ACIM_FLUX #

Brief #

The acim_flux component models the rotor flux of an induction motor in the rotor flux frame and gives the slip that keeps that frame oriented.

Model #

With i_mr the magnetizing current behind the rotor flux (psi_r = Lm * i_mr):

tr * d(i_mr)/dt = id - i_mr slip = iq / (tr * i_mr) [rad/s electrical] torque = 3/2 * pp * lmr * i_mr * iq lmr = Lm^2 / Lr

tr (Lr/Rr) and lmr come from idacim, at rated flux (i_mr = i_n). Below rated flux (field weakening) the iron desaturates and both grow:

x = (i_n - |i_mr|) / (i_n - i_knee), clamped 0..1 tr_act = tr_est * (1 + tr_sat * x) lmr_act = lmr * (1 + lmr_sat * x)

With i_knee > 0 both stop growing below i_knee and stay at their plateau (1 + sat); i_knee 0 is a straight line down to zero flux.

At low induction the iron’s permeability falls again (the foot of the B-H curve): on the spindle the secant lmr was flat from 9 to 19 A and 11% lower at 6.7 A (idacim sweep, 6 Oct). With i_dip > 0 both change below it:

y = (i_dip - |i_mr|) / i_dip, clamped 0..1 lmr_act = … * (1 - lmr_dip * y) tr_act = … * (1 - tr_dip * y)

tr has its own coefficient, as Rr need not stay put at low flux. idacim prints tr_dip = lmr_dip (tr = Lr / Rr follows the secant lmr), which its rotating tr checks confirm on the spindle to a few %; the spindle examples carry that (0.058). A hand value of -0.45 (9 Oct, from a tr that read 0.10-0.11 at 5-8 A) is superseded. i_dip 0 (default) leaves both out; lmr_dip 0 or tr_dip 0 one of them.

The model, slip, psi and torque run on tr_act and lmr_act. tr changes about twice as much as the secant lmr, so the two gains are separate; 0 (default) or i_n 0 keeps both constant. id/iq are normally the measured currents, so a current limit in curpid scales both and the slip stays right.

psi is the rotor flux seen from the stator. With hv0.l = hv0.lq = sigma*Ls (leakage), it turns curpid’s PMSM decoupling psi_d = l * id + psi into the induction motor’s stator flux, so the F3 needs no ACIM code.

en = 0 clears the flux, so every enable starts from a demagnetized rotor.

tr adaptation (reactive power MRAS), off by default #

tr changes with rotor temperature. With tr_ki > 0 the model runs on tr_est, which integrates the reactive power residual

Q = uq id - ud iq Q_m = w (id (l id + psi) + l iq^2) - r_w |w| id iq tr_est -= tr_ki * (Q - Q_m) * sign(w) * period

Q does not depend on r, so neither does the estimate. A positive residual (times sign(w)) means tr_est is too high; the plant gain is a few thousand VA per second of tr, so tr_ki 0.0001 settles in a few seconds. It adapts only while abs(iq) > tr_iq_min and abs(w) > tr_vel_min (slip must be large enough to see) and, with tr_flux_min > 0, |i_mr| >= tr_flux_min * i_n (in deep field weakening the residual is dominated by model errors, not tr; 0.95 keeps it to the base speed range), holds otherwise, and stays within 0.5 to 2 times tr. With tr_ki 0, tr_est = tr.

tr from an encoder in sensorless mode, off by default #

In sl_acim the frame comes from the voltage observer and the MRAS sees no tr. With an encoder, sl_seq0.slip_err = obs0.vel_m - encoder speed is the true slip less the model’s (mechanical rad/s). With tr_ks > 0

tr_est -= tr_ks * tr_est * slip_err / slip_model * period

so tr_ks is a rate [1/s] on the relative slip error (clamped to +-50 %), under the same iq and speed gates as the MRAS. Both adaptations also need a steady speed when tr_acc_max > 0: |acceleration| (5 Hz low pass) below tr_acc_max * max_acc (conf0.max_acc, about 0.3); on a ramp the slip error and the reactive residual carry the inertia and observer lag, not tr.

lmr trim from the q voltage, off by default #

In steady state the q voltage is uq = r iq + w (l id + lmr i_mr). With lmr_ki > 0 the relative residual of that, (uq - r iq - w (l id + lmr i_mr)) / (w lmr i_mr), trims lmr at lmr_ki [1/s], while |w| > tr_vel_min, abs(i_mr) > 20 % of i_n (or 1 A) and the flux is settled (abs(id - i_mr) < 5 % of i_mr). It stays within 0.7 to 1.4 times lmr. Saturation still applies on top.

Pins #

References #

Source: .c File