# How could I compute the stability margin from a closed loop response?

Why the stability margin is typically computed by the open loop response or transfer function rather than the closed loop response or transfer function, how could I measure/compute the stability margin thru a closed loop response or transfer function?

Well the closed loop transfer function is considered stable if no physically feasible frequency can excite the system in such a way the open loop response becomes -1. This can be simply reasoned from the closed loop equation: $$\frac{GC}{1+GC}$$ if $$GC\rightarrow-1$$ the closed-loop gain will explode, hence destabilize the plant.

As such, we evaluate closed-loop stability through the open-loop response.

• Thanks, but I have to verify the margin by checking the closed loop response on the real system, that is doing the frequency sweeping on the command and compare it with the feedback, how could I tell the margin from the closed loop results?
– LHX
Dec 14, 2021 at 1:00
• Are you allowed to introduce or vary the gain in the closed loop system? Or are you only allowed to sweep the input over a frequency range?
– AJN
Dec 14, 2021 at 12:00
• @AJN I can only do the input sweeping.
– LHX
Dec 31, 2021 at 5:37