How to prove stability of discrete time system

ufechner7
Tue, 06 Feb 2024 10:01:48 +0000
Modelling & Simulations

I am simulating the following discrete time feedback system:

How can I prove that it is stable for

K_\mathrm{u} < 2 \frac{1}{T_\mathrm{s} K_2}

?

Code:

using ControlSystemsBase

Ts = 0.01
Ku = 100/5e6
K2 = 5e6

num = [Ku * Ts]
den = [1, -1]
P = tf(num, den, Ts) # plant, the integrator

C = K2               # controller, a constant gain
sys = feedback(P, C)

Output of the command margin:

julia> margin(sys)
(wgm = [NaN;;], gm = [Inf;;], wpm = [NaN;;], pm = [Inf;;])

Does not look like a good answer…

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