Any ideas on how I can fix my controller?

I'm having g an issue with my left controller. It only takes crappy batteries like dollar general brand and will not work if I put in an energizer or Duracell. It will randomly vibrate like crazy and the only way to stop it is to take the battery back out and put it back in. The biggest issue is that if I swing the controller too fast it will disconnect and reconnect. Any ideas what the problem is and how to fix it?