Explain the Ziegler-Nichols tuning methods.

Two classical methods: Ultimate Gain Method - increase P gain until sustained oscillation (Ku), measure period (Pu), apply formulas: P-only Kp=0.5Ku, PI Kp=0.45Ku Ti=Pu/1.2, PID Kp=0.6Ku Ti=Pu/2 Td=Pu/8. Reaction Curve Method - apply step change in manual, measure response curve parameters (dead time L, time constant T, steady-state gain K), apply formulas based on L and T. These methods give aggressive, oscillatory response - usually needs detuning. Better starting point than trial-and-error; modern methods (IMC, Lambda) give less aggressive tuning.