Hello, fellow process engineer! Improving the process is in our job description, so anything that impacts the process, we are responsible for. The best way to tune anything is by trial and error. There are plenty of ways to calculate the PID settings, but typically, as even literature admits, they often fail to produce the best results.
I'm going to assume your operators start the controls in manual, hunt for the settings, and throw it in auto and that's when you're seeing the oscillations? It's always easiest to tune a loop by watching the process variable (PV) and controlled output (CO) on a graph. A good loop will have an overshoot decay of about 25% or less on each swing.
Adjust the PID settings on the master loop first while online after reaching steady state. Follow these guidlines:
GAIN (P) - The gain controls the magnitude of change in the CO in response to error. If you see drastic changes in the CO then reduce the gain. I usually change the gain by 0.25 increments, but of course this depends on your controller and process (every PLC/DCS has their own slightly modified PID equation). If you see not enough change in the CO then increase gain. If the controller operates better in manual mode, then this term needs to be reduced.
RESET (I) - The integral action will adjust for error over time. Say your PV is continuously above or below the setpoint... In this case you need to decrease the integral term. Remember, the equation is 1/Integral gain, so when you increase it, the term drives the CO less and when you decrease it, it drives it more!
RATE (D) - This term is usually not used and set to zero, however, it can be extremely helpful in some cases, especially if a lot of lag time is involved. By lag time, I mean the time it takes to see a change in the PV from when you changed the CO. If you want to minimize overshoot, this may be your solution. The derivative term allows the loop to sense when the rate of change in the process varaible is too much and it changes the CO accordingly.