Find the ultimate gain and frequency for a proportional controller in the case of a process having the transfer function $${{\text{G}}_{\text{p}}}\left( {\text{s}} \right) = \frac{1}{{\left( {4{\text{s}} + 1} \right)\left( {2{\text{s}} + 1} \right)\left( {{\text{s}} + 1} \right)}}.$$

A. $${\text{w}} = \frac{1}{{\sqrt {14} }},\,{{\text{K}}_{\text{c}}} = \frac{{45}}{{7\sqrt {14} }}$$

B. $${\text{w}} = \sqrt {\frac{7}{6}} ,\,{{\text{K}}_{\text{c}}} = \frac{{46}}{3}$$

C. $${\text{w}} = 1,\,{{\text{K}}_{\text{c}}} = 13$$

D. $${\text{w}} = \sqrt {\frac{7}{8}} ,\,{{\text{K}}_{\text{c}}} = \frac{{45}}{4}$$

Answer: Option B