linear control systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/lin... · modern control...

LINEAR CONTROLLINEAR CONTROLSYSTEMSSYSTEMS

Ali KarimpourAssociate Professor

Ferdowsi University of Mashhad

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Dr. Ali Karimpour Sep 2014

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Lecture 1Syllabus

An Introduction to Linear Control Systems. Different Representations of Control Systems. Linearization and More Study on External Description. Internal Description Model. (SS Description). Stability Analysis. Time Domain Analysis of Control Systems. Root Locus Criteria. Controller Design in the Time Domain. Introduction on Frequency Domain Analysis. Nyquist Stability Criteria. Frequency Domain Analysis of Control Systems. Controller Design in the Frequency Domain.

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Prerequisite

English Knowledge

Primary Mathematics

MATLAB Software

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References

Modern Control Systems (12th Edition) By Richard C. Dorf , Robert H. Bishop.

Automatic Control Systems (9th Edition) By FaridGolnaraghi, Benjamin C. Kuo.

Modern Control Engineering (5th Edition) By KatsuhikoOgata

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Any Question?

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Lecture 1

Topics to be covered include: Introduction. Some Advanced Control System. Different Parts of Control Systems. Modelling of Systems. Systems With Time Delay.

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An Introduction to Linear Control An Introduction to Linear Control SystemsSystems

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An Introduction to Linear Control SystemsAn Introduction to Linear Control Systems

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Introduction

Control is the process of causing a system variable such as tempreture to conform to some desired value.

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System An interconnection of elements and devices for a desired purpose.

Control System An interconnection of components forming a system configuration that will provide a desired response.

ProcessThe device, plant, orsystem under control.

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Water-level float regulator (before BC)

RQ-170 unmanned plane(Nowadays)

Introduction - History of Control Engineering

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

1920s Minorsky worked on automatic controllers for steering ships.

1930s Nyquist developed a method for analyzing the stability of controlled systems

1940s Frequency response methods made it possible to design linear closed-loop control systems

1950s Root-locus method due to Evans was fully

developed

1960s State space methods, optimal control,

adaptive control and

1980s Learning controls are begun to investigated

and developed.

……………………….

……………………….


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This photograph shows a flyballgovernor used on a steam enginein a cotton factory near Manchesterin the United Kingdom. Actually, this cotton factory is still running today.


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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 flightiii. Eye

Follow moving objectiv. Hand

Pick up an object and place it at a predetermined locationv. Temperature

Regulated temperature of 36°C to 37°C

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Human System

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Some Control benefits

Enhanced Product Quality.

Waste Minimization.

Environmental Protection.

Greater Throughput for a Given Installed Capacity.

Higher Safety Margins.

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Introduction

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Advanced Control Systems

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A Manual Level Control

Control System for a Boiler of a Thermal Plant

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A Modern High Voltage Transformer


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A Wind Farm


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Different Parts of Control Systems

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As an example consider position control of an aeroplane, or temperature control of a room.

Before designing a control system, it is importantto know the goal, that is, to formulate the control objectives. This includes

what does one want to achieve

what variables need to be controlled to achieve these objectives

what level of performance is necessary (accuracy, speed,...)

Plant

ObjectivesSensorsActuatorsComputingDisturbance & noisesSet pointsUncertainties

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Plant Objectives

Sensors

ActuatorsComputingDisturbance & noisesSet pointsUncertainties

Sensors are the eyes of control enabling one to see whatis going on.

If you can measure it, you can control it.

Once sensors are in place to report on the state of a process, then the next issue is the ability to affect, or actuate, the system in order to move the process from the current state to a desired state.


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In modern control systems, the connection between sensors and actuators is invariably made via a computer of some sort.

Thus, computer issues are necessarily part of the overall design.

Current control systems use a variety of computational devices Including PLC's (Programmable Logic Controllers), PC's (Personal Computers), microcontrollers, etc.

PlantObjectivesSensorsActuators

ComputingDisturbance & noisesSet pointsUncertainties

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One of the things that makes control science interesting is that all real life systems are acted on by noise and external disturbances. These factors canhave a significant impact on the performance of the system.

As a simple example, aircrafts are subject to Disturbances in the form of wind-gusts, and cruise controllers in cars have to cope with different road gradients and different car loadings.

PlantObjectivesSensorsActuatorsComputing

Disturbance & noisesSet pointsUncertainties

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PlantObjectivesSensorsActuatorsComputingDisturbance & noises

Set points

Uncertainties

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Plant Objectives Sensors Actuators Computing Disturbance & noises Set points Uncertainties

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قیف

دهانه مایع

مایع خنک کننده پوسته جامد

نورد

نورد نگهدارنده

مایع خنک کننده ثانویه

Different Part of a Control Systems Plant Objectives Sensors Actuators Computing Disturbance & noises Set points Uncertainties

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نوار ریخته گری در دومین بخش خنک سازی


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Typical flatness control set-up for rolling mill


Plant Objectives Sensors Actuators Computing Disturbance & noises Set points Uncertainties

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Different Parts of Control SystemsSuccess in control engineering depends on some of the issues: Plant Objectives Sensors Actuators Computing Disturbance & noises Set points Uncertainties

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Definition of the control problem

Definition 2.1:The central problem in control is to find a technically feasible way to act on a given process so that the process behaves, as closely as possible, to some desired behaviour. Furthermore, this approximate behaviour should be achieved in the face of uncertainty of the process and in the presence of uncontrollable external disturbances acting on the process.

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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 ActuatorsProvide more Muscle

Better SensorsProvide better Vision

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Control System Design process

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If the performance does not meet specifications, then iterate the configuration and actuator


1. Establish control goals

2. Identify the variables to control

3. Write the specifications for the variables

4. Establish the system configuration and identify the actuator

5. Obtain a model of the process, the actuator and the sensor

6. Describe a controller and select key parameters to be adjusted

7. Optimize the parameters and analyze the performance

If the performance meet the specifications, then finalize design

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Control System Classification

An open-loop control system utilizes an actuating device to control the process directly without using feedback.

A closed-loop feedback control system uses a measurement of the output and feedback of the output signal to compare it with the desired output or reference.

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Control System Classification

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Control System Examples

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Inverted Pendulum.

Ball & Beam.

Ball and plate.

Segway.

Donkey.

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Modeling of Systems

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Model: Relationship among observed signals.

Model types

1- Mental models

2- Graphical models

3- Mathematical (analytical) models

4- Software models • 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 of Systems

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A simplified aeroplane

38Position control system

Modeling of Systems

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A simplified aeroplane

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Modeling of Systems

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Example 2: Dynamics of a electromechanical system

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Position control system

Modeling of Systems

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Example 2: Continue

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خروجی

ورودی

Modeling of Systems

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Example 3: Dynamics of a liquid level system

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ورودی

خروجیکنترلی

مایع خروجی

Modeling of Systems

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Example 4: A system with pure time delay

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سیگنال ورودی

جریان هواسنسوردما

دمای سنجششده

تاخیرزمان

Modeling of Systems

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Example 4: A system with pure time delay

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Modeling of Systems

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1-1 Specify the actuator in following system.

1-2 Specify the disturbance in the system of exercise 1-1.

Exercises

1-3 Specify the actuator (input) and sensor in following system.

1-4 Specify the disturbance in the system of exercise 1-3.

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1-5 Derive the output of example 1 if it is excited by u=sint

1-6 Repeat example 2, but neglect the inductance of the motor.

1-7 Repeat example 2, but consider the motor as a series motor.

Exercises

1-8 Find the mathematical model of the following system.

Final answer is:

ukykybxkkxbxm 12211 )(

xkxbykybym 222

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1-9 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

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1-10 The figure shows a system for extracting water for irrigation by use of solar energy. Draw the block diagram of the system operation.

Exercises

linear control systemskarimpor.profcms.um.ac.ir/imagesm/354/stories/lin... · modern control...

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