How to convert the 0-5V to a 4-20mA current loop?
If all you need is analog 4-20mA loop transmitter, then you need an op-amp, the transistors that its output drives, a sense resistor, and a few other resistors. Note that these are at least 1% resistors. This needs to be built on a printed circuit board, not a solderless breadboard.  Two of my coworkers at Maxim Integrated wrote an applications note about a 4-20mA current-loop transmitter: http://www.maximintegrated.com/en/app-notes/index.mvp/id/5610  see this figure:



Since you are already using a PWM (hopefully with an RC low-pass filter), you just need everything after the DAC output. (Performance will not be as good with an Arduino PWM as it would be with a 16-bit voltage-output DAC, but the general idea would still work.) For your purpose, you can also ignore all of the stuff about the HART modem -- that's an extra feature for sending digital information along the same loop. Only relevant if your PLC receiver was expecting it.

There are also numerous prebuilt 4-20mA transmitter boards available, this has been around many decades in the industrial control market. Since Maxim Integrated makes precision DAC chips, we don't make reference designs that take 0-5V (especially from a PWM!) and convert to 4-20mA -- but we do sell reference design boards that include the DAC. Such as our Monterey system board (MAXREFDES15#). http://www.maximintegrated.com/en/app-notes/index.mvp/id/5683

There's also a 4-20mA Current-Loop Transmitter from ti.com, XTR117: http://www.ti.com/lit/ds/symlink/xtr117.pdf

There's also a board from mikroElektronika, MIKROE-1296 (available through mouser.com) that uses an Analog Devices DAC (through SPI interface) to drive the 4-20mA transmit circuit. Again, this is an idea that's been around many decades, so a search for 4-20mA transmitter should yield lots of useful information.

So your best bet is probably to purchase one of these prebuilt 4-20mA transmitter boards, which most likely will include its own precision DAC. You'll have to modify your Arduino code to drive the SPI interface, specific to whichever DAC you end up using. Or, if you really want to use the PWM to drive 4-20mA (at reduced performance), be sure to at least use an RC low-pass filter to get it as close as possible to a stable DC level.