Bill Goodwine's Courses

Unless otherwise listed below, all the homework problems are assigned in class at the end of every lecture.

1. 1. Determine the equation of motion for an inverted pendulum.
   2. Determine a linear differential equation that approximates
      this system about the “up” position.
   3. If the input is a torque about the pivot for the pendulum,
      design a controller that stabilizes the pendulum in the up
      position.
   4. Use this controller on the nonlinear equations. By
      experimenting with various initial conditions, determine the
      approximate domain in which the controller works.