Post on 29-Mar-2015
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 3
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
Dr. Ungku Anisa, July 2008 4EEEB443 - Control & Drives
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 5
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 6
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 7
Speed Control
Loop
Closed Loop Control with Controlled Rectifiers – Two-quadrantTwo-quadrant Three-phase Controlled Rectifier
DC Motor Drives
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 8
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 9
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 10
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 11
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.
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 12
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 13
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)
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 14
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)
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 15
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 16
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 17
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 18
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)
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 22
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 23
2nd order current loop
model
Approximated by adding Tr to T1
Hence, current model transfer function is given by:
(24)
Design of Controllers– Current loop 1st order approximation
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 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
Design of Controllers– Current loop 1st order approximation
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.
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 25
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 26
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 27
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 30
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 31
Closed Loop Control with Field Weakening – Two-quadrant
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 32
Field weakening
Closed Loop Control with Field Weakening – Two-quadrant
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 33dt
diLiRVe aaaaa
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 35
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 36
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.
Dr. Ungku Anisa, July 2008 37EEEB443 - Control & Drives
DC Motor and Load Transfer Function - Decoupling of Induced EMF LoopStep 1:
Step 2:
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 38
DC Motor and Load Transfer Function - Decoupling of Induced EMF LoopStep 3:
Step 4:
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 39
Back
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 40
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 41
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