In the Aeronautics and Astronautics Department at the Univerisity of Washington, the PhD qualifying exam has two parts: a written exam and an oral exam. In the written exam you are given a journal paper and asked to respond and critique it while providing a sufficient literature review of the field. Then you must make and present a slidedeck to your committee. In the oral part, your committee takes turns asking questions from various courses. For my quals, I got asked questions from convex optimization, structural optimization, nonlinear system theory, and feedback control.