railway DFCCIL Executive 2025 Mock Test Control Systems Time Response Analysis Time Domain Specifications
If ζ is the damping ratio and ωn is the natural frequency, then the expression of Settling time (ts) is
1
\({t_s} \simeq \frac{4}{{\xi {\omega _n}}}\)
2
\(t_s ={e^{\left( { - \frac{{\pi \xi }}{{\sqrt {1 - {\xi ^2}} }}} \right)}}\)
3
\(t_s = \frac{\pi }{{{\omega _n}\sqrt {1 - {\xi ^2}} }}\)
4
\(t_s =\frac{{\pi - {{\tan }^{ - 1}}\left( {\frac{{\sqrt {1 - {\xi ^2}} }}{\xi }} \right)}}{{{\omega _n}\sqrt {1 - {\xi ^2}} }}\)