PMSM-Motor-Control : A research about FOC

PMSM Motor
Control
Motor control refers to the process by which the performance of
the motor is regulated by regulating its speed, torque and other
parameters of the motor. This is really important for having control
over the motor and performing the desired operation needed to be
performed by the motor in the specific application. In this
document, particularly the control of a three phase PMSM motor is
discussed.

PMSM Motor
The PMSM is an AC motor that works on a three phase current supply. A three phase
supply is the one which has three alternating currents which have a phase difference of
120 degrees between each other. The motor contains a stator (stationary part) on which
the three coils carrying the three phase currents are wound and the rotor (rotating part)
that contains permanent magnets on it. This is the differentiating point between
induction and PMSM motors as induction motors do not have permanent magnets on
their rotors.
Stator
The stator is the stationary part of
the motor. It contains the windings
that carry the three-phase currents.
Rotor
The rotor is the rotating part of the
motor. It contains permanent
magnets that interact with the
magnetic field created by the stator
windings.

How PMSM Motors Work
The three phase supply creates a rotating magnetic field (rmf) inside the motor. The poles in the permanent magnets
get coupled with the opposite poles of the rmf and rotate at the same speed as that of the rmf. Hence we have
achieved the rotating motion of the rotor using three phase supply. The speed (rpm) and torque of the motor is equal
to the speed of the rmf and are given by:
Speed Torque
ω = 2πf/p T = k*I (k is a constant and I is phase current)

Controlling Speed and Torque
From the expressions it is clear that the speed of the motor depends on the frequency of the currents in the coils and
the torque depends on the instantaneous values of the currents in the coils. So conclusively, if we want to control the
speed and torque of the motor, we need to have a control on the currents supplied to the motor. This is exactly the
work of a controller.
Current Control
The controller regulates the
current supplied to the motor
windings.
Speed Control
The controller adjusts the
frequency of the current to
control the motor's speed.
Torque Control
The controller adjusts the
magnitude of the current to
control the motor's torque.

Field Oriented Control (FOC)
Field-oriented control (FOC), also known as vector control, is an advanced technique
used to control motors, particularly AC induction motors and permanent magnet
synchronous motors (PMSMs). It provides precise control over a motor's speed and
torque across its entire operating range.
1 Feedback Control Loop
FOC works on a feedback control
loop where reference values
(desired values) are compared to
feedback values (actual values)
measured by sensors.
2 PID Controller
A PID controller processes the
difference between reference and
feedback values to generate a
voltage signal that adjusts the
motor's current.

Transformations in FOC
In FOC there are two types of transforms:
Clarke's Transform
Clarke's transform converts the three AC currents (ia,
ib, ic) into two AC currents (i alpha and I beta). The
formula for Clarke's transform is:
Parkes' Transform
Parkes' transform converts the two AC currents to two
DC currents (id and iq). The formula for Parkes'
transform is:

Algorithm of FOC
The algorithm of one cycle of the closed feedback control loop is described below:
1
Step 1: Measurement
The feedback currents (ia, ib, ic), the angular
velocity of the motor (w) and the angular position
(theta) of the motor are measured using sensors
in the motor.
2 Step 2: Transformation
The feedback currents undergo Clarke's and
Parkes' transform and give d and q feedback
currents (id fb and iq fb).
3
Step 3: Reference Values
The reference d and q currents (id and iq) are
measured using the sensor at the accelerator
pedal. 4 Step 4: PID Control
The reference and feedback currents are fed to
two PID controllers, one for d and one for q
currents. Each controller outputs a voltage signal
(vd and vq).
5
Step 5: Inverse Transformation
The two voltage signals then undergo Clarke's
and Parkes' transforms and we get va, vb, and vc,
that is the voltages in the coils of the windings.
6 Step 6: Inverter
These three voltage signals are then transferred
to a device called an inverter which converts DC
voltage from the battery to AC voltage whose

Simulating FOC
The field oriented control was simulated on Simulink to obtain the speed and torque of the motor. The model is
explained below and also the outputs are graphed and explained. Here the reference d and q currents are chosen
randomly. These values depend on the amount of accelerator pedal pressed. On a particular position pressed on the
accelerator pedal, there is a particular set of reference d and q current values.
Accelerator Pedal
The accelerator pedal
position determines the
reference d and q
currents.
Sensors
Sensors in the motor
measure feedback
values like current,
speed, and position.
PID Controllers
Two PID controllers
regulate the d and q
currents based on
reference and feedback
values.
Inverter
The inverter converts DC
voltage to AC voltage
based on the controller's
output.

PMSM Motor Results
The above graph represents the torque on the y-axis vs time on the x-axis. As the beginning as there is a difference between
reference and feedback values, there is a torque generated in the motor that decreases gradually as the feedback values
approaches the reference values (as torque is proportional to the difference between reference and feedback values) and finally
comes to a stop when then feedback values reach the reference values. Also the speed of the motor rises at the beginning and
becomes constant when the feedback values equal reference values. This all happens within microseconds in the
microcontroller.
Torque vs Time
The graph shows how torque changes over time as the
motor reaches its desired speed.
Speed vs Time
The graph shows how the motor's speed increases and
stabilizes as the feedback values match the reference
values.

Types of motor
control
There are two types of motor control: speed control and torque
control. In this presentation, we will in depth see speed control as
it is easier to understand but both speed and torque control are
based on the same principle

Speed Control
1
Pedal Input
The percentage of the
accelerator pedal
pressed directly
corresponds to the
desired percentage of
the motor's top speed.
This input acts as the
reference value for the
desired speed.
2
Speed Error
The difference between
the reference speed
and the actual motor
speed is known as the
speed error. This error
is proportional to the
torque applied to the
motor.
3
Torque
Adjustment
A higher speed error
results in a higher
torque applied to the
motor. This torque
gradually decreases as
the speed error
approaches zero,
causing the motor to
accelerate until the
desired speed is
reached.
4
Constant Speed
Once the speed error
becomes zero, the
motor operates at a
constant speed. This
process happens very
quickly, typically within
microseconds, thanks
to the efficiency of
Field-Oriented Control
(FOC).

Torque Control
Speed Control
In speed control, the focus is on
regulating the motor's speed, with
the torque being a byproduct of
the speed error.
Torque Control
In torque control, the percentage
of the pedal pressed directly
corresponds to the desired
percentage of the maximum
torque generated by the motor.
The speed is a consequence of
the applied torque.
Similarities
Both speed control and torque
control utilize similar principles
and mechanisms. The primary
difference lies in the control
variable: speed in one case and
torque in the other.

Types of circuits
in controller
The controller is a complex system with various circuits working
together to control the motor. These circuits are responsible for
delivering power, processing signals, and communicating between
different components. Let's explore each type of circuit in detail.

High Voltage Circuit
The high voltage circuit is responsible for delivering power from the battery to the motor. It's located in the inverter
and utilizes IGBT transistors to rapidly switch on and off, generating an AC voltage signal that powers the motor.
IGBT Transistors
These transistors act like switches, rapidly turning on
and off based on signals from the microcontroller. This
switching action creates the AC voltage needed for the
motor.
Inverter
The inverter is the component that houses the high
voltage circuit. It converts the DC power from the
battery into AC power for the motor.

Low Voltage Circuit
The low voltage circuit is the brain of the controller, responsible for controlling the high voltage circuit
and managing the overall system. It houses sensors, microcontrollers, ADC, and DAC, all working
together to process and transmit signals.
1 Sensors
Sensors gather information about the motor's performance and the surrounding environment,
converting it into analog signals.
2 Microcontroller
The microcontroller processes the digital signals from the sensors and sends instructions to
the high voltage circuit.
3 ADC & DAC
The ADC converts analog signals from sensors into digital signals for the microcontroller,
while the DAC converts digital signals from the microcontroller into analog signals for the
motor.

Signal Circuit
The signal circuit is responsible for communication between different components of the controller.
It converts analog signals to digital signals and vice versa, transmitting them efficiently using
optocouplers.
Optocouplers
These devices use light to transmit signals, providing isolation between
components. This allows for efficient signal transmission even with high voltage
differences.
Signal Conversion
The signal circuit converts analog signals from sensors into digital signals for the
microcontroller and vice versa.
Communication
The signal circuit ensures smooth communication between different components,
allowing for coordinated operation of the controller.

Power Circuit
The power circuit acts like a valve, delivering the right amount of
power to each component of the controller. It ensures that each
component receives the necessary power for optimal operation.
Component Power Requirement
Microcontroller Low voltage, low current
Sensors Variable, depending on the
type
IGBT Transistors High voltage, high current

Digital Circuit
The digital circuit is the heart of the controller, containing the microcontroller that processes digital
signals. It receives instructions from the signal circuit and sends commands to the high voltage
circuit.
Processing
The microcontroller processes the digital signals from the sensors and makes decisions based on the
data.
Control
The microcontroller sends commands to the high voltage circuit, controlling the motor's speed and
direction.
Communication
The microcontroller communicates with other components of the controller, ensuring coordinated
operation.

Analog Circuit
The analog circuit contains the sensors that produce analog signals. These signals
are then converted to digital signals by the ADC and sent to the microcontroller for
processing.
Sensors
Sensors measure various parameters like temperature, pressure, and position,
converting them into analog signals.
Analog Signals
Analog signals are continuous and vary smoothly over time, representing the
measured parameter.
ADC Conversion
The ADC converts the analog signals from sensors into digital signals for the
microcontroller to process.

Software of the
Microcontroller
Let us have a look at the microcontroller and the software involved in it. The
microcontroller is the brain of the controller that processes the digital signals to
control the motor. Its working is very similar to that of computers like ram rom
and cpu. Instead of cpu, there is a microcontroller that processes the algorithm
of the motor control and outputs the necessary signals for controlling the motor.

Microcontroller Memory
RAM
For ram, that is storing temporarily the values of
variable for a particular cycle, very small storage units
called registers are used. These are inside the
microcontroller itself hence the access to values of
variable stored in them is very fast and easy for the
processor.
ROM
For rom that is permanent or non volatile memory
there a memory called flash memory that also is in the
microcontroller. This contains the code of the
algorithm that is need to be stored for reading it and
perform the algorithm.

Program Execution
1 Code Compilation
The program is first coded and compiled in a computer and the compiled code that is
in machine language is transferred to the microcontroller where it is stored in its non
volatile flash memory.
2 Module Setup
Setting up of modules: a module is the one that performs a specific task like
production of signal for inverter. Each module has its own registers that are also set
up while setting up the modules.
3 Variable Initialization
Initialization of variables: The variables like d and q currents, rotor angle etc are
defined in the code that is installed in the microcontroller. These variables are
initialized in the starting of the motor control process. Once the process has started,
the values of the variables only get updated in each cycle of the motor control.
4 Main Program Execution
Once the variables’ values are stored in the appropriate registers, the microcontroller
processes them according to the algorithm of the FOC and outputs the signals that

Step 1: Measuremen
Field Oriented Control (FOC) is a powerful technique used to
control electric motors. It involves precisely controlling the
magnetic field within the motor to achieve optimal performance.
The first step in FOC is measurement or sensing, where crucial
information about the motor's state is gathered. This information is
then used in subsequent stages of the FOC process to achieve
precise control.

Measuring the Three Phase Currents
In FOC, the currents flowing through the three windings of the motor (ia, ib, ic) are essential for control. These
currents are measured to provide a real-time understanding of the motor's operation. However, only two
currents (ia and ib) are directly measured using sensors. The third current (ic) is calculated using the
relationship Ia + Ib + Ic = 0. This calculation is performed by the microcontroller, which is a key component in
the FOC system.
1 Current Sensors
Two common types of
sensors are used to
measure the phase
currents: current
transformers (CTs) and
Hall effect sensors. Both
types produce an AC
voltage signal proportional
to the current flowing in
the phase wire.
2 Analog to Digital
Conversion
The AC voltage signal
from the sensor is then
converted to a digital
signal by an analog-to-
digital converter (ADC).
This conversion is
necessary because the
microcontroller can only
process digital
3 Digital Signal Processing
The ADC converts the
continuous AC signal into
discrete digital values. The
microcontroller then
processes these digital
values to determine the
actual current flowing in
each phase winding.

Current Transformer (CT)
A current transformer (CT) is a type of sensor used to measure the current flowing in a wire. It consists of a coil
of wire wound around a magnetic core. When current flows through the wire, it creates a magnetic field that
induces a current in the CT coil. The current in the CT coil is proportional to the current in the wire being
measured.
Operation
The CT encloses the wire
carrying the current. The
magnetic field generated by the
current in the wire induces a
voltage in the CT coil. This
voltage is proportional to the
current flowing in the wire.
Output
The CT produces an AC voltage
signal that is proportional to the
AC current in the phase wire.
This signal is then sent to the
ADC for conversion to a digital
signal.
Advantages
CTs are relatively inexpensive
and reliable. They are also
capable of measuring high
currents with good accuracy.

Hall Effect Sensor
A Hall effect sensor is another type of sensor used to measure current. It is based on the Hall effect, which is
the production of a voltage across a conductor when it is placed in a magnetic field. In a Hall effect sensor, the
magnetic field is generated by the current flowing in the wire being measured.
Operation
The Hall effect sensor is placed
near the wire carrying the
current. The magnetic field
generated by the current
induces a voltage across the
sensor. This voltage is
proportional to the current
flowing in the wire.
Output
The Hall effect sensor produces
an AC voltage signal that is
proportional to the AC current in
the phase wire. This signal is
then sent to the ADC for
conversion to a digital signal.
Advantages
Hall effect sensors are non-
contact sensors, meaning they
do not need to be physically
connected to the wire being
measured. They are also
relatively accurate and reliable.

Rotor Angle Measurement
The rotor angle is the angle between a reference point on the stator and a reference point on the rotor. It is a
crucial parameter in FOC, as it determines the position of the rotor within the motor. There are several
methods for measuring the rotor angle, including using sensors like Hall effect sensors, resolvers, and
encoders. Additionally, sensorless techniques can be employed by measuring the back electromotive force
(EMF) and processing it in the microcontroller.
Hall Effect Sensors
Hall effect sensors are commonly used to
measure the rotor angle. They are placed at
strategic locations on the stator and detect the
magnetic field generated by the rotor.
Resolvers
Resolvers are rotary sensors that provide a
sinusoidal output signal proportional to the rotor
angle. They are more accurate than Hall effect
sensors but also more expensive.
Encoders
Encoders are digital sensors that provide a
pulse output signal for each increment of the
rotor angle. They are highly accurate and widely
used in precision applications.
Sensorless Techniques
Sensorless techniques rely on measuring the
back EMF generated by the motor. This voltage
is proportional to the rotor speed and can be
used to estimate the rotor angle.

Hall Effect Sensors for Rotor Angle
Hall effect sensors are commonly used to measure the rotor angle in electric motors. They are placed at
strategic locations on the stator and detect the magnetic field generated by the rotor. The output of the Hall
effect sensor is a digital signal that indicates the position of the rotor.
Magnetic Field Detection
The Hall effect sensor detects
the magnetic field generated
by the rotor magnets.
Digital Signal Output
The sensor produces a digital
signal that indicates the
position of the rotor.
Microcontroller Processing
The microcontroller processes
the digital signal from the Hall
effect sensor to determine the
rotor angle.

Resolvers for Rotor Angle
Resolvers are rotary sensors that provide a sinusoidal output signal proportional to the rotor angle. They are
more accurate than Hall effect sensors but also more expensive. Resolvers are often used in high-
performance applications where precise rotor angle measurement is critical.
Operation
Resolvers consist of a stator
and a rotor. The stator has two
windings, and the rotor has a
single winding. The rotor rotates
relative to the stator, and the
angle between the rotor and
stator windings determines the
output signal.
Output
Resolvers produce two
sinusoidal output signals that
are 90 degrees out of phase.
These signals are used to
determine the rotor angle.
Advantages
Resolvers are highly accurate
robust and can withstand harsh
environments.

Encoders for Rotor Angle
Encoders are digital sensors that provide a pulse output signal for each increment of the rotor angle. They are
highly accurate and widely used in precision applications. Encoders can be either incremental or absolute,
depending on the type of output signal they provide.
Incremental Encoders
Incremental encoders provide a
pulse output signal for each
increment of the rotor angle.
The number of pulses indicates
the amount of rotation.
Absolute Encoders
Absolute encoders provide a
unique digital code for each
position of the rotor. This code
directly indicates the absolute
position of the rotor.
Advantages
Encoders are highly accurate
relatively inexpensive and easy
to use.

Sensorless Rotor Angle Measurement
Sensorless techniques for rotor angle measurement rely on measuring the back EMF generated by the
motor. This voltage is proportional to the rotor speed and can be used to estimate the rotor angle.
Sensorless techniques are often used in applications where cost or space constraints prevent the use of
sensors.
1 Back EMF Measurement
The back EMF generated by the motor is measured using a voltage sensor.
2 Signal Processing
The measured back EMF signal is processed by the microcontroller to estimate the rotor
speed and angle.
3 Rotor Angle Estimation
The microcontroller uses the processed back EMF signal to estimate the rotor angle.

Step 2:
Transformation
Transformations are a crucial aspect of motor control, simplifying
complex calculations and enhancing the efficiency of the
controller. This process involves representing three sinusoidally
varying currents, representing the three phases of the motor, in
terms of just two constant quantities: d and q currents. This
transformation significantly reduces the workload of the
microprocessor, leading to a faster response time for the
controller.

Understanding the Transformation
1 ABC to Alpha-Beta
The first step in the transformation involves converting the three-phase currents (abc)
into alpha-beta currents. This conversion is achieved by projecting the three-phase
currents onto two perpendicular axes: the alpha axis and the beta axis.
2 Alpha-Beta to D-Q
The second step involves converting the alpha-beta currents into d and q currents.
This is done by aligning the d-axis with the rotor magnetic field and the q-axis
perpendicular to it. The d and q currents represent the components of the stator
magnetic field along these axes.
3 Benefits of Transformation
This transformation simplifies the control process by reducing the number of
variables from three to two. It also allows for easier control of the motor's speed and
torque, as the d and q currents directly relate to the stator magnetic field.

The Role of the Stator
Magnetic Field
The speed and torque of the motor are directly influenced by the
stator magnetic field (rmf). This field is characterized by its
constant magnitude and circular rotation at the motor's speed. The
stator magnetic field is generated by three coils placed at 120-
degree angles to each other, each coil producing a magnetic field
perpendicular to its axis. So, to control the motor, we have to
control this field. By transformations, we make it easy to represent
and control this field.

From Three-Phase to
Two-Phase Currents
The three-phase currents create a rotating magnetic field. To
simplify control, we convert these three currents into two currents:
alpha and beta. This is achieved by projecting the three-phase
currents onto two perpendicular axes, with one axis aligned with
one of the three-phase axes (e.g., the ia axis). The axis aligned
with ia is the alpha axis, and the perpendicular axis is the beta
axis.

Clarke's Transformation
This figure shows
the direction of the
magnetic axes of
the stator windings
in the abc
reference frame
and the stationary
αβ reference frame.
This figure shows
the equivalent α
and β components
in the stationary αβ
reference frame.
These two curves
represent the α and
β currents which
are sinusoidally
varying quantities.
The following
equation describes
the Clarke
transform
computation. fa, fb
and fc are the three
phase currents and
fα and fβ are alpha
and beta currents.

The Importance of D-Q
Currents
While the alpha-beta currents simplify the representation, they are
still sinusoidal and difficult to control. To further simplify the
control, we convert the alpha-beta currents into d and q currents.
The d-axis is aligned with the rotor magnetic field, and the q-axis
is perpendicular to it. The d and q currents represent the
components of the stator magnetic field along these axes.

Parke's Transformation
The diagram shows d and q
axes that rotate at the
speed of the motor. The d
axis makes angle theta with
aplha axis which is
measured by the sensor
The diagram shows d and q
currents (red and blue line)
vs time plot. Hence, we can
see that we made the 3 ac
signals to 2 dc signals
reducing the work of
controller greatly.
This is the formula for
transforming the aplha and
beta current values to d and
q currents.

Advantages of D-Q Transformation
1 Simplified Control
The d-q transformation reduces the number of variables from three to two, simplifying
the control process.
2 Direct Relationship to Stator Field
The d and q currents directly relate to the stator magnetic field, allowing for easier
control of the motor's speed and torque.
3 Improved Efficiency
The transformation reduces the workload of the microprocessor, leading to a faster
response time for the controller.
4 Enhanced Performance
The transformation enables more precise control of the motor, resulting in improved
performance and efficiency.

Sensing the Rotor Angle
The angle between the rotor magnetic field and the alpha axis,
denoted as 'theta,' is crucial for the d-q transformation. This angle
is sensed using a sensor, allowing for accurate determination of
the d and q currents. By knowing the d and q currents, we can
determine the magnitude and angle of the stator magnetic field.

Step 3: Reference
Values
The ultimate goal of motor control is to match the reference and feedback
speed of the motor. The reference speed is determined by the position of
the accelerator pedal pressed by the driver, while the feedback speed is
provided by a sensor in the motor. The difference between these two
values, known as the error, is calculated by the microprocessor. This error
is then used by a PI controller to determine the desired torque, which in turn
determines the necessary d and q currents to be supplied to the motor.

Calculating the Error
1 Reference Speed (wref)
The reference speed, or percentage of maximum speed, is
given by the position of the accelerator pedal pressed by the
driver.
2 Feedback Speed (wfb)
The feedback speed is provided by a sensor in the motor,
giving the actual speed of the motor.
3 Error Calculation
The error is calculated as the difference between the
reference speed (wref) and the feedback speed (wfb): error
= wref - wfb.

Generating the Desired Torque
PI Controller
The PI controller is an algorithm
executed by the microprocessor
that takes the error as input and
outputs the desired torque value.
Torque Proportional to
Error
The principle of vector control or
FOC is that the torque generated
is proportional to the error, which
makes it faster to reduce the
error.
Desired Torque
The desired torque value is then
used to determine the necessary
d and q currents to be supplied to
the motor.

Determining the d and q
Currents
1 Reference Values
The desired torque value is used to determine the reference d and q
currents that need to be supplied to the motor.
2 Feedback Currents
The actual d and q currents being supplied to the motor are measured
by sensors and provided as feedback.
3 Matching Currents
The goal is to match the reference d and q currents with the feedback
currents, ensuring the motor is operating at the desired torque and
speed.

This is the formula for finding reference q current by
using the desired torque.
ψ:Magnetic flux linkage of the permanent magnets
with the stator windings
θ_e:Electrical angle. Electrical angle is given by θ_e=
θ(angle rotated by shaft) *p (number of pairs of poles
in the magnets of rotor)
Te: Desired torque outputted by the PI controller

What about Id?
The formula in the above slide only gives the Iq, now let us see what value does Id take. due to rotation of stator field
a back EMF is induced in stator coils which can negatively affect the working of motor. If the value of Id is negative it
weakens the back EMF.
At low speeds
At low speeds, the back EMF is negligible, hence to
keep the controlling simple, the value of Id is almost
zero (can be assumed zero).
At high speeds
At high speeds, there is a considerable effect of the
back EMF hence, to control this, id is assigned a
negative value which is calculated by certain field
weakening algorithms.

Step 4: PID Control
The principle of vector control, also known as Field-Oriented
Control (FOC), is a fundamental technique used in modern motor
drives. While the desired reference d and q currents can be
calculated, the voltage values required to achieve these currents
may not always produce the desired results due to the non-ideal
behavior of the motor. This is where the importance of feedback
comes into play, allowing the PI controllers to make real-time
adjustments and provide the necessary voltage to the windings.

Calculating Desired D and Q voltages
In the microcontroller, there are two PI controllers (which are algorithms) each controlling separately the d and q
axes. The PI controllers generate voltage signals that are d and q voltages that represent the three phase voltages
upon inverse transformations. So, there is an interesting question that why we need feedback values to calculate the
voltage in windings if we know the currents in the windings (i.e. we know d and q currents)? The values of voltages
can be simply calculated by ohm's law, even if the behavior is non ohmic, there must be a direct relation between
voltage and currents for the windings. This is answered in upcoming slides.

The Challenge of Non-Ideal Motor Behavior
Irregularities in the Motor
The non-ideal behavior of the
motor prevents the calculated
voltage values from always
producing the desired currents.
Factors such as resistance,
inductance, and saturation can
cause the actual currents to
deviate from the reference values.
Unpredictable Variations
These irregularities are often
random and cannot be fully
accounted for in the algorithm.
The motor's performance can be
affected by factors like
temperature, wear, and
manufacturing tolerances, making
it difficult to predict the exact
behavior.
The Need for Feedback
To address these challenges, the
system relies on feedback from
the actual d and q currents. This
allows the PI controllers to make
real-time adjustments and provide
the necessary voltage to the
windings, ensuring the desired
currents are achieved despite the
motor's non-ideal behavior.

Step 5: Inverse
Transformation
Now we have the necessary d and q voltages that are needed to
be transformed back to a,b and c voltages to be fed to inverter.
These processes are called inverse parkes and inverse clarkes
transforms. Both these transformations are taken place in the
microcontroller by using algorithm to calculate them.

Formula for inverse Parke's transformation
Inverse Parke's transformation
In this transformation, we convert back the
constant (DC) D and Q voltages to 2 sinusoidal
AC voltages that are alpha and beta voltages. For
this transformation, the rotor angle theta is also to
be known which is input from the angle sensor.

Formula for inverse Clarke's transformation
Inverse Clarke's transformation
This transformation converts the 2 sinusoidally
varying alpha and beta voltages to 3 AC
sinusoidally varying voltages a, b and c voltages
that can be fed to the inverter to be supplied to the
motor.

Step 6: Inverter
Pulse Width Modulation (PWM) is a crucial technique used in motor control
systems to precisely regulate the voltage applied to the motor windings. By
rapidly connecting and disconnecting the load from the power source, PWM
allows for the effective voltage to be controlled, enabling the desired
sinusoidal AC voltages to be generated and drive the permanent magnet
synchronous motor (PMSM).
ST

Controlling Voltage with PWM
Constant Source
The constant DC voltage from the
battery serves as the power
source. By controlling the PWM, a
percentage of this battery voltage
is effectively applied to the load,
allowing for variable voltage
control.
On/Off Cycling
The PWM rapidly connects and
disconnects the load from the
source, creating an "on" state
where voltage is applied, and an
"off" state where it is not. The
ratio of on-time to total time is the
duty cycle, which determines the
effective voltage.
Effective Voltage
The effective voltage is calculated
as the duty cycle multiplied by the
source voltage. By varying the
duty cycle, the effective voltage
can be adjusted to achieve the
desired AC sinusoidal voltages in
the motor windings.

Space Vector Modulation (SVM)
1 Intermediate Step
Before the PWM signal is generated, an intermediate step called Space Vector
Modulation (SVM) is performed. SVM takes the three-phase voltages from the PI
controller and calculates the optimal switching times for the PWM signal.
2 Switching Time Calculation
SVM determines the on-time for the PWM signal, which is then used to control the
opening and closing of the IGBT switches in the inverter circuit. This ensures the desired
three-phase voltages are accurately generated.
3 Smooth Operation
The PWM signal is repeatedly generated many times per second, allowing for smooth
and continuous operation of the PMSM motor by providing the necessary voltage and
current in the windings.

Inverter and IGBT Switching
Driver Circuit
The PWM signal is received by a driver circuit, which interprets the signal and controls the
switching of the IGBT (Insulated Gate Bipolar Transistor) switches in the inverter circuit.
IGBT Switching
The IGBT switches act as micro-switches, turning on and off in response to the PWM signal.
When the PWM is in the "on" state, the IGBT is turned on, applying voltage to the motor
windings. When the PWM is "off", the IGBT is turned off, removing the voltage.
Positive and Negative Halves
By selectively opening and closing different combinations of IGBT switches, both the positive
and negative halves of the AC voltage waveform can be generated, allowing for the desired
three-phase voltages to be applied to the motor.

Directions of AC current
As seen in the figure, s1, s2, s3 and s4 are 4 IGBT's.
When s2 and s3 are closed, we get a direction of AC
current (or voltage) and when the s1 and s4 are
closed, we get the opposite direction of the current.
Hence, we easily achieved 3 sinusoidal voltage using
PWM and IGBT's (miniature switches).

The Role of PWM in Motor Control
1 Voltage Generation
The PWM signal is used to generate the desired three-phase AC voltages that are
applied to the motor windings, enabling the PMSM to operate effectively.
2 Current Control
By controlling the voltage through PWM, the current flowing through the motor
windings can be precisely regulated, ensuring the motor operates at the optimal
torque and speed.
3 Smooth Operation
The rapid and continuous generation of the PWM signal allows for smooth and
continuous operation of the PMSM motor, providing a stable and reliable power
source.

PWM Frequency and Duty Cycle
Constant Frequency
The PWM signal has a constant frequency, meaning the time period of each
cycle remains the same. This ensures a stable and consistent power delivery to
the motor.
Varying Duty Cycle
By adjusting the duty cycle, or the ratio of on-time to total time, the effective
voltage applied to the motor can be varied, allowing for the desired AC
sinusoidal voltages to be generated.
Effective Voltage
The effective voltage is calculated as the duty cycle multiplied by the source
voltage, providing a means to control the voltage applied to the motor windings.

PWM and the PI Controller
PI Controller Inputs
The three-phase voltages
generated by the PI controller
serve as the input to the PWM
and SVM processes, providing
the necessary information to
generate the appropriate
switching signals.
SVM Calculations
The SVM process takes the
three-phase voltages from the PI
controller and calculates the
optimal switching times for the
PWM signal, ensuring the desired
voltages are applied to the motor
windings.
Integrated System
The PI controller, SVM, and PWM
processes work together as an
integrated system to provide
precise control over the PMSM
motor, enabling smooth and
efficient operation.

Achieving Sinusoidal Voltages with PWM
1
Rapid Switching
The PWM signal rapidly connects and
disconnects the motor windings from the
power source, creating a series of on and off
states.
2 Varying Duty Cycle
By adjusting the duty cycle, or the ratio of on-
time to total time, the effective voltage applied
to the motor can be varied, allowing for the
generation of sinusoidal waveforms.
3
Smooth Operation
The continuous and rapid generation of the
PWM signal ensures a smooth and continuous
supply of power to the motor, resulting in
stable and efficient operation.

So here one cycle of motor control ends. Many such cycles
takes place in a second to ensure smooth and continuous
operation of the motor.
THANK YOU

PMSM-Motor-Control : A research about FOC

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