (xin)
>
> sys becomes an p by m+p LTI model (p outputs and m+p inputs).
> The first m inputs (1:m) are u(t) and the remaining p inputs (m+(1:p)) are e(t)
>
>            A(q) y(t) = B(q) u(t) + e(t)
>
> You are only interested in u(t), therefore select the inputs by  sys(:, 1:m)
>
> lsim (sys(:, 1:m), xin)
>
> Maybe I should improve the documentation of arx.
>
> Best regards,
> Lukas
Dear Lukas,

thank you for the clarifying words!

I deal with the simplest case: single input and single output. Thus xin 
and yout are plain vectors.

With:
octave> [yA,tA,xA] = lsim(sys(:,1),xin);

I get the simulated output of my system: yA    (is this interpretation 
of the output correct?)

and by plotting

octave> plot(ta,yout,'k;measured output;',ta,yA,'r;simulated output;')

I can see how well the LTI system (sys) is able to mimic the physical 
world. (actually not too bad for the beginning)

Now I want to convert the discrete time model to a continuous time model 
with "d2c".

I start with specifying the sample interval dt=0.01s

octave> set(sys,"tsam",0.01);

then do the conversion

octave> Csys = d2c(sys,'bilin');

and run into the next problem if I want to see the contents of Csys:

octave> octave:44> Csys

error: lti: filtdata: require discrete-time system
error: called from:
error:   /Users/widmer/octave/control-2.4.0/@lti/filtdata.m at line 62, 
column 5
error:   /Users/widmer/octave/control-2.4.0/@tf/display.m at line 36, 
column 17

while: octave> get(Csys,"num") returns sensible values.



Then more general questions:
The best model  I have to describe my system is 
H(s)=G*s/((s-p1)(s-p2))   where p1 and p2 are a pair of complex 
conjugate poles and G is a real number.
So far the models I get from arx all look like low-pass filters while my 
system is a band pass (as is obvious from a spectral division of 
output/input).
To evaluate the frequency response of sys I did:

octave> sys = arx (dat,'NA',2,'NB',1);
set(sys,"tsam",0.01);
[H,w,tsam]=frdata(sys(:,1),"v");
loglog(w,abs(H))

Am I not setting NA and NB correctly?

Is there a way to force arx to put the zeros at s=0

Is there a way to estimate the state-space model which is closest to 
some starting model?

           many thanks             -Ruedi