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Electrical Drives I
Week 4-5-6: Solid state dc drives- closed loop control of phase controlled
DC drives
DC Drives control- DC motor without control

Speed Control Strategy:

below base speed: Vt control (terminal voltage control)

above base speed: flux control via Vf control (field weakening)
For the separately excited dc motor, assuming that the field excitation is held constant, the transfer characteristic
between the shaft speed and the applied voltage to the armature can be expressed as:
The feedback is a “naturally existed” loop which
is physically present in the motor itself.
Normally, speed is the subject and is the variable
to be controlled, thus the input signal is NOT
voltage.
Va
-
1
R a  La s
Ia
Td
1
Js  F
KT
Tl
-
Ea
KE
If the load torque is neglected, the transfer characteristics between the motor speed ω and the applied
terminal voltage 𝑉𝑡
𝜔
𝐾𝑇
=
𝑉𝑡
𝑠𝐿𝑎 + 𝑅𝑎 𝐽𝑠 + 𝐹 + 𝐾𝐸 𝐾𝑇

DC Drives control- DC motor without control
The characteristic roots can of the pervious equation can be determined as:
𝑠+
1
𝜏𝑎
𝑠+
𝐹
1
+
𝐽
𝜏𝑎 𝜏𝑚
Where:
𝜏𝑎 = 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑡𝑖𝑚𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 =
𝜏𝑚
𝐿𝑎
𝑅𝑎
𝑅𝑎 𝐽
= 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝑡𝑖𝑚𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 =
𝐾𝐸 𝐾𝑇
The un-damped natural frequency and damping ratio can be given as:
𝜔𝑚 =
1 1
𝐹
+
𝜏𝑎 𝜏𝑚 𝐽
𝜎 = 𝜁𝜔𝑚 =
1 1 𝐹
+
2 𝜏𝑎 𝐽
The speed response over the whole operating range upon the application of a load torque can be determined
by:
Δ𝜔
1 + 𝑠𝜏𝑎
=
𝐾𝐸 𝐾𝑇
Δ𝑇𝐿
1 + 𝑠𝜏𝑎 𝐽𝑠 + 𝐹 +
𝑅𝑎
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

DC motor control normally employ a “two loop control” technique. This has an inner
feedback loop to control the current (and hence torque) and an outer loop to control
speed. When position control is called for, a further outer position loop is added.
Reference
signal
+
Plant
Controller

Output
signal
Sensor
Additional Control variables:
 Protection
 Enhancement of response – fast
response with small overshoot
 Improve steady-state accuracy
Main Control variables:
 Speed
 Torque
 Position
DC Drives control

Normally, a typical drive system would look like the following
assuming the following scenario:

If the motor running light at a set speed and the speed reference
signal is suddenly increased, the reference speed is now greater than
the actual speed and there will be a speed error signal, represented by
the output of the left-hand summing point.

A speed error indicates that acceleration is required, which in turn
means torque, i.e. more current. The speed error is amplified by the
speed controller and the output serves as the reference or input signal
to the inner control system.

Schematic diagram of analogue controlledspeed drive with current and speed
The inner feedback loop is a current-control loop, so when the current
feedback control loops
reference increases, so does the motor armature current, thereby
providing extra torque and initiating acceleration.

As the speed rises the speed error reduces, and the current and torque
therefore reduce to obtain a smooth approach to the target speed.
Closed Loop Control of DC Drives

Cascade control structure

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 Drives-Torque loop
Inner Torque (Current) Control Loop:

Current control loop is used to control torque via armature current (ia) and
maintains current within a safe limit

Amplifies the difference (or current error), and using the resulting amplified
current error signal (an analogue voltage) to control the firing angle α – and hence
the output voltage – of the converter

Accelerates and decelerates the drive at maximum permissible current and torque
during transient operations

Proportional plus integral controller (PI) are usually employed for zero steady state
error operation
Torque
(Current)
Control
Loop. Could
be in terms
of torque or
current
Feedback current signal
is obtained either from a
d.c. current transformer,
or from a.c current
transformer/rectifiers in
the mains supply lines
Closed Loop Control of DC Drives-Torque (current) loop
The inner current loop is usually employed for current limitation. As long as the current control loop functions
properly, the motor current can never exceed the reference value. Hence by limiting the magnitude of the
current reference signal (by means of a clamping circuit), the motor current can never exceed the specified
value.

For small errors in speed, the current reference increases in proportion
to the speed, thereby ensuring ‘linear system’ behavior with a smooth
approach to the target speed.

If the speed error exceeds a limit, the output of the speed-error
amplifier saturates and there is thus no further increase in the current
reference.

Electronic current
limitation!
By arranging for this maximum current reference to correspond to the
full (rated) current of the system there is no possibility of the current in
the motor and converter exceeding its rated value, no matter how large
the speed error becomes.
Closed Loop Control of DC Drives- Speed Loop

Cascade control structure

Speed Control Loop:

Ensures that the actual speed is always equal to reference speed *

Provides response to changes in *, TL and supply voltage without exceeding motor and converter
capability

Proportional plus integral controller (PI) is usually employed
Speed
Control
Loop
Speed feedback is
provided by a d.c.
tachogenerator.
Actual and
reference speeds
are
fed into the speederror amplifier
Closed Loop Control of DC Drives- Speed Loop
 With the motor at rest (and unloaded for the sake of simplicity), we suddenly increase the speed reference from zero
to full value.
 The speed error will be 100%, so the output 𝑰𝒓𝒆𝒇 from the speed error amplifier will immediately saturate at its
maximum value, which has been deliberately clamped so as to correspond to a demand for the maximum (rated)
current in the motor.
 The motor current will therefore be at rated value, and the motor will accelerate at full torque.
 Speed and 𝑬𝒂 will therefore rise at a constant rate, the applied voltage 𝑽𝒕 increasing steadily so that the difference (𝑽𝒕
– 𝑬𝒂 ) is sufficient to drive rated current through the armature resistance.
 The output of the speed amplifier will remain saturated until the actual speed is quite close to the target speed, and
for all this time the motor current will therefore be held at full value.
 Only when the speed is within a few percent of target will the speed-error amplifier come out of saturation. Thereafter,
as the speed continues to rise, and the speed error falls, the output of the speed-error amplifier falls below the
clamped level.
 Speed control then enters a linear regime, in which the correcting current (and hence the torque) is proportional to
speed error, thus giving a smooth approach to final speed.
Closed Loop Control with Controlled Rectifiers – Two-quadrant

Two-quadrant Three-phase Controlled Rectifier DC Motor Drives
 Field is separately excited
and field supply is kept
constant
or
regulated,
depending on the need for
field weakening
 Most important part is the
design of the speed and
current
controllers
time
constants.
System without motor model
Current
Control Loop
Speed
Control
Loop
Closed Loop Control with Controlled Rectifiers

– Two-quadrant
Actual motor speed m measured using the tachogenerator (Tach) is filtered to produce feedback signal
To do list
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
Design 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)
b)
c)
2.
3.
DC Motor & Load
Current feedback loop sensor
Speed feedback loop sensor
Design current (torque) control loop first
Then design the speed control loop
Transfer Function of Subsystems –
DC Motor and Load

Assume load is proportional to speed
TL  BLm
DC motor has inner loop due to 𝐸𝑎 magnetic
coupling, which is not physically seen. This creates
complexity in current control loop design due to the
cross coupling.
 These two loops need to be decoupled by
reconfiguring the block diagram

System without motor block diagram
System with motor block diagram
System without
control
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

Consists of two additional control loops on field circuit:

Field current control loop (inner)

Induced emf control loop (outer): Induced emf loop is estimated and is sensitive to
parameter variation thus needs to be adaptive and also depends on the type of motor
Closed Loop Control with Field Weakening –
Two-quadrant
Field weakening
Closed Loop Control with Field Weakening –
Two-quadrant
Field weakening
Field
current
controller
(PI-type)
Estimated
machine induced emf
dia
e  Va  Ra ia  La
dt
Induced emf
reference
Induced emf
controller
(PI-type with
limiter)
Field current
reference
Closed Loop Control with Field Weakening –
Two-quadrant

The reference 𝑒𝑎∗ is compared to 𝑒𝑎 to obtain the induced emf error signal (for speed above
base speed, 𝑒𝑎∗ kept constant at rated emf value so that 𝜑 ∝ 1 𝜔)

The 𝑒𝑎 (PI) controller processes the error and produces the field current reference 𝑖𝑓∗

𝑖𝑓∗ is limited by the current 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
Closed Loop Control– Four-quadrant

Four-quadrant Three-phase Controlled Rectifier DC Motor Drives
Control operation
of either converter
1 or converter 2
Closed Loop Control– 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 (to transfer control from
one converter to another
Speed and current loops shared by both converters