dan o. popa, linear systems ee 3417, fall 2015 ee 3417 : linear systems continuous signals and...

Dan O. Popa, Linear Systems EE 3417, Fall 2015

EE 3417: Linear SystemsContinuous Signals and Systems

Lectures: Tue/Thu, 12:30-1:50 pm, NH 229 Instructor: Dan Popa, Ph.D., Associate Professor, EECourse TAs: Rommel Alonzo, Yathartha TulhadarLab/Recitation Section for EE 3417 students, Tue/Thu 11:00-12:20, 2:00-

3:20 – ELAB 256Instructor Office hours: Tue/Thu 9:30-11 am NH543Course info: http://www.uta.edu/faculty/popa/linsys Grading policy:

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.

6 Homeworks – 20%Midterm 1 (in-class) – 20%Midterm 2 (take-home) – 20%6 Quizzes – 20%Final (in-class) – 20%


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.


Honor Code

• 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.

• 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 Credit for turned in work may be rescinded for lack of familiarity with your submissions.

• 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.


Textbooks & Description• Textbook:

– B.P. Lathi, Linear Systems and Signals, 2nd ed. (required), Oxford Press, ISBN-13: 978-0-19-515833-5.

• Other materials (on library reserve)– 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: 0-

13-338047-5.– 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: – 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.


Description & Prerequisites• 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).

• The course material is divided between several areas:– 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

• 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.

• EE 3417 prerequisite: Grade C or better in both EE 2347 and EE 2415.


Tentative Course SchedulePart 1: Introduction and Systems Analysis in the time domain• Week 1 - August 27, Lecture 1

– Introduction to signals and systems, syllabus and examples.

• Week 2 - Sept 1, 3 Lectures 2,3 – 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 – 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– Signal Models, step, impulse, exponential, odd, even functions– Quiz 1 @ Lab: Signals Sept 15– Systems: properties and classification (Chapter 1)

• 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


Tentative Course SchedulePart 1: Introduction and Systems Analysis in the time domain• Week 5 - Sept 22, 24, Lectures 8, 9

– Quiz 2 @ Lab : Systems Sept 22– Time domain analysis of systems: (Chapter 2)– Differential equations and solutions– Response: zero input, impulse response

• Week 6 - Sept 29, Oct 1, Lectures 10, 11– 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 – Quiz 3 @ Lab: Time Domain I/O Analysis of Systems, Oct 6– State space analysis of systems: (Chapter 10)

• State equations, Time domain and solutions• System realizations

– Review list for Midterm 1

• Week 8 - Oct 13, 15, Lectures 14, 15– Homework #3 due Oct 13, – In-class Midterm on Oct 13: covers: basic signals, systems, time-domain analysis.


Tentative Course SchedulePart 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)

• Laplace transform

• Week 9 - Oct 20, 22, Lectures 16, 17 – Quiz 4 @ Lab: Laplace transforms Oct 22– Frequency domain analysis of systems: (Chapter 4)

• 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:

• Application to feedback control• Applications to filter design

• Week 11 - Nov. 3, 5 Lectures 20, 21– State space analysis of systems: (Chapter 10)

• Frequency Domain Solutions

– Midterm II (Take-home) handed out Nov 5, covers frequency domain.– Homework #5 due Nov. 5


Tentative Course SchedulePart 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– 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


Tentative Course SchedulePart 2: System Analysis in Frequency Domain• Week 14 – Nov. 24, Lecture 26

– 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


Course Objectives

1. Ability to analyze systems using time-domain methods including impulse response and convolution.

2. Ability to analyze systems using Laplace-domain methods including transfer function and related concepts.

3. Ability to analyze systems using frequency-domain methods including frequency response of a system and Bode plots.

4. Ability to describe systems using modern state-space approaches.

5. Ability to analyze signals using Fourier series and Fourier transform.

6. Ability to appliy systems analysis tools to solve engineering problems.

7. Ability to use MATLAB as an engineering tool.


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– 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.


Research in Multiscale Robotics and Systems – Next Gen Systems (NGS)

Robotics

Control Systems

Manufacturing & Automation

Established Technologies Emerging Technologies

Micromanufacturing

Microrobotics

Microassembly

Micropackaging

Sensors & Actuators

NanoManufacturing

Microsystems & MEMS

Nanotechnology

Biotechnology

Small-scale Robotics & Manufacturing

Modeling & Simulation

Control Theory

Algorithms

Tools and Fundamentals

Sensor networks

Surgical robotics

Human-like robots

Distributed systems

New applicationsfor small-scale systems


Micro-Robotics at Next Gen Systems (NGS)

05/05/11 14

Mobility

Challenge

Micro

Assembly

Event

Vibration

Actuated

Laser

Actuated


“Manufacturable” microrobot families at NGS

04/19/23 15

Copter

quad rotor

Pede

Microcrawler

Blimp

Microballoon

Family of Microrobots made by assembly and 3D die/wafer stacking

Cover (handle)

Cover (device)

Actuator (handle)

ChannelsO/P Port (+x)

O/P Port (-x) Actuator (device)


Human Robot Interaction Research @ NGS

16


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)


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


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


White Box vs Black Box Models

White Box Models Black-Box Models

Information Source First Principle Experimentation

Advantages Good ExtrapolationGood understandingHigh reliability, scalability

Short time to developLittle domain expertise requiredWorks 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 processesExisting systems

This course deals with both white and black continuous models which are linear


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


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


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


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 single-input, single-output (SISO)

• when input & output signal dimensions are more than one, MIMO– Example: Aircraft – MIMO


Week 1, Lectures 1-2: ReviewThese 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


Week 1, Lectures 1-2: ReviewMATLAB 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).


Week 1, Lectures 1-2: Reading and Practice

Reading for week 1:- Chapter B, Lathi textbook, including:

- 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


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 ee 3417 : linear systems continuous signals and...

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