Depends on the exact system. The first Danish ones used 5-speed Ecomat gearboxes adapted from buses, for example the IC3 trains. They then had a small hydraulic torque converter to start on, which locked at around 30km/h after which the train was in first gear. This locking felt like a shift, so the converter plus 5 gears felt like 6. Very smooth.

In these trains I expect the commands mostly increased fuel to the engines, the gearboxes were mostly autonomous, apart from a few exceptions.

Cruise control.

I think they tuned the gearboxes to shift as close together as possible (different wheels may have different wear/diameter).

Maybe they somehow locked them in 1st gear until the startup torque converter was locked.

They did also have an anti-wheelspin system of some sort - certainly in 1st gear full power (400hp on one axle) would otherwise easily spin and wear the wheels.

I think something similar was used in Germany, Norway and a bit in Sweden and a few in England.

I use past tense as the Danes were so fond of the idea that these trains from the nineties were refurbished with 12-speed unsynchronised gearboxes from ZF Friedrichshafen and dry clutches in the 2000s. And they are still going. In this case the engines, clutches and gearboxes are controlled together. For instance lots of power requested when cruising at low RPM, may result in disengaging the clutches, blipping/revving the engines to match the cogwheel speeds like a truck, downshifting 2 gears, reengaging the clutches and then giving the engines fuel.

These were less smooth, but an interesting experience with a few fast shifts when starting (a train is relatively heavy compared to a car, so that is one reason for the many gears, a low gear is required to start even a lightweight train on a dry clutch). Then it would really rev through gear 3 or 4 or so to accelerate quite notably, before behaving more like the original version in the higher gears.

I will update with a couple of videos if they still exist.

Depends on the exact system. The first Danish diesel mechanical multiple units used 5-speed ZF Ecomat gearboxes adapted from buses, for example the IC3 trains. They then had a small hydraulic torque converter to start on, which locked at around 30km/h after which the train was in first gear. This locking felt like a shift, so the converter plus 5 gears felt like 6. Very smooth.

In these trains I expect the commands mostly increased fuel to the engines, the gearboxes were mostly autonomous, apart from a few exceptions.

Cruise control.

I think they tuned the gearboxes to shift as close together as possible (different wheels may have different wear/diameter).

Maybe they somehow locked them in 1st gear until the startup torque converter was locked.

They did also have an anti-wheelspin system of some sort - certainly in 1st gear full power (or torque of a 400HP V8 or 450HP V6 on one axle) would otherwise easily spin and wear the wheels.

I think something similar was used in Germany, Norway and a bit in Sweden and a few in England.

I use past tense as the Danes were so fond of the idea that these trains from the nineties were refurbished with 12-speed unsynchronised gearboxes from ZF Friedrichshafen and dry clutches in the 2000s. And they are still going. In this case the engines, clutches and gearboxes are controlled together. For instance lots of power requested when cruising at low RPM, may result in disengaging the clutches, blipping/revving the engines to match the cogwheel speeds like a truck, downshifting 2 gears, reengaging the clutches and then giving the engines fuel.

These were less smooth, but an interesting experience with a few fast shifts when starting (a train is relatively heavy compared to a car, so that is one reason for the many gears, a low gear is required to start even a lightweight train on a dry clutch). Then it would really rev through gear 3 or 4 or so to accelerate quite notably, before behaving more like the original version in the higher gears.

I will update with a couple of videos if they still exist.