Which quantities does the Ziegler-Nichols tuning method rely on?

• A. Ultimate gain and period of sustained oscillation
• B. Natural frequency and damping ratio
• C. Time constant and steady-state error
• D. Controller bandwidth and rise time

Answer: (A)

The method is built around the point of marginal stability in the feedback loop. You increase the loop gain until the system output just begins to sustain oscillations with constant amplitude—that level is the ultimate gain. Then you measure the period of those sustained oscillations, which is the ultimate period. Those two quantities, ultimate gain and ultimate period, are then used with the Ziegler–Nichols formulas to set the PID (or PI) parameters. The other options describe different modeling or performance metrics (natural frequency and damping ratio describe a second-order model; time constant and steady-state error, or bandwidth and rise time, relate to response characteristics but aren’t the quantities Ziegler–Nichols uses to derive the gains).