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Why does the state transition matrix of a Discrete-PI controller have a real eigenvalue at 1 when $K_I = 0$?

I use python and matrix eigenvalue The the integration / accumulation occurs in the equation $𝑒[π‘˜]=𝑒[π‘˜βˆ’1]βˆ’πΎπ‘’[π‘˜βˆ’2]$. This appears in the first row of the matrix $A$ and is not affected by ...
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Poles of transfer function given a state space model

Let the system be $H(s)$. Laplace transform of the step response is $$ \begin{align} \frac{1}{s}\cdot H(s) &= \mathscr{L}\left(2-2e^{-3t}\right)\\ &= \frac{2}{s} - \frac{2}{s+3}\\ \implies H(s)...
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How to determinine the steady state accuracy (stationäre Genauigkeit) of a disturbance transfer function?

I am assuming that the term disturbance transfer function refers to the ratio of plant output to the disturbance input and that we desire the output to be zero (or as close to zero as possible) at ...
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