Do you have a sample schematic to share, if that's not much of a problem?
I make this project in 1983, I don't have this schematic any more, and I can't have it because I am now living 10.000 Km's far from where I lived in this time and the company where I worked does not exist any more.
I can only give you informations that I can remenber.
That was not a simple tape changer because in such case, triacs had to be high current triacs and this was too expensive.
In my project, it added or substracted voltages with 9 levels, using 6 triacs TIC226.
Nominal input voltage was 80 to 140V, output voltage was 110V or 127Vac +/-5% (two models) 1Kw
Two auxiliary transformers where used, adding or substrating voltages in proportions of 1 and 3.
The steps where:
-4 : triacs of -3 and -1 on
-3: triacs of -3 and 0 on
-2: triacs of -3 and +1 on
-1 ; triacs of 0 and -1 on
0 : both triacs 0 on
+1 : triacs of 0 and +1 on
+2 : triacs of +3 and -1 on
+3: triacs of +3 and 0 on
+4: triacs of +3 and +1 on
To avoid changing of taps continually, comparators had an hysterese.
There also was a delay avoiding changing taps before to stay a complete cycle on the same tap so DC voltage can't be applied to the load.
As the auxiliary transformers had their secundaries in serie with the load, they could not stay with open primary, as they would act as current transformers and develop high primary voltages, I had to accept the occurrence of short circuits during steps changes with inductive loads and protect the triacs with low value power resistors.
Here is an example of a voltage regulator with 115Vac nominal output and 8 taps.