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I know a PID controller. Recently, I heard someone mention a PIAD controller. What is this? Is it a kind of extension of a regular PID controller?

In the control engineering litterature, I have only found a $\text{P}\text{I}^λ\text{D}^µ$ controller yet.

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    $\begingroup$ It looks like the Google search result snippet converts the lambda to an A and ignores mu, resulting in PIAD. $\endgroup$
    – morristtu
    Jul 18 '16 at 12:13
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    $\begingroup$ That's what I thought, too -- $\lambda$ vs. "A" $\endgroup$ Jul 18 '16 at 12:18
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    $\begingroup$ Presumably you don't want the other thing: maguire.com/public/mpi/conversion-kits/… :-) $\endgroup$ Jul 18 '16 at 12:21
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    $\begingroup$ Or maybe the A is for anti-windup? $\endgroup$
    – WG-
    Jul 18 '16 at 14:59
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    $\begingroup$ PIAD or PIADU seems to be a synonym for PIλDµ . $\endgroup$
    – ott--
    Jul 19 '16 at 19:12
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The A could be acceleration. The acceleration part is then used as feedforward or feedback in addition to the ordinary P, I and D parts. Take for instance a height controller for a quadcopter. For an ordinary PID controller the equation would be

$F = K_p \cdot e + K_i \cdot \int e\ dt + K_d \cdot \dot{e}$,

where $e = h_{d} - h$ (error between desired height and actual height above ground) and $F$ is the wanted up-down (heave) force.

What happens if the desired height is 2 m and you let go of the quadcopter at the same height? It probably hits the ground, as the integral term of the controller never had time to wind up, unless you have very high gains. If you modify the PID controller to include a very basic feedforward of the acceleration we get

$F = K_p \cdot e + K_i \cdot \int e\ dt + K_d \cdot \dot{e} + m a$,

where $m$ is the quadcopter mass and $a$ is the acceleration. When you let go of the quadcopter at 2 m the equation reduces to $F = mg$, and the wanted heave force immediately cancels the gravity. The integral part doesn't have to be used. The acceleration has be either measured or calculated.

When I see an A together with PID in my field (motion control) it usually means acceleration, but it could of course be something else in another field.

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