Course refresher

deadmancrossingraceΤεχνίτη Νοημοσύνη και Ρομποτική

13 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

98 εμφανίσεις

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.