# HW8 problem 4

This problem asks you to design a controller for an unstable system (the magnetically levitating ball demonstrated in lecture) and numerically compute Bode's integral formula for the sensitivity function and show that it is equal to \(\pi \Sigma Re (p_k)\), where \(p_k\) are the positions of open-loop right half plane poles.

The controller can be designed in a manner similar to the procedure given in the lecture notes.

However, the problem deson't specify that your controller have good tracking error or phase margin. All you need is for it to stabilize. I like my controllers to work well, but when I made a "good" controller, my integral never seemed to converge to the right answer. Perhaps because of numerical instability.

--Fuller 17:38, 4 December 2007 (PST)