5 Controlled Rectifier DC Drives-closed loop.pps

Closed-loop Control of DC Drives with Controlled Rectifier By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

1

Outline  Closed Loop Control of DC Drives  Closed-loop Control with Controlled Rectifier –

Two-quadrant  Transfer Functions of Subsystems  Design of Controllers  Closed-loop Control with Field Weakening – Two-quadrant  Closed-loop Control with Controlled Rectifier – Four-quadrant  References Dr. Ungku Anisa, July 2008


2

Closed Loop Control of DC Drives  Closed 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 Reference signal

+

Plant

Controller 

Output signal

Sensor Dr. Ungku Anisa, July 2008


3

Closed Loop Control of DC Drives  Feedback loops may be provided to satisfy one or more of

the following:  Protection  Enhancement of response – fast response with small

overshoot  Improve steady-state accuracy

 Variables to be controlled in drives:  Torque – achieved by controlling current  Speed  Position Dr. Ungku Anisa, July 2008


4

Closed Loop Control of DC Drives  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  Torque loop is fastest, speed loop – slower and position loop - slowest



5

Closed Loop Control of DC Drives  Cascade 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 Torque current and torque during transient operations (Current) Control Loop



6

Closed Loop Control of DC Drives  Cascade 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 Dr. Ungku Anisa, July 2008


7

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

Control Loop

DC Motor Drives Speed Control Loop



8

Closed Loop Control with Controlled Rectifiers – Two-quadrant  Actual 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 signal The 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 signal The 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



9

Closed Loop Control with Controlled Rectifiers – Two-quadrant  Design of speed and current controller (gain and time constants) is crucial in meeting the dynamic specifications of the drive system  Controller design procedure: Obtain the transfer function of all drive subsystems

1. a) b) c)

DC Motor & Load Current feedback loop sensor Speed feedback loop sensor

Design current (torque) control loop first 3. Then design the speed control loop 2.



10

Transfer Function of Subsystems – DC Motor and Load  Assume load is proportional to speed

TL  BLm  DC motor has inner loop due to induced emf magnetic coupling, which is not physically seen  This creates complexity in current control loop design



11

Transfer Function of Subsystems – DC Motor and Load  Need to split the DC motor transfer function between m and Va

 where

ωm s  ωm s  Ia s    Va s  Ia s  Va s 

(1)

ωm s  Kb  Ia s  Bt 1  sTm 

(2)

 Ia s  1  sTm   K1 1  sT1 1  sT2  Va s 

(3)

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

diagram. Dr. Ungku Anisa, July 2008


12

Transfer Function of Subsystems – DC Motor and Load  In (2),

- mechanical motor time constant:

J Tm  Bt

- motor and load friction coefficient: Bt  B1  BL  In (3), B K1  2 t K b  Ra Bt

(4) (5) (6)

2

2 1 1 1  Ra Bt  1  Ra Bt   Ra Bt K b         ,         T1 T2 2  La J  4  La J   JLa JLa 

(7)

Note: J = motor inertia, B1 = motor friction coefficient, BL = load friction coefficient Dr. Ungku Anisa, July 2008


13

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

and delay angle  (i.e. using ‘cosine wave crossing’ method) (8) 1  vc    cos    Vcm  where vc = control signal (output of current controller) Vcm = maximum value of the control voltage  Thus, dc output voltage of the three-phase converter  1 vc  3 VLL, m   Vdc  VLL, m cos  VLL, m cos cos vc  Kr vc (9)   Vcm   Vcm  3


3


14

Transfer Function of Subsystems – Three-phase Converter  Gain of the converter

3 VLL, m 3 2V V Kr    1.35  Vcm  Vcm Vcm where V = rms line-to-line voltage of 3-phase supply  Converter also has a delay 1 60 1 1 1 Tr      2 360 f s 12 f s

where fs = supply voltage frequency  Hence, the converter transfer function Kr G r s   1  sTr  Dr. Ungku Anisa, July 2008


(10)

(11)

(12) 15

Transfer Function of Subsystems – Current and Speed Feedback  Current Feedback  Transfer function: H c  No filtering is required in most cases  If filtering is required, a low pass-filter can be included (time constant < 1ms).  Speed Feedback  Transfer function: K G ω s   (13) 1  sT  where K = gain, T = time constant  Most high performance systems use dc tachogenerator and lowpass filter  Filter time constant < 10 ms Dr. Ungku Anisa, July 2008


16

Design of Controllers – Block Diagram of Motor Drive Current Control Loop

Speed Control Loop

 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



17

Design of Controllers– Current Controller Controller

Converter

 PI type current controller: G c s    Open loop gain function:

DC Motor & Load

K c 1  sTc  sTc

 K1K c K r H c  1  sTc 1  sTm  GHol s     T c   s1  sT1 1  sT2 1  sTr 

(14) (15)

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

poles of system) Dr. Ungku Anisa, July 2008


18

Design of Controllers– Current Controller

 If designing without computers, simplification is needed.  Simplification 1: Tm is in order of 1 second. Hence, 1  sTm   sTm

(16)

Hence, the open loop gain function becomes:  K1 K c K r H c  1  sTc 1  sTm  GH ol s     Tc   s 1  sT1 1  sT2 1  sTr   K1 K c K r H c   1  sTc sTm    T c   s 1  sT1 1  sT2 1  sTr   1  sTc  K1 K c K r H cTm (17) GH ol s   K whereK  1  sT1 1  sT2 1  sTr  Tc

i.e. system zero cancels the controller pole at origin. Dr. Ungku Anisa, July 2008


19

Design of Controllers– Current Controller  Relationship between the denominator time constants in (17): Tr  T2  T1  Simplification 2: Make controller time constant equal to T2 Tc  T2 (18)

Hence, the open loop gain function becomes:

1  sTc  1  sT1 1  sT2 1  sTr   1  sT2  K 1  sT1 1  sT2 1  sTr 

GH ol s   K

GH ol s  

KK K HT K where K  1 c r c m 1  sT1 1  sTr  Tc

i.e. controller zero cancels one of the system poles. Dr. Ungku Anisa, July 2008


20

Design of Controllers– Current Controller  After simplification, the final open loop gain function: K GH ol s   1  sT1 1  sTr 

where

K

K1K c K r H cTm Tc

(19) (20)

 The system is now of 2nd order.

GH ol s   From the closed loop transfer function: G cl s   , 1  GH ol s 

the closed loop characteristic equation is:

1  sT1 1  sTr   K

or when expanded becomes: Dr. Ungku Anisa, July 2008


 2  T1  Tr T1Tr s  s  T1Tr 

 K  1    T T 1 r  

(21) 21

Design of Controllers– Current Controller  Design the controller by comparing system characteristic

equation (eq. 21) with the standard 2nd order system equation: s 2  2n s  n2  Hence,

2 n 

(22)

n 

(23)

2

 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


22

Design of Controllers– Current loop 1st order approximation  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

2nd order current loop model Dr. Ungku Anisa, July 2008


23

Design of Controllers– Current loop 1st order approximation  Approximated by adding Tr to T1  T3  T1  Tr

 Hence, current model transfer function is given by: K c K r K 1Tm 1 Tc 1  sT3 Ia s  Ki   * K K K H T 1 Ia s  1  sTi c r 1 c m 1 Tc 1  sT3















1st order approximation of current loop

(24) Full derivation available here. 24

Design of Controllers– Current loop 1st order approximation where

Ti 

T3 1  K fi

(26)

Ki 

K fi

1 H c 1  K fi 

(27)

K fi 

K1K c K r H cTm Tc

(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


25

Design of Controllers– Speed Controller

DC Motor & Load


K s 1  sTs  sTs  Assume there is unity speed feedback:  PI type speed controller: G s s  

G ω s   Dr. Ungku Anisa, July 2008

H 1 1  sT 


(29) (30)

26


DC Motor & Load

1


 Open loop gain function:

 K B K s Ki   1  sTs  GHs     B T  t s  s1  sTi 1  sTm 

(31)

 From the loop gain, the system is of 3rd order.  If designing without computers, simplification is needed. Dr. Ungku Anisa, July 2008


27


 Relationship between the denominator time constants in (31): Ti  Tm (32)  Hence, design the speed controller such that: Ts  Tm

(33)

The open loop gain function becomes:

K K K  1  sTs  GHs    B s i   BtTs  s 1  sTi 1  sTm 

K K K  1  sTm   B s i  BtTs  s 1  sTi 1  sTm  K K K K GHs   where K   B s i s 1  sTi  BtTs

i.e. controller zero cancels one of the system poles. Dr. Ungku Anisa, July 2008


28

Design of Controllers– Speed Controller  After simplification, loop gain function: K GH s   s1  sTi 

where

(34)

K B K s Ki K  BtTs

(35)

 The controller is now of 2nd order. GH s   From the closed loop transfer function: G cl s   ,

the closed loop characteristic equation is:

1  GH s 

s 1  sTi   K

or when expanded becomes: Dr. Ungku Anisa, July 2008


 2  1  K  Ti s  s     Ti  Ti  

(36) 29


 Design the controller by comparing system characteristic

equation with the standard equation: s 2  2n s  n2  Hence:

2 n 

(37)

n 

(38)

2

 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


30

Closed Loop Control with Field Weakening – Two-quadrant  Motor operation above base speed requires field weakening  Field weakening obtained by varying field winding voltage

using controlled rectifier in:  single-phase or

 three-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) Dr. Ungku Anisa, July 2008


31

Closed Loop Control with Field Weakening – Two-quadrant Field weakening



32

Closed Loop Control with Field Weakening – Two-quadrant Field weakening

Field current controller (PI-type)

Estimated machine induced emf

dia e  Va  Raia  La dt Dr. Ungku Anisa, July 2008

Induced emf reference


Induced emf controller (PI-type with limiter)

Field current reference 33

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

dia e  Va  Raia  La dt 

    

(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 signal The 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 flux



34

Closed Loop Control with Controlled Rectifiers – Four-quadrant  Four-quadrant Three-phase Controlled Rectifier DC

Motor Drives



35

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 / rotation

 Converter 2 – for reverse direction / rotation

 Changeover between Converters 1 & 2 handled by monitoring  Speed  Current-command

 Zero-crossing current signals

Inputs to ‘Selector’ block

 ‘Selector’ block determines which converter has to operate by assigning

pulse-control signals  Speed and current loops shared by both converters  Converters switched only when current in outgoing converter is zero (i.e.

does not allow circulating current. One converter is on at a time.) Dr. Ungku Anisa, July 2008


36

References  Krishnan, 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.



37

DC Motor and Load Transfer Function Decoupling of Induced EMF Loop  Step 1:

 Step 2:



38

DC Motor and Load Transfer Function Decoupling of Induced EMF Loop  Step 3:

 Step 4:

Back Dr. Ungku Anisa, July 2008


39

Cosine-wave Crossing Control for Controlled Rectifiers Input voltage to rectifier

Vm 0



2

3

4

Cosine voltage Vcm

vc 

 vc    Vcm 

  cos1 

Results of comparison trigger SCRs Output voltage of rectifier

Cosine wave compared with control voltage vc Vcmcos() = vc



Back Dr. Ungku Anisa, July 2008


40

Design of Controllers– Current loop 1st order approximation Ia s   * Ia s 

K c K r K 1Tm 1

K fi 1 H c 1  sT3   1 1  K fi 1  sT3  1  sT3 

1 1  sT3  Tc K c K r K 1 H cTm 1 Tc K fi Hc

K fi 1 H c 1  K fi 

Ki    1  sT3   K fi  T3  1  sTi   1  s  1  K fi   Back Dr. Ungku Anisa, July 2008


41

5 Controlled Rectifier DC Drives-closed loop.pps

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