Nyquist /Bode Stability Criteria

[ww2i]

How Nyquist or Bode stability criteria is applied to a real plant loop?

[tuan]

Applying Nyquist and Bode stability criteria to a real plant control loop is often quite different from the textbook examples because actual industrial loops contain process dead time, valve nonlinearities, sensor dynamics, noise, and controller limitations. However, the fundamental principle remains the same: evaluate the open-loop transfer function and determine how close the loop is to instability.

[sys1]

For petrochemical and refining applications, Bode analysis is used far more frequently than Nyquist analysis because phase margin and gain margin provide intuitive indicators of control-loop robustness. Nyquist analysis becomes particularly valuable when dealing with loops containing significant dead time, multiple interacting dynamics, advanced process control schemes, or when a rigorous proof of stability is required during control system design and modification studies.

[ww2i]

What we know now is that practically, in modern plants, engineers rarely draw Nyquist plots manually.
Instead they use tools such as:
MATLAB Simulink Control System Toolbox
AspenTech DMC3 Analyzer
Emerson DeltaV Insight
Yokogawa Exaquantum Analytics