So for the record, this is the other thread. The thread started meandering so I suggested a separate thread specific to the matter at hand.
At the risk of providing too-much-information, I'll ramble a bit to collect scattered thoughts and issues that have come up in the past in regards to this application.
To recap, there are 2 fundamental issues. 1) converting TIU AC output to DC, and 2) reverse DC polarity for bi-directional operation.
AC-to-DC is relatively easy. A 10 Amp bridge rectifier is less than $1. Two wire in, two wires out. But no control over polarity so engine goes in one direction. There are many applications where single-direction is good enough considering you have wireless remote control over voltage and hence speed.
Adding DC direction control via polarity reversal can be done with a DPDT switch using the classic cross-connect configuration:
For remote control, this would be a DPDT relay with a basic on/off signal that activates the relay. For example for about $2 here's one with 10 Amp contacts and has a socket so no-soldering required.
There are electronic equivalents of this typically using 4 transistors in a so-called H-bridge configuration. In this case a basic on/off signal turns on 2 of the 4 transistors which effects the DC polarity reversal at the motor. In the diagram, the switch symbol is just transistor.
So a real circuit might look something like this, and there are chips/modules which integrate all this into one component.
The problem is how to integrate the AC-to-DC conversion AND the polarity reversal under DCS control via WiFi tablet controller.
Since the OP has an AIU (per other thread), one idea is to use a relay in the AIU to control a DPDT relay. So the TIU variable channel would alter the AC voltage, an external bridge-rectifier would convert the variable AC to variable DC (of one polarity), and an external DPDT relay would flip the DC polairty under DCS control (via AIU) for direction control. Gets the job done but can be awkward to change directions if having to flip through tablet screens/menus between voltage control and AIU relay control. Maybe not so bad for an occasional direction change but clearly a non-starter for yard switching operations.
The most common method for AC direction control of DC motors is the electronic E-unit which has the bridge rectifier and solid-state H-bridge polarity reversal circuit. And it integrates the direction control using O-gauge AC standard of momentarily removing AC track power (for say, 1 second) to sequence through 4 states, namely forward-neutral-reverse-neutral. There have been slight variants but it is still sold today...$16.50 MSRP.
Two wires in (AC track voltage), two wires out (DC motor voltage). A forum member reverse-engineered this design and published an impressive how this electronic E-unit works.
There are more state-of-the-art electronic E-units that can handle more current, have some additional features such as directional light outputs, more compact by using surface-mount components, etc., but in the end it's 2-wires in, 2 wires out with a direction change method that is part-and-parcel of the O-gauge conventional control method so the tablet interface of the TIU variable channel will have combined speed and direction. I figure there are thousands of E-units sitting in drawers having been removed from conventional-only AC engines that have been converted to command-control.
Here's an example of a modern design using surface-mount components. 2 wires in, 2 wires out.
So the idea would be to place an E-unit at the output of a TIU AC variable channel, and then the DC output of the E-unit feeds the HO DC track. No modification is required to the conventional HO DC engines. Needless to say, an O-gauge E-unit would not even fit in an HO chassis!
My next post will be issues and workarounds for low-voltage operation using electronic E-units.