PMSM-Motor-Control : A research about FOC

This is research about a process called field-oriented control (FOC) that is used to control the pmsm motor.

1. 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.

2. 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.

3. 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)

4. 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.

5. 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.

6. 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:

7. 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 value is given by the voltage signal coming from the controllers. 7 Step 7: Output Finally currents desired are produced due to these voltages and we obtain the desired torque and speed of the motor.

8. 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.

9. 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.

10. 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

11. 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).

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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

18. 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.

19. 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.

20. 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.

21. 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.

22. 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 are transferred to the inverter to control the motor.

23. Step 1: Measurement 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.

24. 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 information. 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.

25. 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.

26. 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.

27. 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.

28. 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.

29. 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 and reliable. They are also robust and can withstand harsh environments.

30. 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 and reliable. They are also relatively inexpensive and easy to use.

31. 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.

32. 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.

33. 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.

34. 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.

35. 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.

36. 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 f α and f β are alpha and beta currents.

37. 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.

38. 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.

39. 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.

40. 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.

41. 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.

42. 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.

43. 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.

44. 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.

45. 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

46. 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.

47. 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.

48. 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.

49. 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.

50. 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.

51. 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.

52. 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.

53. 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

54. 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.

55. 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.

56. 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.

57. 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).

58. 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.

59. 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.

60. 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.

61. 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.

62. 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