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.

-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.