Feedback

Professor Walter W. OlsonDepartment of Mechanical, Industrial and Manufacturing Engineering

University of Toledo

Outline of Today’s Lecture

• Review• Class Policy• What is Control?

• Feedback• Open Loop Systems• Closed Loop System

• Positive Feedback• Negative Feedback• Control actions using feedback

Sense

Compute

Actuate

Class Policies

• Syllabus• Students are expected to be at class on time. • Book: Online at

• http://www.cds.caltech.edu/~murray/amwiki/index.php/Version_2.10e• You will be required to read this BEFORE coming to class.• Recitation points come from your reading!

• Homework is due on the date shown in the syllabus at the beginning of the class period• Late homework will not be accepted• Neatness Counts!• Individual work

• Academic dishonesty (cheating, plagiarizing, and related offenses,) will be harshly dealt with.

Control

• Control =• Sensing +

• {Where are you at? Is it where you want to be?}

• Computation +• {Can you find a path to where you want to go?}

• Actuation• { Make things happen to get you there!}

Why Controls?

• Why Controls?• Things move• Too many things happening• Things move too fast for the human brain to

compute and for muscles to act• Noise and disturbances• Accuracy and precision• Cost

Where Do You Find Controls?

• Everywhere!

Controls: What are differences here?

• Control = Sense + Compute + Actuate

Bench rest• TOW explained

Open Loop Control

• Usually “set point” systems• Advantages

• Simple• Sensitive to environment• Set and forget

• Disadvantages• Non correcting• Sensitive to disturbances• Insensitive to environment

• Examples• Irrigation systems• Washing machines

Sensing Compute Actuate

Closed Loop Control

• Adds a feedback loop to the control system

• For computational purposes, it is shown as

Sense

Compute

Actuate

Controller Plant

Sensor

Input Output

Disturbance

+ or -

+ or -+ or -

+ or -

Positive Feedback

Positive Feedback Clip

Controller Plant

Sensor

++

+ +

VibratingGuitar String

MagneticPickup

AmplifierSpeaker

Plucked String String Vibrations

Controller Plant

Sensor

++

+ + Sound

Guitar String w/ pickup

Amplifier Speaker

Ambient Sound

2 possible models

Background sound

Previous Vibrations

Positive Feedback

• Positive feedback is used to increase the actuation in the loop.• Advantages

• Increased results• Faster results• Finds extremes

• (maxima and minima)• Disadvantages

• Consumes energy• Subject to local extremes (introns)• May become unstable• May destroy system

• Examples:• Metal finders• Searches• Stock market programs• Genetic Algorithm

build population

createmutations

test

performancemeasure

Results

Culled fromPopulation

BestWorst

Negative Feedback

Input Controller Plant

Sensor

Output

Disturbance

+-

+ +

Error Signal

homeostasis

DesiredHeart Beat

Controller Plant

Sensor

Heart Beat

Salt

+-

+ +

Heart

Nerves

Parasympathetic/Sympathetic System

Negative Feedback

• Negative Feedback is used to reduce error• Advantages

• Controls to a set point• Robustness to disturbances (uncertainty)• Rejection of distortion

• Disadvantages• Prone to oscillation• Instability• Complexity• Coupling

• Examples• Set point control• Tracking• Chang the system dynamics

Basic Control Actions

• Bang – Bang• Most are on – off controls where either something

is turned on or turned off in response to sensor:• If the error signal is greater than e1, turn system on

• If error is signal is less than e2, turn system off

• e1 and e2 are usually not be the same value

• The control action could be reversed• Example: Sump pump

• if water level is above 20, turn pump on• if water level is below 5, turn pump off

Basic Control Actions

• Proportional• Control action is

proportional to the error sensed• command = K * error signal• K is often called the “gain” of

the controller

• Example: Volume knob on the radio

Basic Control Actions

• Integral control• control command is based

on the size of the error and the length of time the error has existed

• Example: Ripening of fruit• when fruit ripen they release

ethylene• the ethylene increases the rate

of ripening

command edtRipening fruit

Basic Control Actions

• Derivative control• control command is based

on the magnitude and the rate of change of the error

• Rarely alone used because of instabilities created by the speed of changes

• Example: Pollution control of furnace

ecommand

t

Basic Control Actions

• Combined• PID (Proportional – Integral

– Derivative)• sums all three actions

• Most used control strategy

• Example: Motor controllers

( )( ) ( )p i d

e tcommand K e t K e t dt K

t

Summary

• Open Loop• Closed Loop• Feedback

• Positive feedback• Negative Feedback

• Basic Control Actions• Bang-bang• Proportional• Integral• Deriviative• PID

• Next: Modeling