Lectures related to Harmonic Stability Analysis

Proportional Controller: Error and Setpoint Effects

Explains the necessity of error in a proportional controller and the effects of the setpoint.

Modeling Introduction

Explores the importance of modeling to understand and control complex systems efficiently.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Fourier Series: Harmonic Analysis

Covers the Fourier series representation of periodic signals and harmonic analysis.

Unitary Minimal Models: Representation Theory Insights

Covers the representation theory of unitary minimal models and the Virasoro algebra.

Feedback Control Systems: PID Regulator Synthesis

Explores closed-loop control systems, PID regulator design, and performance analysis.

Structure of Algebras

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Conformal Blocks: Functions on Moduli Spaces

Covers conformal blocks and their significance in complex structures and moduli spaces.

Boundary Conditions in Harmonic Functions

Explains harmonic functions and their boundary conditions, including Dirichlet and Robin conditions.

Density Theorem: Endomorphisms of Simple Modules

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

Machine Learning at the Atomic Scale

Explores simple models, electronic structure evaluation, and machine learning at the atomic scale.

Stability Examples: Routh-Hurwitz Criterion

Illustrates stability examples and the Routh-Hurwitz criterion for closed-loop systems.

Model Reference Method: PID Regulator Design

Explores the Model Reference Method for designing PID regulators and cascade controllers for complex systems.

Signals: Analysis and Synthesis

Introduces the typology of signals and the analysis of deterministic signals.

Heisenberg Groups: Introduction

Introduces the Heisenberg groups, covering representation theory and unique properties.

Multivariable Control: Eigenvalue Assignment and Disturbance Estimation

Discusses closed-loop eigenvalue selection and disturbance impact in multivariable control systems.

Operational Transconductance Amplifiers: Evolution and Frequency Analysis

Explores the evolution and frequency analysis of Operational Transconductance Amplifiers, including stability considerations and the impact of feedback.

Nyquist Criterion: Stability Analysis

Covers the Nyquist criterion for stability analysis in control systems, using the Nyquist diagram to determine closed loop poles.

Monster Group: Representation

Explores the Monster group, a sporadic simple group with a unique representation theory.

Carathéodory's Theorem and Dimension Bound

Explores Carathéodory's Theorem and its dimension implications for set representation.