How about when the minions are hungry they get grumpy, they ignore commands and start eating random stuff?

This way the food mechanic fights against the players goal to use and train the minions, however even if the player forgets to feed them they can drop food near them to help them.

By eating random stuff there is a chance they will eat food and the problem solves itself, also a chance that they will eat some thing they shouldn't, costing a player a useful item or making the minion sick.

Sounds like you have some good ideas already, with hunger and hit points going together in some way.

I love the hunger mechanic in The Long Dark, where conditions like hunger and hypothermia reduce your ability to carry things, which causes you to slow down if you're carrying too much, which means you're out in the cold for even longer. I think what works so well with this is how hunger plays into the games other systems, like collecting items and getting out of the cold.

So it's good when you can figure out what else in your game would work well with a maintenance component like that. It makes sense that more food means you can keep either more minions or keep the minions you have tougher.

Have you thought about having different kind of minions.

I was thinking about warrior minions, and gathering minions. When one minion is well fed, the player has the option to evolve it to a warrior minion. When this happens food gathered from other minions is shared with warrior minions as well. Hunger might de-evolve a warrior minion to a gathering minion.

In Ark when you're hungry your health starts dropping and you start getting "dizzy." But I like the idea of minions not cooperating as well when they're hungry. Just make sure that you test this and it's not frustrating to the player when they really need their minions.

In the good old Dungeon Keeper your Creatures were leaving the dungion if they got unhappy (because of different things like hunger, no bed and so on) so the questions is: Are your minions such important that you need to keep them or is it possible that thay will disapear when they are too hungry