Arizona State University

EEE120 Roadmap: Topics, Terminology, Assignment/Exam Schedule, and General Information

The purpose of the following roadmap is to provide you with a detailed list of topics and terms (terminology, jargon) which you should use to guide you in your studying. You are responsible for learning all terms. The roadmap lets you know what topics we will cover and the general order in which we will cover them. Topics listed below may be rearranged as the semester progresses - depending on class needs. Finally, the roadmap provides you with an assignment/exam schedule and general course information.

WEEK 1 - January 19

Big Picture, Introduction to Feedback and Feedback Systems, Plant, Control, Input, Forcing Function, Output, Disturbances Modeled at Plant Input/Output, Measurement, Sensor Noise, Sensor, Compensator, Unity Feedback, Negative Feedback, Error Signal, Reference Command, Tracking Error, Command Following, Disturbance Rejection, Noise Attenuation, Closed loop stability, Uncertainty, Unmodelled Dynamics, Stability Robustness, Performance Robustness, Fundamental Problem and Issues

Block Diagram Algebra, Relationship between internal signals and external (exogenous) signals, Mason's rule, Sensitivity Function, Complementary Sensitivity Function

HOMEWORK #1
EEE120 Exam #1, Fall 1997
Problem 1 - Laplace, ODEs, Steady State Analysis
Problem 2 - Method of the Transfer Function, Steady State Analysis
Problem 3 - Step Response For High Order System
Problem 4 - Steady State Analysis, Internal Model Principle

EEE120 Final Exam, Fall 1997
Problem 1 - Laplace, ODEs
Problem 2 - Feedback System, Laplace, ODEs, Steady State Analysis

These problems are due in two (2) weeks. Your first objective should be to learn to do problems on EEE120 Exam #1 from Fall 1997 as soon as possible.

WEEK 2 - January 26

Modeling of Dynamical Systems, Input/Output Models, Differential Equations, State Space Models, Cruise Control: An Introductory Example, Simple Model for a Car

Review of Laplace transforms, signals, unit step function, delta distribution (impulse function), impulse family (higher order deltas), real exponentials, introduction to stability ideas, unstable, stable, marginally stable, complex arithmetic, Eulers formulae, complex exponentials, sinusoids, ramps, parabolic signals, region of convergence

Laplace transform properties, multiplication by an exponential - s shift, time multiplication - differentiation in s-domain, differentiation in time - multiplication by s in s-domain, Derivative theorem, Integrators, Differentiators, Time delay theorem, Convolution theorem, Initial Value Theorem, Final Value Theorem

Inverse transforms, Long division, Partial fraction expansions, Solution of Ordinary Differential Equations (Odes) via Laplace, Linear Time Invariant (LTI) Systems

Zero input response (ZIR), Initial conditions, Zero state response (ZSR), Transfer functions, Convolution, Characteristic equation, Poles, Natural modes, Cruise Control System: Analysis of a Feedback System

Steady State Analysis/Calculations, Method of the Transfer Function, Sinusoidal Steady State Analysis, Particular Solutions for Ordinary Differential Equations (ODEs) with Constant Coefficients, Introduction to Frequency Responses

Car Model revisited, State Space, Input/Output to State Space, State Space to Input/Output

Cruise Control System: Analysis of a Feedback System, Proportional Controller, Speed Command Following

WEEK 3 - February 2

Why Feedback? Stabilization, Command Following, Disturbance Rejection, Sensitivity Reduction, An Example: Stabilization of an Unstable Plant, Proportional Control, Minimum gain (bandwidth) to stabilize

Example Continued, Low Frequency Command Following and Disturbance Rejection

WEEK 4 - February 9

Cruise Control Example Revisited, Integral Controller, Step Command Following, Ramp Command Following, Steady State Tracking Error

The Internal Model Principle, Command Following, Disturbance Rejection

Introduction to Root Locus (RL), 1st Order Systems, 2nd Order Systems, Open Loop Poles, Open Loop Zeros, Poles Move Toward Zeros, Stability Robustness with respect to Gain Uncertainty, Gain Margins, Upward Gain Margin, Downward Gain Margin, Imaginary (Phase) Crossovers, Phase Crossover Frequencies, Breakpoints, Complementary Root Locus (CRL)

Stabilizing a system with a Right Half Plane Pole, Gain Stabilization (Proportional Control), Proportional plus Integral (PI) Control, Minimum Gain to Stabilize

System with a Right Half Plane Zero, Destabilization from Increasing Gain, Time Delays

Application of Root Locus Ideas to RLC Circuit, Dependence of Roots on Resistance, Introduction to Damping Ideas, Undamped, Underdamped, Critically Damped, Overdamped

WEEK 5 - February 16

Simple Root Loci continued: 2nd Order Systems

Simple Design Problems

Performance Specifications, Transient Specifications

1st Order Systems: Transient Specifications, Impact of Pole, Time constant, Step response, Settling time, Rise time, Impulse response, Impact of Zero

Examples of 1st order systems: RC circuit - voltage input/voltage output, temperature in a semiconductor fabrication furnace - heat input/temperature output, automobile - force input/speed output, dc motor - voltage input/shaft speed output, airplane - elevator input/altitude output

Standard 2nd Order System: Transient Specifications, Impact of Poles, Damping Factor, Undamped Natural Frequency, Damped Natural Frequency, Nature of roots and dependence on Damping Factor, Overdamped Poles, Critically damped Poles, Underdamped Poles, Undamped Poles, Overshoot, Visualization in complex s-plane, Time to Peak, Overshoot Formula

Examples of 2nd order systems: Car-engine system, DC motor, inverted pendulum

Performance Specifications, Steady State Specifications, Final Value Theorem, Analysis of Feedback Systems

Example: Cruise Control with Integral Controller, Design for Overshoot

WEEK 6 - February 23

Example: Cruise Control with PI Control

Review for EXAM #1

WEEK 7 - March 2

EXAM #1
Topics - Laplace transforms, ODEs, block diagrams, feedback systems, steady state analysis, method of the transfer function, internal model principle, simple design problems, overshoot, simple root loci problems for low order systems.

WEEK 8 - March 9

Introduction to Root Locus Method, Effects of High Frequency Dynamics, 3rd Order System Example, Imaginary Crossovers

WEEK 9 - March 16 (Spring Break)

Please go over Root Locus Rules (see Root Locus Method Handout), Routh Tables, and Bode Plots.

WEEK 10 - March 23

1st, 2nd, and 3rd Order Root Locus Examples Revisited

Root Locus Deformation Concepts

Root Loci Examples, Low and high frequency approximation ideas, Root loci for complex systems, unmodeled dynamics, High frequency actuator dynamics and structural modes

Compensator Implementation Issues: Derivative Action - Feedback, Series, and Feedforward Compensation Structures

Right half plane pole-zero cancellations are not allowed, Can't invert non-invertible stuff!

The Root Locus Method, open loop poles and zeros, closed loop poles, poles move toward zeros, angle criterion, real-axis rule, positive gain rule, negative gain rule, number of loci, number of asymptotes, imaginary crossovers, phase crossover frequecies, angle of asymptotes, center of gravity, break points, magnitude condition, stability summary

Routh Table and Routh Stability Criterion, Computation of Imaginary Crossovers via Routh

Introduction to Frequency Response Methods: Bode Plots, Magnitude approximation ideas, Bode asymptotes for magnitude, systems with 1st order and 2nd order (Overdamped and Critically damped) terms, break frequencies, corrections, gain crossover frequencies, estimation of gain crossover frequencies

Stable Minimum Phase Systems

Phase approximation ideas, Bode asymptotes for phase, phase crossover frequencies, Approximation of imaginary crossovers using Bode asymptotic phase ideas

Stability Robustness: Gain Margins - measured at phase crossovers, Phase Margin - measured at gain crossover, Delay Margin

Root Locus and Bode Plots: Determining Imaginary crossovers from a Bode Plot

Design Problems

WEEK 11 - March 30

Bode Plots for Systems with 2nd Order Underdamped Terms, Resonances due to lightly damped poles, Notches due to lightly damped zeros

Bode Plots for higher order systems

Unstable Systems, Nonminimum Phase Systems

Fitting a Stable Minimum Phase Transfer Function to a Magnitude Response

WEEK 12 - April 6

Nyquist (Polar) Plots, Stability Robustness

Root Locus, Bode Plots, Nyquist Plots

High Frequency Unmodeled Dynamics, Small Gain Theorem: A Stability Robustness Tool

WEEK 13 - April 13

Nyquist Stability Criterion

Stability Summary

Review for EXAM #2

WEEK 14 - April 20

Uncertainty, Design, PID Controllers, Lead-Lag Design

Design Problems

EXAM #2
Topics: Performance Specifications, Transient Specifications, Steady State Specifications, Second Order Systems, Overshoot, Root Locus Rules, Imaginary Crossovers, Phase Crossover Frequencies, Routh Table, Bode Plots, Approximation Ideas, Gain Crossover Frequencies, Simple Design, PID Controllers, Design Implementation, Feedback Compensation, Series Compensation, Feedforward Compensation, Stability Margins

WEEK 15 - April 27

Design Examples

EXAM #3
Topics: Feedback System Transient and Steady State Analysis, Compensator Design, Root Locus, Bode, Nyquist. This exam is intended to be a review for the final exam!

WEEK 16 - May 4

Design Examples

Nonlinear Design, Linearization, Saturating Actuators, Case Studies: Helicopter and Inverted Pendulum, Final Project

Review for FINAL EXAM

TENTATIVE DATES FOR EXAMS

• EXAM #1 - week 7 (Thursday, March 5)
• EXAM #2 - week 14 (Thursday, April 23)
• EXAM #3 - week 15 (Thursday, April 30) - a review for the final!

ALL EXAMS ARE TO BE REDONE AT HOME BY EACH STUDENT. THE REDONE EXAMS WILL BE COLLECTED THE FOLLOWING CLASS. ALL REDONE EXAMS SHOULD REPRESENT THE EFFORT OF THE INDIVIDUAL STUDENT. REDONE EXAMS WILL BE REGARDED AS THE TAKEHOME PORTION OF THE IN CLASS EXAM. PLEASE TAKE THE REDOING SERIOUSLY.

FINAL EXAM - week 16 (Friday, May 8th 10:00 - 11:50 AM, JWS 150)

RESOURCES PERMITTED DURING EXAMS

• ONE SHEET. You are permitted one (1) 8.5" x 11" x 0" sheet on each exam...just one. You may write as small as your eyes will allow you to write.
  
  
• CALCULATORS. You will also be permitted to use calculators or handheld supercomputers on each exam. I strongly recommend that everyone have a good programmable calculator that they know how to use! In this class, you need to be able to find the roots of any polynomial!

GRADING

ADDITIONAL CONTACT

EEE120 Lab GWC-273 965-4375

EEE120 LAB HOURS

TEXTBOOK

"Digital Devices and Systems with PLD Applications," Michael A. Miller, Delmar Publishers, 1997.

FUNDAMENTAL MATERIAL FROM TEXT

MAIN REFERENCE AND SOURCE OF LEARNING

Problems from previous in class exams, takehome exams, and final exams. You will have solutions to most of these. I will assign homework problems from these. Please do not just copy my solutions. Please attempt to understand the main points in the solutions. My solutions, as you will see, are long. They are long because I attempt to make them very complete and self-contained. Most of your learning should come from working out these exam problems.

LOGISTICS: GETTING COURSE MATERIAL

Material will be periodically placed at the Noble Library Copy Center. Please call the Noble Library before making a special trip to pick up course material.

The Noble Library Copy Center Phone Number is 965-7497.

Material which is copyrighted will be left at the Noble Library reserve desk for you to xerox yourselves.

Efforts are being made to make all material available over the web and on CD ROM.

REFERENCES

• Alan V. Oppenheim and Alan S. Willsky with S. Hamid Nawab, Signals and Systems, Prentice Hall, 2nd Edition, 1997.
  
  
• Katsuhiko Ogata, Modern Control Engineering, Prentice Hall, 3rd Edition, 1997.
  
  
• John J. D'Azzo and Constantine H. Houpis, Linear Control System Analysis & Design: Conventional and Modern, McGraw Hill,3rd Edition,1988.
  
  
• Charles E. Rohrs, James L. Melsa, and Donald G. Schultz, Linear Control Systems, McGraw Hill, 1993.
  
  
• Richard C. Dorf and Robert H. Bishop, "Modern Control Systems," Addison Wesley, 8th Edition, 1998.
  
  
• J. Schwarzenbach, "Essentials of Control," Addison Wesley Longman, 1996.
  
  

EXAMS FROM PREVIOUS YEARS

After each test the test questions and answers will be posted here.

• Fall 1991 Exam #1
• Fall 1992 Exam #1, Exam #2, Final
• Spring 1995 Exam #1, Exam #2, Final
• Fall 1995 Exam #1, Exam #2, Final
• Fall 1997 Exam #1, Exam #2, Final

MATLAB M-Files

1. Introduction to Exponential Functions
2. Step Response For First Order System H(s) = a / (s+a) (a > 0) For Different Values of Parameter a, Speed of Response Decreases With Increasing a
3. Frequency Response For First Order System H(s) = a / (s+a) (a > 0) For Different Values of Parameter a, System Bandwidth Increases With Increasing a
4. Pole Dependence on Damping Factor for Standard Second Order Systems
5. Step Response Dependence on Damping Factor for Standard Second Order Systems, Dependence of Overshoot on Damping Factor (Undamped/Underdamped Case)
6. Step Response of a Second Order Underdamped System With Zero In Numerator, Effect of Zero On Step Response, As zero moves further into left half plane its derivative action becomes less pronounced, As zero moves closer to origin its derivative action becomes more pronounced.
7. Root Locus For Nominal Second Order System - Nominal CLS Stable for all Non-negative k, Effect of A Third Pole - CLS Goes Unstable For Large k, Effect of Varying Third Pole With Gain k Fixed
8. Feedforward Compensation Can Reduce Overshoot Caused By Zero (Derivative Action) In Series PI Compensator, Closed loop response to step reference command: (i) with series and no feedforward compensation, (ii) with series and feedforward compensation
9. Introduction to Routh Table: Some Examples
10. Introduction to Frequency Responses: Some Simple SISO Systems
11. Visualization of Typical Open and Closed Loop Frequency Responses: First Order Unstable Plant With Proportional Controller (Open Loop, Sensitivity, Complementary Sensitivity, Input Disturbance to Tracking Error, Reference to Control)
12. Reading Off Stability Margins from A Frequency Response: Unstable Second Order Nonminimum Phase System, Relating Bode and Root Locus Ideas
13. Frequency Response For Second Order Systems In Standard Form
14. Macros Associated With Exam Problems

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    RELEVANT WEB SITES

    Control Tutorials (Carnegie Mellon University, University of Michigan)
    
    Demonstrations in Signals, Systems and Control (Johns Hopkins University)
    
    • System Properties
      
    • Effect of Poles and Zeros on the Step Response of a Finite Dimensional LTI System
      
    • Effect of Open Loop Frequency Response on Closed Loop Properties
      
    
    

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    ADDITIONAL NOTES AND HANDOUTS

    • Laplace Transforms
    • The Root Locus Method
      
    Return to Table of Contents.
    

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    Many exams, problems, and notes on this page can be read using Adobe's Acrobat Reader. A free copy of this program can be downloaded from Adobe for your computer (e.g. Windows 3.1, 95, NT, Mac, Unix).

    Return to Table of Contents.

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    A FINAL NOTE

    I hope that this ROADMAP is helpful. Any feedaback would be greatly appreciated. I hope that you all have a great semester. I will do my best to help you...please help me by asking questions.
    
    Thank you folks.
    
    AAR
    
    

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