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I can't see anything in this annual plot other than that the room temperature switches multiple times between -100 and 220 degC. I suspect you have too high a control action (otherwise you would not get such extreme room temperatures) and your gains are such that the control is unstable. At this experimental stage, I see no reason for adding an integral term in the controller as integral terms can cause instability if incorrectly tuned, and all they do is avoid a steady state error. Your first task should be to get a stable P controller with reasonable actuation power, and then if you need to reduce the steady-state error, add integral action.