| Lecture |
Topics | Additional
material |
| 01 |
dynamics - motion - mathematical model -
prediction - simulation - causes of motion - linearity -
time invariance - LTI (Linear-Time Invariant) system - control system examples |
|
| 02 |
LTI system signals definitions and
dimensions - system as a signal transformer -
abstraction - different systems same description same
behavior - state - system order - Mass/Spring/Damper
from higher order ODE to system of differential
equations - coordinate transformation - equivalent
representations - direct feed-through - examples of
modeling |
MIT - OCW: Signals & Systems - Lecture 1 (with video) |
| 03 |
Time response - zero-input response -
matrix exponential - zero-state response - total
response - superposition principle - Dirac delta -
impulsive response - change of coordinates |
|
| 04 |
Linear algebra - matrices -
eigenvalues/eigenvectors - characteristic polynomial -
algebraic multiplicity - geometric multiplicity -
diagonalization - Jordan form |
Eigenvalues and eigenvectors: MIT - OCW -
Lecture (with video) Diagonalization and powers of A: MIT - OCW - Lecture (with video) |
| 05 2-mass example |
Time domain analysis - modal decomposition - distinct eigenvalues - aperiodic and pseudoperiodic modes - parameters of the natural modes - multiple eigenvalues | MIT - OCW: Differential equations and
exp(At) (video, problems &
solutions) MIT - OCW: Harmonic oscillator (text) |
| 06 stability slides |
Stability of LTI systems - definitions -
Routh stability criterion - Nonlinear systems stability
(slides 1-10 and 14-15 and 41-45, slides done by Prof.
G. Oriolo) |
|
| 07 |
Laplace transform - properties - application - response in the s-domain - transfer function - realizations - poles/zeros - poles vs eigenvalues | |
| 08 |
Zero-State system response - partial
fraction decomposition |
|
| Step response - transient - steady-state | ||
| Bode diagrams |
Bode diagrams summary | |
| Frequency response: system as a filter -
MSD system - first and second order systems -
quarter-car suspension model |
||
| 12 | Interconnected systems: series, parallel
and feedback, appearance of the hidden dynamics |
|
| 13 |
Nyquist stability criterion, stability
margins, Bode stability criterion, delay in the feedback
loop |
|
| Preliminary examples on control - open vs
closed-loop control principles - direct compensation of
the disturbance |
||
| 15 |
Specifications - steady-state and
transient - frequency domain characterization |
|
| 16 |
Loop shaping - choice of the elementary
functions - basic PID |
|
| 17 |
Performance - Sensitivity functions | |
| 18 |
Root locus as an analysis and design tool - Pole placement | |
| 19 |
Controllable and observable system - rank
test - eigenvalue assignment via state feedback -
observability and observer design - separation principle |
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