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Discrete emulator of simple feedback

Discrete emulator of simple feedback

Discrete emulator of simple feedback

(OP)
I'm interested in a discrete time simulation for the simple unity feedback control loop.

The simple unity feedback loop has only gain, no phase changes. There is a gain element (no phase shift) in the forward path, and no gain in the feedback path. The loop will track the input with an accuracy determined by the gain, which is itself unlimited. The circuit is always stable.

When this simple circuit is translated directly from continuous to discrete a delay element is added in the feedback. This discrete circuit is then unstable for any gain >= 1. It is unstable because the pole is outside the unit circle (regardless of phase). Hence, the simple translation does not emulate the continuous system.

Is there a discrete emulator for the continuous unity feedback loop?

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