automotive control project

8/10/2019 Automotive Control Project

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5430577521

5430578121

2103408 Automotive Control

1 2556


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1

Introduction 2

System Description 2

Objective 2

Model 2 - 5

Needs of Control 6

PID Controller Design 6 - 8

System Hardware and Software 8 - 12

References 13

Appendix 14


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Mathematic Model of DC Motor

In general, the torque generated by a DC motor is proportional to the armature current and the

strength of the magnetic field. In this example we willassume that the magnetic field is constant and,therefore, that the motor torque is proportional to only the armature current i by a constant factor Kt as

shown in the equation below. This is referred to as an armature-controlled motor.

The back emf, e , is proportional to the angular velocity of the shaft by a constant factor Ke .

In SI units, the motor torque and back emf constants are equal, that is, Kt = Ke ; therefore, we willuse K to represent both the motor torque constant and the back emf constant. From the figure above, we can derive the following governing equations based on Newton's 2nd law and

Kirchhoff's voltage law.

From FBD of the motor: = = ; = (1)

From KVL: (2)

Laplace transform (1) and (2),

TransferFunction:

Input: ( ) Output: ( ) State-Space:


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J: Moment of inertia of the rotor

R = 0.01m z = 0.015m

=13

2

3 w = 0.015m h = 0.035m D = 0.005m d = 0.035/2 + 0.01 = 0.0275m

=

HDPE = 930 / 3

=

= 0.3 2+ 3 1

12(

2+ 2) + 2

= 0.029223 2 K t: Motor torque constant

Maximum efficiency Data sheet Appendix 1

= =0.0010297

(0.36 )= 2.8603

10 3

K e: Electromotive force constant

K t

= 2.8603 10 3

B: Motor viscous friction constant

no load Data sheet Appendix 1


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= = 2.8603 10 3 (0.1 ) = 2.8603 10 4

= =(2.8603 10 3 )

6700

260

= 4.0767

10 7

R: Electric resistance

Maximum efficiency Data sheet Appendix 1

= =3

0.36 = 8.3333

L: Electric inductance

= 0.001

TransferFunction

( ) = ( )( ) =2.8603

10 32.922 10 52+ 0.2435 + 1.158 10 5

Transfer Function Second order


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Needs of Control

3000 rpm

Rise time < 1 s

Setting time < 3 s

%MP < 20 %

Steady-State Error=0

PID Controller Design

PI Root-Locus Method Block Diagram

Transfer Function

( ) ( ) =

( ) ( )1 + ( ) ( )

( ) =2.8603 10 3

2.922 10 52+ 0.2435 + 1.158 10 5

Plant

( ) = 231 +0.035

PI Kp = 231 Ki = 0.035 Root-Locus Method MATLAB Sisotool

( ) ( ) ( ) ( ) ( )


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Design Requirements Root-Locus


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Design Requirements

Rise time = 0.806 s

Setting time 1.43 s %MP = 0 %

Steady-State Error=0

System Hardware and Software


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1. ET-Easy STAMP Arduino Board

2. H-Bridge Circuit Motor Driver

3. 3V 5240 RPM DC Motor ( Data Sheet Appendix 1)

4. 4x 1.5V AA Battery


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5.

6. TCRT5000 Reflective Optical Sensor

sensor

7. Arduino

//control parameter for tuningdouble Kp = 231;

double Ki = 0.035; double Kd = 0;

double lastVal = 0; // for D action double Integral = 0;

double IntegratorUpperLimit = 50000;

double IntegratorLowerLimit = -50000;

double V = 0; //voltage double Speed = 0; //read speeddouble Period = 0.1;


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//Serial.print(" ");

}

void UpdateSpeed(){counter++; if(counter==9) {

Speed = (180)/(samplingCount*Period); counter = 0;

samplingCount = 0;

}}


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Appendix 1

Data Sheet 3V 5240 RPM DC Motor

automotive control project

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