Table 4 Numerical values for time responses obtained via mNRBO, NRBO, HO, GEO and SMA.

From: Enhanced PID controller tuning for nonlinear continuous stirred-tank heaters using a modified Newton-Raphson optimizer with random opposition and Lévy-flight learning

Stability metric

mNRBO

NRBO

HO

GEO

SMA

\({N}_{rt}\) (s)

62.0506

136.7929

140.4278

149.7403

139.9460

\({N}_{st}\) (s)

206.8783

288.1727

293.0011

308.4895

296.1712

\({N}_{po}\) (%)

1.4098

1.8669

1.9479

1.7929

1.9921

\({N}_{pse}\) (%)

0.0060

0.0728

0.0657

0.0213

0.0644

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