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document parameter b
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baggepinnen committed Jun 7, 2022
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Expand Up @@ -15,6 +15,7 @@ where
- $T_i$ is the integral time
- $T_d$ is the derivative time
- $N$ is the maximum derivative gain
- $b \in [0, 1]$ is the proportion of the reference signal that appears in the proportional term.

The controller further has output saturation controlled by `umin, umax` and integrator anti-windup controlled by the tracking time $T_t$.

Expand Down Expand Up @@ -62,5 +63,5 @@ plot(res, plotu=true); ylabel!("u + d", sp=2)
![Simulation result](https://user-images.githubusercontent.com/3797491/172366365-c1533aed-e877-499d-9ebb-01df62107dfb.png)

## Details
- The derivative term only acts on the (filtered) measurement and not the command signal. It is thus safe to pass step changes in the reference to the controller.
- The derivative term only acts on the (filtered) measurement and not the command signal. It is thus safe to pass step changes in the reference to the controller. The parameter $b$ can further be set to zero to avoid step changes in the control signal in response to step changes in the reference.
- Bumpless transfer when updating `K` is realized by updating the state `I`. See the docs for `set_K!` for more details.

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