W1-Introduction of Control System

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BMFA 2413Introduction To Control

Systems

Lecturer

Silah Hayati binti KamsaniFaculty of Manufacturing Engineering

Department of Robotics and AutomationEmail: [email protected] Phone: 06-

3316401

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mailto:[email protected]:[email protected]


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Learning Outcomes

At the end of this course, students should be ableto:

Identify basic control system theory such as transferfunction, Laplace Transform, stability analysis, linearequation, time respond and others.

Model linear and time invariant system using frequencydomain and state space method.

Model linear and time invariant system for mechanicaland electromechanical systems by manipulating block

diagrams and signal flow diagram. Apply commercially available mathematical software to

solve control theory problems.

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References

Text books: Nise, S Norman, Control Systems Engineering, 5th Edition, John

Wiley & Sons Inc., United State of America, 2008.

Ogata, Katsuhiko, Modern Control Engineering, 4th Edition,

Prentice Hall, 2002

Palm W. J, Control System Engineering, John Wiley, 2002

Bishop, Dorf, Modern Control Systems, 10th Edition, PrenticeHall, 2005.

Ogata, Katsuhiko, MATLAB for Control Engineers, Prentice Hall,

2008.

Computer Usage:

MATLAB and Simulink Programming

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Course EvaluationsNO. COURSE WORK PERCENTAGE, %

1 Laboratory activities x 6Laboratory work basis in maximum 2 persons/group withindividual short lab report

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2 Project x 1Group activities with maximum 4 persons/groupTo measure the students understanding and analysis on aproblem-based task

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3 Test x 2Test on students knowledge and understanding about therecent topic.

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4 Practical Assessment x 1Hands-on test on students knowledge and understandingabout the laboratory and practical activities.

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5 Assignment x 1Critical review on any journal/article regarding controlsystem (max. 2 persons/group)

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6 Final ExamUnderstanding, applications, problem solving and decision

making.

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TOTAL 100

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Introduction

Control systems are important and are present almost everywhere in our

daily lives.

Examples of man-made control systems: CD player, radio antenna,

rockets/missiles, robots, oven, room air condition.

Examples of God-created control systems : level of adrenalin in the human

body, entry of light through the human eye, holding and carrying things

using hand, human riding a bicycle.

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Introduction

Generally, control system can be classified into threecategories;

nature control system created by God (example human body immunization, etc.)

automatic / modern control system created by human(example auto pilot flight operation, satellite system,space shuttle, robotic system and etc.)

combination between nature and automatic controlsystem (example human driving of car)

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What are the advantages ofcontrol system?

Advantages of control systems - 4 primary reasons:

Power amplification Radar rotation.

Remote control Robot for picking material in

hazardous environment.

Convenience of input form Any type of input -

mechanical, electrical, air etc.

Compensation of disturbance - Measure thedisplacement of the antenna cause by wind and return

the antenna to the position commanded by the input.

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The earliest complete control systems are water clock invented and a double

acting pump by al-Jazari, 1206.

History of Control Systems

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a. Early elevators were

controlled by hand ropes or

an elevator operator. Here, a

rope is cut to demonstrate

the safety brake, an

innovation in earlyelevators;

b. Modern Duo-lift elevators

make their way up the

Grande Arche in Paris,

driven by one motor, witheach car counterbalancing

the other. Today, elevators

are fully automatic, using

control systems to regulate

position and velocity.Photos courtesy of UnitedTechnologies Otis Elevator.

History of Control Systems

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What is SystemA system might be considered as an assemblage of

components that provide interactions.

M

f (t) Input

Spring

(K)

ViscousDamper

(C)

x (t)Output

Mass spring damper system

Disassembly system

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What is Control SystemA control system consists ofsubsystems and processes (orplants) assembled for the purpose ofcontrolling theoutputs of the processes.

Input Sensing DevicesInput Sensing Devices Output Load DevicesOutput Load Devices

Visual &Sound

Signals

Visual &Sound

Signals

Local PLC

cont rol ler

Local

Process

Cont rol

System

Local PC

Central

PLC

cont roller

Comput er

System

Other part

of indus try

Indus trial

network

(high level)

Indus trial

network

(middl e level)

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What are the areas of applicationof control engineering?

Examples of application:

Home appliances: microwave, telephone, computer, VCD player, clocketc..

Industry: CNC machine tool, robot, conveyor, AGV etc..

Biological: Animals, plants, ants, human ..etc

Social: Country, districts, society, etc.

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Controlled variable the quantity/condition that is measured andcontrolled (normally controlled variable is the output of the system)

Manipulated variable the quantity/condition that is varied by thecontroller so as affect the value of the controlled variable

Plants a piece of equipment/set of a machine functioning together,which perform a particular operation

Process progressively continuously operation that consists of aseries of controlled action to achieve a particular result.

Systems a combination of components that act together andperform a certain objective

Definitions of Terms in

Control Systems

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Disturbance a signal that tends to adversely affect the valueof the output of the system. There are two types ofdisturbance; internal disturbance generated within the system external disturbance generated outside the system and is

an input

Automatic control system a control system that is self-

regulating without human intervention

Process control system an automatic regulating system in

which the output is a variable such as temperature, pressure,

flow, liquid level or pH is called process control system

Definitions of Terms in

Control Systems

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Fundamental blocks

Represents components or subsystems such as controller, amplifier, etc.

Each block may have one or more inputs which affects the output of the

components.

The input and output signals may have the same form or they may be

changed into a different form depending on the function of the component or

subsystem.

System Representation

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Take-off point

V V

V

-allows a signal to be taken from any

components output. Assume that it does not

load any components output (the signals are not

changed).

Summing junction V=V1-V2+

-

V1

V2

-allows 2 or more signals to beadded/subtracted. The +, - sign indicates

whether the signals are added or

subtracted.

Components/subsystems


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Components/subsystems (others)Controllers, plants

Actuators

Sensors

Amplifiers

Signals in Control Systems

Input/reference [u(t),r(t),R(s)] represented by an arrow pointing into

the block, can be manipulated or controlled

Output [y(t), c(t), C(s)] represented by an arrow pointing away from theblock, the needed signal

Error [e(t)=r(t)-c(t)]

Feedback

Disturbances/noise is also an input signal that cannot be controlled


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Input

Transducer

Input

R(s)+ Plant+

Noise 1 Noise 2

++ Output

C(s)

+ Controller

Summer

Output

Transducer

-

Error (E(s))

Plant


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Examples of system


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Examples of systemrepresentation

A motorcycle can be considered as a system.

The main input to the system is the throttle angle and the main output is the motorcycle speed.

This system can be represented as follow:

Fuel flow rate, q Motorcycle speed, n

The arrows represent variable while the components arerepresented by blocks.

Each blockhas an input and an output variable.

The output variables of a component can bethe input variable for another component ! !!

Throttle Engine Gear Wheel

Throttle angle, Engine speed, N Wheel speed, n


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This control function or the interference to the process is introduced by an

organization of parts (including operators in manual control) that, when

connected together is called the Control System.

Depending on whether a human body (the operator) is physically involved in

the control system, they are divided into Manual Control and Automatic

Control. Due to its efficiency, accuracy and reliability, automatic control is

widely used in chemical processed.

Control Systems Categories

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It can be seen that this control system, completed by theoperator, possesses

the following functions:

Measurement

This is essentially an estimate or appraisal of the process

being controlled by the system. In this example, this is

achieved by the right hand of the operator.Comparison

This is an examination of the likeness of the measured

values and the desired values. This is carried out in the

brain of the operator.

Control Systems Functions

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Computation

This is a calculated judgment that indicates how much the measuredvalue and the desired values differ and what action and how much

should be taken. In this example, the operator will calculate thedifference between the desired temperature and the actual one.Accordingly the direction and amount of the adjustment of the valveare worked out and the order for this adjustment is sent to the lefthand from the brain of the operator. If the outlet water temperatureis lower, then the brain of the operator will tell the left hand to open

the steam valve wider. If there is any disturbance, or variation of flowrate in water to the shower inlet, some adjustment must be made tokeep the outlet water temperature at a desired value.


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Correction

This is ultimately the materialization of the order for the adjustment.

The left hand of the operator takes the necessary actions following

the order from brain.

Therefore, for a control system to operate satisfactorily, it must have

the abilities of measurement, comparison, computation and

correction.

Of course, the manual operation has obvious disadvantages e.g. the

accuracy and the continuous involvement of operators. Althoughaccuracy of the measurement could be improved by using an

indicator, automatic control must be used to replace the operator. In

industry, it is automatic control that is widely used.


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Firstly, we can use a temperature measurement device to measure the

water temperature, which replaces the right hand of the operator. This

addition to the system would have improved accuracy.

Instead of manual valves, we use a special kind of valve, called a

control valve, which is driven by compressed air or electricity. This will

replace the left hand of the operator.

We put a device called a controller, in this case a temperature

controller, to replace the brain of the operator. This has the functions

of comparison and computation and can give orders to the control

valve.

The signal and order connections between the measurement device,

control valve and controller are transferred through cables and wires,

which replace the nerve system in the operator.

Automatic Control Systems

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Examining the automatic control system, it is found that it

contains the following hardware.

Sensor - a piece of equipment to measure system variables.

It serves as the signal source in automatic control.

Controller - a piece of equipment to perform the functions of

comparison and computation.

Control Element - a piece of equipment to perform the control

action or to exert direct influence on the process. This element

receives signals from the controller and performs some type of

operation on the process. Generally the control element is

simply a control valve.

Control Systems Hardware

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Associated with a control system are a number of different types of variables.

First we have the Controlled Variable. This is the basic process value being regulated by

the system. It is the one variable that we are specially interested in - the outlet water

temperature in the example above.

An important concept related to the controlled variable is the Setpoint. This is the

predetermined desired value for the controlled variable. The objective of the control

system is to regulate the controlled variable at its setpoint.

To achieve the control objective there must be one or more variables we can alter or

adjust. These are called the Manipulated Variables. In the above example this was the

input hot water flow rate.

Conclusively, in the control system we adjust the manipulated variable to maintain thecontrolled variable at its setpoint. This meets the requirement of keeping the stability of

the process and suppressing the influence of disturbances.

Control Systems Principle

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What is the objective of control


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What is the objective of controlsystems?

Objective of Control System

A control system provides an output or response for a given input orstimulus.

It is designed such that the output variable equals to the desired variable.

(Example: Air-Conditioning System desire temperature is 16C,so the output temperature of air-conditioner system should be16C)

A controlled variable normally determines the inputand outputof a controlsystem.

Control strategies are needed to achieve this objective.

Basically there are two control strategies open loop control and closed

loop control.34

Ex.: Elevator buttons and the desired level (Input), actual level ofelevator (Output), elevator level -> controlled variable.

O L C l S


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Open Loop Control Systems (OLCS):The output signal of an OLCS is not fed back to influence

the control action.

Inputtransducer

Input

R(s)

+ Plant+

Noise 1 Noise 2

++ Output

C(s)Controller

The control action of an OLCS depends only on the input

signal. OLCS are not capable of filtering disturbances/noise.

Examples: toaster, washing machine, studying time, electric

fan, traffic light, ceiling fan and oven.

Open Loop Control Systems

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Open loop control system a control system in which thecontrol/regulating action is independent of the output (output has no

effect on the control action)

In other words; the output of open loop control system is not

compared with the reference input

Input transduceris functioning to converts the form of the input tothat used by controller.

The controlleris functioning to drives the process/plant

The inputcan be called reference/set pointand the outputcan be

called controlled variable

Disturbances also called as input to the system and affect theoutput/controlled variable. Open loop controlled system cannot

compensate the disturbance and do not correct for the disturbance

signal .

Example : Washing machine operated on time basis, does not

measure the output signal (cleanliness of the clothes)


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In general, any control systems that operated on a time basis isopen loop control system

Open loop control system is easier to build because systemstability is not a major problem

Advantages & Disadvantages of open loop control system; Advantages:

simple construction

easy maintenance no stability problem convenient when output is hard to measured & not economy

to produced

Disadvantages: the output may different from desired input if there is

calibration error causes by disturbance/changes re-calibration is required from time to time to maintain the

required output


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Example of oven open

loop systemSWITCH

1

21

3

1 ~10000C2 ~

20000C3 ~30000C

CONTROLLER

PROCESS

OVEN

Oven system

Example of oven open loop


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Example of oven open loopsystem

Open Loop System:

The temperature of the oven is controlled by setting the switch toposition 1, 2 and 3.The controller is designed such that for each setting differentelectrical current is supplied to the heating element whichcorrespondingly generating the heat to the oven and set thetemperature 1000C, 2000C and 3000C response.If the desired temperature by user is 2000C the user will set theswitch to position 2. The performance of this system will dependon the accuracy of the controlled designed .

Switch Controller Oven

Set point Temp (T)

Current (i)


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Closed loop control system control system in which the

control/regulating action is influence by the output

In other word; the output is fed back to the input reference for

comparison The actuating error signal (differential between input and the

output signal) is fed back to the controller to reduce the error

and bring the output of the system to desired value

Input transduceris functioning to converts the form of the

input to that used by controller.

Output transducer/sensoris functioning to measure the

controlled variable/output response and convert into the form

used by controller (example ; potentiometer, thermistor,

tachometer, and etc.)

Closed Loop Control Systems

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At the 1st summing junction, the output and disturbance

which fed back via feedback path is compared with the

input reference where the output signal is subtracted from

the input signal. The result called actuating signal/error.

The controller will make correction and drive theplant/process if any error/actuating signal generated. If no

error, plants response is already the desired response.

Example : Room temperature control by measuring the

actual room temperature and comparing it with reference

temperature (desired temperature), the thermostat turns

the heating/cooling equipment on/off in such way to ensure

the room temperature at comfortable level.

Closed Loop Control Systems

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Feedback control systems are often referred to as closed

loop control system. A system that maintains a prescribed

relationship between output and input and using the

difference by comparing them is called feedback controlsystem.

There are numerous example of closed loop/feedback control

system and not limited to engineering but can be found in

various non-engineering fields.

Feedback Control Systems

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Examples of oven closed


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Examples of oven closedloop system

Switch Controller Oven

Set point

Operator

Sensor

Manually


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OLCS vs CLCS


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Open Loop System Closed Loop System

Does not have the feedback path. Have the feedback path.

Low accuracy. Greater accuracy

Sensitive to noise, disturbances andchanges in the environment.

Less sensitive to noise, disturbances andchanges in the environment.

The system cannot compensate and

correct disturbance

The system can compare the output

response with the input and make acorrection if there is any difference

Simple and inexpensive Complex and expensive

The differences between open and closed-loop system are

shown in table below;

OLCS vs. CLCS

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Car Speed Control

The car speed is controlled by pressed or depressed theaccelerator pedal, which is, controls the fuel quantity to carengine.

Figure below shows the equivalent block diagram for car speed

controller(humandriver)

carengine

transducer(speedometer

)

i/p reference(desiredspeed)

o/p response(actualspeed)

Control Systems Example

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The following term can identify from the block diagram;

Process/plant engine car

Controller human driver

Sensor/transducer speedometerInput reference desired speed (example: 110 km/h)

Controlled variable actual speed

Manipulated variable fuel quantity

The controller (human driver) is measure the car speed through speedometer.

If the speed of the car exceed than desire speed (example 110 km/h), thedriver will depressed the accelerator pedal.

Car speed control is classified as closed loop/feedback control system


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Liquid Level Control

Figure below shows the block diagram of simple liquid levelcontrol

The objective of this control system is to maintain/controlthe liquid level in the tank at desire value

controlvalve

liquid tank

level sensor

error /actuating signal

actual level

actual level

controller


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From the block diagram, the following term can be identifying;

Controlled variable liquid level

Manipulated variable liquid flow

Transducer level sensor

Process/plant liquid tank

The fluid level in the tank cannot be directly controlled. It can be controlled

only by changing/manipulating the water flow into the tank

The differences between input reference (set point) and output signal

generate an error / actuating signal.

If the error signal is positive, it indicates to controller that actual level is lower

than desired level. Than its drive controller to open the control valve to allow ahigher flow rate into the tank

If the actual level is higher than desired level, the control valve turn close to

reduce the inflow rate

The liquid level control can classify as closed loop/feedback control system.


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Analysis and Design


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Objectives

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Control systems are dynamic: it responds to the input by going through atransient phase before settling to the steady state phase. Normally, we would

like the steady state signal to be the same as the input signal.

transient response steady state

Three major analysis and design objectives are:

1. Producing the desired transient response: Transient response is the case when the plant is

changing from one steady state to another, when there are changes in the input signal.

Example: elevator.

2. Achieving stability: A system that can produce a consistent/steady output is a stable

system. An unstable system is harmful to the plant and may cause serious accidents.

3. Reducing steady state error: Steady state response only exists for stable systems. An

important characteristic for design is the steady state error. Example: an elevator that

does not stop at the same level at the floor may cause serious accidents to its passengers.

Control Systems Response


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Characteristics

Response Characteristics of elevator:

Transient response Gradual increase from 1st floor to 4th floor.Steady state response When the elevator reaches to the desiredfloor.

Steady state error The accuracy of the elevators leveling with thefloor.

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Input:desiredlevelOutput: actualelevator level(control variable)

Control Systems Design:


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Time,s

Floor

G

1

2

3

4

5

6

7

y g

Analysis & Objectives

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Control Systems Design:


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Draw aschematic.

Step 3

Simplify theblock

diagrams.

Step 5 Step 4

Determine aphysical

system from

requirements.

Step 1 Step 2

Analysis anddesign.

Step 6

Build aprototype.

Step 7

Draw afunctional

block

diagram.

Draw aschematic.

Form themathematical

model andblock

diagrams.

Step 4

Simplify the

blockdiagrams.

Step 5

Analysis and

design.

Step 6

Process

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Design Process of Control


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System HOW TO START THE ANALYSIS OF DESIGN PROCES:

1.Transform requirements into physical system2.Draw a functional block diagram

3.Create a schematic4.Develop a mathematical model (Block Diagram)

1.Kirchhoffs voltage law2.Kirchhoffs current law3.Newtons laws

5.Reduce the block diagram6.Analyze and design

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MathematicalModel

Mathematical model of Spring Damper System:K, C and M are spring constant, damping coefficient and massresponse. The variables are force, f (t) and displacement x (t).

We would like to develop a mathematical model relating f (t) as inputand x (t) as the output.

f (t) Input

x (t) Output

f (t) Input x (t) Output

?=f

x

K C

M

Spring damper


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Mathematical

Model

Free Body Diagram of Spring Damper System:

K, C and M are spring constant, damping coefficient and massresponse. The variables are force, f (t) and displacement x (t).We would like to develop a mathematical model relating f (t) as inputand x (t) as the output.

f s (t)

Spring damper

M

f d (t)

f (t)

x(t)


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Testwaveforms

used in

controlsystems

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W1-Introduction of Control System

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