The Black Square fleet-wide ILS tracking issue continues
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BKSQ AP Issues.
Example - Bonanza Pro - Flying a short route as follows:Airport to a VOR using AP in HDG then NAV mode using KX155. Having previously set up the KNS-81 to use the same VOR as ref, I made an "Offset" WP1 from that, so after passing the VOR I Use the KNS-81 & RNAV mode to nav to WP1. I switch over HSI Source to RNAV, AND also Press the NAV/GPS Button to set AP to follow RNAV. I Then line up the AC towards WP1 with HDG Mode, and then Activate NAV mode on the AP, and it steers correctly towards WP1, also showing "DME Data" in the DME Display that has been set to show RNAV. - Perfect!
At WP1 I switch to HDG mode and turn towards the ILS (Set in KX155 NAV1) Feathers at a 30 Deg Angle and some miles out from where feathers start. Making sure HSI Source is now set to "NAV 1" & NAV/GPS mode to NAV, i activate APR Mode on the AP and get the correct AP Mode Annunciators APR & GS, and HSI indicates the Needle /CDI correctly. - . So Far So Good...
Entering LOC Center line the Needle starts moving but nothing happens, the AP does not capture the LOC at all, and I have tried lots of sets of Approaches and trying different things to get it to capture.
Finally I found, that If I immediatly after seeing the LOC Needle starts to move Press NAV/GPS mode to RNAV and then again back to NAV, Then the AP will capture the LOC/ILS correctly and the full ILS Phaze works as expected.
It seems that If I DO NOT use the KNS-80/81 during a Flight, The LOC/ILS Works as it should, and If I have used it, I must Restart the flight from the World map to "Reset" the AP system.
One more note only: When the AP does capture it almost always "aims" the AC towards the Rwy threshold and reaches LOC "center line" very late in my opinion
Hope this helps to find the "Bug"

@ErnieBall I tried your exact procedure with the Bonanza Pro in FS24, and got the same result twice in two tries. Also tried flying the exact same flight, but flying normal VOR instead of KNS, and it caught the ILS first try. If I use the KNS, but using NAV instead of HDG when arming the APR, it also caught the ILS. Then I tried all again, this time in FS20 and got the exact same results. The problem seemed to be when switching from HDG to APR, after having used the KNS.
It all seemed 100% reproducible, but as I’m writing this, I’m doing yet another try at the original procedure, and this time it worked as expected, going from HDG to APR, having used the KNS during the flight. So, now I don’t know.
Does the distance away from the center line, when arming the APR, affect its functioning? I’m not a pilot, so I don’t know the proper procedures, but when do you usually arm the APR?