The process variable has slow decaying oscillations. Control theory text books indicate decreasing the PID gain should make the loop more stable. You decrease the PID gain. The oscillation gets worse. You decrease the gain again. The amplitude and the period get bigger. You repeatedly decrease the PID gain.

Do you lie awake at night wondering what the source of process dynamics is? Do you wonder why temperature and composition controllers tend to oscillate at low production rates and low levels? Are you perplexed why some controllers need a lambda factor of 2 and others need a lambda factor...