Draw the bode diagram of the compensator draw the bode

Question

Assignment

Problem 1

Consider the control system shown in the figure. Design a phase lag compensator using bode diagram method to make the phase margin P.M.≥45°

Draw the bode diagram of the uncompensated system and show the phase margin.
Design a phase lag compensator G_c(s) = k[(s+z) / (s+p)] using bode diagram. You need steps to determine the values of the new cross-over frequency, z, p, and k.
Draw the Bode diagram of the compensator
Draw the Bode diagram of the compensated system and show the phase margin.
Draw the Bode diagram of the closed loop system
Calculate the poles of the closed loop system
Show the response and performance to the step input and indicate the settling time.

Problem 2

For the close loop system

y(t) = [1 0] x(t) + [0] u(t)

Determine the controllability and observability of the system.