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GEE 514 Solar Energy Institute,Dr.Mutlu BOZTEPE 1

Introduction to Control

Systems

G(s)+

_

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Course Objectives

To provide a general understanding of thecharacteristics of dynamic systems and feedbackcontrol.

To teach classical methods for analysing controlsystem accuracy, stability and dynamicperformance.

To teach classical control system designmethods.

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Course Contents

Introduction to control systems Modelling of the physical systems Time domain analysis, Laplace transforms, Transfer

functions, System Responses Closed loop control systems Classical design in the s-domain Classical design in the frequency domain

Digital control systems Nonlineer control systems, on/off control Design examples

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Course Book

Advanced Control Engineering

Roland S. Burns

Butterworth-HeinemanPaperback, 464 pages, publication date: OCT-2001

ISBN-13: 978-0-7506-5100-4ISBN-10: 0-7506-5100-8

http://www.elsevier.com/wps/find/bookdescription.cws_home/677158/description#description

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Introduction to Control

Systems

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Control System Concepts

A system is a collection of components whichare co-ordinated together to perform a function.

Systems interact with their environment across aseparating boundary.

The interaction is defined in terms ofvariables.

system inputs

system outputs

environmental disturbances

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Systems

Disturbance Inputs

Control Inputs

System Outputs

Engineering systems

Biological systems

Information systems

Subsystem

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System Variables

The systems boundarydepends upon thedefined objective function of the system.

The systems function is expressed in terms of

measured output variables.The systems operation is manipulated through

the control input variables.

The systems operation is also affected in anuncontrolled manner through the disturbanceinput variables.

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Car and Driver Example

Objective function: to control the direction andspeed of the car.

Outputs: actual direction and speed of the car

Control inputs: road markings and speed signs

Disturbances: road surface and grade, wind,

obstacles. Possible subsystems: the car alone, power

steering system, braking system, . . .

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Antenna Positioning Control System

Original system: the antenna withelectric motor drive systems.

Control objective: to point theantenna in a desired reference direction.

Control inputs: drive motor voltages.

Outputs: the elevation and azimuth of theantenna.

Disturbances: wind, rain, snow.

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Antenna Control System

Functional Block Diagram

Physical VariablesInformation Variables

AntennaMotorPoweramp

Diff.amp

Ref.

input

Angle

sensor

volts volts

volts

+

_

power torqueAngular

position

Antenna System

Wind force

Feedback Path

Error

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Control System Components

System or process (to be controlled)Actuators (converts the control signal to a power

signal)

Sensors (provides measurement of the systemoutput)

Reference input (represents the desired output)

Error detection (forms the control error) Controller (operates on the control error to form the

control signal, sometimes called compensators)

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Feedback System Characteristics

Consider the following speed control system

Load

KlMotor

Km

Amp

Ka

Speed sensorKs

Reference

speed

u+

_

Disturbance

torque

wo

Open loop system

Feedback Path

wr+

+

Td

Tm

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Open Loop System Characteristics

The accuracy of the open loop system depends upon the calibrationof the gains and prior knowledge of the disturbance (choose thecontrol uto give the desired w

o).Problems:

nonlinear or time varying gains

unknown and varying disturbances

Load

KlMotor

Km

Amp

Ka

u

Disturbance

torque

wo

Open loop system

+

+

Td

Tm

dllma

dmlo

TKuKKK

TTK

)(w

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Closed Loop Characteristics

IfKa

is very large such that,

then,

Ksis the sensor gain in units of volts per rad/s.

The input/output relationship is not verysensitive todisturbances or changes in the system gains

slmaslmaKKKKKKKK 1

d

sma

r

s

oT

KKKK

11 ww

rad/s volts 0

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Closed Loop Characteristics

System Error

The control error is

Again, if the loop gain, KaK

mK

lK

sis large, then the

error is small.

d

slma

sl

r

slma

d

slma

slr

slma

slma

osr

TKKKK

KK

KKKK

TKKKK

KK

KKKK

KKKK

Ke

11

1

111

)(

w

w

ww

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Note: Gain Definitions

forward gain: KaK

mK

l

feedback gain: Ksloop gain: K

aK

mK

lK

s

closed loop gain: forward gain1 + loop gain

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System Dynamics

Consider a sudden change in the speed reference,w

r.

The output speed, wowill not respond

instantaneously due to the inertial characteristics ofthe motor and load, i.e. their dynamiccharacteristics.

The motor and load need to be represented by

dynamic equations rather than simple gains. The output response will generallylagthe input and

may be oscillatory.

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System Dynamics

Step Responses

0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Step Response, Ka=2

0 2 4 6 8 10-0.5

0

0.5

1

1.5

2Step Response, Ka=20

wo wowr

wr

Tm

Tm

Ka

= 2 Ka = 20

Assume Ks

= 1.0

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Control System Design Objectives

Primary Objectives:

1. Dynamic stability

2. Accuracy

3. Speed of response

Addition Considerations:

4. Robustness (insensitivity to parameter variation)

5. Cost of control

6. System reliability

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Control System Design Steps

Define the control system objectives.

Identify the system boundaries.

define the input, output and disturbance variables

Determine a mathematical model for thecomponents and subsystems.

Combine the subsystems to form a model forthe whole system.

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Applyanalysis and design techniques todetermine the control system structure andparameter values of the control components, to

meet the design objectives.

Test the control design on a computersimulation of the system.

Implement and test the design on the actualprocess or plant.

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Examples of Control SystemsRoom Temperature Control System

Proportionalmode: Betteraccuracy,complex

On/Off controlmode:

Thermostaticcontrol, simple,

low accuracy

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Examples of Control SystemsAircraft Elevator Control System

Hydraulicservomechanismshave a goodpower/weight

ratio, and are idealfor applicationsthat require largeforces to be

produced by smalland light devices.

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Examples of Control SystemsComputer Numerically Controlled (CNC) Machine

The purpose ofthis latter device,

which produces ananalog signal

proportional tovelocity, is to forman inner, or minorcontrol loop inorder to dampen,

or stabilize theresponse of thesystem.

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Examples of Control SystemsShip Autopilot Control System

Actual heading ismeasured by a gyro-compass (or magneticcompass), compared

with desired value.Error are send toautopilot (Course-keeping system)

Actual rudder angle is

sensed, and autopilotcontrols the shipcourse by steering-gear.

gee 514 lecture 1

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