Transcript EE 3417: Linear Systems Continuous Signals and Systems Lectures: Tue/Thu, 12:30-1:50 pm, NH 229 Instructor: Dan Popa, Ph.D., Associate Professor, EE Course TAs: Rommel.

EE 3417: Linear Systems
Continuous Signals and Systems
Lectures: Tue/Thu, 12:30-1:50 pm, NH 229
Instructor: Dan Popa, Ph.D., Associate Professor, EE
Course TAs: Rommel Alonzo, Yathartha Tulhadar
Lab/Recitation Section for EE 3417 students, Tue/Thu 11:00-12:20, 2:003:20 – ELAB 256
Instructor Office hours: Tue/Thu 9:30-11 am NH543
Course info: http://www.uta.edu/faculty/popa/linsys
Grading policy:
6 Homeworks – 20%
Midterm 1 (in-class) – 20%
Midterm 2 (take-home) – 20%
6 Quizzes – 20%
Final (in-class) – 20%
Grading criteria: on curve based on class average, generally
>80% will be an A, 60-80% B, 50-60% C, 30-50% D, <30% F.
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Syllabus
• Assignments:
– Homeworks: 6 Homeworks contain both written and/or computer
simulations using MATLAB. Submit code to TA’s if it is part of the
assignments.
– Reading Assignments: After each course. The assigned reading
material is given out in order to make you better understand the
concepts. Materials from the reading assignments may be part of
course exams.
– Examinations: Midterm 1(in-class), Midterm 2 (take-home), 6
quizzes (at lab for EE 3417) and one final (in-class).
– EE 3417 students – LAB session in ELAB 256, Tue/Thu, covers
– problems (recitation), MATLAB and SIMULINK, LABVIEW
– In rare circumstances (medical emergencies) exams may be
retaken and assignments can be resubmitted without penalty.
– Missed deadlines for take-home exams and homeworks:
Maximum grade drops 25% per late day.
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Honor Code
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Academic Dishonesty will not be tolerated. All homeworks and exams are
individual assignments. Discussing homework assignments with your
classmates is encouraged, but the turned-in work must be yours. Discussing
exams with classmates is not allowed. Your take-home exams and homeworks
will be carefully scrutinized to ensure a fair grade for everyone.
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Random quizzes on turned-in work: Every student will be required to answer
quizzes in person at least twice during the semester for homework and take
home exam. You will receive invitations to stop by during office hours. Credit for
turned in work may be rescinded for lack of familiarity with your submissions.
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Attendance and Drop Policy: Attendance is not mandatory but highly
encouraged. If you skip classes, you will find the homework and exams much
more difficult. Assignments, lecture notes, and other materials re going to be
posted here, however, due to the pace of the lectures, copying someone else's
notes may be an unreliable way of making up an absence. You are responsible
for all material covered in class regardless of absences.
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Textbooks & Description
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Textbook:
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Other materials (on library reserve)
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B.P. Lathi, Linear Systems and Signals, 2nd ed. (required), Oxford Press, ISBN-13: 978-019-515833-5.
Student Edition of MATLAB Version 5 for Windows by Mathworks, Mathworks Staff,
MathWorks Inc.
R.D. Strum, D.E. Kirk, Contemporary Linear Systems using MATLAB, PWS Publishing,
1994, ISBN: 0-534-93273-8.
B.W. Dickinson, Systems: Analysis, Design and Computation, Prentice Hall, 1991, ISBN: 013-338047-5.
G.F. Franklin, J.D. Powell, A. Emami-Naeni, Feedback Control of Dynamic Systems, 5th
edition, Prentice Hall, 2006, ISBN: 0-13-149930-0.
Catalog description:
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EE 3317. LINEAR SYSTEMS (3-0) For non-electrical engineering majors. Time-domain
transient analysis, convolution, Fourier Series and Transforms, Laplace Transforms and
applications, transfer functions, signal flow diagrams, Bode plots, stability criteria, and
sampling. Classes meet concurrently with EE 3417.
EE 3417 CONTINUOUS SIGNALS AND SYSTEMS (3-3) Time-domain transient analysis,
convolution, state-space analysis, frequency domain analysis, Laplace transforms and
transfer functions, signal flow and block diagrams, Bode plots, stability criteria, Fourier series
and transforms. Applications from control systems and signal processing. Problems and
numerical examples using MATLAB will be covered during recitation and computer
laboratory sessions.
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Description & Prerequisites
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This is an introductory signal and systems course. It presents a broad
overview of continuous linear systems concepts and techniques, and
focuses on fundamentals such as time-domain and frequency domain
analysis, stability, and discretization (sampling).
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The course material is divided between several areas:
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Signals and systems: classification, manipulation, modeling
Continuous time-domain analysis of systems
Continuous frequency domain analysis of systems
Sampling and Fourier analysis of signals
Programming excercises using MATLAB
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ME Majors Prerequisite: Grade C or better in MATH 3330, ME Majors
Corequisite: EE 2320 or equivalent. BE Majors Prerequisite: Grade C or
better in MATH 3319.
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EE 3417 prerequisite: Grade C or better in both EE 2347 and EE 2415.
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Tentative Course Schedule
Part 1: Introduction and Systems Analysis in the time domain
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Week 1 - August 27, Lecture 1
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Week 2 - Sept 1, 3 Lectures 2,3
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Review of basics: Matrix and vector algebra, complex numbers, integrals and series.
(Background), MATLAB programming
Homework #1 handed out on Sept 1
Week 3 - Sept 8, 10, Lectures 4,5
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Introduction to signals and systems, syllabus and examples.
Signals: classification, operations, standard signals (Chapter 1)
Operations: Time Shifting, Scale, Reversal
Classification: analog, digital, periodic, aperiodic, finite, infinite, causal, anticausal, energy and
power signals, deterministic and stochastic.
Measures: Power, Energy
Signal spaces
Week 4 - Sept 15, 17, Lectures 6, 7
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Signal Models, step, impulse, exponential, odd, even functions
Quiz 1 @ Lab: Signals Sept 15
Systems: properties and classification (Chapter 1)
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LTI/LTV, memory/dynamic, causal/anticausal, invertible/non-invertible
Basic models: electrical/mechanical, internal and external description
Homework #1 due Sept 15, Homework #2 handed out
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Tentative Course Schedule
Part 1: Introduction and Systems Analysis in the time domain
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Week 5 - Sept 22, 24, Lectures 8, 9
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Week 6 - Sept 29, Oct 1, Lectures 10, 11
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Quiz 2 @ Lab : Systems Sept 22
Time domain analysis of systems: (Chapter 2)
Differential equations and solutions
Response: zero input, impulse response
Time domain analysis of systems: (Chapter 2)
Convolution integral
Response: zero state
Stability: internal/external
Intuitive insights into system behavior
Homework #2 due Sept 29, Homework #3 handed out
Week 7 - Oct 6, 8, Lectures 12, 13
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Quiz 3 @ Lab: Time Domain I/O Analysis of Systems, Oct 6
State space analysis of systems: (Chapter 10)
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State equations, Time domain and solutions
System realizations
Review list for Midterm 1
Week 8 - Oct 13, 15, Lectures 14, 15
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Homework #3 due Oct 13,
In-class Midterm on Oct 13: covers: basic signals, systems, time-domain analysis.
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Tentative Course Schedule
Part 2: System Analysis in Frequency Domain
• Week 8 - Oct 13, 15, Lectures 14, 15
– Homework #4 handed out Oct 15
– Frequency domain analysis of systems: (Chapter 4)
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Laplace transform
• Week 9 - Oct 20, 22, Lectures 16, 17
– Quiz 4 @ Lab: Laplace transforms Oct 22
– Frequency domain analysis of systems: (Chapter 4)
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Properties and use of Laplace transform
Transfer functions and block diagrams
Frequency response - Bode plots
• Week 10 - Oct 27, 29, Lectures 18, 19
– Homework #4 due Oct 29 , Homework #5 handed out
– Frequency domain analysis of systems:
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Application to feedback control
Applications to filter design
• Week 11 - Nov. 3, 5 Lectures 20, 21
– State space analysis of systems: (Chapter 10)
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Frequency Domain Solutions
– Midterm II (Take-home) handed out Nov 5, covers frequency domain.
– Homework #5 due Nov. 5
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Tentative Course Schedule
Part 2: System Analysis in Frequency Domain
• Week 12 - Nov. 10, 12 Lectures 22, 23
– Midterm #2 due Nov. 10 in class. Midterm 2 grades will be returned
only by appointment (see instructions).
– Homework #6 handed out on Nov. 10
– Fourier analysis of signals (Chapter 6)
• Fourier series: existence, calculation
• Trigonometric and exponential series
• Fourier series: convergence
• Week 13 - Nov. 17, 19 Lectures 24, 25
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Parseval's theorem
LTI system response to periodic inputs
Quiz 5 @ Lab: Fourier Series, Nov 19
Fourier analysis of systems (Chapter 7)
• The Fourier Transform and its properties
• Connection between Laplace and Fourier Transform
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Tentative Course Schedule
Part 2: System Analysis in Frequency Domain
• Week 14 – Nov. 24, Lecture 26
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Application to signal processing: filters and window functions
Parseval's Theorem
Homework #6 due Nov. 24
• Week 15 - Dec 1, 3 Lectures 27, 28
– Quiz 6 @ Lab: Fourier Transforms, Dec 1
– Sampling (Chapter 8)
• Week 16 - Dec 8 Lecture 29
– Couse Recap
• Week 17- Dec 14
– Final exam (in-class) (comprehensive) TBD
– Bring a 5-page, double-sided cheat sheet, handwriting only
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Course Objectives
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Ability to analyze systems using time-domain methods including
impulse response and convolution.
Ability to analyze systems using Laplace-domain methods
including transfer function and related concepts.
Ability to analyze systems using frequency-domain methods
including frequency response of a system and Bode plots.
Ability to describe systems using modern state-space approaches.
Ability to analyze signals using Fourier series and Fourier
transform.
Ability to appliy systems analysis tools to solve engineering
problems.
Ability to use MATLAB as an engineering tool.
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Textbook Reading and Review
• Course Refresher:
– Math: complex numbers, matrix algebra, vectors and
trigonometry, differential equations.
– Programming: MATLAB
• For weeks 1,2
– Read Preface, and Background section of Textbook
• Purpose of weekly assigned textbook readings
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To solidify concepts
To go through additional examples
To expose yourselves to different perspectives
Reading is required. Problems or questions on exams might
cover reading material not covered in class.
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Research in Multiscale Robotics and
Systems – Next Gen Systems (NGS)
Tools and Fundamentals
Established Technologies
Modeling & Simulation
Microsystems &
MEMS
Robotics
Control Systems
Control Theory
Nanotechnology
Manufacturing &
Automation
Algorithms
Sensor networks
New applications
for small-scale
systems
Emerging Technologies
Surgical robotics
Human-like robots
Distributed systems
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Biotechnology
Micromanufacturing
Microrobotics
Microassembly
Micropackaging
Sensors & Actuators
NanoManufacturing
Small-scale
Robotics &
Manufacturing
Micro-Robotics at Next Gen Systems (NGS)
IEEE Mobile Micro-Robotics Challenge
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Wireless, fully autonomous mobile microrobots.
Mobility
Challenge
Vibration
Actuated
Micro
Assembly
Event
Laser
Actuated
Dan O. Popa, Linear Systems EE 3417, Fall 2015
05/05/11
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“Manufacturable” microrobot families at NGS
Family of Microrobots made by
assembly and 3D die/wafer stacking
Copter
quad rotor
Pede
Microcrawler
Blimp
Microballoon
Cover (handle)
Channels
O/P Port
(+x)
Cover (device)
O/P Port
(-x)
Actuator (device)
Actuator (handle)
Dan O. Popa, Linear Systems EE 3417, Fall 2015
11/6/2015
15
Human Robot Interaction Research @ NGS
Co-botics
w/
Physical
Interaction
Advanced
HumanRobot
Interfaces
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Realistic &
Intuitive
HumanRobot
Interaction
Real-Time
Visual
Servoing
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Lecture 1: Intro to Linear Signals
and Systems
• What are linear systems and why is it important
to study them?
– Signal:
• Conventional Electrical or Optical signals
• Any time dependent physical quantity
– System:
• Object in which input signals interact to produce output
signals.
• Static vs dynamic systems
• 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)
Dan O. Popa, Linear Systems EE 3417, Fall 2015
System Modeling
• Building mathematical models based on
observed data, or other insight for the
system.
– Parametric models (analytical): ODE, PDE
– Non-parametric models: ex: graphical models
- plots, or look-up tables.
– Mental models – Ex. Driving a car and using
the cause-effect knowledge
– Simulation models – ex: Many interconnect
subroutines, objects in video game
Dan O. Popa, Linear Systems EE 3417, Fall 2015
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
Dan O. Popa, Linear Systems EE 3417, Fall 2015
White Box vs Black Box Models
White Box Models
Black-Box Models
Information Source
First Principle
Experimentation
Advantages
Good Extrapolation
Short time to develop
Good understanding
Little domain expertise
High reliability, scalability 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
This course deals with both white and black continuous models which are linear
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Application Areas for This
Course
• 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 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
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Linear vs. Nonlinear
• Why study continuous linear analysis of signals
and systems when many systems are nonlinear
in practice?
– Basis for digital signals and systems
– Many dynamical systems are nonlinear but some
techniques for analysis of nonlinear systems are
based on linear methods
– Methods for linear systems often work reasonably
well, for nonlinear systems as well
– If you don’t understand linear dynamical systems you
certainly can’t understand nonlinear systems
Dan O. Popa, Linear Systems EE 3417, Fall 2015
LTI Models
• Continuous-time linear dynamical system
(LDSC) has the form
dx/dt= A(t)x(t) + B(t)u(t),
y(t) = C(t)x(t) + D(t)u(t)
• where:
– t  R denotes time
– x(t)  Rn is the state (vector)
– u(t)  Rm is the input or control
– y(t)  Rp is the output
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Linear Systems in Practice
• most linear systems encountered are time-invariant: A,
B, C, D are constant, i.e., don’t depend on t
– Examples: second-order electromechanical systems with
constant coefficients
• when there is no input u (hence, no B or D) system is
called autonomous
– Examples: filters, uncontrolled systems
• when u(t) and y(t) are scalar, system is called singleinput, single-output (SISO)
• when input & output signal dimensions are more than
one, MIMO
– Example: Aircraft – MIMO
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Week 1, Lectures 1-2: Review
These lectures cover math concepts related to:
- White Box Systems Examples: RLC circuit, MSD
mechanical system
- 1st order ODE equations – solving
- Review of Taylor series, derivation, integration
- Complex numbers and examples, rings and fields
- Rational polynomials fractions and partial fraction
expansions
- Vectors and matrices, vector spaces, linear mappings
- Systems of linear equations
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Week 1, Lectures 1-2: Review
MATLAB functions:
- Simple commands: whos (who), clear, clf, clc, load, save,
print, plot (xlabel, ylabel, xlim, ylim, semilogx, semilogy,
plot3, contour, legend, )
- Complex numbers: real, imag, conj, abs, angle, log, log10,
cart2pol, pol2cart
- PFE: residue
- Vector operations, element by element operations,
matrices, matrix operations (inv, det).
Dan O. Popa, Linear Systems EE 3417, Fall 2015
Week 1, Lectures 1-2: Reading and
Practice
Reading for week 1:
- Chapter B, Lathi textbook, including:
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MATLAB session B
B.7 tables
B.1-2 – complex numbers
B-5 – PFE
B-6, B-4 – Vectors and Matrices
B-2, B-3 – sinusoids and sketching signals
- Example exercises:
- B.1, B.2: polar to cartesian, cartesian to polar conversion
- B.3, B.4: multiplication/division and addition/subtraction of complex
numbers
- B.5 – Functions of complex variable
- B.8, B.9, B.10 – Partial fraction expansions
- B.12, B.13 – Matrix operations
Dan O. Popa, Linear Systems EE 3417, Fall 2015
MATLAB Exercises
• Run the following MATLAB demos:
– Type “demo” at the MATLAB prompt
– Watch “Getting Started” Videos
– Run as many Simulink Demos as you can.
For each one:
• Double click all the model boxes and look inside
• Try to modify parameters which make sense to you
and see their effects by running the model.
Dan O. Popa, Linear Systems EE 3417, Fall 2015