HW 6 Question 4
First, this problem has a small bug: in part (a), the problem asks for a gain crossover frequency of 1 rad/sec. It should ask for a bandwidth of 1 rad/sec. There are various definitions of the bandwidth, and the gain crossover frequency is one of them, but satisfying that definition is impossible in this particular problem. You'll need to use a different definition of the bandwidth to find a feasible result.
This problem is meant to help you start thinking about how to "place" poles and zeros intelligently so that you don't have to resort to ridiculously high gains (>1000). Intelligence in this case manifests itself as observing that if you place the controller zero at the right distance between the controller pole and one of the process poles, you can add large amounts of phase, which gives you room to play with the proportional gain to adjust your bandwidth.
So I recommend taking a step back from Matlab, and starting this problem with pencil and paper, so you get an idea of the relative sizes of \(k_p\) and \(k_d\) before stumbling blindly into a guess/check cycle.
--George Hines 16:43, 16 November 2007 (PST)