1. EEEB443 Control & Drives Closed-loop Control of DC Drives with ChopperBy
Dr. Ungku Anisa Ungku Amirulddin
Department of Electrical Power Engineering
College of Engineering
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Dr. Ungku Anisa, July 2008

2. Outline Closed Loop Control of DC Drives with Choppers
Current Control for DC Drives with Choppers
Pulse-Width-Modulation (PWM) Controller
Hysteresis-Current Controller
Comparison between PWM and Hysteresis Controller
Transfer Function of PWM-Controlled Chopper
Two-quadrant
Four-quadrant
Design of Controllers
References
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

3. Closed Loop Control of DC Drives
Closed loop control is when the duty cycle 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
Reference signal
Output
signal +
Controller
Plant 
Sensor
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

4. Closed Loop Control of DC Drives
Feedback loops may be provided to satisfy one or more of the following:
Protection
Enhancement of speed response
Improve steady-state accuracy
Variables to be controlled in drives:
Torque – achieved by controlling current
Speed
Position
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

5. Closed Loop Control of DC Drives
For DC Drive, this can be:
Controlled rectifier or
DC-DC converter
Cascade 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
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

6. Closed Loop Control for DC Drives with Choppers
Outer speed loop very similar to that in the controlled rectifier dc drive
Inner current control loop – different
Current Control Loop
Speed Control Loop
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

7. Current Control for DC Drives with Choppers
Current control loop is used to control torque via armature current (ia)
Output of current controller determines duty cycle (i.e. switching) of DC-DC converter
Current controller can be either:
Pulse-Width-Modulation (PWM) Controller
contain PI controllers, i.e. linear
fixed switching frequency
Hysteresis (bang-bang) controller
on-off controllers, i.e. non-linear
varying switching frequency
Selection of controller affects current control loop transient response
Hence, affects speed loop bandwidth.
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

8. Current Control for Chopper Drives – PWM Controller
In two quadrant chopper, upper and lower switches are complementary
Only ONE control signal required
Current error is passed to PI controller to produce control voltage vc
vc is then passed to a PWM circuit to produce the switching signal q.
q = 1  T1 ‘on’, T2 ‘off’  Va = Vdc
q = 0  T1 ‘off’, T2 ‘on’  Va = 0
vc > Vtri
vc < Vtri
T1 ‘on’, Va = Vdc
T2 ‘on’, Va = 0
Vdc
Pulse Width
Modulator
(PWM) vc
ia* PI +  q T1 T2 D1 Va - D2 ia
vtri
ierr
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

9. Current Control for Chopper Drives – PWM Controller
In the PWM circuit:
vc is compared with a triangular waveform
if vc > Vtri  ‘on’ signal is produced (q = 1)
if vc < Vtri  ‘off’ signal is produced (q = 0)
(1)
Chopper switching frequency is fixed by triangular waveform frequency regardless of operating conditions
Bandwith of current loop controller is limited by frequency of Vtri
vc > Vtri
vc < Vtri
Ttri
ton 1 vc
Vdc
vc > Vtri
vc < Vtri q va
q = 1 
T1 ‘on’, va = Vdc
q = 0 
T2 ‘on’, va = 0
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Dr. Ungku Anisa, July 2008

10. Current Control for Chopper Drives – PWM Controller
Ttri
ton 1 vc
Vdc Va
In the PWM circuit:
Average value of q over a cycle determines duty cycle  of chopper:
Average armature voltage: q  va
va switches between Vdc and 0
average armature voltage Va depends on duty cycle (i.e. how long T1 is on)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

11. Current Control for Chopper Drives – PWM Controller
PWM controls chopper duty cycle  once in every cycle
Frequency of Va fixed by frequency of Vtri
Hence, chopper is a variable voltage source with average current control
Instantaneous current control is not exercised
Current can exceed maximum armature current between two consecutive switching
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

12. Current Control for Chopper Drives – Hysteresis Controller
ia  ia* - ia
ia  ia* + ia
Instantaneous current control
Current controlled within a narrow band of excursion from the desired value ia*
Hysteresis window determines allowable deviation of ia
Vdc
ia* q T1 T2 D1 + Va - D2 ia 
ierr
ia* q ia
ia
Hysteresis Controller
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

13. Current Control for Chopper Drives – Hysteresis Controller
Actual current ia compared with reference current ia* to obtain error signal ierr
If ia  ia* + ia  q = 0, T2 ‘on’ and Va = 0
If ia  ia* - ia  q = 1, T1 ‘on’ and Va = Vdc
Value of ia can be externally set or made to be a fraction of ia
Chopper switching frequency is not fixed
ia  ia* + ia
ia* q ia
ia
ia  ia* - ia
ia  ia* + ia
ia  ia* - ia
q = 1 
T1 ‘on’, va = Vdc
q = 0 
T2 ‘on’, va = 0
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

14. Current Control for Chopper Drives – Qualitative Comparison
Characteristics
Hysteresis Controller
PWM Controller
Switching frequency
Varying
Fixed
(follows sawtooth waveform frequency i.e. carrier frequency)
Switching losses
High (due to varying switching frequency)
Low
Speed of response
Fastest (due to instantanous change in current)
Fast
Ripple current
Adjustable
(depends on hysteresis window ia )
Filter size
Depends on ia
Small
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Preferred method !

15. Closed Loop Control for DC Drives with Choppers
Controller design procedure:
Obtain the transfer function of all drive subsystems
DC Motor & Load
Current feedback loop sensor
Speed feedback loop sensor
Design torque (current) control loop first
Two options to choose from:
Hysteresis Controller – to design just choose value of ia
PWM Controller (contains PI controller)
determine transfer function of PWM-controlled chopper
design PI controller using the same procedure as in closed loop control using controlled rectifier
Exactly the same as before (i.e. transfer functions obtained in closed loop control using controlled rectifier)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

16. Closed Loop Control for DC Drives with Choppers
Controller design procedure (continued):
Then design the speed control loop
Obtain 1st order model of the designed current controller
Design the speed PI controller using the same procedure as in closed loop control using controlled rectifier
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

17. Transfer Function of PWM-Controlled Chopper
PWM current controller is preferred over Hysteresis Controller
Before we can design the PI controller, need to obtain linear relationship between control input vc and average armature voltage Va for PWM method
Need transfer function for PWM-controlled chopper
vtri
ia*
Pulse Width
Modulator
(PWM)
Chopper
DC motor + vc q Va ia PI  ia
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

18. Transfer Function of PWM-Controlled Two-quadrant Chopper
Need to obtain linear relationship between control input vc and average armature voltage Va for PWM method
Case 1:
vc > Vtri
vc < Vtri
Vtri
-Vtri vc 
T1 off all the time
i.e. ton, T1 = 0 vc
-Vtri
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

19. Transfer Function of PWM-Controlled Two-quadrant Chopper
Case 2:
Vtri
-Vtri vc
vc > Vtri
vc < Vtri 
T1 on ½ cycle
i.e. ton, T1 = 0.5Ttri
0.5 vc
-Vtri
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

20. Transfer Function of PWM-Controlled Two-quadrant Chopper
Case 3:
vc > Vtri
vc < Vtri
Vtri
-Vtri vc 
T1 on all the time
i.e. ton, T1 = Ttri 1
Vtri
0.5 vc
-Vtri
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

21. Transfer Function of PWM-Controlled Two-quadrant Chopper
Relationship between  and vc :
(2)
For the two-quadrant chopper:
(3)
Hence, considering only the term due to vc, the two–quadrant chopper gain is:
(4)
0.5 vc 
-Vtri
+Vtri 1
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

22. Transfer Function of PWM-Controlled Four-quadrant Chopper
Recap Chopper operation:
Positive current:
Va = Vdc when T1 and T2 on
Va = 0 when current freewheels through T2 and D4
+ Va - T1 D1 T2 D2 D3 D4 T3 T4 +
Vdc -
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

23. Transfer Function of PWM-Controlled Four-quadrant Chopper
Recap Chopper operation:
Positive current:
Va = Vdc when T1 and T2 on
Va = 0 when current freewheels through T2 and D4
Negative current:
Va = -Vdc when T3 and T4 on
Va = 0 when current freewheels through T4 and D2
Output voltage can swing between:
Vdc and -Vdc
Vdc and 0
+ Va - T1 D1 T2 D2 D3 D4 T3 T4 +
Vdc -
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

24. Transfer Function of PWM-Controlled Four-quadrant Chopper
Need to obtain linear relationship between control input vc and average armature voltage Va for PWM method
Four quadrant chopper has two legs, so it requires two switching signals (one for each leg)
Depending on relationship between the two switching signals, 4-quadrant chopper has two switching schemes:
Bipolar switching
Unipolar switching
Switching scheme determines output
voltage swing between
Vdc and -Vdc or Vdc and 0. +
Vdc −
+ Va - T1 D1 T2 D2 D3 D4 T3 T4
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Leg A
Leg B

25. Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching)
Bipolar Switching PWM
Leg A and Leg B obtain switching signals from the same control signal vc
Switching of Leg A and Leg B are always complementary
vc > Vtri
vc < Vtri
+ Va - T1 D1 T2 D2 D3 D4 T3 T4 +
Vdc − vc
vtri q
Leg A
q = 1,q =0
 T1 on, T2 on
 Va= Vdc
q = 0, q =1
 T4 on, T3 on
 Va= -Vdc
Leg B
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

26. Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching)
Bipolar Switching PWM
Va = Va+- Va-
Leg A q
2vtri vc +
Vdc − D1 D3 T1 T3
+ Va -
Va+
Vdc
vtri
Va-
Vdc T4 T2 D2 D4 Va
Vdc
-Vdc vc q
Leg B
Va+
Va-
Va jumps between +Vdc and –Vdc  Bipolar Switching PWM
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

27. Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching)
Bipolar Switching PWM
2vtri vc
2vtri vc
vc > Vtri
vc < Vtri q
Vdc q
Vdc
Va+
Vdc
Va-
Vdc
Va = Va+- Va- Va
Vdc
-Vdc
Va jumps between +Vdc and –Vdc
 Bipolar Switching PWM
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

28. Transfer Function PWM-Controlled Four-quadrant Chopper (Bipolar Switching)
Each leg is a two-quadrant chopper.
Output of Leg A (average):
(5)
where
(6)
Output of Leg B (average):
(7)
(8)
Hence, average voltage across the motor:
(9)
Subt. (6) into (9)
Bipolar Switching PWM
2vtri vc
Vdc
Va+
Vdc
Va-
Vdc Va
Vdc
-Vdc
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

29. Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching)
Unipolar Switching PWM
Leg B switching signals obtained from the inverse of control signal for Leg A
vc > Vtri
vc < Vtri
+ Va - T1 D1 T2 D2 D3 D4 T3 T4 +
Vdc − vc
vtri qa
-vc qb
Leg A
-vc > Vtri
-vc < Vtri
Leg B
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

30. Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching)
Unipolar Switching PWM
2Vtri vc
-vc qa
Leg A
vtri +
Vdc −
Va+
Vdc D1 D3 vc T1 T3
+ Va -
Va-
Vdc
vtri T4 T2 D2 D4
-vc Va
Vdc qb
Va+
Va-
Leg B
Va = Va+- Va-
Va jumps between +Vdc and 0  Unipolar Switching PWM
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

31. Unipolar Switching PWM
Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching)
Unipolar Switching PWM
2Vtri vc
-vc
2Vtri vc
-vc
vc > Vtri
vc < Vtri qb
Vdc
-vc > Vtri
-vc < Vtri qa
Vdc
Va+
Vdc
Va-
Vdc
Va = Va+- Va- Va
Vdc
Va jumps between +Vdc and 0 
Unipolar Switching PWM
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

32. Unipolar Switching PWM
Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching)
Each leg is a two-quadrant chopper.
Output of Leg A (average):
(10)
where
(11)
Output of Leg B (average):
(12)
(13)
Hence, average voltage across motor armature:
(14)
Unipolar Switching PWM
2Vtri vc
-vc
Va+
Vdc
Va-
Vdc Va
Vdc
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Same as Bipolar Switching Scheme!

33. PWM-Controlled Four-quadrant Chopper Comparison between Bipolar & Unipolar Switching
Bipolar Switching PWM Unipolar Switching PWM
2Vtri vc
-vc
2vtri vc
Va+
Vdc
Va+
Vdc
Va-
Vdc
Va-
Vdc Va
Vdc
-Vdc Va
Vdc
Output voltage swings from Vdc and –Vdc
Output voltage frequency equal to frequency of triangle voltage (ftri)
Output voltage swings from Vdc and 0
Output voltage frequency equal to times frequency of triangle voltage (ftri)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

34. ftri = frequency of Vtri
PWM-Controlled Four-quadrant Chopper Comparison between Bipolar & Unipolar Switching
Characteristics
Bipolar Switching
Unipolar Switching
Output voltage swing
Vdc and -Vdc
Vdc and 0
Output voltage frequency
ftri = frequency of Vtri
2ftri
Current ripple =
For same ftri and Vdc, unipolar scheme gives:
better output voltage waveform (less ripple)
lower current ripple
better frequency response
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

35. Transfer Function PWM-Controlled Chopper: Two and Four Quadrant
Gain of the PWM-controlled chopper:
Two -quadrant: (15)
Four–quadrant: (16)
where Vdc = dc link voltage
Vtri = maximum control voltage
(i.e. peak of the triangular waveform)
Chopper also has a delay:
(17)
where fc = carrier (triangular) waveform frequency
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

36. Transfer Function of Subsystems
PWM-controlled Chopper: (18)
Note: Kr and Tr as given in equations (15) – (17) above.
Other subsystem transfer functions are as observed in ‘Closed-loop Control of DC Drives with Controlled Rectifier’.
DC Motor and Load:
Current Feedback:
Speed feedback:
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

37. Design of Controllers – Block Diagram of Motor Drive
Current Control Loop
Speed Control Loop
Assume that we are using PWM controlled chopper
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

38. Design of Controllers– Current Controller
DC Motor & Load
PWM-controlled Chopper
PI type current controller: (19)
Loop gain function:
(20)
Design procedure - same as for current controller in closed-loop control using controlled rectifiers
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

39. Design of Controllers– Current loop 1st order approximation
Approximated by adding Tr to T1 
(21)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

40. Design of Controllers– Current loop 1st order approximation
where (22)
(23)
(24)
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

41. Design of Controllers– Speed Controller
DC Motor & Load
PI type current controller: (25)
Assume there is unity speed feedback:
(26)
1st order approximation of current loop
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

42. Design of Controllers– Speed Controller
Loop gain function:
(27)
Design procedure - same as for speed controller in closed-loop control using controlled rectifiers 1
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

43. References
Krishnan, R., Electric Motor Drives: Modeling, Analysis and Control, Prentice-Hall, New Jersey, 2001.
Mohan, Underland, Robbins, Power Electronics: Converters, Applications and Design, 2nd ed., John Wiley & Sons, USA, 1995.
Nik Idris, N. R., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008.
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives