Thanks for posting that part number; I was just typing a request for that !
There are two obstacles between that Serial Server and the 1747-L20 controller: the electrical signal and the application protocol.
Data Highway 485, as the name suggests, uses a differential serial signalling system that is based on
EIA-485, aka "RS-485".
The serial server you have has, like most devices in its class, a serial port based on
EIA-232, aka "RS-232".
These two signalling methods are not interchangeable; they use different wiring methods, voltage levels, and interface chips.
There are many electrical converters available to convert RS-232 to RS-485, and some networked Serial Servers implement multiple electrical standards (RS-232, RS-422, and RS-485). So why not just add one of those ?
The reason is the application protocol.
Data Highway 485 is a type of serial network that uses a "token passing" protocol, and it requires very fast responses from the network nodes. The process of taking a packet from the serial side, wrapping it up in a TCP/IP protocol header, transmitting it over Ethernet, getting a response from a software package, transmitting that over Ethernet, unwrapping it from TCP/IP and sending it out on the serial port..... takes too long.
In fact, even the Windows serial driver isn't fast enough for the DH485 protocol. Rockwell Automation gave up on trying to circumvent Windows as of Windows XPSP3; the Rockwell driver for the 1747-PIC interface module won't even try to run under Vista or Windows 7.
Other protocols that are
asynchronous and can allow relatively long delays between packets will work with a Serial Server. The Allen-Bradley DF1 protocol is a good example; you could connect that serial server to the Channel 0 port of an SLC-5/03, 5/04, 5/05 or MicroLogix controller and run DF1 through the "COM Port Redirector" utility just fine.
To connect to this particular SLC, the best thing to use is a 1747-UIC interface. This is a USB to DH485 interface box built by Rockwell Automation specifically to connect to DH485 networks. It performs all the token-passing and network handshaking right there onboard the box and plugs into any USB computer port, with drivers for Windows XP and Windows 7.