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Lecture Notes



Lecture Notes

TOPIC #CONTENTSLECTURE NOTES
Topic 1

Introduction


Motivation

Basic linear system response

(PDF)
Topic 2

Basic root locus


Basic aircraft control concepts

Basic control approaches

(PDF)
Topic 3

Frequency response methods


Analysis

Synthesis

Performance

Stability

(PDF)
Topic 4

Stability in the frequency domain


Nyquist stability theorem

Examples

Appendix

This is the basis of future robustness tests

(PDF)
Topic 5

Control design using Bode plots


Performance issues

Synthesis

Lead/Lag examples

(PDF)
Topic 6

State-space systems


What are state-space models?

Why should we use them? How are they related to the transfer functions used in classical control design and how do we develop a state-space model? What are the basic properties of a state-space model, and how do we analyze these?

(PDF)
Topic 7

State-space systems (cont.)


What are state-space models?

Why should we use them?

How are they related to the transfer functions used in classical control design and how do we develop a state-space model?

What are the basic properties of a state-space model, and how do we analyze these?

(PDF)
Topic 8

State-space systems (cont.)


What are the basic properties of a state-space model, and how do we analyze these?

State-space (SS) to transfer function (TF)

(PDF)
Topic 9

State-space systems (cont.)


What are the basic properties of a state-space model, and how do we analyze these?

Time domain interpretations

System modes

(PDF)
Topic 10

State-space systems (cont.)


System zeros

Transfer function matrices for multiple-input and multiple-output (MIMO) systems

(PDF)
Topic 11

State-space systems (cont.)


State-space model features

Observability

Controllability

Minimal realizations

(PDF)
Topic 12

State-Space Systems (cont.)


State-space model features

Controllability

(PDF)
Topic 13

State-space systems (cont.)


Full-state feedback control

How do we change the poles of the state-space system?

Or, even if we can change the pole locations

Where do we change the pole locations to?

How well does this approach work?

(PDF)
Topic 14

State-space systems (cont.)


Full-state feedback control

How do we change the poles of the state-space system?

Or, even if we can change the pole locations

Where do we put the poles?

  • Heuristics
  • Linear quadratic regulator (LQR)

How well does this approach work?

(PDF)
Topic 15

State-space systems (cont.)


Open-loop estimators

Closed-loop estimators

Observer theory (no noise) — Luenberger

Estimation theory (with noise) — Kalman

(PDF)
Topic 16

State-space systems (cont.)


Closed-loop control using estimators and regulators

Dynamics output feedback

"Back to reality"

(PDF - 1.3 MB)
Topic 17

Deterministic linear quadratic regulator (LQR)


Optimal control and the Riccati equation

Weight selection

(PDF)
Topic 18

Optimal estimators


Applied optimal control (Chapter 12) — Bryson and Ho

Applied optimal estimation — Gelb

Optimal estimation of dynamic systems — Crassidis and Junkins

(PDF)
Topic 19

Feedback control systems


Stengel (Chapter 6)

Question: How well do the large gain and phase margins discussed for LQR map over to dynamics output feedback (DOFB) using LQR and linear quadratic estimator (LQE) (called linear quadratic Gaussian (LQG))?

(PDF)
Topic 20

Closed-loop system analysis


Bounded gain theorem

Robust stability

(PDF)
Topic 21

Robustness analysis


Model uncertainty

Robust stability (RS) tests

RS visualizations

(PDF)
Topic 22

Feedback control systems (cont.)


Robust stability (RS)

Nominal performance (NP)

Robust performance (RP)

Small gain theorem

(PDF)
Topic 23

MIMO systems


Singular value decomposition

Multivariable frequency response plots

(PDF)
Topic 24

Feedback control systems (cont.)


H∞ synthesis

(PDF)

 








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