Prelab - Lead

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A recap.

What have we learned so far? Perhaps more than we wanted about the propeller arm (about its angular velocity and acceleration, its forces, and the how fast it build up thrust), lots about system functions (poles, natural frequencies, step responses and frequency responses, in both discrete and continuous time), but only about one control scheme, PID. And the "D" part of PID has always been a problem. Whether the "D" meant "delta" in DT or derivative in CT, it was always a source of undesirable noise.

That resistor mystery.

When we had you add a small resistor in series with the capacitor when using an op-amp PD controller, it dramatically reduced the noise in the motor command. What we did was bound the high frequency gain of the PD controller, but we can be more deliberate in designing such a "bounded" PD controller, as it is what we call a lead network. In order to design lead controllers, one needs to understand an aspect of the open-loop frequency response, phase and gain margin, and its relation to stability and step responses.

The Maglev Lab

This week you will set up the magnetic levitation system, determine a one-pole model for how fields build up in your electromagnet, calibrate a cancellation circuit needed to measure a levitating body's position, and finally, design an analog controller that will "levitate" a magnetized object (hold it in a stable free-floating position below the electromagnet). It is a big lab, but there are no labs for two weeks, and we will be scheduling plenty of virtual office hours, so there is no reason to rush through it. Please do try to keep up with the pre-pre-prelab, pre-prelab, and prelab for the first state space lab if you can.

This prelab

We have included notes reviewing transforms, and Bode plots from poles examples in the lecture notes section for this week, along with extensive notes for the virtualized lectures. We will also try to post videos covering this material throughout the week. In addition, for constructing frequency response plots from H(s) poles and zeros, a good review can be found in Professor Siebert's Chapter 4. Professor Joel Dawson's notes on lead and lag networks are also excellent: R14, R15, R16, R17.

Please review the week five lecture material and notes here and the week eight/lecture 6 material and review notes here before trying the exercises below. They are intended to help you solidify your understanding of lead compensators, and to indicate some of the issues in using them in three-pole systems. Since the magnetic levitation system can be modeled as a three-pole system, we hope this prelab will help you focus your search for an effective design.