Question

The transfer function of a phase lead controller is $\frac{1+3Ts}{1+Ts}.$ The maximum value of phase provided by this controller is

• A. ${90}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is D ${30}^{\circ }$

For lead compensator
$T.F=\frac{\alpha (1+T^{\prime }s)}{1+\alpha T^{\prime }s}=\frac{1+3Ts}{1+Ts}$
$So,T^{\prime }=3T$
$\alpha T^{\prime }=T$
$\alpha 3T=T$
$\alpha =\frac{1}{3}$
${\varphi }_{max}=si{n}^{-1}\left(\frac{1-\alpha }{1+\alpha }\right)=si{n}^{-1}\left(\frac{1-1/3}{1+1/3}\right)$
${\varphi }_{max}=si{n}^{-1}\left(\frac{2/3}{4/3}\right)=si{n}^{-1}\left(\frac{1}{2}\right)={30}^{\circ }$