The transfer function of a first-order controller is given as $${G_c}(s) = {{K\left( {s + a} \right)} \over {s + b}}$$

where k, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is

The magnitude plot of a rational transfer function G(s), with real coefficient is shown in figure. Which of the following compensators has such a magnitude plot?

The pole-zero plot given below corresponds to a

The transfer function of a phase-lead compensator is given by $${G_c}(s) = {{1 + 3Ts} \over {1 + Ts}}$$

where T > 0. The maximum phase-shift provided by such a compesator is