Assignment

1. Design a lead controller for the plant G (s) = 5 / [s(s+1)(0.2s+1)] by following the process outlined below.

a. Draw (or use MATLAB) the Bode plot for the plant and determine the phase margin of the system.

b. Design a lead compensator with a gain (K) of 1 that provides a phase margin of 40^o.

c. Verify that your design works in MATLAB and include a Bode plot for your controlled system.

d. What is the approximate bandwidth of the controlled system?

2. The fuselage of an airplane has yaw dynamics that are captured by

Y(s) = [ {8.45 (45² + 0.4s + 1)} / {(100s + 1) (s² + 0.24s + 1) (0.01s² + 0.004s + 1)}] δ(s)

where y is the plane's yaw rate and δ is the rudder angle.

a. Make a Bode plot of the plant and determine the phase margin and gain margin.

b. There is a lightly damped mode that is causing a peak around 10 rad/s. If the fuselage is excited at that frequence, it may cause excessive bending. To eliminate this behavior, design a notch controller. Show that your controller works by plotting a Bode plot of your closed loop system.