Summary of ECE 3085
System - A collection of components that together perform a
function. (eg., circuit, car engine, car, airplane, chemical
process)
Systems can be linear or nonlinear, causal or noncausal, static
(memoryless) or have memory, finite dimensional or
infinite dimensional, time varying or time invariant,
continuous time or discrete time
In this course, we have introduced the mathematical tools to
analyze and design linear, time-invariant systems.
ECE 3085, Spring 2000
Notes written by Dr. Heck
Analysis Tools
CONTINUOUS-TIME SYSTEMS
DISCRETE-TIME SYSTEMS
Laplace
Transform
Cont. Time
Conv.
Fourier
Transform
Z-transform
Discrete
Time Conv
Discrete
Time Fourier
Transform
Solving for
response to input
X
X
X
X
X
X
Solving for
steady state
response to
sinusoid
X
X
X
X
X
X
Understanding
filtering
characteristics
Understanding
characteristics of
system response
(stability,
transient
behavior, etc)
X
X
X
X
Transfer
function
Transfer
function
ECE 3085, Spring 2000
Notes written by Dr. Heck
Control Design Methods
• Root Locus - Plot of the closed loop poles as a function of
gain (can be used in the s-domain or the z-domain to
determine the K that yields desirable closed loop pole
positions)
• Frequency Response - Bode plot design (not covered in this
course, but a common method)
• Simulation - after the root locus or the Bode plot methods
are used to get an initial design, the system is simulated and
the controller can be adjusted for better performance
• Implementation - either as an analog circuit or a computer
that implements a difference equation
ECE 3085, Spring 2000
Notes written by Dr. Heck
Digital Control
• Mappings - Euler approximation for differentiation, bilinear
transformation (or Tustin’s rule or trapezoidal rule), step
response matching (or zero order hold)
• Direct Method of Design - Map plant to discrete time and
do the design directly in the discrete-time domain
• Indirect Method of Design - Design the controller in the
continuous-time domain, then map it to discrete time
• Implementation - computer algorithm implementing a
difference equation
ECE 3085, Spring 2000
Notes written by Dr. Heck
State Space Methods
Alternative method to representing systems (as opposed to
transfer functions)
• Motivation for using:
– represents internal model behavior
– matrix representation easier for computers to use
– easier for multi-input and multi-output systems
• What have we learned to do with it?
– Put systems into state space form
– Solve system response to IC (zero input response) and to the input
(zero state response)
– Find transfer function
ECE 3085, Spring 2000
Notes written by Dr. Heck