DC Motor Control docx

DC Motor Transient Running Operation This demo simulates the running of a DC motor with constant field or pm excitation 5 hp 240V 1200 rpm rated torque Tr = 30 N.m BLOCK DIAGRAM MODEL OF

DC Motor Control: Theory and Implementation

By Chung Tan Lam

CIMEC Lab.

I Introduction

A DC motor speed drive

The mathematical model of dc motor (permanent magnet type) can be expressed by these equations

where

a

V : Armature voltage [V]

a

i : Armature current [A]

e

T : Electromagnetic torque [N.m]

L

T : Load torque [N.m]

a

L : Armature inductance [H]

a

R : Armature resistance [Ω ]

K : Coupling coefficient [N.m/A]

J : Momen of inertia [Kg.m 2 ]

m

B : Damping coefficient

The block diagram of a cascade closed-loop speed control of the dc motor is shown below.

DC MOTOR MODEL

CASCADE SPEED CONTROL OF A DC MOTOR DRIVE

Typical dynamic responses are also shown The motor is initially at standstill and

at no load when a step command in speed is applied; when steady-state conditions are reached, a reversal of speed is commanded followed by a step load application

The system is highly nonlinear due to the introduction of saturation needed to limit both the current delivered and the voltage applied to the motor The system is in the saturation mode when the errors are large; as a consequence, the controller functions as a constant current source, that is torque, resulting in the ramping of the speed since the load

in this example is a pure inertia The inclusion of saturation limits on the PI integrator is therefore necessary to provide antiwindup action The presence of the signum function in the torque expression is required in order to insure that the load is passive whether the speed is positive or negative (as is the case here)

1 DC Motor Transient Running Operation

This demo simulates the running of a DC motor with constant field or pm excitation (5 hp 240V 1200 rpm) rated torque Tr = 30 N.m

BLOCK DIAGRAM MODEL OF A DC MOTOR

MOTOR TRANSIENT RUNNING OPERATION

Electrical system equation:

va = Ra.ia + La.dia/dt + ea

where ea = K.wm

Mechanical system equation:

Te = J.dwm/dt + Tl.signum(wm) + f(wm)

where Te = K.ia

Simulation Results

MOTOR SPEED [rad/s]

MOTOR CURRENT [A]

2 DC Motor with bipolar PWM excitation

This demo simulates the running of a DC motor with PWM (bipolar) excitation (5

hp 240V 1200 rpm) rated torque Tr = 30 N.m

DC Motor With Bipolar PWM Excitation

DC Motor Model

Simulation Results

Voltage Average Applied To Motor

MOTOR SPEED (rad/s)

Motor Current (A)

3 DC Motor with unipolar PWM excitation

This demo simulates the running of a DC motor with PWM (unipolar) excitation (5

hp 240V 1200 rpm) rated torque Tr = 30 N.m

DC Motor Model

Simulation Results

Voltage Average Applied To Motor

Motor Speed (Rad/S)

Motor Current (A)

4 Automatic Starter of a DC Motor

This demo simulates the starting of a DC motor with automatic starter

(5 hp 240V 1200 rpm) rated torque Tr = 30 N.m The starter is simulated by a speed-dependent effective armature resistance using a look-up table Mathematical model of the dc machine



















=

=

+ +

=

+ +

=

a e

m a

L m

m e

a a a

a a a

Ki T

K e

T B dt

d J T

e i R dt

di L V

ω ω

where

a

V : Armature voltage [V]

a

i : Armature current [A]

e

T : Electromagnetic torque [N.m]

L

T : Load torque [N.m]

a

L : Armature inductance [H]

a

R : Armature resistance [Ω ]

K : Coupling coefficient [N.m/A]

J : Momen of inertia [Kg.m 2 ]

m

B : Damping coefficient

Simulation Results

MOTOR SPEED

MOTOR CURRENT

H-BRIDGE DRIVER MODULE

T itle

F u ll B rid g e D riv e r

A 4

W e d n e s d a y , M a y 1 1 , 2 0 0 5

R 5

1 K

A N 1

1

C T

E 1 7

A N 2

3

C T

4

E 2 5

C 2 6

U 7 P C 8 1 7

A N 1

1

C T

E 1 7

A N 2

3

C T

4

E 2 5

C 2 6

U 6 P C 8 1 7

1 2 3 4 5 6 7 8 9

1 0

1 1

1 2

1 3

1 4

J 5

C O N 1 4

O u t2

O u t1

R 1 3

4 x 4 7 0

D 1

R C 0 /T 1 C K I

C 6

1 0 3

V c c

1

IN

2

C O M

3

L O

4

V b 8

H O 7

V s 6

N C 5

U 1

IR 2 1 0 5

D 5 _ P W M 1

2 4 V D C

1 5 V D C

R 6

5 0 K

O u t1

D 7 _ P W M 2

2 4 V D C

1 5 V D C

O u t2

H O 1

H O 1

R C 2 /C A P 1

3

2 1

-+

U 3 A

L M 3 5 8

5

6 7

-+

U 3 B

L M 3 5 8

V s 1

2 3 4 5

R 2 4

4 x 4 7 0

D 1 3

D 0

D 1

D 1 4

D 2

D 3

D 1 5 D 1 6

L O 1

+ C 1 2

3 3 u F -6 4 V

D 5

C 1

1 0 4

H O 2

R E 2

V s 2

2 3 4 5

R 1 4

4 x 2 2 K

L O 1

L O 2

5 V D C

In 4

In 3

D 6

V s 1

L O 2

5 V D C

In 2

D 7

In 1

+ C 1 3

3 3 u F -1 6 V

5 V D C

R 1 5 4 7 K

S e n s in g

D 8

In 1

R E 1

5 V D C

D 2

D 1

C 9

1 0 4

D 4

D 3

D 6

D 5 _ P W M 1

R 1 6 4 7 K

R C 4 /S D I

D 7 _ P W M 2

R B 0 /IN T 0

R B 4

R B 1 /IN T 1

R C 5 /S D O

In 2

A N 0

R E 2

R E 1

R B 5

2 4 V D C

G N D

R C 1

R C 2 /C A P 1

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

J 1

C O N 1

1 2 3 4 5 6 7 8 9

1 0

1 1

1 2

1 3

1 4

J 2

C O N 1

P O R T V C C

R C 0 /T 1 C K I

V C C _ IO

E X T V C C

R E 0 /R D

R E S E T #

R C 3 /S C K

D 0

S e n s in g

In 4

R 1 8 4 7 K

A N 0

D 2

V c c

1

IN

2

C O M

3

L O

4

V b 8

H O 7

V s 6

N C 5

U 2

IR 2 1 0 5

C 2

1 0 4

H O 2

IN

1

O U T 3

U 4 K I7 8 1 5

V s 2

1

2

3

4

5

J 3

E n c o d e r

R B 0 /IN T 0

2 3 4 5

R 1 9

4 x 4 7 0

2 4 V D C

R 2 0

4 x 1 5 0

R B 5

2 3 4 5

R 2 1

4 x 2 2 K

1 5 V D C

2 3 4 5

R 2 2

4 x 4 7 0

A N 1

1

C T

E 1 7

A N 2

3

C T

4

E 2 5

C 2 6

U 5 P C 8 1 7

R B 4

D 4

D 3

O u t2

C 7

1 0 4

O u t1

5 V D C

R 4

1 K

R B 1 /IN T 1

R C 1

5 V D C

(H-Bridge Driver + 2 output +4 input + 4 Indicator LED’s)

T it le

H -B rid g e P o w e r M O S F E T A

W e d n e s d a y , M a y 1 1 , 2 0 0 5

G N D

O u t p u t 2

O u t p u t 1

I n p u t 3

G N D 3

I n p u t 4

G N D 4

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

J 3

T o H -B rid g e D riv e r

O u t 2

O u t 1

V s 1

H O 1

V s 2

I n p u t 1

I n p u t 2

I n p u t 3

C u r rA m p

1

T 1

I R F 5 4 0

1

Q D

I R F 5 4 0

O u t p u t 1

O u t 1

1

Q C

I R F 5 4 0

M 1

C 3

1 0 4

V S 1

V S 2

H V

H V

1

Q B

I R F 5 4 0

+

C 4

1 0 0 0 u F -6 4 V

1

T 2

I R F 5 4 0

O u t p u t 2

O u t 2

1

Q A

I R F 5 4 0

R 1

0 0 1 -1 W + C 53 3 u F -6 4 V

F 1

F U S E

1 2 3 4 5 6 7 8

J 1

O u t p u t 1

1 2 3 4 5 6 7 8

J 2

O u t p u t 2

M 2

H V

G N D

H V

C 6

1 0 4

R 2

0 0 1 -1 W

C u rrA m p

R 3

1 0

R 4

1 0

R 5

1 0

R 6

1 0

H O 1

L O 1

H O 2

L O 2

I n p u t 1

G N D 1

I n p u t 2

G N D 2

Power MOSFET Module

T itle

C A N _ U S B In te rf a c e

A 4

W e d n e s d a y , J u ly 2 8 , 2 0 0 4

D B 2

D B 1

P O R T V C C

E X T 5 V

D B 4

D B 3

1 2

J P 2

U S B 5 V

D B 6

D B 5

1 2

J P 3

E x t 5 V

D B 7

R C 4 /S D I

R B 4

R C 1

R B 0 /IN T 0

R C 5 /S D O

V C C

R B 1 /IN T 1

(11,12,13,14): Only for USB Controller

1 2 3

C N 1 3

A D 2

V C C

A N 2

C 7

1 0 4

M C L R

R E 2 /C S

R e s e t_ S W

A N 0

1 2 3

C N 1 1

A D 0

R B 5

R E 1 /W R

R C 0

S W 2

S ta rt

1 2 3

C N 1 4

A D 3

V C C

A N 3

C 8

1 0 4

1

2

3

4

C N 5

A u x _ P o w e r

M C L R

(10): V+=12 or 24VDC depend on Extended board

R 6

1 0 K

R C 3 /S C K

1 2 3 4 5 6

C N 1 0

IC D 2

V C C

1 2 3

C N 1 5

A D 4

V C C

A N 4

C 9

1 0 4

R 7

1 5 0

1

2

3

C N 7

E x t_ 5 V

R B 3 /C A N R X

Power Management

R C 3 /S C K

A N 3

R B 2 /C A N T X

R A 4

1 2

9

1 0

R L Y 1

R e s e t

R A 4

V +

A N 4

R E 0 /R D

R 1

1 0 K

T X D

1

G N D

2

V C C

3

R X D

4

R s 8

C A N H 7

C A N L 6

V re f 5

U 2

M C P 2 5 5 1

V C C

V C C

S W 1

R e s e t

1 2 3 4 5

C N 8

S P I

C 2

E X T 5 V

V C C

V C C

R C 7 /R X

R C 2 /P W M 1

SDO

E X T 5 V

SDI

V C C

SCK

R E 1 /W R

R C 3 /S C K

R E 2 /C S

R B 4

CA NL

CA NH

C 4

1 0 4

CA NL

CA NH

R B 0 /IN T 0

R e s e t_ S W

R A 0 /A N 0

2

R A 1 /A N 1

3

R A 2 /A N 2

4

R A 3 /A N 3

5

R A 4

6

R A 5 /A N 4

7

R B 0 /IN T 0 3 3

R B 1 /IN T 1 3 4

R B 2 /C A N T X 3 5

R B 3 /C A N R XR B 4 3 6

3 7

R B 5 /P G M 3 8

R B 6 /P G C 3 9

R B 7 /P G D 4 0

R C 0

1 5

R C 1

1 6

R C 2 /C C P 1

1 7

R C 3 /S C K

1 8

R C 4 /S D I 2 3

R C 5 /S D O 2 4

R C 6 /T X 2 5

R C 7 /R X 2 6

G N DV D D 3 1

3 2

M C L R

1

O S C 1

1 3

O S C 2

1 4

V D D

1 1

G N D

1 2

R E 0 /R D /A N 5

8

R E 1 /W R /A N 6

9

R E 2 /C S /A N 7

1 0

R D 0 /P S P 0

1 9

R D 1 /P S P 1

2 0

R D 2 /P S P 2 2 1

R D 3 /P S P 3 2 2

R D 4 /P S P 4 2 7

R D 5 /P S P 5 2 8

R D 6 /P S P 6 2 9

R D 7 /P S P 7 3 0

U 1

P IC 1 8 F 4 5 8

V C C

8

O U T 5

G N D 4

N C

1

Y 2

O S C 4 0

V C C

D 1

L E D

R 2

1 2 0

R B 1 /IN T 1

D B 2

D B 3

D B 4

C 3

1 0 4

D B 5

D B 6

1 2

C N 1

R e m o te C P U R e s e t

D B 7

R 3

3 3 0

R C 7 /R X

R B 2 /C A N T X

1 2 3 4

C N 2

R S 2 3 2

R C 4 /S D I

R 4

1 5 0

SCK

D B 0

J P 1

J U M P _ 1

R B 3 /C A N R X

D B 1

R 5

1 5 0

SDI

1 2 3 4 5

C N 6

S P I

V C C RX

SDO

TX

A N 0

A N 1

V +

C 1

1 0 4

A N 2

V C C

G N D

R C 4 /S D I

V C C

1 2 3 4

C N 4

C A N _ O U T

R B 5

V C C

V +

1 2 3 4

C N 3

C A N _ IN

G N D

R B 7

A N 0

R C 6 /T X

R C 5 /S D O

E X T 5 V

1 2 3 4

C N 9

A u x _ P o w e r

G N D

V +

R e s e t_ S W

R C 6 /T X

E X T V C C

R C 5 /S D O

R B 6

R C 2 /P W M 1

C 5

1 0 4

R C 1

1 2 3 4 5 6 7 8 9

1 0

1 1

1 2

1 3

1 4

J 1

C O N 1 4

1 2 3 4 5 6 7 8 9

1 0

1 1

1 2

1 3

1 4

J 2

C O N 1 4

R B 7

R C 4 /S D I

R C 0

R E S E T #

G N D

R C 5 /S D O

E X T V C C

P O R T V C C

R E S E T #

V C C _ IO

R B 6

1 2 3

C N 1 2

A D 1

R E 0 /R D

V C C

A N 1

C 6

1 0 4

V C C _ IO

D B 0

R C 3 /S C K

Motor Controller (PIC18F458 + 5AD’s + CAN Comm.)

MEASURING MOTOR PARAMETERS

These are the motor parameters that are need:

Note that the above values are stated for a single winding with dc motors, and are the phase values for a BLDC motor Brushless dc motors (BLDC) are usually 3 phase synchronous motors used in a configuration to be treated as dc drives Also note, it is assumed that dc motors being discussed have a permanent magnet field supply Wound field motors are not part of this discussion

MOTOR RESISTANCE

For the winding resistance use an ohmmeter For a DC motor measure the armature resistance between the 2 armature wires The ohmic value of the armature resistance will

be very small, thus a high sensitivity ohmmeter will be needed If it is a WYE connected BLDC motor, the armature resistance is the line-to-line resistance Thus divide the resistance (l-l) by 2 to get the phase resistance The ohmic value will also be very small

shaft at some speed [rpm] such as 1000rpm With a dc motor, use a DC voltmeter to

rad/sec Convert rpm to rad/sec as

] [

] [

or sec]

/ [

] [

sec sec

60

min radias

2 min

rpm speed

v Volts rad

speed

v Volts K

rad x

rev x

rev









= π

With a BLDC motor use an ac voltmeter to measure the voltage between any 2 wires of the 3 motor wires and then convert the line-to-line voltage to the phase voltage

73 1

) (

) (phase K line to line

as-











=











rpm

volts K

amp

in lb

T

) (

00684 0

The derivation for the above equation is Equate Electrical Power to Mechanical Power converted to Watts

356 1

x 12

T

x

x 60

2

x

x

Where

N:rpm

Rearranging terms and simplifying:

I

T N

E

x 00684 0

= Where







=

=









=

A

in lb K

I

T

rpm

volts K

N

E

T

l l rms e

constant, Torque

constant, emf

Converting rpm to rad/sec





















=





















=





















−

sec

554 9 2

x sec

60

x min

x 2 min

sec 60

x

rad

v rad

v rev

rev v

π π

Thus



















=











 −

=

=

−

sec

8 1396

00684 0

554 9

00684 0 554 9

) (

rad

v K amp

in lb K

K K

K K

l l e T

e T

T e

Motor rotor inertia can be measured by making an experiment The inertia can be calculated from the equation





=

sec

rad on accelerati

x sec -in -lb Inertia ]

[

on torque

Also (rearranging terms)

[ sec 2] on

accelerati

torque accel Inertia = lb−in−

DC MOTORS

To do this test it is necessary to measure the acceleration of the motor rotor and the acceleration torque of the motor rotor These two parameters are described as follows:

ACCELERATION – This parameter is determined by putting a step in current into the

motor winding to bring the motor up to rated speed The motor will accelerate exponentially The acceleration is a measure of the rate of change of velocity over a period of time To make this test, a dc tachometer should be connected to the motor shaft The output of the tachometer should be connected to a strip chart recorder When a step input in current is applied to the motor winding, the chart recorder will plot the rate of change of the motor shaft velocity as a function of the tachometer output voltage The tachometer calibration can be used to convert volts to rpm The acceleration is therefore the change in velocity for the linear part of the exponential curve (sometimes refered to

as the 66% response of the exponential change in velocity) divided by the time elapsed for the detected rate of change in velocity The resulting calculation of the acceleration must have the dimensions changed to be in units of rad/sec2

TORQUE- An ammeter must be inserted in series with the motor input winding When the step in input current is applied to the motor input, the maximum value of current should be noted This current must be converted to torque The torque is equal to the maximum value of current observed multiplied by the motor torque constant Torque [lbin]= amps[a] x KT [lb-in/a] The inertia is then the acceleration torque divided by the acceleration - Inertia= Accel torque[lb-in]/acceleration[rad/sec2]=lb-in-sec2

BLDC MOTORS- The tests described thus far must be modified for a bldc motor A

bldc motor must be tested with its servo amplifier The step input will be a step in dc voltage to the servo amplifier input The voltage step should be large enough to cause the motor to reach rated speed With bldc motors it is not possible to measure the high frequency phase current in a WYE connected motor Thus some other procedure must be used to measure the current or torque and velocity Commercial bldc servo amplifiers have two dc output test points One output is a dc voltage proportional to velocity with a given calibration The voltage can be directly connected to a strip chart as described previously to measure the motor acceleration, A second test output provides a dc voltage proportional to torque or a percentage of rated torque This calibrated voltage can also be recorded with a stripchart recorder to observe its maximum value for a step voltage input

to the servo amplifier The inertia can thus be calculated as done previously

MOTOR INDUCTANCE L

This procedure assumes a model as a series equivalent R L circuit To measure the motor inductance uses a very low voltage ac source to the motor winding The resistance and inductance will be very small values For a magnetic flux field dc motor, apply the ac voltage to the armature winding For a BLDC motor apply the ac voltage to one pair of the three wires In both cases measure the voltage and the current

Remember that the BLDC motor is usually connected in WYE Thus the readings will be line-to-line You want the phase values for the voltage, so divide the voltage by 2 The impedance of the dc motor or the BLDC motor phase winding is

then-2 2

2 2

tan impedance

s]

var reactance[

] [ tan

reacctance impedance

The

] [ [amps]

current line

[volts]

voltage phase

or voltage Armature

Impedance

ce resis

ohms ce

resis

ohms

−

=

= +

=

=

=

Solve for the reactance from this equation Note that the phase resistance was measured previously and will be small in value The inductance can than be calculated from

inductance

x frequency

x 2 s]

var Reactance[ = π The frequency is probably going to be from the ac source at 60 Hz Thus

Hz]

frequency[

x 2

s]

var reactance[

[henries]

Inductance

π

=