EE/ME/AE324:
Dynamical Systems
Chapter 3: Standard Forms for System Models
StateVariables
A common way to model systems is using statevariables:
y
y
g
independent variables that completely describe the system
response for all t t 0 given knowledge of the
EE/ME/AE324:
Dynamical Systems
Chapter 4: Block Diagrams
and Computer Simulation
Block Diagrams
A block diagram is an interconnection of:
Blocks representing math operations
Wires representing signals (info.) and their flow
Commonly used to analyze/simul
EE/ME/AE324:
Dynamical Systems
Chapter 7: Transform Solutions
of Linear Models
The Laplace Transform
Converts systems or signals from the real time
domain, e.g., functions of the real variable t, to the
complex frequency domain, e g functions of the
doma
EE/ME/AE324:
Dynamical Systems
Chapter 8: Transfer Function
Analysis
The System Transfer Function
Consider the system described by the nth-order I/O eqn.:
y ( n ) + an 1 y ( n 1) +
+ a0 y = bmu ( m ) +
+ b0u
Taking the Laplace transform of the system eq
EE/ME/AE324:
Dynamical Systems
Chapter 9: Developing Linear
Models
From there to here.
From here to there
there.
Nonlinearities are everywhere.
Linearization of Nonlinear Elements
Most real world systems have significant nonlinear elements
The objective
EE/ME/AE324:
Dynamical Systems
Chapter 5: Modeling Rotational
Mechanical Systems
Common Variables Used
Assume 1 rotational DoF per mass i e all motion scalar
mass, i.e.,
Angular Displacement: (t ) [rad]
d (t )
[rad/s]
Angular Velocity: (t ) =
dt
d (t )
EE/ME/AE324:
Dynamical Systems
Chapters 1011:
Electromechanical, Thermal
and Fluid Systems
Electromechanical Coupling by Magnetic Fields
current-carrying
Many electromechanical devices contain current carrying
wires that can move within a magnetic field,