5 controlled rectifier dc drives-closed loop.pps

Closed-loop Control of DC Drives with Controlled RectifierByDr. Ungku Anisa Ungku AmirulddinDepartment of Electrical Power EngineeringCollege of Engineering

Dr. Ungku Anisa, July 2008 1EEEB443 - Control & Drives

OutlineClosed Loop Control of DC DrivesClosed-loop Control with Controlled Rectifier –

Two-quadrantTransfer Functions of SubsystemsDesign of Controllers

Closed-loop Control with Field Weakening – Two-quadrant

Closed-loop Control with Controlled Rectifier – Four-quadrant

References

Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 2

Closed Loop Control of DC DrivesClosed loop control is when the firing angle is varied

automatically by a controller to achieve a reference speed or torque

This requires the use of sensors to feed back the actual motor speed and torque to be compared with the reference values


Controller Plant

Sensor

+

Referencesignal

Outputsignal

Closed Loop Control of DC DrivesFeedback loops may be provided to satisfy one or more

of the following:ProtectionEnhancement of response – fast response with small

overshootImprove steady-state accuracy

Variables to be controlled in drives:Torque – achieved by controlling currentSpeedPosition


Closed Loop Control of DC DrivesCascade control structure

Flexible – outer loops can be added/removed depending on control requirements.

Control variable of inner loop (eg: speed, torque) can be limited by limiting its reference value

Torque loop is fastest, speed loop – slower and position loop - slowest


Closed Loop Control of DC DrivesCascade control structure:

Inner Torque (Current) Control Loop: Current control loop is used to control torque via armature current

(ia) and maintains current within a safe limit Accelerates and decelerates the drive at maximum permissible

current and torque during transient operations


Torque (Current)

Control Loop

Closed Loop Control of DC DrivesCascade control structure

Speed Control Loop: Ensures that the actual speed is always equal to reference speed * Provides fast response to changes in *, TL and supply voltage (i.e. any

transients are overcome within the shortest feasible time) without exceeding motor and converter capability


Speed Control

Loop

Closed Loop Control with Controlled Rectifiers – Two-quadrantTwo-quadrant Three-phase Controlled Rectifier

DC Motor Drives


Current Control Loop

Speed Control Loop

Closed Loop Control with Controlled Rectifiers – Two-quadrantActual motor speed m measured using the tachogenerator (Tach) is

filtered to produce feedback signal mr

The reference speed r* is compared to mr to obtain a speed error signalThe speed (PI) controller processes the speed error and produces the

torque command Te*Te* is limited by the limiter to keep within the safe current limits and the

armature current command ia* is produced ia* is compared to actual current ia to obtain a current error signalThe current (PI) controller processes the error to alter the control signal vc

vc modifies the firing angle to be sent to the converter to obtained the motor armature voltage for the desired motor operation speed


Closed Loop Control with Controlled Rectifiers – Two-quadrantDesign of speed and current controller (gain and

time constants) is crucial in meeting the dynamic specifications of the drive system

Controller design procedure:1. Obtain the transfer function of all drive subsystems

a) DC Motor & Loadb) Current feedback loop sensorc) Speed feedback loop sensor

2. Design current (torque) control loop first3. Then design the speed control loop


Assume load is proportional to speed

DC motor has inner loop due to induced emf magnetic coupling, which is not physically seen

This creates complexity in current control loop design

Transfer Function of Subsystems – DC Motor and Load


mLL BT

Transfer Function of Subsystems – DC Motor and LoadNeed to split the DC motor transfer function between m and Va

(1)

where(2)

(3)

This is achieved through redrawing of the DC motor and load block diagram.


sV

sI

sI

sω

sV

sω

a

a

a

m

a

m

mt

b

sTB

K

1sI

sω

a

m

21

1a

a

11

1

sV

sI

sTsT

sTK m

Transfer Function of Subsystems – DC Motor and LoadIn (2),

- mechanical motor time constant: (4)

- motor and load friction coefficient: (5)In (3),

(6)

(7)

Note: J = motor inertia, B1 = motor friction coefficient, BL = load friction coefficient


tm B

JT

Lt BBB 1

a

b

a

tat

a

at

a

a

JL

K

JL

BR

J

B

L

R

J

B

L

R

TT

22

21 4

1

2

11,

1

tab

t

BRK

BK

21

Transfer Function of Subsystems – Three-phase ConverterNeed to obtain linear relationship between control signal vc

and delay angle (i.e. using ‘cosine wave crossing’ method)(8)

where vc = control signal (output of current controller)

Vcm = maximum value of the control voltageThus, dc output voltage of the three-phase converter

(9)


cm

c

V

v1cos

crccm

m

cm

cmmdc vKv

V

V

V

vVVV

L,L

L,L L,L

3

coscos3

cos3 1

Transfer Function of Subsystems – Three-phase ConverterGain of the converter

(10)

where V = rms line-to-line voltage of 3-phase supplyConverter also has a delay

(11) where fs = supply voltage frequencyHence, the converter transfer function

(12)


rr

sT

K

1sG r

cmcmcm

mr V

V

V

V

V

VK 35.1

233

L,L

ssr ffT

1

12

11

360

60

2

1

Transfer Function of Subsystems – Current and Speed FeedbackCurrent Feedback

Transfer function:No filtering is required in most casesIf filtering is required, a low pass-filter can be included (time

constant < 1ms).Speed Feedback

Transfer function:(13)

where K = gain, T = time constantMost high performance systems use dc tachogenerator and low-

pass filterFilter time constant < 10 ms


sT

K

1sGω

cH

Design of Controllers – Block Diagram of Motor Drive

Control loop design starts from inner (fastest) loop to outer(slowest) loop

Only have to solve for one controller at a time Not all drive applications require speed control (outer loop) Performance of outer loop depends on inner loop


Speed Control Loop

Current Control Loop

PI type current controller: (14)Open loop gain function:

(15)

From the open loop gain, the system is of 4th order (due to 4 poles of system)

Design of Controllers– Current Controller


c

cc

sT

sTK

1sGc

r

mc

c

crc

sTsTsTs

sTsT

T

HKKK

111

11sGH

21

1ol

DC Motor & LoadConverterController

Design of Controllers– Current ControllerIf designing without computers, simplification is needed.Simplification 1: Tm is in order of 1 second. Hence,

(16)Hence, the open loop gain function becomes:

i.e. system zero cancels the controller pole at origin.Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 19

mm sTsT 1

c

mcrc

r

c

r

mc

c

crc

r

mc

c

crc

T

THKKKK

sTsTsT

sTK

sTsTsTs

sTsT

T

HKKK

sTsTsTs

sTsT

T

HKKK

1

21ol

21

1

21

1ol

where111

1sGH

111

1

111

11sGH

(17)

Design of Controllers– Current ControllerRelationship between the denominator time constants in

(17):Simplification 2: Make controller time constant equal to T2

(18) Hence, the open loop gain function becomes:

i.e. controller zero cancels one of the system poles.Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 20

12 TTTr

2TTc

c

mcrc

r

r

r

c

T

THKKKK

sTsT

K

sTsTsT

sTK

sTsTsT

sTK

1

1ol

21

2

21ol

where11

sGH

111

1

111

1sGH

Design of Controllers– Current ControllerAfter simplification, the final open loop gain function:

(19)

where (20)

The system is now of 2nd order.From the closed loop transfer function: , the closed loop characteristic equation is:

or when expanded becomes: (21)


rsTsT

K

11sGH

1ol

c

mcrc

T

THKKKK 1

KsTsT r 11 1

sGH1

sGHsG

ol

olcl

rr

rr TT

K

TT

TTssTT

11

121

1

Design of Controllers– Current ControllerDesign the controller by comparing system characteristic

equation (eq. 21) with the standard 2nd order system equation:

Hence,(22)

(23)

So, for a given value of :use (22) to calculate n Then use (23) to calculate the controller gain KC


22 2 nnss

n2

2n

To design the speed loop, the 2nd order model of current loop must be replaced with an approximate 1st order model

Why?To reduce the order of the overall speed loop gain function

Design of Controllers– Current loop 1st order approximation


2nd order current loop

model

Approximated by adding Tr to T1

Hence, current model transfer function is given by:

(24)



i

c

m

c

m

sT

K

sTT

THKKKsTT

TKKK

i

crc

rc

11

11

11

sI

sI

3

1

3

1

*a

a

rTTT 13

Full derivation available here.

1st order approximation of current loop


where (26)

(27)

(28)

1st order approximation of current loop used in speed loop design.

If more accurate speed controller design is required, values of Ki and Ti should be obtained experimentally.


c

mcrcfi T

THKKKK 1

fii K

TT

13

fic

fii KH

KK

1

1

PI type speed controller: (29)

Assume there is unity speed feedback: (30)

Design of Controllers– Speed Controller


s

sss sT

sTK

1sG

11

sGω

sT

H

DC Motor & Load

1st order approximation of current

loop

Open loop gain function:

(31)

From the loop gain, the system is of 3rd order.If designing without computers, simplification is needed.

1

Design of Controllers– Speed Controller


mi

s

st

isB

sTsTs

sT

TB

KKK

11

1sGH

DC Motor & Load

1st order approximation of current

loop

Design of Controllers– Speed ControllerRelationship between the denominator time constants in (31):

(32)Hence, design the speed controller such that:

(33) The open loop gain function becomes:

i.e. controller zero cancels one of the system poles.Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 28

mi TT

ms TT

st

isB

i

mi

m

st

isB

mi

s

st

isB

TB

KKKK

sTs

K

sTsTs

sT

TB

KKK

sTsTs

sT

TB

KKK

where

1sGH

11

1

11

1sGH

Design of Controllers– Speed ControllerAfter simplification, loop gain function:

(34)

where (35)

The controller is now of 2nd order.From the closed loop transfer function: ,

the closed loop characteristic equation is:

or when expanded becomes: (36)Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 29

isTs

K

1sGH

st

isB

TB

KKKK

KsTs i 1

sGH1

sGHsGcl

iii T

K

TssT 12

Design of Controllers– Speed ControllerDesign the controller by comparing system characteristic

equation with the standard equation:

Hence:(37)

(38)

So, for a given value of :use (37) to calculate n Then use (38) to calculate the controller gain KS


22 2 nnss

n2

2n

Motor operation above base speed requires field weakeningField weakening obtained by varying field winding voltage

using controlled rectifier in:single-phase orthree-phase

Field current has no ripple – due to large Lf

Converter time lag negligible compared to field time constant Consists of two additional control loops on field circuit:

Field current control loop (inner)Induced emf control loop (outer)

Closed Loop Control with Field Weakening – Two-quadrant




Field weakening


Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 33dt

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Induced emf controller

(PI-type with limiter)

Field weakening

Field current

controller(PI-type)

Field current reference

Estimated machine -induced emf

Induced emf reference

Closed Loop Control with Field Weakening – Two-quadrantThe estimated machine-induced emf is obtained from:

(the estimated emf is machine-parameter sensitive and must be adaptive)The reference induced emf e* is compared to e to obtain the induced emf

error signal (for speed above base speed, e* kept constant at rated emf value so that 1/)

The induced emf (PI) controller processes the error and produces the field current reference if*

if* is limited by the limiter to keep within the safe field current limits if* is compared to actual field current if to obtain a current error signalThe field current (PI) controller processes the error to alter the control signal

vcf (similar to armature current ia control loop) vcf modifies the firing angle f to be sent to the converter to obtained the

motor field voltage for the desired motor field fluxDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 34

dt

diLiRVe aaaaa

Four-quadrant Three-phase Controlled Rectifier DC Motor Drives

Closed Loop Control with Controlled Rectifiers – Four-quadrant


Control very similar to the two-quadrant dc motor drive.Each converter must be energized depending on quadrant of operation:

Converter 1 – for forward direction / rotationConverter 2 – for reverse direction / rotation

Changeover between Converters 1 & 2 handled by monitoringSpeedCurrent-commandZero-crossing current signals

‘Selector’ block determines which converter has to operate by assigning pulse-control signals

Speed and current loops shared by both convertersConverters switched only when current in outgoing converter is zero (i.e.

does not allow circulating current. One converter is on at a time.)

Closed Loop Control with Controlled Rectifiers – Four-quadrant


Inputs to ‘Selector’ block

ReferencesKrishnan, R., Electric Motor Drives: Modeling, Analysis and

Control, Prentice-Hall, New Jersey, 2001.Rashid, M.H, Power Electronics: Circuit, Devices and

Applictions, 3rd ed., Pearson, New-Jersey, 2004.Nik Idris, N. R., Short Course Notes on Electrical Drives,

UNITEN/UTM, 2008.


DC Motor and Load Transfer Function - Decoupling of Induced EMF LoopStep 1:

Step 2:


DC Motor and Load Transfer Function - Decoupling of Induced EMF LoopStep 3:

Step 4:


Back


Vm

Vcmvc

0 2 3 4

Input voltageto rectifier

Cosine wave compared with control voltage vc

Results of comparison trigger SCRs

Output voltageof rectifier

Vcmcos() = vc

cm

c

V

v1cos

Cosine voltage

Back


i

cc

c

c

m

c

m

sT

K

K

Ts

KH

K

KsT

H

K

sTK

sTH

K

sTT

THKKKsTT

TKKK

i

fi

fi

fi

fi

fi

fi

fi

crc

rc

1

11

11

1

11

1

11

11

1

11

sI

sI

33

3

3

3

1

3

1

*a

a

Back

5 controlled rectifier dc drives-closed loop.pps

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