control applying input to cause system variables to conform to desired values called the reference. ...

Control

Applying input to cause system variables to conform to desired values called the reference.

Cruise-control car:f_engine(t)=? speed=60 mph

E-commerce server:Resource allocation? T_response=5 sec

Embedded networks:

Flow rate? Delay = 1 sec Computer systems: QoS guarantees

Feedback (close-loop) Control

Acturator

Sensor

reference

control input

controlled variable

manipulatedvariable

Controlled System( “plant” )

+ -

error

controlfunction

Controller

sample

(efector, etc)

(monitor etc)

Open-loop control

Compute control input without continuous variable measurement Simple Need to know EVERYTHING ACCURATELY to work right

Cruise-control car: friction(t), ramp_angle(t) E-commerce server: Workload (request arrival rate?

resource consumption?); system (service time? failures?)

Open-loop control fails when We don’t know everything We make errors in estimation/modeling Things change

Acturator

reference

control input

controlled variable

manipulatedvariable

Controlled System( “plant” )

+-

error

controlfunction

Controller

(efector, etc)

Feedback control theory, vs …

Adaptive resource management heuristics Laborious design/tuning/testing iterations Not enough confidence in face of untested workload

Queuing theory Doesn’t handle feedbacks Not good at characterizing transient behavior in overload

Feedback control theory Systematic theoretical approach for analysis and design Predict system response and stability to input

Control design methodology

Controller Design

Requirement Analysis

System model Dynamic model Control algorithm

Performance Specifications

Satisfy

Linear vs. non-linear Time-invariant vs. Time-varying

Are coefficients functions of time?

Continuous-time vs. Discrete-time


Example: Control of Lotus NotesArchitecture

RIS = RPCs in System

Actual RIS

DesiredRIS

RPCsMaxUsers

Server

ControllerAdmin

Control Model

ControllerNotesServer

MaxUsersDesiredRIS

ActualRIS

r(k)

e(k)u(k) y(k) Control error: e(k)=r(k)-y(k)

System model: y(k)=(0.43)y(k-1)+(0.47)u(k-1)

P controller: u(k)=Ke(k) ?

© 2004 HellersteinFeedback Control of Computing Systems: M1 - Introduction

Example: Control & Responsein an Email Server

Control(MaxUsers)

Response(queue length)

Good

Slow

Bad

Useless


ComponentsTarget system: what is controlledController: exercises controlTransducer: translates measured outputs

DataReference input: objectiveControl input: manipulated to affect outputDisturbance input: other factors that affect the target systemTransduced output: result of manipulation

Given target system, transducerControl theory finds controller

that adjusts control inputto achieve measuredoutput in the presence of disturbances.

ControllerTargetSystem

Transducer

ReferenceInput

ControlInput

MeasuredOutput

TransducedOutput

Disturbance InputControl System Architecture


ArchitectureMaxUsers

NotesClient

NotesClient

NotesServer

ServerLog

RPCs RPCRecords

Administrative Tasks

MeasuredRIS

Block Diagram

ControllerNotesServer

MaxUsersReferenceRIS

Sensor

Target SystemActualRIS

Administrative Tasks

IBM Lotus Domino Server


Unstable System

Stability Accuracy Short settling Small Overshoot

Properties of Control Systems – SASO

Performance specifications

Settling time

Overshoot

Controlledvariable

Time

Referencevalue

%

Steady StateTransient State

Steady state error


Control Theory in Two Slides: System Identification

Notes ServerMaxUsers Actual RIS

)(ky)(ku

0 20 40 60 80 100020406080

100

Measured RIS

Pre

dict

ed R

IS

055.0

913.0

1

1

b

a

97.2 R

Model of System Dynamics

)1()1()( 11 kubkyaky

1

1)(az

bzN

Transfer Function


Poles of H(z)

ControllerG(z)

Notes ServerN(z)

SensorS(z)-

+

H(z) = Closed Loop Transfer Function

)(te

Integral Control Law

)()1()( tKetutu

K=1 K=5K=.1

Control Theory in Two Slides: Control Designr*

control applying input to cause system variables to conform to desired values called the reference. ...

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