CDS 101: Lecture 1.1 Introduction to Feedback and Control

Richard M. Murray

27 September 2004

Goals:Give an overview of CDS 101/110; describe course structure, administration Define feedback systems and learn how to recognize main featuresDescribe what control systems do and the primary principles of feedback

Reading (available on course web page): Åström and Murray, Analysis and Design of Feedback Systems, Ch 1

(available from course web page)

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Course Administration

Course syllabusCDS 101 vs CDS 110abLectures, recitationsOffice hoursGradingHomework policyCourse text and referencesClass homepageSoftwareCourse outline

Signup sheet, mailing listLecture DVDs: 102 Steele, Box GCourse load: keep track of hoursCourse ombuds: Wednesday

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CDS 101/110 Instructional Staff

Lecturer: Richard Murray (CDS)

Co-InstructorsAnand Asthagiri (ChE)Tim Colonius (ME)Ali Hajimiri (EE)Steven Low (CS/EE)Hideo Mabuchi (Ph/CDS)

Head TA: Steve Waydo (CDS)

TAsDomitilla Del VecchioAsa HopkinsHaomiao “H” Huang Hao JiangMorr Mehyar/Kevin Tang

MabuchiLow

Murray Asthagiri Colonius

Hajimiri

Steve Domitilla Asa H

KevinMorrHao

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Mud Cards

Mud cards3 x 5 cards passed out at beginning

of each lectureDescribe “muddiest” part of the

lecture (or other questions)Turn in cards at end of classResponses posted on FAQ list by 8

pm on the day of the lecture (make sure to look!)

Class FAQ listSearchable database of responses

to mud cards and other frequently asked questions in the class

What does closed loop mean? You used this term without defining it.

FAQ

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What is Feedback?

Miriam Webster: the return to the input of a part of the

output of a machine, system, or process (as for producing changes in an electronic circuit that improve performance or in an automatic control device that provide self-corrective action) [1920]

Feedback = mutual interconnection of two (or more) systemsSystem 1 affects system 2System 2 affects system 1Cause and effect is tricky; systems

are mutually dependent

Feedback is ubiquitous in natural and engineered systems

Terminology

System 2

System 1

System 2System 1

System 2System 1

ClosedLoop

OpenLoop

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Example #1: Flyball Governor

“Flyball” Governor (1788) Regulate speed of steam engine Reduce effects of variations in load

(disturbance rejection) Major advance of industrial revolution

Balls fly out as speed increases,

Valve closes,slowing engine

http://www.heeg.de/~roland/SteamEngine.htmlBoulton-Watt steam engine

Flyballgovernor

Steamengine

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Other Examples of Feedback

Biological SystemsPhysiological regulation (homeostasis)Bio-molecular regulatory networks

Environmental SystemsMicrobial ecosystemsGlobal carbon cycle

Financial SystemsMarkets and exchangesSupply and service chains

ESE

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Control = Sensing + Computation + Actuation

SenseVehicle Speed

ComputeControl “Law”

ActuateGas Pedal

In Feedback “Loop”

GoalsStability: system maintains desired operating point (hold steady speed)Performance: system responds rapidly to changes (accelerate to 6 m/sec)Robustness: system tolerates perturbations in dynamics (mass, drag, etc)

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Two Main Principles of Feedback

Robustness to Uncertainty through FeedbackFeedback allows high performance in the

presence of uncertaintyExample: repeatable performance of

amplifiers with 5X component variationKey idea: accurate sensing to compare

actual to desired, correction through computation and actuation

Design of Dynamics through FeedbackFeedback allows the dynamics (behavior)

of a system to be modifiedExample: stability augmentation for highly

agile, unstable aircraftKey idea: interconnection gives closed

loop that modifies natural behaviorX-29 experimental aircraft

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Example #2: Speed Control

engine hill

engine desired( )

mv bv f f

f k v v

Control System++-

disturbance

reference

Stability/performanceSteady state velocity approaches

desired velocity as k Smooth response; no overshoot or

oscillations

Disturbance rejectionEffect of disturbances (eg, hills)

approaches zero as k RobustnessResults don’t depend on the specific

values of b, m or k, for k sufficiently large

ss des hill

1kv v u

b k b k

time

velocity

vdes

1 ask

0 ask

“Bob”

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Example #3: Insect Flight

More information: M. D. Dickinson, Solving the mystery of

insect flight, Scientific American, June 2001

CDS 101 seminar : Friday, 10 Oct 03

ACTUATION

two wings(di-ptera)

specialized“power”muscles

SENSING

neuralsuperposition

eyes

hind winggyroscopes(halteres)

COMPUTATION

~500,000 neurons

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Control Tools

Modeling Input/output representations for subsystems +

interconnection rulesSystem identification theory and algorithms Theory and algorithms for reduced order modeling

+ model reduction

AnalysisStability of feedback systems, including

robustness “margins”Performance of input/output systems (disturbance

rejection, robustness)

SynthesisConstructive tools for design of feedback systemsConstructive tools for signal processing and

estimation (Kalman filters)

MATLAB Toolboxes SIMULINK Control System Neural Network Data Acquisition Optimization Fuzzy Logic Robust Control Instrument Control Signal Processing LMI Control Statistics Model Predictive Control System Identification µ-Analysis and

Synthesis 

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Overview of the Course

Wk Mon/Wed Fri

1 Introduction to Feedback and Control MATLAB tutorial, Steve W.

2 System Modeling Linear algebra/ODE review, Steve W.

3 Stability and Performance Control of cavity oscillations, T. Colonius

4 Linear Systems Internet Congestion Control, S. Low

5 Controllability and Observability Midterm exam

Review for midterm, Steve W.

6 Transfer Functions Piloted flight, D. McRuer (tentative)

7 Loop Analysis of Feedback Systems Stability in Electronic Circuits, A. Hajimiri

8 Frequency Domain Design Molecular Feedback Mechanisms, A. Asthagiri

9 Limits on Performance Thanksgiving holiday

10 Uncertainty Analysis and Robustness Final exam

Review for final, TBD

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Summary: Introduction to Feedback and Control

Sense

Compute

Actuate

Control =

Sensing + Computation +Actuation

Feedback PrinciplesRobustness to UncertaintyDesign of Dynamics

Many examples of feedback and control in natural & engineered systems:

BIO

BIOESE

ESE

CS

Lecture 2.1: System Modeling

Model = state, inputs, outputs, dynamics

Principle: Choice of model depends on the questions you want to answer

( , )

( )

dxf x u

dty h x

b

k3

m1m2

q1

u(t)

q2

k2k1

function dydt = f(t,y, k1, k2, k3, m1, m2, b, omega)

u = 0.00315*cos(omega*t);

dydt = [

y(3);

y(4);

-(k1+k2)/m1*y(1) +

k2/m1*y(2);

k2/m2*y(1) - (k2+k3)/m2*y(2)

- b/m2*y(4) + k3/m2*u ];

1

1 1

( , )

( )k k k

k k

x f x u

y h x

What’s Next

Homework problems: due 10/65 examples of control systemsMATLAB cruise control example

(hint: get this running now)CDS 110: steady cam example plus

more MATLAB

Wednesday: 1-3 pm, 74 JRGReview of linear algebra and ODEs

Friday: 2-3 pm, 74 JRGMATLAB tutorial – plan on attending

if you have never used MATLAB before

Next week: System Modeling Define what a model is and what types

of questions it can be used to answer Introduce the concepts of state,

dynamic, and inputs Provide examples of common modeling

techniques Describe common modeling tradeoffs

Don’t forget to fill out MUD CARDS

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Welcome to

CDS 101 – Design and Analysis of Feedback Systems

CDS 110a – Introductory Control Theory

Instructor: Richard M. Murray

PICK UP HANDOUTS OUTSIDEOF LECTURE HALL