Table 2: Comparative presentation of the results of design of the PI controller with performances for three methods.

Method Overshoot (%)Settling time (ms)Phase margin   (degrees)Gain margin Stability margin

Ziegler-Nichols (ZN)13.6775341.887562.3148281.890.48
Tyreus-Luyben (TL)9.437989.374113.619554.63.050.62
Proposed method (PM)10.7857.159.987256.52.740.64