I'm sorry, dyan, I don't think you have a chance in hell of running an A/C with a 200 W solar panel setup. Even with an inverter that could put out the needed power, you would drain your batteries in a heartbeat.
IF (and this is a big "IF") your solar panels were putting out 14.5 Volts at 200 Watts, your theoretical Amperage would be just under 13.8 Amps. This is ALMOST enough to run an A/C (probably not enough to start it though), but - I think you're going to be lucky to see about 6-7 Amps output, even if the panels are oriented exactly 90 degrees to the sun's rays.
I've installed virtually the same setup as you have on our trailer, except I used a 20 Amp MPPT controller. My hope is that it will provide sufficient charge to the batteries that I won't need to use my generator when boondocking. But, I will not be using the A/C (we camp where it's cool) and I've replaced all lighting in the trailer with LEDs.
However, you can certainly get enough power to supply AC through an inverter to recharge cell phones, run a PC, and so on. You can probably even power something like a microwave if you get a large enough inverter. And, you WILL have to buy an inverter. The trailer does not have one installed. Inverters are "Watt" rated, so you will want to buy one that can handle the largest demand you expect to place on it. AND, for best results on some items, you need a "true" or "pure" sine wave inverter like this one:
http://www.amazon.com/gp/product/B0..._m=ATVPDKIKX0DER&pf_rd_r=0M5M23Q4DHHNZS48BF8F These are more expensive than the "modified" or "square wave" inverters, but some electronic devices can be damaged with square wave input.
You could possibly increase your solar panel array, maybe up to 600 Watts? and that might power an A/C in full sunlight. You might have to get a larger MPPT controller too (40 Amps), though.
Edit: If you were to power your A/C with an inverting generator, you would need one capable of putting out about 3000 Watts at 110 V. This gives you around 27 Amps, which is enough to "start" the A/C. Once it has started, it will take less power, maybe around 2000 Watts.
- Jack