# Physics projects for Y3 and Y4 students

## Project description

### Feedback & Control for Physicists: Michelson Interferometer

#### (supervisor: John Gough)

Nature of project: theory, software

Available to students on full-time physics degree schemes only.

#### Project description and methodology

The aim of this project is to develop control theory approaches relevant to a physical system. We begin with a study of the basic concepts with a special focus on linear systems. The key idea will be feedback and how it is applied in practice.

Ideally, the student will be taking or have taken PH33310 (Engineering Control).

The core skills needed will be the ability to work with linear systems and knowledge of Fourier/Laplace transform analysis. (This project will make extensive use of matrix theory and Fourier analysis!)

In this project we will study how feedback is used in a practical way to control the Michelson Interferometer.

A successful project will develop beyond the above in one/some of the following directions:
We will use various software facilities online (eg Wolfram's transfer function application) to analysis the properties of the transfer function for specific situations. Here it will be essential to have developed a thorough understanding of the basic concepts.

Further reading of the literature should reveal more sophisticated applications of feedback control which can be outlined in the project.

We will also seek to develop a systems theory approach. Additional properties such as sensitivity analysis, robustness will be accounted for.

When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.

This project is only available as a Y3 project.

Please speak to John Gough (jug) if you consider doing this project.

Initial literature for students:

1. Feedback for Physicists: A tutorial essay, J. Bechhoefer
2. Book, Feedback systems: an introduction for scientists and engineers, KJ AstrĂ¶m, RM Murray
3. Control: A perspective PR Kumar - Automatica, 2014

#### Novelty, degree of difficulty and amount of assistance required

Feedback and control are important ideas in instrumentation, but typically left off the Physics curriculum. This is taught here in PH33310 which is recommended as a pre- or co-requisite.

The core skills needed will be the ability to work with linear systems and knowledge of Fourier/Laplace transform analysis. (This project will make extensive use of matrix theory and Fourier analysis!)

#### Project milestones and deliverables (including timescale)

milestoneto be completed by
basic theory and referencesend of October
formulation of problem - outlook end of November
use of software (Wolfram)Christmas
First applicationsmid-March