Modeling, investigating and design control system of the direct curent motor

Trang 1 Hanoi University of IndustryFaculty: Mechatronics---MAJOR ASSIGNMENT REPORT OF INTRODUCTION TOAUTOMATIC CONTROL SYSTEMSMODELING, INVESTIGATING AND DESIGN CONTROL SYSTEM OF THE DI

Hanoi University of Industry Faculty: Mechatronics -

MAJOR ASSIGNMENT REPORT OF INTRODUCTION TO

AUTOMATIC CONTROL SYSTEMS

MODELING, INVESTIGATING AND DESIGN CONTROL SYSTEM OF

THE DIRECT CURENT MOTOR

Supervisor: Master Bui Huy Anh Student: Do Manh Dung

Class: ME6159.TA1 - Course 17 Student ID: 20226006516

Hanoi - 2023

INTRODUCTION 2

SECTION 1: BRIEFT OVERVIEW OF THE DESIGNED SYSTEM 3

1.1: System modeling 3

1.2: Transfer function 4

1.3: The stability of the control system 5

1.4: The system respone 6

SECTION 2: THE INFLUENCE OF PARAMETERS ON SYSTEM QUALITY 8

2.1: The influence of electric inductance L on system quality 8

2.2: The influence of electric resistance R on system quality 10

2.3: The influence of Moment of inertia of the rotor J on system quality. 11

SECTION 3: DESIGN THE PHASE DELAY CONTROLLER FOR THE SYSTEM 13

3.1: Phase delay controller 13

3.2: Investigate the dependence of position control quality on controller parameters 14

3.3: Investigate the influence of a to the quality of the control system 15

3.4: Investigate the influence of Kc to the quality of the control system.17 3.5: Investigate the influence of T to the quality of the control system 18

IN CONCULSION 20

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The direct current motor is a peripheral device that is widely used because of its simple control and affordable price A direct current motor DC (DC is stand for

“Direct Current Motors”) is a mortor controlled bt a current with a fixed direction

of in other words, this is a type of motor that runs on a DC voltage source – a direct voltage (Different from AC alternating voltage) The ouput wires of the motor usually consist of two wires (power wire – VCC and ground wire – GND)

DC motor is a direct curent motor with continuous rotation function

DC motors come in many types, each with different specific functions Around

us, small DC motors are used in tools, toys, and various household appliances Inindustry, applications of DC motors include conveyors and turntables, … using large power DC motors in applications such as brakes and reversing… We have some examples such as DC motor in fan, hydraulic pumps, direct current DC motor used in the robot manufacturing industry

This article aims to simulate and design the control system through the

application of DC motor

SECTION 1: BRIEFT OVERVIEW OF THE

DESIGNED SYSTEM

1.1: System modeling

In general, the torque generated by a DC (direct current) motor (động cơ) isproportional to the armature current and the strength of the magnetic field In thisexample we will assume that the magnetic field is constant and, therefore, thatthe motor torque is proportional to only the armature current i by a constantfactor K

t as shown in the equation below This is referred to as an controlled motor

In SI units, the motor torque and back emf constants are equal, that is, K e=K t=K

; therefore, we will use K to represent both the motor torque constant and theback emf constant

From the figure above, we can derive the following governing equations based

on Newton's 2nd law and Kirchhoff's voltage law

(4) L di

dt +Ri=V L +V R =V −e=V −K θ

.

(2.2)Applying the Laplace transform, the above modelling equations can be expressed

in terms of the Laplace variable s.

1.2: Transfer function

G (s)= Θ (s)

V (s)

We arrive at the following open loop transfer function by eliminating I(s)

between the two above equations

However, during this example we will be looking at the position as the output

From the concept: 𝑅 = 1Ω, 𝐿 = 0.5𝐻, 𝑏 = 0.1𝑁𝑚𝑠, (K=Ke=Kt) = 0,01 Nm/Amp

1.3: The stability of the control system

Matlab is used to enter the parameters and transfer function just found, type the codes below in m-file and run in Command Window:

The bode plot is shown below

⇒ The Gm is infinity value, which means that the amplitude of the system does not exceed the steady stae It is an indicator of the maximum amplitude that the system can achieve before becoming unstable Pm is infinity value, due to the phase of the system never meet -180 degrees, which is positive because a phase near -180 degrees can leed to unstable

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1.4: The system respone

The following codes are used in Matlab to find the system respone diagram:

 Steady state: infinity

⇒ The motor DC can’t meet the system respone requirements because of the large steady state

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SECTION 2: THE INFLUENCE OF PARAMETERS

ON SYSTEM QUALITY.

2.1: The influence of electric inductance L on system quality

The following codes are used in Matlab

The diagram is created by the codes above.

Comment: When L increases from 0.5 to 5:

 Peak respone does not change

 Steady state is reduced

 Settling time is increasing

 Rise time is increased

⇒Increasing L reduces the error, but the system response time increases a lot

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2.2: The influence of electric resistance R on system quality

The following codes are used in Matlab

 Peak respone is reduced.

 Steady state is reduced

 Settling time is reduced

 Rise time is reduced

⇒The system takes less time to be stable

2.3: The influence of Moment of inertia of the rotor J on system

quality.

J=0.01;

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The diagram is created by the codes above.

In conculsion, we can derive the change in the moment of inertia J of the rotor does not seem to affect the peak response nor does improve the steady state of the system However, as the moment of inertia J becomes larger, the rise time and the response time is longer

⇒ The rise time and the response time of the DC motor system is proportional to the moment of inertia of the rotor

SECTION 3: DESIGN THE PHASE DELAY

CONTROLLER FOR THE SYSTEM.

3.1: Phase delay controller.

The phase delay controller is a low-pass filter Using the phase delay stage will narrow the system’s bandwidth, causing the system’s gain coefficient for high frequency input signals to decrease, due to the phase delay stage having no effect

on the respone

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Because of reducing the gain coefficient in the high frequency domanin, the phase delay has the effect of filrtering high frequency noise that affects the system.

Because the gain coefficient in the low frequency domain is large, the phase delay stage reduces the system’s steady state

The transfer function of the phase delay stage is written as:

Therefore, the structure of the phase delay stage as below:

The parameters of the phase delay controller that need to be investigated are Kc,

From the diagram, the parameters are identified below:

 Peak respone: -2.75 (5.58s)

 Steady state: 0.44

 Settling time: 38.8s

3.2: Investigate the influence of a to the quality of the control system.

Kc=8 and T=100 are kept the same , a is changed as follows: 0; 0.2; 0.4; 0.6; 0.8; -1

-The following codes are excuted as:

legend('a= 0','a= -0.2','a= -0.4','a=-0.6','a=-0.8','a=-1')

Comment: a is increased from -1 to 0

 Overshoot = 0

 The settling value are all equal to 0.444

 Settling time increased from 38.8s to 217s

 Time gradually increases from 15.2s to 122s

 Increasing a causes the system to quickly meet the steady state

3.3: Investigate the influence of Kc to the quality of the control system.

a=-1 and T=100 are kept the same , Kc is changed as follows: 0; 2; 4; 6; 8; 10The following codes are excuted as:

 When increasing Kc from 2 to 8, the settling time decreases from 263 to 38.8, but when changing Kc=10, the settling time increases to 886

 The settling value increases from 0 to 0.5 when changing Kc from 0 to 10

3.4: Investigate the influence of T to the quality of the control system.

a=-1 and Kc=8 are kept the same, T is changed as follows: 0; 20; 40; 60; 80; 100.The following codes are excuted as:

IN CONCULSION

 Control and position control of DC motors is an interesting topic This is ahighly practical research model, the basis for machine control, robot

control, and the foundation for developing future automation models

 After completing the major assignment, we can understand how the modelsimulates a real system Know how to use Matlab simulation software and

test the system on the simulink model Know how to investigate an

automatic system and depend on the system response to external

parameters (specifically in the article, the dynamic response depends on

the moment of inertia of the rotor) The major assignment created

conditions for practicing the design of the controller and testing it on the

machine Surveying and giving results of the system response dependence

on controller parameters, the system response can be self-aligned as

desired

 Advantages in the process of carrying out major assignment: abundant resources and close to the topic, enthusiastic support from teachers,

provision of complete documents The long period of study and research,

with the support of the internet combined with the knowledge

accumulated during the classroom learning process, helps complete large

assignments quickly

 However, there are still many difficulties in the implementation process, the conditions for practicing and working on computers are still limited, so

exposure to this type of exercise is still confusing In the process of

writing, mistakes will be inevitable Therefore, with the goal of

completing major assignments completely, all comments and

contributions from teachers and readers will be seriously accepted

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