Nature of project: **theory**, software

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

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 proportional feedback is used in a practical way to design and control the Operational Amplifier (Op Amp).

*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** if you consider doing this project.

*Initial literature for students:*

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

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!)

milestone | to be completed by |
---|---|

Locating source material | end of October |

overview of theory/formulating basic physical systems as control problems | end of November |

looking at applications/ underlying principles of op amps | Christmas |

Further directions and Analysis | mid-March |