Overview

Description

COURSE DETAILS:

Motivation:

In late 1867, taking a break from his study of electricity and magnetism, James Clerk Maxwell had two important but seemingly disconnected ideas.  First, he analyzed the steam-engine “governor,” which uses feedback to keep the engine speed constant under varying load.  He explained (using techniques he had previously developed to analyze the rings of Saturn) why the regulation sometimes became unstable.  The February, 1868, paper that followed was the first theoretical study on control theory and is a founding document in that field of engineering.  Indeed, Norbert Wiener’s term for control theory, “cybernetics,” was derived from the Greek word κυβερνήτης (kybernetes) for governor, to honour Maxwell’s contribution.  “Cyberspace” and similar words derive from the same root.

At roughly the same time, in December, 1867, Maxwell wrote a letter to Tait introducing the thought experiment now known as Maxwell’s demon.  In order to show that the second law of thermodynamics was only statistically true, he imagined a “neat-fingered being” that could sort slow- and fast-moving molecules in a box, developing a temperature difference at seemingly no cost.  This challenge to the second law of thermodynamics produced much heated argument, raising many subtle issues that have only recently been understood and only very recently been tested experimentally.

This mini-course will be a quick introduction to key ideas about control.   Experimentalists will gain much practical knowledge on making better experiments.  Theorists will learn useful tools to make physical systems behave in desired ways and to make a start on a different way of thinking that is having more and more impact on physics itself..  

Topics:

• Control of linear systems in the frequency domain (transfer functions, sensitivity, PID control)
• Control of linear systems in the time domain (state-space formulation, controllability and observability, separation principle)
• Optimal control for nonlinear feedforward plus LQR and MPC feedback for robustness plus Kalman filter for noise:  the grand synthesis

Text:  Control Theory for Physics, JB, Cambridge Univ. Press, 2021

Course level:  The background assumed is the standard “Mathematics for Physics” preparation of a Physics undergrad (e.g., Phys 384 or equivalent).  You should be familiar with Fourier transforms (and at least a little bit, Laplace transforms), standard linear algebra (eigenvalues, etc.), calculus of variations (Euler-Lagrange), and the matrix solutions of systems of linear ordinary different equations.

Grading

Materials

REQUIRED READING NOTES: