Problem 2.
The disturbance is not correctly specified; it should read that the spectrum is S(omega)=A/(omega^2+1) for A chosen such that the rms amplitude is 0.1 N. (Since if the spectrum is known, the rms is known.)
The disturbance is also incorrectly specified because if it acted purely on the horizontal position, then (A,F) would not be reachable (the theta states would not be affected by the disturbance). Instead, assume that the disturbance acts on the system in the same way that the control force acts (this means that it has the same effective moment arm as the control force, which isn't very realistic, but allows a solution to be generated).
Also, for part (a), it would be useful to plot the step response of the controller to a step command in the horizontal position (as you did for both the LQR and classical-control designs).
- DGM, 2009.02.22 8:30p (updated 2/23 8:08pm)