How to verify if my system (Z-domain) is stable in MATLAB

Hello,

I designed a transfer function, then I plotted the root locus, and found what is the gain my TF needs to have my desired poles.

Those poles are inside the unit circle, which means my system is stable.

But i want to test if it is actually stable and if it's time response follow my requirements.

However, this is the plot i get when i check its impulse response (K is the gain that makes my tf have those poles, which are inside the unit circle):

impulse(feedback(K*TF,-1))

The function is supposed to stabilize in 0. Why would this go to -Inf?

Am I doing the plot wrong?

step function gives me something similar.

Thanks in advance

Answer 1

[Sam Chak]

Hi @Rafael

Most probably because you did a "positive feedback".

Try do this

impulse(feedback(K*TF, 1))

instead of

impulse(feedback(K*TF, -1))

Also check:

help feedback

 FEEDBACK  Feedback connection of two input/output systems. 
 
    M = FEEDBACK(M1,M2) computes a closed-loop model M for the feedback loop: 
 
           u --->O---->[ M1 ]----+---> y
                 |               |           y = M * u
                 +-----[ M2 ]<---+
 
    Negative feedback is assumed and the model M maps u to y. To apply 
    positive feedback, use the syntax M = FEEDBACK(M1,M2,+1).
 
    M = FEEDBACK(M1,M2,FEEDIN,FEEDOUT,SIGN) builds the more general feedback 
    interconnection:
 
                       +------+
           v --------->|      |--------> z
                       |  M1  |
           u --->O---->|      |----+---> y
                 |     +------+    |
                 |                 |
                 +-----[  M2  ]<---+
 
    The vector FEEDIN contains indices into the input vector of M1 and
    specifies which inputs u are involved in the feedback loop. Similarly, 
    FEEDOUT specifies which outputs y of M1 are used for feedback. If SIGN=1 
    then positive feedback is used. If SIGN=-1 or SIGN is omitted, then 
    negative feedback is used. In all cases, the resulting model M has the 
    same inputs and outputs as M1 (with their order preserved).
 
    If M1 and M2 are arrays of models, FEEDBACK returns a model array M of 
    the same dimensions where 
       M(:,:,k) = FEEDBACK(M1(:,:,k),M2(:,:,k)) .
 
    For dynamic systems SYS1 and SYS2, 
       SYS = FEEDBACK(SYS1,SYS2,'name') 
    connects SYS1 and SYS2 by matching their I/O names. The I/O names of 
    SYS1 and SYS2 must be fully defined.
 
    See also LFT, PARALLEL, SERIES, CONNECT, INPUTOUTPUTMODEL, DYNAMICSYSTEM.

    Documentation for feedback
       doc feedback

    Other uses of feedback

       iddata/feedback     InputOutputModel/feedback    lti/feedback
       idmodel/feedback

[Rafael]

Unfortunatly that did not work, but thank you anyway for correcting me on how to use feedback()!