1
Dan O.
Popa, EE 1205 Intro. to EE
1
Systems Concepts
Dan Popa, Ph.D., Associate Professor
popa@uta.edu
,
http://ngs.uta.edu
•
Systems
Approach
and Related Concepts
•
Modeling
: Physical, mathematical
•
System
identification, block diagrams, subsystems, modules,
interconnection
•
Input/output, environmental effects, linear

nonlinear, dynamic,
causal

noncausal
•
Examples of complex robotic systems
2
Dan O.
Popa, EE 1205 Intro. to EE
2
Signals and Systems
–
Signal:
•
Any time dependent physical quantity
•
Electrical, Optical, Mechancal
–
System:
•
Object in which input signals interact to
produce output signals.
•
Some have fundamental properties that make
it predictable:
–
Sinusoid in, sinusoid out of same frequency (when
transients settle)
–
Double the amplitude in, double the amplitude out
(when initial state conditions are zero)
?
x
(
t
)
u
(
t
)
y
(
t
)
3
Dan O.
Popa, EE 1205 Intro. to EE
3
Signal Classification
–
Continuous Time vs.
Discrete Time
•
Telephone line signals,
Neuron synapse
potentials
•
Stock Market, GPS
signals
–
Analog vs. Digital
•
Radio Frequency (RF)
waves, battery power
•
Computer signals, HDTV
images
4
Dan O.
Popa, EE 1205 Intro. to EE
4
Signal Classification
–
Deterministic vs. Random
•
FM Radio Signals
•
Background Noise Speech
Signals
–
Periodic vs. Aperiodic
•
Sine wave
•
Sum of sine waves with non

rational frequency ratio
5
Dan O.
Popa, EE 1205 Intro. to EE
5
System Classification
–
Linear vs. Nonlinear
•
Linear systems have the property of
superposition
–
If U
→Y,
U1
→Y1,
U2
→Y2 then
»
U1+U2
→ Y1+Y2
»
A*U
→A*Y
•
Nonlinear systems do not have this property,
and the I/O map is represented by a
nonlinear mapping.
–
Examples: Diode, Dry Friction, Robot Arm at
High Speeds.
–
Memoryless vs. Dynamical
•
A memoryless system is represented by a
static (non

time dependent) I/O map:
Y=f(U).
–
Example: Amplifier
–
Y=A*U, A

amplification
factor.
•
A dynamical system is represented by a
time

dependent I/O map, usually a
differential equation:
–
Example: dY/dt=A*u, Integrator with Gain A.
Mandelbrot set, a fractal image,
result of a Nonlinear Discrete
System Z
n+1
=Z
n
²+C
0
0
)
sin(
2
2
2
2
L
g
dt
d
L
g
dt
d
Exact Equation,
nonlinear
Approximation
around vertical
equilibrium, linear
6
Dan O.
Popa, EE 1205 Intro. to EE
6
System Classification
–
Time

Invariant vs. Time Varying
•
Time

invariant system parameters do not change over time. Example: pendulum, low power
circuit
•
Time

varying systems perform differently over time. Example: human body during exercise.
–
Causal vs. Non

Causal
•
For a causal system, outputs depend on past inputs but not future inputs.
Examples: most
engineered and natural systems
•
A non

causal system, outputs depend on future inputs. Example: computer simulation
where we know the inputs a

priori, digital filter with known images or signals.
–
Stable vs. Unstable
•
For a stable system the output to bounded inputs is also bounded. Example: pendulum at
bottom equilibrium
•
For an unstable system the ouput diverges to infinity or to values causing permanent
damage. Example: short circuit on AC line.
7
Dan O.
Popa, EE 1205 Intro. to EE
7
System Modeling
•
Building mathematical models based on observed
data, or other insight for the system.
–
Parametric models (analytical): ODE, PDE
–
Non

parametric models: graphical models

plots,
look

up cause

effect tables
–
Mental models
–
Driving a car and using the
cause

effect knowledge
–
Simulation models
–
Many interconnect
subroutines, objects in video game
8
Dan O.
Popa, EE 1205 Intro. to EE
8
Types of Models
•
White Box
–
derived from first principles laws: physical,
chemical, biological, economical, etc.
–
Examples: RLC circuits, MSD mechanical models
(electromechanical system models).
•
Black Box
–
model is entirely derived from measured data
–
Example: regression (data fit)
•
Gray Box
–
combination of the two
9
Dan O.
Popa, EE 1205 Intro. to EE
9
White Box Systems: Electrical
•
Defined by Electro

Magnetic Laws of Physics:
Ohm’s Law, Kirchoff’s Laws, Maxwell’s Equations
•
Example: Resistor, Capacitor, Inductor
u
R
i
u
i
C
u
i
L
10
Dan O.
Popa, EE 1205 Intro. to EE
10
RLC Circuit as a System
Kirchoff’s Voltage Law (KVL):
u
1
L
C
R
u
u
3
u
2
RLC
q
(
t
)
u
(
t
)
i
(
t
)
11
Dan O.
Popa, EE 1205 Intro. to EE
11
White Box Systems: Mechanical
Newton’s Law:
M
K
B
F
MSD
x
(
t
)
F
(
t
)
x
(
t
)
Mechanical

Electrical
Equivalance:
F (force)
~V (voltage)
x
(displacement) ~ q (charge)
M (mass) ~ L (inductance)
B (damping) ~ R (resistance)
1/K (compliance) ~ C (capacitance)
12
Dan O.
Popa, EE 1205 Intro. to EE
12
White

Box vs. Black

Box Models
Newton

Euler
Law
:
Lawn
Mower
x
,
y
,
θ
ω
_
r
(
t
)
,
ω
_
l
(
t
)
X
(
t
)
,
Y
(
t
)
Θ
(
t
)
13
Dan O.
Popa, EE 1205 Intro. to EE
13
Grey

Box Models
14
Dan O.
Popa, EE 1205 Intro. to EE
14
White Box vs Black Box Models
White
Box Models
Black

Box Models
Information Source
First Principle
Experimentation
Advantages
Good Extrapolation
Good
understanding
High reliability, scalability
Short time to develop
Little domain expertise
required
Works for not well
understood systems
Disadvantages
Time consuming
and
detailed domain expertise
required
Not
scalable, data restricts
accuracy, no system
understanding
Application Areas
Planning, Construction,
Design, Analysis,
Simple
Systems
Complex processes
Existing systems
Start to understand simple white continuous time models
which are
linear
Eventually deal with grey

box or black

box models in real

life
15
Dan O.
Popa, EE 1205 Intro. to EE
15
Linear vs. Nonlinear
•
Why study continuous linear analysis of signals and
systems when many systems are nonlinear in
practice?
–
Linear systems have generic, predictable performance.
–
Nonlinear systems can be approximated and transformed
into linear systems.
–
S
ome techniques for analysis of nonlinear systems are
based on linear methods
–
If you don’t understand linear dynamical systems you
certainly can’t understand nonlinear systems
16
Dan O.
Popa, EE 1205 Intro. to EE
16
Application Areas for Systems Thinking
•
Classical circuits & systems (1920s
–
1960s) (transfer
functions, state

space description of systems).
•
First engineering applications: military

aerospace 1940’s

1960s
•
Transitioned from specialized topic to ubiquitous in 1980s
with EE applications to:
–
Electronic circuit design
–
Signal and image processing
•
Networks (wired, wireless), imaging, radar, optics.
–
Control of dynamical systems
•
Feedback control, prediction/estimation/identification of systems, robotics, micro
and nano systems
17
Dan O.
Popa, EE 1205 Intro. to EE
17
Diagram Representation of Systems
Top
Bottom 1
Bottom 2
Bottom 3
Middle
Graph
Node 1
Graph
Node 3
Graph
Node 5
Graph
Node 4
Graph
Node 2
Hierarchical Diagram: Organizations
Undirected Graph: Networks
Flowchart: Procedures, Software
18
Dan O.
Popa, EE 1205 Intro. to EE
18
System Simulation Software
•
Matlab Simulink
–
http://www.mathworks.com/support/2010b/simu
link/7.6/demos/sl_env_intro_web.html
•
National Instruments Labview
–
http://www.ni.com/gettingstarted/labviewbasics/
environment.htm
19
Dan O.
Popa, EE 1205 Intro. to EE
19
EE

Specific Diagrams
•
Block Diagram Model:
–
Helps understand flow of information (signals) through a complex system
–
H
elps visualize I/O dependencies
–
E
quivalent to a set of linear algebraic equations.
–
Based on a set of primitives:
Transfer Function
Summer/Difference
Pick

off point
•
Signal Flow Graph (SFG):
–
Directed Graph alternative
H
(
s
)
U
(
s
)
Y
(
s
)
+
+
U2
U1
U1+U2
U
U
U
20
Dan O.
Popa, EE 1205 Intro. to EE
20
EE

Specific Diagrams: Signal Flow Graph
(SFG
–
Directed Graph)
2

port circuit SFG
Multi

loop Control SFG
21
Dan O.
Popa, EE 1205 Intro. to EE
21
EE

Specific Diagrams:
Block Diagram Simplification Rules
22
Dan O.
Popa, EE 1205 Intro. to EE
22
EE

Specific Diagrams:
Block Diagram Reduction Rules
23
Dan O.
Popa, EE 1205 Intro. to EE
23
EE

Specific Diagrams:
Block Diagram Reduction Rules
24
Dan O.
Popa, EE 1205 Intro. to EE
24
Robots as Complex Systems
G. Bekey definition: an entity that can sense, think and act.
Extensions: communicate, imitate, collaborate
Classification: manipulators, mobile robots, mobile manipulators.
Sense
Think
Act
Robot
25
Dan O.
Popa, EE 1205 Intro. to EE
Research in Multiscale Robotics at
Next Gen Systems (NGS) Group
Robotics
Control Systems
Manufacturing &
Automation
Established Technologies
Emerging Technologies
Micromanufacturing
Microrobotics
Microassembly
Micropackaging
Sensor
&
Actuator Arrays
NanoManufacturing
Microsystems &
MEMS
Nanotechnology
Biotechnology
Small

scale
Robotics &
Manufacturing
Modeling & Simulation
Control Theory
Algorithms
Tools and Fundamentals
Assistive Robots
Human

like
robots
Distributed
and
wireless sensor
systems
New applications
for
robot
systems
26
Dan O.
Popa, EE 1205 Intro. to EE
26
Control System Block Diagram
27
Dan O.
Popa, EE 1205 Intro. to EE
27
Automatic Control
•
Control: process of making a system variable
converge to a reference value
•
If r=ref_value=changing

servo (tracking control)
•
If r=ref_value=constant

regulation (stabilization)
•
Open loop vs. closed loop (feedback) control
Controller
K(s
)
Plant
G(s)
+

Sensor Gain
H(s)
+
+
Controller
K(s
)
Plant
G(s)
r
r
y
y
28
Dan O.
Popa, EE 1205 Intro. to EE
28
Brief History of Feedback Control
•
The key developments in the history of mankind that affected
the progress of feedback control were:
•
1. The preoccupation of the Greeks and Arabs with keeping accurate track
of time. This represents a period from about 300 BC to about 1200 AD.
(Primitive period of AC)
•
2. The Industrial Revolution in Europe, and its roots that can be traced
back into the 1600's. (Primitive period of AC)
•
3. The beginning of mass communication and the First and Second World
Wars. (1910 to 1945). (Classical Period of AC)
•
4. The beginning of the space/computer age in 1957. (Modern Period of
AC).
29
Dan O.
Popa, EE 1205 Intro. to EE
29
Primitive Period of AC
Float Valve for tank level regulators
Drebbel incubator furnace control (1620)
(antiquity)
30
Dan O.
Popa, EE 1205 Intro. to EE
30
Primitive Period of AC
James Watt
Fly

Ball Governor
For regulating steam
engine speed
(late 1700’s)
31
Dan O.
Popa, EE 1205 Intro. to EE
31
Classical Period of AC
•
Stability Analysis:
Maxwell, Routh, Hurwitz, Lyapunov (before 1900).
•
Electronic Feedback Amplifiers with Gain for long distance
communications (Black, 1927)
–
Stability analysis in frequency domain using Nyquist criterion (1932),
Bode Plots (1945).
•
PID controller (Callender, 1936)
–
servomechanism control
•
Root Locus (Evans, 1948)
–
aircraft control
•
Most of the advances were done in Frequency Domain.
32
Dan O.
Popa, EE 1205 Intro. to EE
32
Modern Period of AC
•
Time domain analysis (state

space)
•
Bellmann, Kalman: linear systems (1960)
•
Pontryagin: Nonlinear systems (1960)
–
IFAC
•
Optimal controls
•
H

infinity control (Doyle, Francis, 1980’s)
–
loop shaping (in
frequency domain).
•
MATLAB (1980’s to present) has implemented math behind
most control methods.
33
Dan O.
Popa, EE 1205 Intro. to EE
33
Feedback Control
•
Role of feedback:
–
Reduce sensitivity to system parameters (robustness)
–
Disturbance rejection
–
Track desired inputs with reduced steady state errors,
overshoot, rise time, settling time (performance)
•
Systematic approach to analysis and design
–
Select controller based on desired characteristics
•
Predict system response to some input
–
Speed of response (e.g., adjust to workload changes)
•
Approaches to assessing stability
34
Dan O.
Popa, EE 1205 Intro. to EE
34
Feedback System Block Diagram
•
Temperature control system
35
Dan O.
Popa, EE 1205 Intro. to EE
35
Feedback System Block Diagrams
•
Automobile Cruise Control
36
Dan O.
Popa, EE 1205 Intro. to EE
Key Transfer Functions
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
2
1
s
G
s
G
s
E
s
U
s
U
s
Y
s
E
s
Y
:
eedforward
F
)
(
)
(
)
(
)
(
)
(
:
Loop
2
1
s
H
s
G
s
G
s
E
s
B
)
(
)
(
)
(
1
)
(
)
(
)
(
)
(
:
2
1
2
1
s
H
s
G
s
G
s
G
s
G
s
R
s
Y
Feedback
Plant
Controller
S
)
(
s
U
)
(
s
Y
)
(
s
R
)
(
s
E
Transducer
)
(
s
B
+
–
)
(
1
s
G
)
(
2
s
G
)
(
s
H
Reference
37
Dan O.
Popa, EE 1205 Intro. to EE
Transient Response Characteristics
state
steady
of
%
specified
within
stays
time
Settling
:
reached
is
value
peak
which
at
Time
:
value
state
steady
reach
first
until
delay
time
Rise
:
value
state
steady
of
50%
reach
until
Delay
:
s
p
r
d
t
t
t
t
0.5
1
1.5
2
2.5
3
0.25
0.5
0.75
1
1.25
1.5
1.75
2
overshoot
M
p
s
t
p
t
r
t
d
t
38
Dan O.
Popa, EE 1205 Intro. to EE
Effect of pole locations
Faster Decay
Faster Blowup
Oscillations
(higher

freq)
Im(s)
Re(s)
(
e

at
)
(
e
at
)
in
out
V
A
A
V
1
Negative feedback
Pole at

1/A (stable)
in
out
V
A
A
V
1
Positive feedback
Pole at 1/A
(unstable)
39
Dan O.
Popa, EE 1205 Intro. to EE
Basic Control Actions: u(t)
:
control
al
Differenti
:
control
Integral
:
control
al
Proportion
s
K
s
E
s
U
t
e
dt
d
K
t
u
s
K
s
E
s
U
dt
t
e
K
t
u
K
s
E
s
U
t
e
K
t
u
d
d
i
t
i
p
p
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
0
40
Dan O.
Popa, EE 1205 Intro. to EE
40
Summary of Basic Control
•
Proportional control
–
Multiply e(t) by a constant
•
PI control
–
Multiply e(t) and its integral by separate constants
–
Avoids bias for step
•
PD control
–
Multiply e(t) and its derivative by separate constants
–
Adjust more rapidly to changes
•
PID control
–
Multiply e(t), its derivative and its integral by separate constants
–
Reduce bias and react quickly
41
Dan O.
Popa, EE 1205 Intro. to EE
Conclusion: Control Systems
•
Abstraction is the basis for system level thinking. Abstraction requires
advanced mathematics, and it is especially required of Electrical and
Computer Engineers.
•
Control Theory contains abstractions and generalizations able to
guarantee predictable performance of systems under control.
•
Negative feedback offers numerous advantages: noise rejection,
robustness to plant variations,
dynamical tracking performance.
•
Examples of popular control schemes include Proportional

Integral

Derivative (PID) schemes.
•
Modern control is primarily based on time

domain analysis of state

equations using matrices.
•
Control engineers can find jobs in any industry. Control concepts can be
applied in any engineering industry.
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