That behavior is caused by the fact that you switch to a hard coded constant current reference whenever the V_Highest is less than V_top. Since you have tracking turned on for your PID, every time you briefly jump to this set point, the controller resets to this point as well, and then has to lower again. The problem isn't your gains, the problem is your logic in determining when to switch between the PID logic and the PID controller. Also, it can't tune your system because it is a discontinuous system with discrete switching devices. You'd have to use a frequency response estimation to use the tune function. You will likely need to manually tune the PI values and be more careful about when you switch between the closed loop controller and the fixed constant current reference.
Essentially, your PI controller is working, because it is trying to reduce the difference between V_highest and V_top, Which it is doing, but whenever it gets them close, it triggers the logic to 'reset' the controller (switch to the constant value reference which, because tracking is on the PID, 'resets' it), and it has to start over.
