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.
We are aware that too high of a PID gain can cause excessive oscillations and even instability. The ultimate gain for processes with no steady state on PID horizon is usually much higher than our comfort level.
Many of the most important process variables, such as vessel and column composition, pressure and temperature, do not reach a steady state in the time frame of PID action. Batch composition, pH and temperature and, of course, level have no steady state.
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...