LINEAR CONTROL SYSTEMSkarimpor.profcms.um.ac.ir/imagesm/354/.../lec1_introduction_sep20… · Dr. Ali Karimpour Sep 2016 Modeling of Systems 21 Model: Relationship among observed

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Dr. Ali Karimpour Sep 2016

LINEAR CONTROL

SYSTEMS

Ali Karimpour

Associate Professor

Ferdowsi University of Mashhad

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2

Prerequisite

v English Knowledge

v Primary Mathematics

v MATLAB Software

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Syllabus

v An Introduction to Linear Control Systems.(Lecture 1)

v Different Representations of Control Systems. (Lecture 2)

v Linearization. (Lecture 3)

v Internal and External Description. (Tf and SS Description). (Lecture 4)

v Stability Analysis. (Lecture 5)

v Time Domain Analysis of Control Systems. (Lecture 6)

v Root Locus Criteria. (Lecture 7)

v Controller Design in the Time Domain. (Lecture 8)

v Frequency Domain Analysis of Control Systems.(Lecture 9)

v Nyquist Stability Criteria. (Lecture 10)

v Controller Design in the Frequency Domain. (Lecture 11)

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Grading

No delay policy. Bonus(on your participation) up to 5%

v Exercises (1-2, 3-4, 6, 7, 9 and10 each 2%) 12%

v Midterm1 (Lectures 1, till 5) 18%

v Midterm2 (Lectures 6, 7 and 8) 20%

v Final 50%

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References

v Modern Control Systems (12th Edition) By Richard C. Dorf ,

Robert H. Bishop.

v Automatic Control Systems (9th Edition) By Farid Golnaraghi,

Benjamin C. Kuo.

v Control Systems Engineering (Wiley 2000) By Norman S. Nise

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Lecture 1

Topics to be covered include:

v Introduction.

v Some Advanced Control System.

v Different Parts of Control Systems.

v Modelling of Systems.

v Systems With Time Delay.

6

An Introduction to Linear Control

Systems

v Introduction.


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Introduction

7

Control System An interconnection of components forming a system

configuration that will provide a desired response.

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8

Water-level float regulator

(before BC)RQ-170 unmanned plane

(Nowadays)

Introduction - History of Control Engineering

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9

18th Century James Watt’s centrifugal governor for the speed control of a steam

engine.

Introduction - History of Control Engineering

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Introduction - Earliest Control Systems?

i. Pancreas

Regulates blood glucose level

ii. Adrenaline

Automatically generated to increase the heart rate and oxygen in times of flight

iii. Eye

Follow moving object

iv. Hand

Pick up an object and place it at a predetermined location

v. Temperature

Regulated temperature of 36°C to 37°C

10

Human System

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Some Control benefits

v Enhanced Product Quality.

v Waste Minimization.

v Environmental Protection.

v Greater Throughput for a Given Installed Capacity.

v Higher Safety Margins.

11

Introduction

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Advanced Control Systems

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A Manual Level Control

An Automatic Control

System

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A Modern High Voltage Transformer

Advanced Control Systems

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v Introduction.





14

An Introduction to Linear Control Systems

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Different Parts of Control Systems

15

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Success in control engineering depends on some of the issues:

v Plant

v Objectives

v Sensors

v Actuators

v Computing

v Disturbance & noises

v Set points

v Uncertainties

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قيف

دهانه مايع

مايع خنک کننده پوسته جامد

نورد

نورد نگهدارنده

مايع خنک کننده ثانويه

Different Part of a Control Systems

v Plant

v Objectives

v Sensors

v Actuators

v Computing

v Disturbance & noises

v Set points

v Uncertainties

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In summary:

Sensors provide the eyes and actuators the muscle but

control science provides the finesse.

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Better Control(Computing)

Provides more finesse by combining sensors and

actuators in more intelligent ways

Better Actuators

Provide more Muscle

Better Sensors

Provide better Vision

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Control System Examples

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v Inverted Pendulum.

v Ball & Beam.

v Ball and plate.

v Segway.

v Donkey.

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v Introduction.





20

An Introduction to Linear Control Systems

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Modeling of Systems

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Model: Relationship among observed signals.

• Split up system into subsystems,

• Joined subsystems mathematically, 1- Modeling

2- System identification

• Does not necessarily involve any experimentation

on the actual system.Building

models • It is directly based on experimentation.

• Input and output signals from the

system are recorded.3- Combined

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Example 1: Dynamics of a mechanical system

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ورودی

خروجی

Modeling

xMxbu

uM

xM

bx

1

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Example 2: Dynamics of a electromechanical system

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Position control system

Modeling

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Example 2: Continue

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خروجی

ورودی

Modeling

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A simplified aeroplane

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Position control system

Modeling

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t (Time)

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Example 3: A thermal system یک سيستم حرارتی: 3مثال

Input signal is an step function so:

00

01)(

t

ttu

ssu

1)(

00

0)(

t

tkekty

t

/1)(

s

k

s

ksy

Input signal1

Output signal

k

?)(

)()(

su

sysg

1

s

k

System Identification

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1-1 Specify actuator and disturbance in the following system.

Exercises

1-2 Specify actuator, sensor and disturbance in the following system.

خروجی

ورودی

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1-3 Derive the output of following

system if it is excited by u=sint

1-4 Derive model of following system, but neglect the inductance of the

motor.

1-5 Repeat exercise 1-4, but consider the motor as a series motor.

Exercises

خروجی

ورودی

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Exercises

1-6 Find the mathematical model of the system.

Final answer is:

ukykybxkkxbxm 12211 )(

xkxbykybym 222

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1-7 In a control system of an industrial composition process , it is very

important to control the chemical composition of the output. There is

an infrared analyzer for measurement and the valve of additive stream

is controllable. Complete the feedback loop and find the block diagram

of the process.

Exercises

Documents

LINEAR CONTROL SYSTEMSkarimpor.profcms.um.ac.ir/imagesm/354/.../lec1_introduction_sep20… · Dr. Ali Karimpour Sep 2016 Modeling of Systems 21 Model: Relationship among observed