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

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Rafael 2022년 11월 11일
편집: Rafael 2022년 11월 11일
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.

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### 답변(1개)

Sam Chak 2022년 11월 11일
Most probably because you did a "positive feedback".
Try do this
impulse(feedback(K*TF, 1))
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
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Rafael 2022년 11월 11일
편집: Rafael 2022년 11월 11일
Unfortunatly that did not work, but thank you anyway for correcting me on how to use feedback()!

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