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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

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Control

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

Feedback (close-loop) Control

Controlled System( “plant” )

Controller

control

function

control

input

manipulated

variable

Acturator

(efector, etc)

error

sample

controlled

variable

Sensor

+

-

(monitor etc)

reference


Open loop control

Controlled System( “plant” )

Controller

control

function

control

input

manipulated

variable

Acturator

(efector, etc)

error

controlled

variable

+

-

reference

Open-loop control

  • Compute control input without continuous variable measurement

    • Simple

    • Need to know EVERYTHINGACCURATELY 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


Feedback control theory vs

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

Control design methodology

Controller Design

System model

Dynamic model

Control algorithm

Satisfy

Requirement Analysis

Performance Specifications

  • Linear vs. non-linear

  • Time-invariant vs. Time-varying

    • Are coefficients functions of time?

  • Continuous-time vs. Discrete-time


Example control of lotus notes

Controller

Control Model

MaxUsers

Actual

RIS

Desired

RIS

e(k)

+

u(k)

y(k)

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

Controller

Notes

Server

r(k)

System model: y(k)=(0.43)y(k-1)

+(0.47)u(k-1)

-

Example: Control of Lotus Notes

Architecture

Admin

RPCs

MaxUsers

Server

RIS = RPCs in System

Desired

RIS

Actual RIS

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


Example control response in an email server

Example: Control & Responsein an Email Server

Response

(queue length)

Good

Bad

Control

(MaxUsers)

Slow

Useless


Control system architecture

Disturbance Input

Control System Architecture

Reference

Input

Control

Input

Measured

Output

Controller

Target

System

Transduced

Output

Transducer

Components

Target system: what is controlled

Controller: exercises control

Transducer: translates measured outputs

Given target system, transducer

Control theory finds controller

that adjusts control input

to achieve measured

output in the presence of

disturbances.

Data

Reference input: objective

Control input: manipulated to affect output

Disturbance input: other factors that affect the target system

Transduced output: result of manipulation


Ibm lotus domino server

Administrative

Tasks

Target System

MaxUsers

Reference

RIS

Actual

RIS

Measured

RIS

Controller

Notes

Server

MaxUsers

Sensor

Block Diagram

Administrative

Tasks

IBM Lotus Domino Server

Notes

Client

RPC

Records

RPCs

Server

Log

Notes

Server

Notes

Client

Architecture


Properties of control systems saso

Unstable System

Stability

Accuracy

Short settling

Small Overshoot

Properties of Control Systems – SASO


Performance specifications

Performance specifications

Controlled

variable

Overshoot

Steady state error

%

Referencevalue

Transient State

Steady State

Time

Settling time


Control theory in two slides system identification

Model of System Dynamics

Transfer Function

100

80

60

Predicted RIS

40

20

0

0

20

40

60

80

100

Measured RIS

Control Theory in Two Slides: System Identification

MaxUsers

Actual RIS

Notes Server


Control

Poles

of

H(z)

Integral Control Law

K=5

K=1

K=.1

Control Theory in Two Slides: Control Design

+

r*

Controller

G(z)

Notes Server

N(z)

Sensor

S(z)

-

H(z) = Closed Loop Transfer Function


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