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I have a combination of a feedback control loop and feedforward compensation

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where $\tilde{E}$ represents a fluctuation of the system input (namely a input voltage of a dc-dc converter) which is directly measured. The $\tilde{E}$ is basically a step change or a sine with a given frequency.

The transfer function in the feedforward path can be found as

$H_{ff}(s) = \frac{W(s)}{G(s)}$.

In my particular case following holds

$G(s) = \frac{K_1}{s\cdot\tau + 1}\cdot e^{-s\cdot T_d}$

$W(s) = \frac{K_2}{s\cdot\tau + 1}$.

Based on that I have

$H_{ff}(s) = \frac{K_2}{K_1}\cdot e^{s\cdot T_d}$.

It means that for the feedforward compensation I would need a time shift forward. My question is how can be this time shift forward implemented in digital control?

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  • $\begingroup$ Depends on what you mean by "forward". Time shifts are implemented as delays, but they can only go backwards in time (i.e. only have access to past samples). The other way around is non-causal and violates the laws of physics. Can't be done. $\endgroup$ Commented Nov 8, 2024 at 12:41
  • $\begingroup$ @Hilmar thank you very much for your reaction. The above mentioned feedforward compensation leads to a non-causal $H_{ff}(s)$ which can be realized neither in digital nor in analog domain. My question is whether there is some method how to approximate the phase lead which is basically hidden in the $e^{s\cdot T_d}$ term. The only one idea which I have is the lead compensator. But there will be some amplification present. $\endgroup$ Commented Nov 8, 2024 at 12:59

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