EEE-480/591: Feedback Control Systems
Arizona State University
EEE-480/591: Feedback Control Systems
Table of Contents
Course Objective
Prerequisites and Assessment Quiz
Selected Topics
Roadmap
Textbook
Laboratories
Matlab M-files
Class Notes/Exams/Homework
Videos
Related Materials
References
Under Development
Course Objective
This course is designed to provide students with an understanding of fundamental principles, concepts, and techniques for feedback system analysis and design. Emphasis will be placed on relating engineering concepts to real-world problems and applications. Practical computer aided analysis and design will be a central component of the course. Application areas include: robotics, aerospace systems, and semiconductor manufacturing processes.
Guiding Principles: Philosophy, Approach, and Perspective
The following principles will be used to guide all developments:
- Material will proceed from particular (concrete) examples to more general (abstract) examples.
- All concepts will be motivated via simple examples.
- Progressively complex examples will be used to illustrate how ideas, concepts, and techniques
may be readily applied.
- Emphasis will be placed on relating mathematical and engineering concepts to real-world applications.
- Emphasis will be placed on computer aided analysis and design.
- Visualization will be used to reinforce concepts and to enhance the learning process.
- ``Mulitple concept examples'' will be used to cover essential (fundamental) ideas as quickly as possible.
This will permit students to cover main ideas in a short period - providing crucial perspective and
leaving time to focus on applications to real problems. By so doing, it will permit us to spend more time on how ideas, concepts, techniques are used to address real-world problems.
It is hoped that this should enhance integration and coherence as well.
Prerequisites and Assessment Quiz
PREREQUISITES
While each of the following topics will be visited, students are expected to be familiar with:
- Ordinary differential equations, elementary Laplace transforms, system concepts (e.g. linearity, time invariance, transfer function, poles, zeros, stability, impulse response, step response, sinusoidal analysis, etc.), complex arithmetic.
RULES FOR 480 ASSESSMENT QUIZ
Here is information regarding the upcoming EEE480 Assessment Quiz (next week).
NOTE:
Studying for your assessment quiz will significantly help you with the course material.
Come see me if you need suitable references to study from.
In order to better understand the concepts, it is highly recommended to make use of the resources available in the lab website.
The INTERACTIVE EXAMPLES (Wolfram demo programs) can be accessed from Lab Website -> Resources -> Matlab M-files
(Note: You need to view the site with IE or Firefox, and need to download the Wolfram plugin to see the interactive programs. If you see a warning about security, make sure you allow all contents to be displayed)
MATERIAL FOR EEE480 ASSESSMENT QUIZ
:
Solving a first order differential equation
Basic transform concepts
Transfer function
Poles
Zeros
Linearity
Zero input response
Zero state response
General solution
Stability
Step response
Time constant
Settling time
Frequency response
Magnitude and phase
Steady state response to a constant input
Steady state response to a sinusoidal input
3dB frequency
Unity gain crossover frequency
Complex Arithmetic
45-45-90 right triangle
30-60-90 right triangle
37-53-90 (3-4-5) right triangle
Block diagram algebra (including feedback loop)
RLC Circuit Transfer Function
Selected Topics
- Need for Feedback
- Laplace Transforms and LTI Concepts
- Modeling of Dynamical Systems
- Fundamental Feedback Concepts
- Root Locus, Bode Plot, and Nyquist Methods
- Design Examples and Applications
Learning Objectives
Upon successful completion of this course, the student will be able to
- Model a variety of dynamical systems.
- Analyze and design automatic control systems.
- Use state-of-the-art computer aided analysis and design tools
for control system analysis and design.
- Implement practical control systems.
Roadmap, Topics, Terms, and Assignments
- Fundamental Feedback System Concepts (5 Weeks, 10 Lectures, 1 credit)
The purpose of this module is to provide an overview of fundamental feedback control system analysis and design concepts. Students will be exposed to block diagram analysis, analysis using Laplace transforms, modeling of dynamical systems, linearization, transient analysis, sinusoidal steady state analysis, stability, design specifications, internal model principle, root locus and Bode plot analysis, polar plots, stability margins, and computer aided design. All concepts are motivated via simple examples which are made progressively more complex to illustrate real-world problems and issues. Application areas will include robotics, aerospace systems, and semiconductor manufacturing. Upon successful completion of this module, students will be able to analyze and design simple control systems using computer aided analysis and design tools.
- Analysis and Design Tools (5 Weeks, 10 Lectures, 1 credit)
The purpose of this module is to develop an in-depth understanding of classical control
methods and their application to real-world engineering problems. Methods to be covered include the Root Locus method, Bode plot methods, Nyquist methods. Application areas will include robotics, aerospace systems, and semiconductor manufacturing. Upon successful completion of this module, students will be able to analyze and design control systems (of intermediate complexity) using computer aided analysis and design tools.
- Control System Design (5 Weeks, 10 Lectures, 1 credit)
The purpose of this module is to develop expertise in designing
relatively complex control systems. Design methods will include lead-lag design and loop shaping methods. Application areas will include robotics, aerospace systems, and semiconductor manufacturing. Upon successful completion of this module, students will be able to design relatively complex control systems using computer aided analysis and design tools.
- Laboratory ( 1 credit)
The purpose of the laboratory is to master computer aided control system analysis and design tools.
Emphasis will be placed on real-world problems and applications. Upon successful completion of this module, students will be able to analyze and design relatively complex control systems using state-of-the-art computer aided analysis and design tools.
Future Updates
This roadmap will be updated as the semester progresses. All updates will be publicized via email.
Textbook
A.A. Rodriguez, ``Analysis and Design of Feedback Systems,'' Control3D, 2003.
Laboratories
The EEE480 laboratory is VERY DIFFERENT! It is a fun laboratory!
The purpose of the lab is to teach students how to design and implement
practical control systems.
Goals of the lab are to:
- shed light on material covered in lectures and homeworks; i.e. connect
theory with reality;
- prepare students for exams;
- master state-of-the-art control system design tools (e.g. MATLAB,
SIMULINK, Control System Toolbox, etc.);
- prepare students for a neat senior design project;
- HAVE FUN!
TA: Karan Puttannaiah - kputtann@asu.edu
Location: GWC 379
Lab Software
In this lab,we use ModelExplorer to analyse systems and controllers for all the lab exercises. The latest version of ModelExplorer can be downloaded from BlackBoard (you will need an ASU ID to access the website). The screenshot below shows the ModelExplorer main screen. Some features of ModelExplorer are:
- Easy analysis of systems - one click plotting of time domain and frequency domain responses, root loci, nyquist plots.
- Impact of different designs - specify the plant/controller and easily study all the important properties of the system with just a few clicks.
- Saving your work - Simple to save a copy of your work so you can resume anytime, without starting from scratch.
- Easy access to references - Directly access relevant references (websites, documents, videos) from within ModelExplorer.
- Animations - All lab modules come with animations to help visualize the systems so you can easily see the impact of your designs in a real-world setting.
- Matlab based - Since ModelExplorer runs from Matlab, it works on Windows, Linux and Macs, so that you can use the system of your choice.
(Click for a larger image)
Several demonstration videos below show some of the features of ModelExplorer and how they are used with the lab.
Cruise Control for a Car
In this lab, we look at designing a cruise control system for a car. The model for this lab is one of the pre-installed models for ModelExplorer, and can be
loaded from the Model menu. This lab supports real-world effects like comparing linear and nonlinear models, and adding disturbances like wind.
The lab manual can be found under the References menu in ModelExplorer, and The screenshot shows the integrated animation/plot view for this lab.
(Click for a larger image)
The video below gives an overview of ModelExplorer and the lab.
If the video
appears clipped, try using a different player like VLC
Position Control for a Cart
This lab looks at controlling the position of a cart on track. To load the model, select the "Cart on Track" model from ModelExplorer (under the Models menu).
The track is two meters long, and we examine how to position the cart to the desired set point without overshooting the track rails. The figure below shows a
screenshot of the lab animation (including graphs).
(Click for a larger image)
Angle Control for an Inverted Pendulum
This lab looks at controlling the angle of an inverted pendulum. To load the model, select the "Inverted Pendulum" model from ModelExplorer (under the Models menu).
The length of the pendulum (equivalently the instability) can be modified by choosing different plants from under the "Plants" menu. In this lab, we examine
how changing the instability impacts the open loop and closed loop pendulum. Students play a game where they try to maintain the pendulum angle within a region for
different pendulum lengths. Once they see the difficulty of open look control of unstable systems, an automatic controller is designed and implemented.
The figure below shows a screenshot of the lab animation (including graphs).
(Click for a larger image)
Pitch Control of an Unstable Aircraft
The previous lab introduced students to the difficulty of controlling unstable systems.
In this lab, we look at controlling the pitch angle of an unstable aircraft (F-35). To load the model, select the "Unstable Aircraft" model from ModelExplorer (under the Models menu).
We examine the tracking accuracy of the automatic controller for different references, and look at how the frequency response can inform us about the limitations
of the closed loop system.
The figure below shows a screenshot of the lab animation (including graphs).
(Click for a larger image)
The video below gives an overview of ModelExplorer and the lab.
If the video
appears clipped, try using a different player like VLC
MATLAB M-Files
- Introduction to Exponential Functions
- 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
- 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
- Pole Dependence on Damping
Factor for Standard Second Order Systems
- Step Response Dependence on
Damping Factor for Standard Second Order Systems, Dependence of Overshoot
on Damping Factor (Undamped/Underdamped Case)
- 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.
- 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
- 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
- Introduction to Routh Table: Some
Examples
- Introduction to Frequency Responses:
Some Simple SISO Systems
- Reading Off Stability Margins from A
Frequency Response: Unstable Second Order Nonminimum Phase System,
Relating Bode and Root Locus Ideas
- SISO Analysis
- Impact of Plant Coupling on Decentralized PI Control Law m-file, Slides
Class Notes/Exams
Review Notes - Exam 1 - Sample 1(Spring 2016)
Review Notes - Exam 1 - Sample 2(Spring 2016)
Review Notes - Exam 1 (Fall 2015)
Chapter on Laplace Transforms from Text
EEE480 Student Class Notes (Spring 2012, 22 pages, 2MB)
Previous Exams
- Fall 2017: Exam1, Exam2, Exam2 m-file (1integrator, 2instabilities), Final Exam
- Spring 2017: Exam1, Exam2, Exam 2 Solutions, Exam2 m-file (4integrators), Final Exam, Final Exam m-file (2integrators, 2instabilities)
- Fall 2016: Exam1, Root Locus for 3 Poles with Breakpoints m-file, Exam2, Final Exam
- Spring 2016: Exam1, Exam2, Exam2 m-file, Final Exam, Final Exam m-file, Problem 2 Lead Design m-file
- Fall 2015: Exam1, Exam1-SampleStudentSoln, Exam2, Exam 2 Fourth Order CLS m-file, Final Exam, Final Fourth Order CLS m-file
- Spring 2015: Exam1, Exam2, Final Exam , Exam 2 m-file , Final Exam m-file , BW_PM m-file
- Fall 2014: Exam1, Exam2, Final Exam
- Spring 2014: Exam1, Exam2, Final Exam
- Fall 2013: Exam1, Exam2, Final Exam
- Fall 2012: Final Exam
- Spring 2012: Exam 1 ,Final Exam
- Fall 2011: Final Exam
- Spring 2010: Exam 1, Exam 2
- Spring 2008: Exam 1 with solutions, Exam 2 with solutions (Spring 2008)
- Spring 2001: Exam1, Exam1 Solution
- Fall 2000: Exam1
- Spring 2000: Exam1
- Fall 1999: Exam1, Exam1 Solution
- Spring 1999: Exam1, Exam1 Solution
- Spring 1998: Exam1, Exam1 Solution
- Fall 1997: Exam1, Exam1 Solution
- Fall 1995: Exam 1 Practice, Exam1 with Solution Exam2, Final Exam , Final Exam Solution
- Spring 1995: Exam1, Exam1 Solution , Exam2, Exam2 Solution, Final Exam ,Final Exam Solution
- Fall 1994: Exam1, Exam1 Solution
- Fall 1992: Exam1 with Solution, Exam2 with Solution, Final Exam with Solution)
- Fall 1991: Exam1, Exam1 Solution
Class Homework: Sample solutions