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.
Severely dead-time-dominant loops are particularly challenging because a control loop cannot see and start to correct for an unmeasured disturbance until after one dead time. Complete correction takes at least two dead times. Also, such loops are more susceptible to noise, since there is not a major process time constant...
Nearly all loops have noise. Whether you see the noise is a matter of amplitude, frequency, resolution, and data compression. Signal filters and damping can reduce noise but the penalty is a measurement lag and deterioration in the ability to reject disturbances.