When I had some inherited tenants I wanted gone in neighboring RI recently (criminal record, needed to fix up the unit) I actually gave them a heads up in advance, which a lot of people wouldn't recommend and I get why. But I had "the talk" with them about 3 months in advance and told them it was coming and I was trying to give them as much heads up as possible. Then around when I said it was going to happen, and I was ready to think about working on that unit I gave them the 30-day termination notice. They did complain about financial situation so I offered up the remaining month as free rent and told them they would get the security deposit back the day they moved out as long as there was no gross and obvious damage. I made them sign an agreement that the month of free rent was for moving costs and if they didn't move after the month they would owe the money as back rent. That seemed to do the trick and they moved out without much of a fuss.
I was told at the time by an attorney that I could send a termination notice and evict for being a hold-over tenant, but I decided it was well worth the one month's rent to try and make it civil and smooth and to help them transition. I wouldn't have been able to file an eviction until that one month was up anyway. It did work but you have to figure out if they are going to be honest and what their intentions are.