The cart with an inverted pendulum, shown below, is "bumped" with an impulse
force, F. Determine the dynamic equations of motion for the system, and lin
earize about the pendulum s angle, theta = Pi (in other words, assume that p
endulum does not move more than a few degrees away from the vertical, chosen
to be at an angle of Pi). Find a controller to satisfy all of the design re
quirements given below.
