digital-brain/content/websites/control_bootcamp.md

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+++ title = "Control Bootcamp" author = ["Dehaeze Thomas"] draft = false +++

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https://www.youtube.com/playlist?list=PLMrJAkhIeNNR20Mz-VpzgfQs5zrYi085m

Overview

Linear Systems

Stability and Eigenvalues

Linearizing Around a Fixed Point

Controllability

Controllability, Reachability, and Eigenvalue Placement

Controllability and the Discrete-Time Impulse Response

Degrees of Controllability and Gramians

Controllability and the PBH Test

Cayley-Hamilton Theorem

Reachability and Controllability with Cayley-Hamilton

Inverted Pendulum on a Cart

Eigenvalue Placement for the Inverted Pendulum on a Cart

Linear Quadratic Regulator (LQR) Control for the Inverted Pendulum on a Cart

Motivation for Full-State Estimation

Observability

Full-State Estimation

Kalman Filter

Observability Example in Matlab

Observability Example in Matlab (Part 2)

Kalman Filter Example in Matlab

Linear Quadratic Gaussian (LQG)

LQG Example in Matlab

Introduction to Robust Control

Three Equivalent Representations of Linear Systems

Example Frequency Response (Bode Plot) for Spring-Mass-Damper

Laplace Transforms and the Transfer Function

Benefits of Feedback on Cruise Control Example

Benefits of Feedback on Cruise Control Example (Part 2)

Cruise Control Example with Proportional-Integral (PI) control

Sensitivity and Complementary Sensitivity

Sensitivity and Complementary Sensitivity (Part 2)

Loop shaping

Loop Shaping Example for Cruise Control

Sensitivity and Robustness

Limitations on Robustness

Cautionary Tale About Inverting the Plant Dynamics

Control systems with non-minimum phase dynamics

Bibliography