A controller  of the form  is to be designed for the plant  as shown in the figure. The value of  that yields a phase margin of  at the gain cross-over frequency of  is ___________ (round off to one decimal place).

Consider a unity-gain negative feedback system consisting of the plant (s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are

Consider a lead compensator of the form

The frequency at which this compensator produces maximum phase lead is . At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of , is . The values of , respectively, are