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NEWCASTLE UNIVERSITY
__________________________
SEMESTER 2, 2019/2020
__________________________
CONTROL OF ELECTRIC DRIVES
Time allowed – 24 hours
Your completed work must be submitted by 2pm (UK time) on
22/05/2020
You are not expected to, and it is not advisable to, work on this
assessment constantly for the 24-hour period. This assessment has
been designed to be worked on for a much shorter period of time in
line with the length of a standard exam sitting.
Guidance on exam time: 3 hours
Instructions for candidates:
Candidates must answer TWO questions from SECTION A,
and ALL THREE questions from SECTION B
All questions carry equal marks
[Marks shown for subsections are indicative only]
The standard 2nd order form is given by
2 + 2 +
2
The quadratic solution to 2 + + = 0 is =
±√
2

2 4
[More instructions, and how to fill in the exam script, are on
following page]
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CONTROL OF ELECTRIC DRIVES
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It is important to show the method of calculation and the steps taken
to achieve the results.
Exam Script Preparation:
1) Answers must be either typed or clearly written. The most
convenient way to answer your questions is to write them out on a
blank A4 sheet of paper with a 1” (2.5cm) margin on the left.
2) Please clearly number your pages so that we can understand the
order. Also please make sure your questions, and subsections, are
clearly numbered.
3) You can then either scan your pages, or photograph them with
your mobile phone. It is your responsibility to ensure that the exam
script is legible when you submit it. Please ensure any scanned
documents / photos are not blurred. Please combine your scanned
documents / photos into a single PDF file. You can do this in
PowerPoint or Word.
4) Upload your answers as a PDF file to the EEE8014 Blackboard page
by going to ‘Assignments’, selecting ‘Exam’ and following the
instructions.
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CONTROL OF ELECTRIC DRIVES
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SECTION A
Question 1
1a) A separately excited DC machine is modelled using:
= +

+
=
=
=

=
i) Assuming that the flux ( ) is a constant, convert the above
equations to the s-domain
[3 Marks]
ii) Then develop the transfer function

(
(

)
)
[6 Marks]
1b) Two time constants can be defined as =

and =

2

0
2
.
During field weakening the flux is described by = 0, where
0 is the rated flux. Using the developed transfer function ( )
( )
equate this to the standard 2nd order form and derive
expressions for damping factor ( ) and natural frequency ( )
in terms of , , and .
[9 Marks]
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1c) A separately excited DC motor drive uses an H-bridge converter
to supply voltage to the armature winding. A constant flux
level has been established in the machine. The H-bridge
converter is switched using unipolar pulse width modulation.
The motor parameters are = 0.1 Nm/A, = 0.1 Ω, and
= 8 mH. The drive is used for a hoist application where a
constant load torque of 2 Nm must be produced at standstill.
Assuming the DC bus voltage is 24 V, calculate the modulation
index.
[6 Marks]
1d) Assuming the operating conditions of 1c), for a carrier
frequency of 10 kHz, estimate the peak to peak value of the
armature current ripple.
[6 Marks]
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Question 2
2a) A DC motor drive employs a cascaded control structure as
shown in Fig.1. The inner armature current loop has been
previously tuned to give a first order closed loop response and
is represented in the diagram by a first order transfer function.
The mechanical components of the drive have been modelled
with inertia ( ) and a friction coefficient ( ). The motor flux is
assumed to be constant and the relationship between
armature current and torque given by = . The speed
loop is controlled by a proportional term .
Fig.1
i) Define the open loop transfer function for the system in
Fig.1.
ii) Derive an expression for the closed loop transfer function

( )

( )
.
For the final expression ensure that the denominator
isolates the
2
term.
[10 Marks]
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2b) By comparing the denominator of the closed loop transfer
function with the standard 2nd order form, derive expressions
for natural frequency ( ) and damping factor ( ) in terms of
the other system parameters.
[5 Marks]
2c) Assuming a critically damped closed loop response ( = 1),
calculate the speed loop gain when the system parameters
are:
= 0.35 kgm2
, = 1.5 Nm/A, = 2, = 0.05 s, = 2.5
[6 Marks]
2d) Calculate the steady state speed error ( ( )) when the
demanded speed

is 5rad/s.
[9 Marks]
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Question 3
3a) In an induction machine, the relationship between the rotor
flux vector (

), and the stator current vector (

), can be
described by the following space vector differential equation:

=

1

+

( )

The model parameters are defined as:
= mutual inductance, = rotor time constant, =
excitation frame angular velocity, and = rotor shaft electrical
angular velocity.
Derive a steady state algebraic expression for the rotor flux in
terms of the stator current vector.
[5 Marks]
3b) A 4-pole, induction machine, vector controlled drive, is
operating at a constant speed of 900 revs/min. At a particular
instant the stator current vector is

= (10 + 17) A and the
slip is 0.03 per unit. Calculate the e-frame flux components

and

. The machine parameters are = 0.103 H,
= 0.11 H, and = 0.703 Ω.
[11 Marks]
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3c) The electromagnetic torque developed by the drive is given by
the following e-frame expression:
=
3
2

2

(

)
Using the current and flux components calculated in 3b),
determine:
i) The torque
ii) The mechanical output power.
[4 Marks]
3d) In an induction machine vector controlled drive, it is essential
to know the slip frequency ( or 2) to allow for accurate
orientation of the reference frame, and hence torque control.
Show the equation that you would implement in a vector
controlled drive which takes into account transient operation of
the flux. Using this equation, calculate the slip frequency
required for the torque of 3c)
[3 Marks]
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3e) In an electric drive it is useful to be able to estimate the stator
voltage required corresponding to a particular rotor flux vector
(

), and the stator current vector (

), to determine if the
inverter is capable of producing this voltage. Using the
following equations, derive a steady state expression which
would allow the stator voltage requirement to be estimated.

=

+

+

=

+

=

+

[7 Marks]
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SECTION B
Question 4
4a) An induction machines dynamic performance can be described
by space vector theory. The stator current space vector can be
written as:

=
2
3
(
+
+
2

) where = ( 120
)
Carefully derive the scalar expressions which relate the
rectangular components of

to the phase currents.
[6 Marks]
4b) A 3-phase, 2-pole, induction machine drive includes current
sensors for measurement of the stator currents. During each
PWM cycle the controller samples the stator phase currents
and performs a 3-phase to 2-phase transformation. During one
of the cycles the sampled values of the stator currents are
given as:

= 17.31 A,
= 3.11 A,
= 20.41 A
Using the transformations derived in 4a) calculate the
rectangular components of the stator current vector.
[4 Marks]
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4c) During the same PWM cycle the position of the rotor flux
vector was determined to be at an angle of = 80 with
respect to the d-axis of the stator reference frame. Assuming
vector controlled conditions are in operation (i.e. the d-axis of
the e-frame is aligned with the rotor flux vector), determine the
flux (

) and torque (

) producing components of the
current. Show diagrams to help explain your calculations and
relationships.
[9 Marks]
4d) A model for a field orientated induction machine can be
described by the following equations:
=
3
2

2

+
1

=

Using the currents calculated in 4c), calculate the rotor flux
magnitude and the torque. It can be assumed that the rotor
flux has reached a steady state level, the mutual inductance is
91 mH, and the rotor self-inductance is 77 mH.
[5 Marks]
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4e) During the next PWM cycle the rotor flux vector can be
considered to be in the same position as 4c). A speed reversal
is to be performed whilst keeping the rotor flux level constant.
Determine the magnitude and angle of the stator current
vector (

) during this cycle, and the values of the

and

.
Show diagrams to help explain your calculations and
relationships.
[6 Marks]
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Question 5
5a) The 3-phase voltage source inverter for a 15 kW, 50 Hz, 4-pole,
vector controlled induction machine, has a DC link voltage of
720 V. It can be assumed that the machine is a balanced starconnected set of coils, and each coil can be modelled as a series
connected resistance (0.215 Ω) and inductance (0.065 H). It
can also be assumed that the machines star-point is isolated,
the inverter is switched using sine-triangle PWM, the inverters
power devices are ideal, and that inverter dead-time is not
present.
For the inverter, the phase modulation signals applied ( 1, 2,
and 3) are given as:
1 = 0.25 sin(15 . )
2 = 0.25 sin(15 . + 120
)
3 = 0.25 sin(15 . + 240
)
Using this information, calculate the magnitude and phase
angle of the fundamental component of the coils currents.
[8 Marks]
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5b) An induction machine can be modelled by the following eframe equations:

=
1

+

( )

=
3
2

2

(

)
Show, that by alignment of the e-frame d-axis with the rotor
flux vector, simplified equations for the flux, torque, and slip
frequency can be derived for a vector controlled induction
motor. Clearly show all of the steps in the derivation.
[8 marks]
5c) The 15 kW, 50 Hz, 4-pole, vector controlled induction machine
is used to drive a mechanical load which has an inertia (J) and
viscous friction (B). A simplified model of the system is shown
in Fig. 2. The flux producing current demand

is held
constant at 14 A and the flux is assumed to have settled to a
steady state. The machines parameters are:
= 0.215 Ω, = 0.221 Ω, = = 0.065 H,
= 0.064 H, = 0.04 kgm2
, = 0.2 Nm/rad/s
s
1
J
1B
r
e* i
ds
e* i
qs T
e r
vector controller
Fig. 2
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i) If the torque producing current demand

is subjected
to a step change from 0 A to 9 A, calculate the torque
produced.
[4 marks]
ii) Using the simplified model of the system, derive a
transfer function ( )
( )
for the mechanical part of the
system.
[3 marks]
iii) In response to the step change in torque, the rotor speed
will increase. Calculate the stator frequency applied (in
Hz) after the steady state speed has been reached.
[7 marks]
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Question 6
6a) The block diagram of a digitally controlled DC drive simulation
model is shown in Fig.3.
Fig.3
i) Explain the function of the Zero Order Hold (ZOH) and
why it is necessary.
ii) What is the purpose of the limiter block on the armature
current demand
iii) What is the purpose of the Delay block
iv) Explain why the speed loop PI controller has an antiwindup feature.
v) It is common to sample the armature current in
synchronism with the inverter PWM carrier signal. Why is
this done
[5 Marks]
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6b) The DC motor model block in Fig.3 contains a structure based
on the following equations:
= +

+
=
2 +

+
=
=
=
i) Rearrange these equations into a state space form to find

and

, which uses armature current and angular
velocity as state variables.
ii) Using these state space equations from part i), draw a
MATLAB Simulink block diagram of the DC motor.
[8 Marks]
6c) A control loop is employed to hold the armature current
constant regardless of the motor back emf. After an initial
transient the angular velocity settles to a constant value.
Develop an algebraic equation which can be used to predict the
steady state speed based on a constant armature current.
(Hint: It will result in a quadratic equation).
[6 Marks]
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6d) A DC motor drive described in 6b) has the following
parameters:
= 0.35 kgm2
, = 1.5 Nm/A, = 0.5, = 0.005 Nms
2
Calculate the steady state angular velocity corresponding
to a constant armature current of 5 A.
[4 Marks]
6e) The control system described in 6b) uses an H-bridge
converter connected to a 240 V DC supply. The converter is
switched using pulse width modulation. In a speed loop
application, the angular velocity demand is set to a constant
value of 50 rads
1
. After an initial transient, the motor
angular velocity error reduces to 0 rads
1
and the motor
electromagnetic torque settles to a steady state value of
10Nm. The armature resistance is 1 Ω and the torque
constant is = 1.5 Nm/A.
i) Calculate the back EMF for the angular velocity of
50 rads
1
ii) Calculate the armature voltage required to maintain
this steady state condition.
iii) Determine the PWM modulation index (m) output
required during this steady state condition.
[7 Marks]
[END]