$9$ Consider a phase lead controller whose transfer function is $C(s)=k_1^{1+T_1}1.5$ where $k>0$ and

a$)$ Construct the Nyquist diagram of $C(s),$ marking all important points.

$q,$

$q,$

$q,$

$q,$

$q,$

$q,$

$q,$

$q,$

$q,$

b$)$ Using the Nyquist diagram, prove that the maximum phase addition ${}_m$ possibl by $C(s)$ can be given by

$sin9m+\frac{1-}{1+}$