Linear Control Systems

1. Introduction

Amin Rezaeizadeh Linear Control Fall 1396 1-1

Amin Rezaeizadeh

Fall 1396

Logistics

Linear ControlAmin Rezaeizadeh

Lecturer: Amin Rezaeizadeh aminre@sharif.ir Office 717

Lectures: Sat. and Mon. 9:00 – 10:30Lab: Sat 13:30 – 15:30Exercise: Mon. 12-13:30

Assessment: 10 (final) + 7(Quiz) + 3(Lab)

There will be approx. 3 Quizzes

Web-site: http://control.ee.sharif.ir/~controlsys

Fall 1396 1-2

Logistics

Linear ControlAmin Rezaeizadeh Fall 1396 1-3

Logistics

Linear ControlAmin Rezaeizadeh

The course book

Fall 1396 1-4

G.F. Franklin, J.D. Powell, A.

Emami-Naeini. Feedback Control of Dynamic

Systems. 4th international edition, Pearson

Higher Education, 2002

Course Planning

Linear ControlAmin Rezaeizadeh

Introduction

Model formation, differential equations, linearization

Laplace transforms

Frequency domain analysis, stability, Nyquist plot, Bode plot

Second order systems

State variables, sensitivity

PID Control

Root locus method

Controller design in the time domain

Controller design in the frequency domain

Phase lead and phase lag compensation

Extension to the control structure: feedforward, cascade

Spring 1396 1-5

abb.com

robohub.org

control.ee.ethz.ch

airbus.com

Automatic ControlThe Hidden Technology You Meet Every Day [Karl Aström]

Amin Rezaeizadeh Linear Control Spring 1396 1-8

ControlThe Main Idea

Amin Rezaeizadeh Linear Control Fall 1396 1-9

Introduction

ControlThe Main Idea

model dynamicsẋ = f(x, u, t)

feedback stability

Amin Rezaeizadeh Linear Control Fall 1396 1-10

Introduction

Process Control Example

I Heater

Amin Rezaeizadeh Linear Control Fall 1396 1-11

Introduction

Process Control Example

I Heater

Plant

Amin Rezaeizadeh Linear Control Fall 1396 1-12

Introduction

Process Control Example

I Heater

PlantActuator

Amin Rezaeizadeh Linear Control Fall1396 1-13

Introduction

Process Control Example

I Heater

PlantActuatorControlI

Amin Rezaeizadeh Linear Control Fall 1396 1-14

Introduction

Process Control Example

I Heater

PlantActuatorControlI

+-T0

T

SensorT

Amin Rezaeizadeh Linear Control Fall 1396 1-15

Introduction

Process Control Example

I Heater

PlantActuatorControlI

+-T0

T

SensorT

++

noiseAmin Rezaeizadeh Linear Control Fall 1396 1-16

Introduction

Process Control Example

I Heater

PlantActuatorControlI

+-T0

T

SensorT

++

noise

Tout

Tout

Amin Rezaeizadeh Linear Control Fall 1396 1-17

Introduction