FCL analytical PI controller gains documentation

Natan Vachon

Intellectual 470 points

Hello,

Is there a documentation available concerning the computation of the PI controller gains in the FCL library.

Because the gain are computed from the motor constants, it seems that you computed those gains analytically.

Is there a documentation available for this ?

Best

Natan

over 5 years ago

0 Ramesh Ramamoorthy over 5 years ago

TI__Mastermind 27240 points

Recommend reviewing this

e2e.ti.com/.../teaching-your-pi-controller-to-behave-part-i

0 Natan Vachon over 5 years ago in reply to Ramesh Ramamoorthy

Intellectual 470 points

Hello,

I figured it out by doing the calculation. Maybe it can help someone.

The thoretical plant transfer function is Iq / Uq = H(s) = 1 / (R + L*s)

We take a PI controller whose transfer function is K(s) = (Kp * s + Ki) / s

And we introduce a constant k such as Kp = k*L, and Ki = k*R, then the open loop becomes:

OL(s) = K(s) * H(s) = k * (L*s + R) / s * 1 / (R + L*s) = k / s

So the open loop transfer function is the same as a pure integrator transfer function. Then the phase margin is 90degrees and the gain margin is infinite.

Also, the closed loop transfer function is :

CL(s) = 1 / (1 + s / k)

So the k parameter is equal to the closed loop bandwidth.

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FCL analytical PI controller gains documentation